https://chemwiki.ch.ic.ac.uk/api.php?action=feedcontributions&feedformat=atom&user=Jjserran 2026-07-15T22:17:40Z User contributions MediaWiki 1.43.8 https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=248051 2012-03-13T14:40:38Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> amber=(softonly,lastequiv) test nosymm geom=connectivity SP&lt;br&gt;<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)&lt;br&gt;<br /> <br /> MMVB analysis&lt;br&gt;<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). The C-H bonds are described just by MM (1.0). <br /> <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. For instance, in a system with just three configurations, we can write the vector after the connection matrix (leaving a blank line): <br /> <br /> 1 1.000000&lt;br&gt;<br /> 2 1.000000&lt;br&gt;<br /> 3 1.000000&lt;br&gt;<br /> <br /> <br /> In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. The labeling for C atoms (in MMVB) or localized molecular orbitals (in ''ab initio'') are: <br /> <br /> &lt;p&gt;&lt;br&gt;<br /> [[Image:benzenes.png|200px|thumb|center|Labeling in MMVB (left) and ab initio (right)]]&lt;br&gt;<br /> &lt;/p&gt;&lt;br&gt;<br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> <br /> Here go the inputs/outputs:<br /> <br /> MMVB single point: <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_S0_mmvb.gjf]]&lt;br&gt;<br /> [[Media:benzene_S0_mmvb.log]]&lt;br&gt;<br /> &lt;/p&gt;<br /> <br /> MMVB optimization: <br /> <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_S0_mmvb_opt.gjf]]&lt;br&gt;<br /> [[Media:benzene_S0_mmvb_opt.log]]&lt;br&gt;<br /> &lt;/p&gt;<br /> <br /> ''ab initio'' Pij analysis: <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_cas_pij_S0.gjf]]&lt;br&gt;<br /> [[Media:benzene_cas_pij_S0.log]]&lt;br&gt;<br /> &lt;/p&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=248042 2012-03-13T14:38:06Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> amber=(softonly,lastequiv) test nosymm geom=connectivity SP&lt;br&gt;<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)&lt;br&gt;<br /> <br /> MMVB analysis&lt;br&gt;<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). The C-H bonds are described just by MM (1.0). <br /> <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. The labeling for C atoms (in MMVB) or localized molecular orbitals (in ''ab initio'') are: <br /> <br /> &lt;p&gt;&lt;br&gt;<br /> [[Image:benzenes.png|200px|thumb|center|Labeling in MMVB (left) and ab initio (right)]]&lt;br&gt;<br /> &lt;/p&gt;&lt;br&gt;<br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> <br /> Here go the inputs/outputs:<br /> <br /> MMVB single point: <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_S0_mmvb.gjf]]&lt;br&gt;<br /> [[Media:benzene_S0_mmvb.log]]&lt;br&gt;<br /> &lt;/p&gt;<br /> <br /> MMVB optimization: <br /> <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_S0_mmvb_opt.gjf]]&lt;br&gt;<br /> [[Media:benzene_S0_mmvb_opt.log]]&lt;br&gt;<br /> &lt;/p&gt;<br /> <br /> ''ab initio'' Pij analysis: <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_cas_pij_S0.gjf]]&lt;br&gt;<br /> [[Media:benzene_cas_pij_S0.log]]&lt;br&gt;<br /> &lt;/p&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=248039 2012-03-13T14:36:19Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> amber=(softonly,lastequiv) test nosymm geom=connectivity SP&lt;br&gt;<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)&lt;br&gt;<br /> <br /> MMVB analysis&lt;br&gt;<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). The C-H bonds are described just by MM (1.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. The labeling for C atoms (in MMVB) or localized molecular orbitals (in ''ab initio'') are: <br /> <br /> &lt;p&gt;&lt;br&gt;<br /> [[Image:benzenes.png|200px|thumb|center|Labeling in MMVB (left) and ab initio (right)]]&lt;br&gt;<br /> &lt;/p&gt;&lt;br&gt;<br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> <br /> Here go the inputs/outputs:<br /> <br /> MMVB single point: <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_S0_mmvb.gjf]]&lt;br&gt;<br /> [[Media:benzene_S0_mmvb.log]]&lt;br&gt;<br /> &lt;/p&gt;<br /> <br /> MMVB optimization: <br /> <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_S0_mmvb_opt.gjf]]&lt;br&gt;<br /> [[Media:benzene_S0_mmvb_opt.log]]&lt;br&gt;<br /> &lt;/p&gt;<br /> <br /> ''ab initio'' Pij analysis: <br /> <br /> &lt;p&gt;<br /> [[Media:benzene_cas_pij_S0.gjf]]&lt;br&gt;<br /> [[Media:benzene_cas_pij_S0.log]]&lt;br&gt;<br /> &lt;/p&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=File:Benzene_S0_mmvb_opt.log&diff=247998 2012-03-13T14:20:31Z

<p>Jjserran: </p> <hr /> <div></div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=File:Benzene_S0_mmvb.log&diff=247995 2012-03-13T14:20:16Z

<p>Jjserran: </p> <hr /> <div></div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=File:Benzene_cas_pij_S0.log&diff=247992 2012-03-13T14:20:01Z

<p>Jjserran: </p> <hr /> <div></div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=File:Benzene_S0_mmvb_opt.gjf&diff=247991 2012-03-13T14:19:45Z

<p>Jjserran: </p> <hr /> <div></div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=File:Benzene_S0_mmvb.gjf&diff=247982 2012-03-13T14:19:25Z

<p>Jjserran: </p> <hr /> <div></div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=File:Benzene_cas_pij_S0.gjf&diff=247980 2012-03-13T14:19:10Z

<p>Jjserran: </p> <hr /> <div></div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247977 2012-03-13T14:18:27Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> amber=(softonly,lastequiv) test nosymm geom=connectivity SP&lt;br&gt;<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)&lt;br&gt;<br /> <br /> MMVB analysis&lt;br&gt;<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). The C-H bonds are described just by MM (1.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. The labeling for C atoms (in MMVB) or localized molecular orbitals (in ''ab initio'') are: <br /> <br /> &lt;p&gt;&lt;br&gt;<br /> [[Image:benzenes.png|200px|thumb|center|Labeling in MMVB (left) and ab initio (right)]]&lt;br&gt;<br /> &lt;/p&gt;&lt;br&gt;<br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> <br /> Here go the inputs/outputs:<br /> <br /> <br /> &lt;p&gt;<br /> [[Media:benz_rhf.gjf]]&lt;br/&gt;<br /> [[Media:benz_rhf.log]]<br /> &lt;/p&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247940 2012-03-13T14:12:14Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> amber=(softonly,lastequiv) test nosymm geom=connectivity SP&lt;br&gt;<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)&lt;br&gt;<br /> <br /> MMVB analysis&lt;br&gt;<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). The C-H bonds are described just by MM (1.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. The labeling for C atoms (in MMVB) or localized molecular orbitals (in ''ab initio'') are: <br /> <br /> &lt;p&gt;&lt;br&gt;<br /> [[Image:benzenes.png|200px|thumb|center|Labeling in MMVB (left) and ab initio (right)]]&lt;br&gt;<br /> &lt;/p&gt;&lt;br&gt;<br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=File:Benzenes.png&diff=247926 2012-03-13T14:07:45Z

<p>Jjserran: </p> <hr /> <div></div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247920 2012-03-13T14:05:42Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> amber=(softonly,lastequiv) test nosymm geom=connectivity SP&lt;br&gt;<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)&lt;br&gt;<br /> <br /> MMVB analysis&lt;br&gt;<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). The C-H bonds are described just by MM (1.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. <br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247906 2012-03-13T14:02:41Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> %chk=/work/jjserran/MMVB/meta_dist_MMVB_2r.chk<br /> %mem=1500MB<br /> #p amber=(softonly,lastequiv) test nosymm geom=connectivity SP<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)<br /> <br /> MMVB analysis<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). The C-H bonds are described just by MM (1.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. <br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247722 2012-03-13T12:53:05Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> %chk=/work/jjserran/MMVB/meta_dist_MMVB_2r.chk<br /> %mem=1500MB<br /> #p amber=(softonly,lastequiv) test nosymm geom=connectivity SP<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)<br /> <br /> MMVB analysis<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)&lt;br&gt;<br /> C IOp(117) ... MMVB control:&lt;br&gt;<br /> C 0 ... No MMVB&lt;br&gt;<br /> C 1 ... Do MMVB calculation.&lt;br&gt;<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)&lt;br&gt;<br /> C 0000 ... No Conical Intersection Search (Default)&lt;br&gt;<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)&lt;br&gt;<br /> C 00000 ... Do not Delete any Coulombic Qij.&lt;br&gt;<br /> C 10000 ... Specify Qij to delete.&lt;br&gt;<br /> C 0000000 ... Solve VB problem numerically with Lanczos&lt;br&gt;<br /> C 1000000 ... Solve VB problem analytically&lt;br&gt;<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets&lt;br&gt;<br /> C 10000000 ... Slater determinant&lt;br&gt;<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)&lt;br&gt;<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)&lt;br&gt;<br /> C -1 ... Read guess by card in input file&lt;br&gt;<br /> C -2 ... Use the largest elements of H as a guess&lt;br&gt;<br /> C -3 ... Use the five largest contributions of H as a guess&lt;br&gt;<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==<br /> <br /> <br /> For the ground state of benzene, the value for the &lt;math&gt; P_{ij} &lt;/math&gt; between neighbouring C atoms are (theoretically) 0.40. <br /> <br /> The MMVB &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1 0.434 2 2 0.000&lt;br&gt;<br /> 3 1-0.914 3 2 0.434 3 3 0.000&lt;br&gt;<br /> 4 1-0.041 4 2-0.914 4 3 0.434 4 4 0.000&lt;br&gt;<br /> 5 1-0.914 5 2-0.041 5 3-0.914 5 4 0.434 5 5 0.000&lt;br&gt;<br /> 6 1 0.434 6 2-0.914 6 3-0.041 6 4-0.914 6 5 0.434 6 6 0.000&lt;br&gt;<br /> <br /> In this case, as you can see in the input below, the following &lt;math&gt; Q_{ij} &lt;/math&gt; are deleted: <br /> <br /> Pairs of Qij integrals deleted in MMVB:&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 3 1&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 4 1&lt;br&gt;<br /> 4 2&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> 5 1&lt;br&gt;<br /> 5 2&lt;br&gt;<br /> 5 3&lt;br&gt;<br /> 6 2&lt;br&gt;<br /> 6 3&lt;br&gt;<br /> 6 4&lt;br&gt;<br /> <br /> You can see an example of optimization as well. <br /> <br /> <br /> On the other hand, the ''ab initio'' &lt;math&gt; P_{ij} &lt;/math&gt; are: <br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.174&lt;br&gt;<br /> 2 0.130 0.174&lt;br&gt;<br /> 3 -0.076 0.337 0.174&lt;br&gt;<br /> 4 0.337 -0.076 0.130 0.174&lt;br&gt;<br /> 5 -0.076 0.337 -0.076 0.337 0.174&lt;br&gt;<br /> 6 0.337 -0.076 0.337 -0.076 0.130 0.174&lt;br&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247678 2012-03-13T12:33:39Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> %chk=/work/jjserran/MMVB/meta_dist_MMVB_2r.chk<br /> %mem=1500MB<br /> #p amber=(softonly,lastequiv) test nosymm geom=connectivity SP<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)<br /> <br /> MMVB analysis<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)<br /> C IOp(117) ... MMVB control:<br /> C 0 ... No MMVB<br /> C 1 ... Do MMVB calculation.<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)<br /> C 0000 ... No Conical Intersection Search (Default)<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)<br /> C 00000 ... Do not Delete any Coulombic Qij.<br /> C 10000 ... Specify Qij to delete.<br /> C 0000000 ... Solve VB problem numerically with Lanczos<br /> C 1000000 ... Solve VB problem analytically<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets<br /> C 10000000 ... Slater determinant<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)<br /> C -1 ... Read guess by card in input file<br /> C -2 ... Use the largest elements of H as a guess<br /> C -3 ... Use the five largest contributions of H as a guess<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. In addition, it is advisable to delete the coulombic &lt;math&gt; Q_{ij} &lt;/math&gt; integrals between non-neighbouring atoms if your aim is to optimize a structure.<br /> <br /> On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> <br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.<br /> <br /> The route section must be similar to:<br /> <br /> #p CASSCF(8,8,nofulldiag)/6-31G*,Pop=AllOrbitals,gfinput,iop(4/46=1,5/39=2300001,5/42=1),nosymm,guess=read,<br /> scf=maxcycle=999,geom=check<br /> <br /> The IOP 5/42=1 is needed to localize the MOs. The results are given in the output as: <br /> <br /> Pij Operator.&lt;br&gt;<br /> The signs are fixed to have E=Sum Pij*Kij with Kij&lt;0&lt;br&gt;<br /> e.g. Pij=1 for singlet 2e/2o&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 -0.490 0.170&lt;br&gt;<br /> 3 -0.525 -0.490 0.163&lt;br&gt;<br /> 4 0.455 -0.490 -0.398 0.163&lt;br&gt;<br /> 5 -0.455 0.150 -0.559 -0.449 0.137&lt;br&gt;<br /> 6 -0.538 -0.684 -0.311 -0.311 0.143 0.063&lt;br&gt;<br /> 7 -0.392 0.150 -0.449 -0.559 -0.773 0.143 0.137&lt;br&gt;<br /> 8 -0.394 -0.490 0.455 -0.525 -0.392 -0.538 -0.455 0.167&lt;br&gt;<br /> <br /> Pij a a a a&lt;br&gt;<br /> 1 0.000&lt;br&gt;<br /> 2 -0.495 0.000&lt;br&gt;<br /> 3 -0.504 -0.490 0.000&lt;br&gt;<br /> 4 -0.092 -0.490 -0.444 0.000&lt;br&gt;<br /> 5 -0.493 -0.239 -0.522 -0.470 0.000&lt;br&gt;<br /> 6 -0.503 -0.555 -0.406 -0.406 -0.290 0.000&lt;br&gt;<br /> 7 -0.473 -0.239 -0.470 -0.522 -0.603 -0.290 0.000&lt;br&gt;<br /> 8 -0.444 -0.495 -0.092 -0.504 -0.473 -0.503 -0.493 0.000&lt;br&gt;<br /> <br /> Pij a a b b&lt;br&gt;<br /> 1 0.168&lt;br&gt;<br /> 2 0.005 0.170&lt;br&gt;<br /> 3 -0.021 0.000 0.163&lt;br&gt;<br /> 4 0.547 0.000 0.046 0.163&lt;br&gt;<br /> 5 0.039 0.389 -0.037 0.021 0.137&lt;br&gt;<br /> 6 -0.035 -0.128 0.095 0.095 0.433 0.063&lt;br&gt;<br /> 7 0.081 0.389 0.021 -0.037 -0.170 0.433 0.137&lt;br&gt;<br /> 8 0.050 0.005 0.547 -0.021 0.081 -0.035 0.039 0.167&lt;br&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == Example: benzene ==</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247663 2012-03-13T12:25:33Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> %chk=/work/jjserran/MMVB/meta_dist_MMVB_2r.chk<br /> %mem=1500MB<br /> #p amber=(softonly,lastequiv) test nosymm geom=connectivity SP<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)<br /> <br /> MMVB analysis<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 2.140507&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 2.137967&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 -1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 -1.210918&lt;br&gt;<br /> H-MM5 1.670182 -1.111139 1.222392&lt;br&gt;<br /> H-MM5 0.338023 -2.313857 1.210918&lt;br&gt;<br /> <br /> (The geometry must include the type of atom)<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0&lt;br&gt;<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0&lt;br&gt;<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0&lt;br&gt;<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0&lt;br&gt;<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0&lt;br&gt;<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0&lt;br&gt;<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0&lt;br&gt;<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0&lt;br&gt;<br /> 9 1 1.0&lt;br&gt;<br /> 10 2 1.0&lt;br&gt;<br /> 11 3 1.0&lt;br&gt;<br /> 12 4 1.0&lt;br&gt;<br /> 13 5 1.0&lt;br&gt;<br /> 14 6 1.0&lt;br&gt;<br /> 15 7 1.0&lt;br&gt;<br /> 16 7 1.0&lt;br&gt;<br /> 17 8 1.0&lt;br&gt;<br /> 18 8 1.0&lt;br&gt;<br /> <br /> (This is the connection matrix: 21.0 stands for a double bond interaction, 10.0 for a single-bond interaction. For instance, in benzene all the connections between neighbouring C atoms must be 21.0, and between non-neighbouring C atoms must be 10.0; in the case of optimizations, it is better to change 10.0 to 11.0). <br /> <br /> And then the MM parameters. <br /> <br /> The IOP 117 controls the calculation. The main parameters are: <br /> <br /> C2IOp(117)<br /> C IOp(117) ... MMVB control:<br /> C 0 ... No MMVB<br /> C 1 ... Do MMVB calculation.<br /> C 000 ... Activate Bridging Corrections to Kij and Qij (Default)<br /> C 0000 ... No Conical Intersection Search (Default)<br /> C 1000 ... Search For Conical Intersection For (LRoot,LRoot-1)<br /> C 00000 ... Do not Delete any Coulombic Qij.<br /> C 10000 ... Specify Qij to delete.<br /> C 0000000 ... Solve VB problem numerically with Lanczos<br /> C 1000000 ... Solve VB problem analytically<br /> C 00000000 ... Hartree-Waller functions for singlets or triplets<br /> C 10000000 ... Slater determinant<br /> <br /> The IOP 119 is also important: <br /> <br /> C2IOp(119)<br /> C IOp(119) ... Control Initial Lanczos Vector (ILzVec)<br /> C -1 ... Read guess by card in input file<br /> C -2 ... Use the largest elements of H as a guess<br /> C -3 ... Use the five largest contributions of H as a guess<br /> <br /> <br /> Sometimes there may be a problem in solving the eigenvalue problem due to the initial vector in the Lanczos method (an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix). Then it is advisable to use, by default, the option &quot;-3&quot; to make sure that your initial vector is well-balanced. Another option is to use an initial vector in the input file. On the other hand, the IOPs 4/31=2,4/33=2 are for the number of states and to print everything, respectively. <br /> <br /> In the output we can find the &lt;math&gt; K_{ij} &lt;/math&gt; as well as the elements of the density matrix, &lt;math&gt; P_{ij} &lt;/math&gt; and the transition density matrix elements: <br /> <br /> Pi Kij and Qij for I,J= 2 1&lt;br&gt;<br /> K0ij= -0.56278165E-01 Kij= -0.50723878E-01&lt;br&gt;<br /> Q0ij= -0.25559997E-01 Qij= -0.31740808E-01&lt;br&gt;<br /> Pi Kij and Qij for I,J= 3 1&lt;br&gt;<br /> K0ij= -0.56034953E-01 Kij= -0.55333517E-01&lt;br&gt;<br /> Q0ij= -0.31493372E-01 Qij= -0.32273930E-01&lt;br&gt;<br /> Sigma Kij and Qij for I,J= 3 2&lt;br&gt;<br /> K0ij= -0.53944673E-02 Kij= -0.46567881E-02&lt;br&gt;<br /> Q0ij= -0.18172581 Qij= -0.18395974&lt;br&gt;<br /> <br /> Spin Density Matrix&lt;br&gt;<br /> Root 1&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.423 2 2 0.000&lt;br&gt;<br /> 3 1-0.424 3 2 0.478 3 3 0.000&lt;br&gt;<br /> 4 1-0.548 4 2-0.984 4 3 0.480 4 4 0.000&lt;br&gt;<br /> 5 1-0.581 5 2 0.478 5 3-0.974 5 4 0.480 5 5 0.000&lt;br&gt;<br /> 6 1-0.497 6 2-0.423 6 3-0.581 6 4-0.548 6 5-0.424 6 6 0.000&lt;br&gt;<br /> 7 1 0.979 7 2-0.563 7 3-0.569 7 4-0.440 7 5-0.410 7 6-0.506&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.506 8 2-0.563 8 3-0.410 8 4-0.440 8 5-0.569 8 6 0.979&lt;br&gt;<br /> 8 7-0.490 8 8 0.000&lt;br&gt;<br /> &lt;S**2&gt; 0.0000&lt;br&gt;<br /> <br /> Transition Density Matrix&lt;br&gt;<br /> 1 1 0.000&lt;br&gt;<br /> 2 1-0.564 2 2 0.000&lt;br&gt;<br /> 3 1 0.386 3 2 0.151 3 3 0.000&lt;br&gt;<br /> 4 1-0.097 4 2 0.000 4 3-0.263 4 4 0.000&lt;br&gt;<br /> 5 1 0.254 5 2-0.151 5 3 0.000 5 4 0.263 5 5 0.000&lt;br&gt;<br /> 6 1 0.000 6 2 0.564 6 3-0.254 6 4 0.097 6 5-0.386 6 6 0.000&lt;br&gt;<br /> 7 1 0.045 7 2 0.523 7 3-0.382 7 4 0.151 7 5-0.363 7 6 0.024&lt;br&gt;<br /> 7 7 0.000&lt;br&gt;<br /> 8 1-0.024 8 2-0.523 8 3 0.363 8 4-0.151 8 5 0.382 8 6-0.045&lt;br&gt;<br /> 8 7 0.000 8 8 0.000&lt;br&gt;<br /> &lt;S**2&gt; -8.0000&lt;br&gt;<br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247617 2012-03-13T11:59:38Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> %chk=/work/jjserran/MMVB/meta_dist_MMVB_2r.chk<br /> %mem=1500MB<br /> #p amber=(softonly,lastequiv) test nosymm geom=connectivity SP<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)<br /> <br /> MMVB analysis<br /> <br /> 0 1&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 -1.190099&lt;br&gt;<br /> C-MM101 -1.416685 -0.268994 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 -1.204823&lt;br&gt;<br /> C-MM101 0.545282 1.753453 0.000000&lt;br&gt;<br /> C-MM101 0.174614 1.160606 1.204823&lt;br&gt;<br /> C-MM101 -0.620151 -0.067453 1.190099&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 -0.728991&lt;br&gt;<br /> C-MM101 0.777908 -1.455653 0.728991&lt;br&gt;<br /> H-MM5 -1.036876 -0.367046 -2.137967&lt;br&gt;<br /> H-MM5 -2.183420 -1.024540 0.000000&lt;br&gt;<br /> H-MM5 0.533588 1.549366 -2.140507&lt;br&gt;<br /> H-MM5 1.140713 2.649438 0.000000<br /> H-MM5 0.533588 1.549366 2.140507<br /> H-MM5 -1.036876 -0.367046 2.137967<br /> H-MM5 1.670182 -1.111139 -1.222392<br /> H-MM5 0.338023 -2.313857 -1.210918<br /> H-MM5 1.670182 -1.111139 1.222392<br /> H-MM5 0.338023 -2.313857 1.210918<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0<br /> 9 1 1.0<br /> 10 2 1.0<br /> 11 3 1.0<br /> 12 4 1.0<br /> 13 5 1.0<br /> 14 6 1.0<br /> 15 7 1.0<br /> 16 7 1.0<br /> 17 8 1.0<br /> 18 8 1.0<br /> <br /> StrUnit 1<br /> BndUnit 1<br /> SBUnit 1<br /> MM2VDW 3.311 336.176 290000.0 12.50 2.25<br /> NonBon 5 10 0 0 0.000 0.000 1.000 0.000 0.000 1.000<br /> DielC 1.5000<br /> VDW MM5 1.5000 0.0470<br /> VDW MM101 1.9000 0.0440<br /> VDWShf1 * 1 0.0<br /> VDWShf1 MM5 2 -1.0<br /> VDWShf2 1 2 0.9150<br /> CubStr2 MM101 MM101 4.4000 1.5230 2.000<br /> CubStr2 MM101 MM5 4.6000 1.1130 2.000<br /> SixBndI-0-0-1-3 MM101 MM101 MM101 0.4500 109.5000 0.00000007 -1.0<br /> SixBndI-0-0-5-3 MM101 MM101 MM101 0.4500 109.5000 0.00000007 -1.0<br /> SixBndI-0-0-1-3 MM101 MM101 MM5 0.3600 110.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-3 MM101 MM101 MM5 0.3600 110.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-2 MM5 MM101 MM5 0.3200 109.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-3 MM5 MM101 MM5 0.3200 109.4700 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM5 MM101 MM5 0.3200 109.4000 0.00000007 -1.0<br /> SixBndI-0-0-5-2 MM5 MM101 MM5 0.3200 109.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-3 MM5 MM101 MM5 0.3200 109.4700 0.00000007 -1.0<br /> SixBndI-0-0-4-1 MM101 MM101 MM101 0.3400 109.4700 0.00000007 -1.0<br /> SixBndI-0-0-4-3 MM101 MM101 MM101 0.3400 109.5000 0.00000007 -1.0<br /> SixBndI-0-0-4-1 MM101 MM101 MM101 0.2900 0.0000 0.00000007 -1.0<br /> SixBndI-0-0-4-2 MM101 MM101 MM101 0.2900 109.5100 0.00000007 -1.0<br /> SixBndI-0-0-1-1 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-2 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-1 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-2 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-1 MM5 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-2 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-2 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM5 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> MM2Tors-0-0-1 MM101 MM101 MM101 MM101 0.2000 0.2700 0.0930<br /> MM2Tors-0-0-4 MM101 MM101 MM101 MM101 0.2000 0.2700 1.5330<br /> MM2Tors-0-0-5 MM101 MM101 MM101 MM101 0.2000 0.2700 0.0930<br /> MM2Tors-0-0-1 MM101 MM101 MM101 MM5 0.0000 0.0000 3.2670<br /> MM2Tors-0-0-5 MM101 MM101 MM101 MM5 0.0000 0.0000 0.2670<br /> MM2Tors-0-0-1 MM5 MM101 MM101 MM5 0.0000 0.0000 0.2360<br /> MM2Tors-0-0-5 MM5 MM101 MM101 MM5 0.0000 0.0000 0.2370<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247615 2012-03-13T11:58:55Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> The typical input file may be: <br /> <br /> %chk=/work/jjserran/MMVB/meta_dist_MMVB_2r.chk<br /> %mem=1500MB<br /> #p amber=(softonly,lastequiv) test nosymm geom=connectivity SP<br /> iop(1/19=11,1/117=00001,1/119=-3,2/15=1,4/31=2,4/33=2)<br /> <br /> MMVB analysis<br /> <br /> 0 1<br /> C-MM101 -0.620151 -0.067453 -1.190099<br /> C-MM101 -1.416685 -0.268994 0.000000<br /> C-MM101 0.174614 1.160606 -1.204823<br /> C-MM101 0.545282 1.753453 0.000000<br /> C-MM101 0.174614 1.160606 1.204823<br /> C-MM101 -0.620151 -0.067453 1.190099<br /> C-MM101 0.777908 -1.455653 -0.728991<br /> C-MM101 0.777908 -1.455653 0.728991<br /> H-MM5 -1.036876 -0.367046 -2.137967<br /> H-MM5 -2.183420 -1.024540 0.000000<br /> H-MM5 0.533588 1.549366 -2.140507<br /> H-MM5 1.140713 2.649438 0.000000<br /> H-MM5 0.533588 1.549366 2.140507<br /> H-MM5 -1.036876 -0.367046 2.137967<br /> H-MM5 1.670182 -1.111139 -1.222392<br /> H-MM5 0.338023 -2.313857 -1.210918<br /> H-MM5 1.670182 -1.111139 1.222392<br /> H-MM5 0.338023 -2.313857 1.210918<br /> <br /> 1 2 21.0 3 21.0 4 10.0 5 10.0 6 10.0 7 10.0 8 10.0 9 1.0<br /> 2 1 21.0 3 10.0 4 10.0 5 10.0 6 21.0 7 10.0 8 10.0 10 1.0<br /> 3 1 21.0 2 10.0 4 21.0 5 10.0 6 10.0 7 10.0 8 10.0 11 1.0<br /> 4 1 10.0 2 10.0 3 21.0 5 21.0 6 10.0 7 10.0 8 10.0 12 1.0<br /> 5 1 10.0 2 10.0 3 10.0 4 21.0 6 21.0 7 10.0 8 10.0 13 1.0<br /> 6 1 10.0 2 21.0 3 10.0 4 10.0 5 21.0 7 10.0 8 10.0 14 1.0<br /> 7 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 8 21.0 15 1.0 16 1.0<br /> 8 1 10.0 2 10.0 3 10.0 4 10.0 5 10.0 6 10.0 7 21.0 17 1.0 18 1.0<br /> 9 1 1.0<br /> 10 2 1.0<br /> 11 3 1.0<br /> 12 4 1.0<br /> 13 5 1.0<br /> 14 6 1.0<br /> 15 7 1.0<br /> 16 7 1.0<br /> 17 8 1.0<br /> 18 8 1.0<br /> <br /> StrUnit 1<br /> BndUnit 1<br /> SBUnit 1<br /> MM2VDW 3.311 336.176 290000.0 12.50 2.25<br /> NonBon 5 10 0 0 0.000 0.000 1.000 0.000 0.000 1.000<br /> DielC 1.5000<br /> VDW MM5 1.5000 0.0470<br /> VDW MM101 1.9000 0.0440<br /> VDWShf1 * 1 0.0<br /> VDWShf1 MM5 2 -1.0<br /> VDWShf2 1 2 0.9150<br /> CubStr2 MM101 MM101 4.4000 1.5230 2.000<br /> CubStr2 MM101 MM5 4.6000 1.1130 2.000<br /> SixBndI-0-0-1-3 MM101 MM101 MM101 0.4500 109.5000 0.00000007 -1.0<br /> SixBndI-0-0-5-3 MM101 MM101 MM101 0.4500 109.5000 0.00000007 -1.0<br /> SixBndI-0-0-1-3 MM101 MM101 MM5 0.3600 110.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-3 MM101 MM101 MM5 0.3600 110.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-2 MM5 MM101 MM5 0.3200 109.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-3 MM5 MM101 MM5 0.3200 109.4700 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM5 MM101 MM5 0.3200 109.4000 0.00000007 -1.0<br /> SixBndI-0-0-5-2 MM5 MM101 MM5 0.3200 109.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-3 MM5 MM101 MM5 0.3200 109.4700 0.00000007 -1.0<br /> SixBndI-0-0-4-1 MM101 MM101 MM101 0.3400 109.4700 0.00000007 -1.0<br /> SixBndI-0-0-4-3 MM101 MM101 MM101 0.3400 109.5000 0.00000007 -1.0<br /> SixBndI-0-0-4-1 MM101 MM101 MM101 0.2900 0.0000 0.00000007 -1.0<br /> SixBndI-0-0-4-2 MM101 MM101 MM101 0.2900 109.5100 0.00000007 -1.0<br /> SixBndI-0-0-1-1 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-2 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-1 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-2 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-1-1 MM5 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-2 MM101 MM101 MM101 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-2 MM101 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> SixBndI-0-0-5-1 MM5 MM101 MM5 0.5900 120.0000 0.00000007 -1.0<br /> MM2Tors-0-0-1 MM101 MM101 MM101 MM101 0.2000 0.2700 0.0930<br /> MM2Tors-0-0-4 MM101 MM101 MM101 MM101 0.2000 0.2700 1.5330<br /> MM2Tors-0-0-5 MM101 MM101 MM101 MM101 0.2000 0.2700 0.0930<br /> MM2Tors-0-0-1 MM101 MM101 MM101 MM5 0.0000 0.0000 3.2670<br /> MM2Tors-0-0-5 MM101 MM101 MM101 MM5 0.0000 0.0000 0.2670<br /> MM2Tors-0-0-1 MM5 MM101 MM101 MM5 0.0000 0.0000 0.2360<br /> MM2Tors-0-0-5 MM5 MM101 MM101 MM5 0.0000 0.0000 0.2370<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247612 2012-03-13T11:57:12Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then &lt;math&gt; K_{ij} &lt;/math&gt; = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> The idea is to use a combination of molecular mechanics (MM) and valence bond (VB) theory to simulate MC-SCF results. <br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For a detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> This is a CASSCF implementation of VB based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix '''P''' with localized MOs. The index &lt;math&gt; P_{ij} &lt;/math&gt; evaluates the contributions of the determinants to the CASSCF wave function and is used to generate resonance formulas. <br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247594 2012-03-13T11:47:46Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since &lt;math&gt; K_{ij} &lt;/math&gt; depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that &lt;math&gt; K_{ij} &lt;/math&gt; = 0) as well as their directionality (that is, if two ''p'' orbitals in adjacent bonds are perpendicular, then Kij = 0 whatever the distance is). Therefore, if ''T'' = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247591 2012-03-13T11:46:11Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since ( = &lt;math&gt; K_{ij} &lt;/math&gt; ) depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that Kij = 0) as well as their directionality (that is, if two p orbitals in adjacent bonds are perpendicular, then Kij = 0 whatever the distance is). Therefore, if T = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247580 2012-03-13T11:42:51Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> where the first term is the two-electron-exchange repulsion integral, and the second one is the one-electron-exchange integral (nuclear-electron attraction) times the overlap integral between orbitals ''i'' and ''j''. <br /> <br /> Then the essence of the theory is that paired spins correspond to chemical bonds. The paired spins label regions in the molecule where we might expect chemical bonds to occur. Then we can construct spin eigenfunctions (with associated Rumer diagrams) using the spin-pairing method. A function constructed in this way is associated pictorically with a possible way of drawing classical chemical bonds in order to accommodate all the electrons from a set of singly occupied valence orbitals. In this way, each Rumer diagram acquires a certain “chemical” significance. It is then plausible to assume that in favourable cases a single spin-paired structure may give a reasonably good description of the electronic state.<br /> <br /> On the other hand, since Kij depends on orbital overlap, then we have to take into account the distance between them (if the distance is too large, we can assume that Kij = 0) as well as their directionality (that is, if two p orbitals in adjacent bonds are perpendicular, then Kij = 0 whatever the distance is). Therefore, if T = 0, the total energy will be the same for both states (crossing). You can find a detailed discussion in: <br /> &lt;p&gt;<br /> *F. Bernardi, M. Olivucci, M.A. Robb. '''Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization'''. ''Acc. Chem. Res.'' 23 (1990) 405-412.<br /> *S. Vanni, M. Garavelli, M.A. Robb. '''A new formulation of the phase change approach in the theory of conical intersections'''. ''Chem. Phys.'' 347 (2008) 46-56. <br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247569 2012-03-13T11:34:25Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> &lt;math&gt;K_{ij} = \left&lt;{ij|ij}\right&gt;&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247565 2012-03-13T11:32:09Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = [ij|ij] +2S_ij&lt;i|h|j&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> &lt;math&gt;K_{ij} = \langle \mathbf{x},\mathbf{y}\rangle &lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi. '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb. '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247515 2012-03-13T10:25:19Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = \langle{ij|\frac{1}{r_12}|ji}\rangle +2S_ij\left&lt;{i|\hat{H}|j}\right&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> &lt;math&gt;K_{ij} = \langle \mathbf{x},\mathbf{y}\rangle &lt;/math&gt;<br /> <br /> &lt;math&gt;E^{*,ONIOM} = E_{model}^{*,high} + E_{real}^{*,low} - E_{model}^{*,low}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=247514 2012-03-13T10:24:17Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”).<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_{ij} = \langle{ij|\frac{1}{r_12}|ji}\rangle +2S_ij\left&lt;{i|\hat{H}|j}\right&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> &lt;math&gt;K_{ij} = \langle \mathbf{x},\mathbf{y}\rangle &lt;/math&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=User_talk:Jjserran&diff=247491 2012-03-13T10:11:18Z

<p>Jjserran: </p> <hr /> <div>&lt;math&gt;\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}&lt;/math&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=User_talk:Jjserran&diff=247490 2012-03-13T10:11:03Z

<p>Jjserran: </p> <hr /> <div>&lt;math&gt;&lt;math&gt;\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}&lt;/math&gt;&lt;/math&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=User_talk:Jjserran&diff=247487 2012-03-13T10:09:51Z

<p>Jjserran: </p> <hr /> <div>&lt;math&gt;E= Q \Pm K&lt;/math&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=User_talk:Jjserran&diff=247485 2012-03-13T10:08:49Z

<p>Jjserran: Created page with &quot;&lt;math&gt;1+1=2&lt;/math&gt;&quot;</p> <hr /> <div>&lt;math&gt;1+1=2&lt;/math&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=246372 2012-03-12T18:14:07Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”). &lt;math&gt;E_{real}^{low} - E_{model}^{low}&lt;/math&gt;&lt;/p&gt;<br /> <br /> In general, the total energy of a system is, according to the London formula:&lt;math&gt;E_{real}^{low} - E_{model}^{low}&lt;/math&gt;&lt;math&gt;E = Q \Pm K&lt;/math&gt;<br /> <br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_ij = \left&lt;{ij|\displaystyle\frac{1}{r_12}|ji}\right&gt; +2\cdot{S_ij}\left&lt;{i|\hat{H}|j}\right&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> <br /> == MMVB ==<br /> <br /> See the article: F. Bernardi, M. Olivucci, M.A. Robb. '''Simulation of MC-SCF Results on Covalent Organic Multi-Bond Reactions: Molecular Mechanics with Valence Bond (MM-VB)'''. ''J. Am. Chem. Soc.'' 114 (1992) 1606-1616. <br /> <br /> For detailed description of the VB applications in photochemistry, see: <br /> <br /> *F. Bernardi, M. Olivucci, M.A. Robb, G. Tonachini. '''Can a Photochemical Reaction Be Concerted? A Theoretical Study of the Photochemi18cal Sigmatropic Rearrangement of But-1-ene'''. ''J. Am. Chem. Soc.'' 114 (1992) 5805-5812. <br /> <br /> *M.J. Bearpark, M. Deumal, M.A. Robb, T. Vreven, N. Yamamoto, M. Olivucci, F. Bernardi '''Modelling Photochemical [4+4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene+Butadiene'''. ''J. Am. Chem. Soc.'' 119 (1997) 709-718. <br /> <br /> <br /> <br /> == Ab initio Pij's ==<br /> <br /> See the article: L. Blancafort, P. Celani, M.J. Bearpark, M.A. Robb '''A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules'''. ''Theor. Chem. Acc.'' 110 (2003) 92-99.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=246317 2012-03-12T17:27:11Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”). <br /> <br /> In general, the total energy of a system is, according to the London formula: <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;E = Q \pm K&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> being Q the Coulomb integral and K the exchange integral, whose behaviour can be rationalized by using the Heitler-London expression for two electrons: <br /> <br /> <br /> &lt;p&gt;<br /> &lt;math&gt;K_ij = \left&lt;{ij|\displaystyle\frac{1}{r_12}|ji}\right&gt; +2\cdot{S_ij}\left&lt;{i|\hat{H}|j}\right&gt;&lt;/math&gt;<br /> &lt;/p&gt;<br /> <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> == Ab initio Pij's ==</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=246299 2012-03-12T17:22:06Z

<p>Jjserran: </p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> The physical basis of VB theory is the notion that a chemical bond is associated with the pairing of the electrons in the (singly occupied) valence orbitals of the atoms concerned, and its aim is to construct wave functions in which all possible bonds are described in terms of spin pairing. Mathematically, this means that one must deal with many-determinant wave functions constructed directly from atomic orbitals by admitting all allocations of spin factors and coupling the spins in pairs to a resultant ''S'' = 0. In essence, in the VB formalism there is a direct connection between the electron pairs which are spin coupled and molecular structure (i.e. the geometry corresponds to “where the bonds are”). <br /> <br /> &lt;math&gt;\vec{r}(t) = y\cdot{\vec{j}}&lt;/math&gt; <br /> <br /> <br /> <br /> == MMVB ==<br /> <br /> == Ab initio Pij's ==</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=246290 2012-03-12T17:18:25Z

<p>Jjserran: /* The Photochemical Isomerisation of Benzene to Benzvalene */</p> <hr /> <div>== Valence Bond Analysis ==<br /> <br /> == Introduction ==<br /> <br /> == MMVB ==<br /> <br /> == Ab initio Pij's ==<br /> <br /> <br /> &lt;h4&gt;Introduction&lt;/h4&gt;<br /> &lt;p&gt;<br /> We shall study the valence isomeristion of benzene to benzvalene using CASSCF methods. There are many critical points on the S&lt;sub&gt;0&lt;/sub&gt; (singlet ground state), S&lt;sub&gt;1&lt;/sub&gt; (singlet first excited state), S&lt;sub&gt;2&lt;/sub&gt; (singlet second excited state) surfaces associated with the photochemical isomerisations of benzene. Here we only detail some points on the reaction path of benzene(a) to benzvalene(e).<br /> &lt;/p&gt;<br /> <br /> &lt;p&gt;<br /> This work is extract from the article : &lt;br/&gt;<br /> [http://pubs.acs.org/doi/pdf/10.1021/ja00055a042 An MC-SCF study of the S1 and S2 photochemical reactions of benzene, Ian J. Palmer, Ioannis N. Ragazos, Fernando Bernardi, Massimo Olivucci, and Michael A. Robb ; ''J. Am. Chem. Soc.'', 1993, 115 (2), 673-682 ] <br /> &lt;/p&gt;<br /> <br /> [[Image:window_benzene_schemagen.jpg]]<br /> <br /> &lt;p&gt;<br /> The starting geometry comes can come from your favourite molecular modelling package. Any similar package could also be used to generate the cartesian coordinates to start with.<br /> &lt;/p&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo/VB&diff=246288 2012-03-12T17:17:19Z

<p>Jjserran: Created page with &quot;== The Photochemical Isomerisation of Benzene to Benzvalene == &lt;h4&gt;Introduction&lt;/h4&gt; &lt;p&gt; We shall study the valence isomeristion of benzene to benzvalene using CASSCF methods. ...&quot;</p> <hr /> <div>== The Photochemical Isomerisation of Benzene to Benzvalene ==<br /> <br /> <br /> &lt;h4&gt;Introduction&lt;/h4&gt;<br /> &lt;p&gt;<br /> We shall study the valence isomeristion of benzene to benzvalene using CASSCF methods. There are many critical points on the S&lt;sub&gt;0&lt;/sub&gt; (singlet ground state), S&lt;sub&gt;1&lt;/sub&gt; (singlet first excited state), S&lt;sub&gt;2&lt;/sub&gt; (singlet second excited state) surfaces associated with the photochemical isomerisations of benzene. Here we only detail some points on the reaction path of benzene(a) to benzvalene(e).<br /> &lt;/p&gt;<br /> <br /> &lt;p&gt;<br /> This work is extract from the article : &lt;br/&gt;<br /> [http://pubs.acs.org/doi/pdf/10.1021/ja00055a042 An MC-SCF study of the S1 and S2 photochemical reactions of benzene, Ian J. Palmer, Ioannis N. Ragazos, Fernando Bernardi, Massimo Olivucci, and Michael A. Robb ; ''J. Am. Chem. Soc.'', 1993, 115 (2), 673-682 ] <br /> &lt;/p&gt;<br /> <br /> [[Image:window_benzene_schemagen.jpg]]<br /> <br /> &lt;p&gt;<br /> The starting geometry comes can come from your favourite molecular modelling package. Any similar package could also be used to generate the cartesian coordinates to start with.<br /> &lt;/p&gt;</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo&diff=246287 2012-03-12T17:16:57Z

<p>Jjserran: /* Computational Photochemistry Research Group Wiki, Imperial College London */</p> <hr /> <div>= Computational Photochemistry Research Group Wiki, Imperial College London =<br /> <br /> A place to write something about computing facilities (e.g. CX1),<br /> documenting codes (Gaussian + dynamics; latest versions)<br /> and example input files.<br /> -[[User:Mjbear|Mjbear]] 16:16, 17 October 2008 (BST)<br /> <br /> Please amend and update this! Log in using your IC account.<br /> <br /> == Computing Resources ==<br /> === [[Resgrp:comp-photo-hpc|Using College HPC to run Gaussian: CX1]] ===<br /> ===== [[Resgrp:comp-photo-hpc-ax1|- AX1 / AX2 ]] =====<br /> === [[Resgrp:comp-photo-owncomp|Group-managed computers]] ===<br /> === [[Resgrp:utilities|Utilities]] ===<br /> <br /> == Codes ==<br /> === [[Resgrp:comp-photo-gaussian|Gaussian versions]] ===<br /> ===== [[Resgrp:comp-photo-gaussian_problems|- known problems ]] =====<br /> === [[Resgrp:comp-photo-dyn|MCTDH (DD-vMCG)]] ===<br /> === [[Resgrp:comp-photo-onthefly|Direct CAS/RAS]] ===<br /> <br /> == Example Calculations / Tutorials ==<br /> === [[Resgrp:comp-photo-benzene-tutorial|Benzene CASSCF tutorial (G03)]] ===<br /> === [[Resgrp:comp-photo-CHD|Seam calculations of CHD]] ===<br /> ===== [[Resgrp:comp-photo-seam|- Current Seam Frequency Code ]] =====<br /> === [[Resgrp:comp-photo/sh|Surface Hopping]] ===<br /> <br /> === [[Resgrp:comp-photo/VB|Valence-Bond analysis]] ===<br /> <br /> <br /> === [[Resgrp:comp-photo-visualise|GaussView, visualisation etc]] ===<br /> <br /> === [[ONIOM]] ===<br /> <br /> == Calculations ==<br /> === [[Resgrp:comp-photo-calculations|Examples]] ===</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo&diff=246285 2012-03-12T17:16:28Z

<p>Jjserran: /* Computational Photochemistry Research Group Wiki, Imperial College London */</p> <hr /> <div>= Computational Photochemistry Research Group Wiki, Imperial College London =<br /> <br /> A place to write something about computing facilities (e.g. CX1),<br /> documenting codes (Gaussian + dynamics; latest versions)<br /> and example input files.<br /> -[[User:Mjbear|Mjbear]] 16:16, 17 October 2008 (BST)<br /> <br /> Please amend and update this! Log in using your IC account.<br /> <br /> == Computing Resources ==<br /> === [[Resgrp:comp-photo-hpc|Using College HPC to run Gaussian: CX1]] ===<br /> ===== [[Resgrp:comp-photo-hpc-ax1|- AX1 / AX2 ]] =====<br /> === [[Resgrp:comp-photo-owncomp|Group-managed computers]] ===<br /> === [[Resgrp:utilities|Utilities]] ===<br /> <br /> == Codes ==<br /> === [[Resgrp:comp-photo-gaussian|Gaussian versions]] ===<br /> ===== [[Resgrp:comp-photo-gaussian_problems|- known problems ]] =====<br /> === [[Resgrp:comp-photo-dyn|MCTDH (DD-vMCG)]] ===<br /> === [[Resgrp:comp-photo-onthefly|Direct CAS/RAS]] ===<br /> <br /> == Example Calculations / Tutorials ==<br /> === [[Resgrp:comp-photo-benzene-tutorial|Benzene CASSCF tutorial (G03)]] ===<br /> === [[Resgrp:comp-photo-CHD|Seam calculations of CHD]] ===<br /> ===== [[Resgrp:comp-photo-seam|- Current Seam Frequency Code ]] =====<br /> === [[Resgrp:comp-photo/sh|Surface Hopping]] ===<br /> <br /> === [[Resgrp:comp-photo/VB|Valence-Bond analysis]] ===<br /> <br /> == The Photochemical Isomerisation of Benzene to Benzvalene ==<br /> <br /> <br /> === [[Resgrp:comp-photo-visualise|GaussView, visualisation etc]] ===<br /> <br /> === [[ONIOM]] ===<br /> <br /> == Calculations ==<br /> === [[Resgrp:comp-photo-calculations|Examples]] ===</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo&diff=246284 2012-03-12T17:15:31Z

<p>Jjserran: /* Valence-Bond analysis */</p> <hr /> <div>= Computational Photochemistry Research Group Wiki, Imperial College London =<br /> <br /> A place to write something about computing facilities (e.g. CX1),<br /> documenting codes (Gaussian + dynamics; latest versions)<br /> and example input files.<br /> -[[User:Mjbear|Mjbear]] 16:16, 17 October 2008 (BST)<br /> <br /> Please amend and update this! Log in using your IC account.<br /> <br /> == Computing Resources ==<br /> === [[Resgrp:comp-photo-hpc|Using College HPC to run Gaussian: CX1]] ===<br /> ===== [[Resgrp:comp-photo-hpc-ax1|- AX1 / AX2 ]] =====<br /> === [[Resgrp:comp-photo-owncomp|Group-managed computers]] ===<br /> === [[Resgrp:utilities|Utilities]] ===<br /> <br /> == Codes ==<br /> === [[Resgrp:comp-photo-gaussian|Gaussian versions]] ===<br /> ===== [[Resgrp:comp-photo-gaussian_problems|- known problems ]] =====<br /> === [[Resgrp:comp-photo-dyn|MCTDH (DD-vMCG)]] ===<br /> === [[Resgrp:comp-photo-onthefly|Direct CAS/RAS]] ===<br /> <br /> == Example Calculations / Tutorials ==<br /> === [[Resgrp:comp-photo-benzene-tutorial|Benzene CASSCF tutorial (G03)]] ===<br /> === [[Resgrp:comp-photo-CHD|Seam calculations of CHD]] ===<br /> ===== [[Resgrp:comp-photo-seam|- Current Seam Frequency Code ]] =====<br /> === [[Resgrp:comp-photo/sh|Surface Hopping]] ===<br /> <br /> === [[Resgrp:comp-photo/VB|Valence-Bond analysis]] ===<br /> <br /> == The Photochemical Isomerisation of Benzene to Benzvalene ==<br /> <br /> <br /> &lt;h4&gt;Introduction&lt;/h4&gt;<br /> &lt;p&gt;<br /> We shall study the valence isomeristion of benzene to benzvalene using CASSCF methods. There are many critical points on the S&lt;sub&gt;0&lt;/sub&gt; (singlet ground state), S&lt;sub&gt;1&lt;/sub&gt; (singlet first excited state), S&lt;sub&gt;2&lt;/sub&gt; (singlet second excited state) surfaces associated with the photochemical isomerisations of benzene. Here we only detail some points on the reaction path of benzene(a) to benzvalene(e).<br /> &lt;/p&gt;<br /> <br /> &lt;p&gt;<br /> This work is extract from the article : &lt;br/&gt;<br /> [http://pubs.acs.org/doi/pdf/10.1021/ja00055a042 An MC-SCF study of the S1 and S2 photochemical reactions of benzene, Ian J. Palmer, Ioannis N. Ragazos, Fernando Bernardi, Massimo Olivucci, and Michael A. Robb ; ''J. Am. Chem. Soc.'', 1993, 115 (2), 673-682 ] <br /> &lt;/p&gt;<br /> <br /> [[Image:window_benzene_schemagen.jpg]]<br /> <br /> &lt;p&gt;<br /> The starting geometry comes can come from your favourite molecular modelling package. Any similar package could also be used to generate the cartesian coordinates to start with.<br /> &lt;/p&gt;<br /> <br /> === [[Resgrp:comp-photo-visualise|GaussView, visualisation etc]] ===<br /> <br /> === [[ONIOM]] ===<br /> <br /> == Calculations ==<br /> === [[Resgrp:comp-photo-calculations|Examples]] ===</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo&diff=246274 2012-03-12T17:07:43Z

<p>Jjserran: /* Example Calculations / Tutorials */</p> <hr /> <div>= Computational Photochemistry Research Group Wiki, Imperial College London =<br /> <br /> A place to write something about computing facilities (e.g. CX1),<br /> documenting codes (Gaussian + dynamics; latest versions)<br /> and example input files.<br /> -[[User:Mjbear|Mjbear]] 16:16, 17 October 2008 (BST)<br /> <br /> Please amend and update this! Log in using your IC account.<br /> <br /> == Computing Resources ==<br /> === [[Resgrp:comp-photo-hpc|Using College HPC to run Gaussian: CX1]] ===<br /> ===== [[Resgrp:comp-photo-hpc-ax1|- AX1 / AX2 ]] =====<br /> === [[Resgrp:comp-photo-owncomp|Group-managed computers]] ===<br /> === [[Resgrp:utilities|Utilities]] ===<br /> <br /> == Codes ==<br /> === [[Resgrp:comp-photo-gaussian|Gaussian versions]] ===<br /> ===== [[Resgrp:comp-photo-gaussian_problems|- known problems ]] =====<br /> === [[Resgrp:comp-photo-dyn|MCTDH (DD-vMCG)]] ===<br /> === [[Resgrp:comp-photo-onthefly|Direct CAS/RAS]] ===<br /> <br /> == Example Calculations / Tutorials ==<br /> === [[Resgrp:comp-photo-benzene-tutorial|Benzene CASSCF tutorial (G03)]] ===<br /> === [[Resgrp:comp-photo-CHD|Seam calculations of CHD]] ===<br /> ===== [[Resgrp:comp-photo-seam|- Current Seam Frequency Code ]] =====<br /> === [[Resgrp:comp-photo/sh|Surface Hopping]] ===<br /> <br /> === [[Resgrp:comp-photo/VB|Valence-Bond analysis]] ===<br /> <br /> === [[Resgrp:comp-photo-visualise|GaussView, visualisation etc]] ===<br /> <br /> === [[ONIOM]] ===<br /> <br /> == Calculations ==<br /> === [[Resgrp:comp-photo-calculations|Examples]] ===</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo-hpc&diff=220417 2012-01-13T10:24:34Z

<p>Jjserran: /* New nodes */</p> <hr /> <div>IC has two centrally-managed HPC computer systems: a PC cluster CX1, and a small Silicon Graphics AX1.<br /> We mainly use CX1, as it has many more accessible nodes and processors. Also, we own two nodes, which have a dedicated batch queue (pqmb) for the group, mainly for short test calculations. The chemistry queue is pqchem.<br /> <br /> More details here: [http://www.hpc.ic.ac.uk high performance computing]<br /> <br /> Join the [https://mailman.ic.ac.uk/mailman/listinfo/hpc-announce mailing list]. If you have problems, ask around within the group first, otherwise contact Matt Harvey in HPC support directly (m.j.harvey@imperial.ac.uk).<br /> <br /> == Using The Cluster ==<br /> Before running calculations on the cluster, look at the tutorial:<br /> <br /> [https://www.ch.ic.ac.uk/wiki/index.php/Using_the_cluster_:_tutorial%2C_examples Using the cluster : tutorial and examples]<br /> <br /> Below is a summary / reminder.<br /> <br /> == Connecting ==<br /> To connect to the PC cluster and forward display information for X-windows, use '''ssh -Y myname@login.cx1.hpc.ic.ac.uk'''<br /> <br /> Use your IC college account (as 'myname').<br /> <br /> This connects to one of two front-end nodes. All cluster nodes (the rest are for running calculations through a queueing system) share common file systems.<br /> (To compile Gaussian code, need to specify login-0 explicitly when connecting, as this is the node the supported Gaussian compiler is licensed for).<br /> <br /> Once connected, using the command id should give something like the following:<br /> <br /> [login-0 ~]$ id<br /> uid=45751(mjbear) gid=11000(hpc-users) groups=1010(gaussian-users),11000(hpc-users),11100(gaussian-devel),11232(pgi-users)<br /> <br /> To access the current development version of Gaussian, you will need to be in the ''gaussian-devel'' group (and sign the developer's license agreement).<br /> To access run-time libraries to run Gaussian, you also need to be in the ''pgi-users'' groups.<br /> Both should have been set up when your account was created.<br /> <br /> == Queuing system ==<br /> <br /> PBS queuing system. '''xpbs''' gives you an interactive display.<br /> Need to supply a script for this queuing system that requests the resources to run the calculation you want.<br /> Examples in <br /> /home/gaussian-devel/test_h11<br /> (This is for the development version of Gaussian that was current as of --[[User:Mjbear|Mjbear]] 11:46, 23 March 2011 (UTC))<br /> <br /> <br /> Using files in this directory, the command '''qsub jobscript_test009''' sends the following script to the queueing system:<br /> <br /> [login-0 test_g01]$ cat jobscript_test009<br /> #PBS -l ncpus=2<br /> #PBS -l mem=1700mb<br /> #PBS -l walltime=00:09:00<br /> #PBS -joe<br /> <br /> module load gaussian/devel-modules<br /> module load gdvh11<br /> <br /> gdv &lt; /home/mjbear/test_h11/test009.com &gt; $WORK/test009.log<br /> <br /> In general, it's best to request the resources you really need! Rather than try to second-guess the queueing system.<br /> <br /> Queue suggestion: ''xdbg'' is for 4 processor calculations using up to 15600 MB for 15 mins. This is basically for running calculations on one node - but an nprocshared=2 nproclinda=2 calculation will also work if there's space.<br /> <br /> We have two of our own nodes, which are 8 processor and 12 GB.<br /> These have slow memory access, so are best used for short test calculations to check larger jobs will run.<br /> <br /> To run a calculation on our private nodes you need to:<br /> <br /> 1) use qsub -q pqmb<br /> to send the job to our private queue.<br /> (This can be included in the job script itself, as a PBS option)<br /> <br /> 2) '''select=1:ncpus=8'''<br /> -will give you 8 cores, 1 node (shared memory parallelism only).<br /> <br /> '''select=2:ncpus=8'''<br /> -will give you 16 cores, 2 nodes (shared + distributed memory parallelism). See test160.com for an example.<br /> <br /> Output files go on $WORK filesystem. This is not backed up!<br /> <br /> To Do:<br /> # using '''cpsub''' and '''cpcomchk'''<br /> <br /> <br /> == New nodes ==<br /> <br /> We have an own queue named &quot;pqmb&quot; on CX1 (see above). There are two kinds of nodes on pqmb:rather old 8 core nodes and two new ones which have 12 cores.<br /> <br /> There is 48 GB of physical memory on this node type, so you can request a maximum of 47800mb of user memory.<br /> <br /> Example: <br /> <br /> #PBS -l select=1:ncpus=6:mem=10000mb:westmere=true<br /> #PBS -l walltime=96:00:00<br /> #PBS -q pqmb<br /> <br /> These sentences may be written in a job script asking for 1 node and 6 cores in this node.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo-hpc&diff=220416 2012-01-13T10:24:01Z

<p>Jjserran: /* New nodes */</p> <hr /> <div>IC has two centrally-managed HPC computer systems: a PC cluster CX1, and a small Silicon Graphics AX1.<br /> We mainly use CX1, as it has many more accessible nodes and processors. Also, we own two nodes, which have a dedicated batch queue (pqmb) for the group, mainly for short test calculations. The chemistry queue is pqchem.<br /> <br /> More details here: [http://www.hpc.ic.ac.uk high performance computing]<br /> <br /> Join the [https://mailman.ic.ac.uk/mailman/listinfo/hpc-announce mailing list]. If you have problems, ask around within the group first, otherwise contact Matt Harvey in HPC support directly (m.j.harvey@imperial.ac.uk).<br /> <br /> == Using The Cluster ==<br /> Before running calculations on the cluster, look at the tutorial:<br /> <br /> [https://www.ch.ic.ac.uk/wiki/index.php/Using_the_cluster_:_tutorial%2C_examples Using the cluster : tutorial and examples]<br /> <br /> Below is a summary / reminder.<br /> <br /> == Connecting ==<br /> To connect to the PC cluster and forward display information for X-windows, use '''ssh -Y myname@login.cx1.hpc.ic.ac.uk'''<br /> <br /> Use your IC college account (as 'myname').<br /> <br /> This connects to one of two front-end nodes. All cluster nodes (the rest are for running calculations through a queueing system) share common file systems.<br /> (To compile Gaussian code, need to specify login-0 explicitly when connecting, as this is the node the supported Gaussian compiler is licensed for).<br /> <br /> Once connected, using the command id should give something like the following:<br /> <br /> [login-0 ~]$ id<br /> uid=45751(mjbear) gid=11000(hpc-users) groups=1010(gaussian-users),11000(hpc-users),11100(gaussian-devel),11232(pgi-users)<br /> <br /> To access the current development version of Gaussian, you will need to be in the ''gaussian-devel'' group (and sign the developer's license agreement).<br /> To access run-time libraries to run Gaussian, you also need to be in the ''pgi-users'' groups.<br /> Both should have been set up when your account was created.<br /> <br /> == Queuing system ==<br /> <br /> PBS queuing system. '''xpbs''' gives you an interactive display.<br /> Need to supply a script for this queuing system that requests the resources to run the calculation you want.<br /> Examples in <br /> /home/gaussian-devel/test_h11<br /> (This is for the development version of Gaussian that was current as of --[[User:Mjbear|Mjbear]] 11:46, 23 March 2011 (UTC))<br /> <br /> <br /> Using files in this directory, the command '''qsub jobscript_test009''' sends the following script to the queueing system:<br /> <br /> [login-0 test_g01]$ cat jobscript_test009<br /> #PBS -l ncpus=2<br /> #PBS -l mem=1700mb<br /> #PBS -l walltime=00:09:00<br /> #PBS -joe<br /> <br /> module load gaussian/devel-modules<br /> module load gdvh11<br /> <br /> gdv &lt; /home/mjbear/test_h11/test009.com &gt; $WORK/test009.log<br /> <br /> In general, it's best to request the resources you really need! Rather than try to second-guess the queueing system.<br /> <br /> Queue suggestion: ''xdbg'' is for 4 processor calculations using up to 15600 MB for 15 mins. This is basically for running calculations on one node - but an nprocshared=2 nproclinda=2 calculation will also work if there's space.<br /> <br /> We have two of our own nodes, which are 8 processor and 12 GB.<br /> These have slow memory access, so are best used for short test calculations to check larger jobs will run.<br /> <br /> To run a calculation on our private nodes you need to:<br /> <br /> 1) use qsub -q pqmb<br /> to send the job to our private queue.<br /> (This can be included in the job script itself, as a PBS option)<br /> <br /> 2) '''select=1:ncpus=8'''<br /> -will give you 8 cores, 1 node (shared memory parallelism only).<br /> <br /> '''select=2:ncpus=8'''<br /> -will give you 16 cores, 2 nodes (shared + distributed memory parallelism). See test160.com for an example.<br /> <br /> Output files go on $WORK filesystem. This is not backed up!<br /> <br /> To Do:<br /> # using '''cpsub''' and '''cpcomchk'''<br /> <br /> <br /> == New nodes ==<br /> <br /> We have an own queue named &quot;pqmb&quot; on CX1. There are two kinds of nodes on pqmb:rather old 8 core nodes and two new ones which have 12 cores.<br /> <br /> There is 48 GB of physical memory on this node type, so you can request a maximum of 47800mb of user memory.<br /> <br /> Example: <br /> <br /> #PBS -l select=1:ncpus=6:mem=10000mb:westmere=true<br /> #PBS -l walltime=96:00:00<br /> #PBS -q pqmb<br /> <br /> These sentences may be written in a job script asking for 1 node and 6 cores in this node.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo-hpc&diff=220415 2012-01-13T10:23:42Z

<p>Jjserran: /* Queuing system */</p> <hr /> <div>IC has two centrally-managed HPC computer systems: a PC cluster CX1, and a small Silicon Graphics AX1.<br /> We mainly use CX1, as it has many more accessible nodes and processors. Also, we own two nodes, which have a dedicated batch queue (pqmb) for the group, mainly for short test calculations. The chemistry queue is pqchem.<br /> <br /> More details here: [http://www.hpc.ic.ac.uk high performance computing]<br /> <br /> Join the [https://mailman.ic.ac.uk/mailman/listinfo/hpc-announce mailing list]. If you have problems, ask around within the group first, otherwise contact Matt Harvey in HPC support directly (m.j.harvey@imperial.ac.uk).<br /> <br /> == Using The Cluster ==<br /> Before running calculations on the cluster, look at the tutorial:<br /> <br /> [https://www.ch.ic.ac.uk/wiki/index.php/Using_the_cluster_:_tutorial%2C_examples Using the cluster : tutorial and examples]<br /> <br /> Below is a summary / reminder.<br /> <br /> == Connecting ==<br /> To connect to the PC cluster and forward display information for X-windows, use '''ssh -Y myname@login.cx1.hpc.ic.ac.uk'''<br /> <br /> Use your IC college account (as 'myname').<br /> <br /> This connects to one of two front-end nodes. All cluster nodes (the rest are for running calculations through a queueing system) share common file systems.<br /> (To compile Gaussian code, need to specify login-0 explicitly when connecting, as this is the node the supported Gaussian compiler is licensed for).<br /> <br /> Once connected, using the command id should give something like the following:<br /> <br /> [login-0 ~]$ id<br /> uid=45751(mjbear) gid=11000(hpc-users) groups=1010(gaussian-users),11000(hpc-users),11100(gaussian-devel),11232(pgi-users)<br /> <br /> To access the current development version of Gaussian, you will need to be in the ''gaussian-devel'' group (and sign the developer's license agreement).<br /> To access run-time libraries to run Gaussian, you also need to be in the ''pgi-users'' groups.<br /> Both should have been set up when your account was created.<br /> <br /> == Queuing system ==<br /> <br /> PBS queuing system. '''xpbs''' gives you an interactive display.<br /> Need to supply a script for this queuing system that requests the resources to run the calculation you want.<br /> Examples in <br /> /home/gaussian-devel/test_h11<br /> (This is for the development version of Gaussian that was current as of --[[User:Mjbear|Mjbear]] 11:46, 23 March 2011 (UTC))<br /> <br /> <br /> Using files in this directory, the command '''qsub jobscript_test009''' sends the following script to the queueing system:<br /> <br /> [login-0 test_g01]$ cat jobscript_test009<br /> #PBS -l ncpus=2<br /> #PBS -l mem=1700mb<br /> #PBS -l walltime=00:09:00<br /> #PBS -joe<br /> <br /> module load gaussian/devel-modules<br /> module load gdvh11<br /> <br /> gdv &lt; /home/mjbear/test_h11/test009.com &gt; $WORK/test009.log<br /> <br /> In general, it's best to request the resources you really need! Rather than try to second-guess the queueing system.<br /> <br /> Queue suggestion: ''xdbg'' is for 4 processor calculations using up to 15600 MB for 15 mins. This is basically for running calculations on one node - but an nprocshared=2 nproclinda=2 calculation will also work if there's space.<br /> <br /> We have two of our own nodes, which are 8 processor and 12 GB.<br /> These have slow memory access, so are best used for short test calculations to check larger jobs will run.<br /> <br /> To run a calculation on our private nodes you need to:<br /> <br /> 1) use qsub -q pqmb<br /> to send the job to our private queue.<br /> (This can be included in the job script itself, as a PBS option)<br /> <br /> 2) '''select=1:ncpus=8'''<br /> -will give you 8 cores, 1 node (shared memory parallelism only).<br /> <br /> '''select=2:ncpus=8'''<br /> -will give you 16 cores, 2 nodes (shared + distributed memory parallelism). See test160.com for an example.<br /> <br /> Output files go on $WORK filesystem. This is not backed up!<br /> <br /> To Do:<br /> # using '''cpsub''' and '''cpcomchk'''<br /> <br /> <br /> == New nodes ==<br /> <br /> We have an own queue named &quot;pqmb&quot; on CX1. There are two kinds of nodes on pqmb:rather old 8 core nodes and two new ones which have 12 cores.<br /> <br /> There is 48 GB of physical memory on this node type, so you can request a maximum of 47800mb of user memory.<br /> <br /> Example: <br /> <br /> #PBS -l select=1:ncpus=6:mem=10000mb:westmere=true<br /> #PBS -l walltime=96:00:00<br /> #PBS -q pqmb<br /> <br /> These sentences may be written in a job script asking for 1 node and 6 cores in this node.</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:utilities&diff=181940 2011-05-10T15:48:31Z

<p>Jjserran: </p> <hr /> <div>Here there is useful information and people to get in touch with: <br /> <br /> Chief Service Technician (Mr. Peter Sulsh): p.sulsh@imperial.ac.uk‎<br /> <br /> ICT Service Desk: service.desk@imperial.ac.uk‎<br /> <br /> Allowances (Mrs. Althea Hartley-Forbes): a.hartley-forbes@imperial.ac.uk<br /> <br /> HPC Systems Support Specialist (Mr. Matt Harvey): m.j.harvey@imperial.ac.uk<br /> <br /> Printing posters: get in touch with ‎Dr. Ian R. Gould (i.gould@imperial.ac.uk). More information: http://www3.imperial.ac.uk/people/i.gould/poster%20printing1</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:utilities&diff=181939 2011-05-09T17:38:46Z

<p>Jjserran: </p> <hr /> <div>Here there is useful information and people to get in touch with: <br /> <br /> Chief Service Technician (Mr. Peter Sulsh): p.sulsh@imperial.ac.uk‎<br /> <br /> ICT Service Desk: service.desk@imperial.ac.uk‎<br /> <br /> Allowances (Mrs. Althea Hartley-Forbes): a.hartley-forbes@imperial.ac.uk<br /> <br /> HPC Systems Support Specialist (Mr. Matt Harvey): m.j.harvey@imperial.ac.uk<br /> <br /> Printing posters: get in touch with ‎Dr. Ian R. Gould (i.gould@imperial.ac.uk)</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:utilities&diff=181938 2011-05-09T17:30:21Z

<p>Jjserran: New page: IC has several centrally-managed HPC computer systems: mainly we use the PC cluster CX1, but there is also a small Silicon Graphics AX1. This and an older separate machine AX2 (added as an...</p> <hr /> <div>IC has several centrally-managed HPC computer systems: mainly we use the PC cluster CX1, but there is also a small Silicon Graphics AX1.<br /> This and an older separate machine AX2 (added as an AX1 queue) are soon to be replaced,<br /> but they are still useful for larger shared memory parallel</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo&diff=181937 2011-05-09T17:26:34Z

<p>Jjserran: /* Utilities */</p> <hr /> <div>= Computational Photochemistry Research Group Wiki, Imperial College London =<br /> <br /> A place to write something about computing facilities (e.g. CX1),<br /> documenting codes (Gaussian + dynamics; latest versions)<br /> and example input files.<br /> -[[User:Mjbear|Mjbear]] 16:16, 17 October 2008 (BST)<br /> <br /> Please amend and update this! Log in using your IC account.<br /> <br /> == Computing Resources ==<br /> === [[Resgrp:comp-photo-hpc|Using College HPC to run Gaussian: CX1]] ===<br /> ===== [[Resgrp:comp-photo-hpc-ax1|- AX1 / AX2 ]] =====<br /> === [[Resgrp:comp-photo-owncomp|Group-managed computers]] ===<br /> === [[Resgrp:utilities|Utilities]] ===<br /> <br /> == Codes ==<br /> === [[Resgrp:comp-photo-gaussian|Gaussian versions]] ===<br /> ===== [[Resgrp:comp-photo-gaussian_problems|- known problems ]] =====<br /> === [[Resgrp:comp-photo-dyn|MCTDH (DD-vMCG)]] ===<br /> === [[Resgrp:comp-photo-onthefly|Direct CAS/RAS]] ===<br /> <br /> == Example Calculations / Tutorials ==<br /> === [[Resgrp:comp-photo-benzene-tutorial|Benzene CASSCF tutorial (G03)]] ===<br /> === [[Resgrp:comp-photo-CHD|Seam calculations of CHD]] ===<br /> ===== [[Resgrp:comp-photo-seam|- Current Seam Frequency Code ]] =====<br /> === [[Resgrp:comp-photo/sh|Surface Hopping]] ===<br /> <br /> === [[Resgrp:comp-photo-visualise|GaussView, visualisation etc]] ===<br /> <br /> === [[ONIOM]] ===<br /> <br /> == Calculations ==<br /> === [[Resgrp:comp-photo-calculations|Examples]] ===</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo&diff=181936 2011-05-09T17:26:21Z

<p>Jjserran: /* Utilities */</p> <hr /> <div>= Computational Photochemistry Research Group Wiki, Imperial College London =<br /> <br /> A place to write something about computing facilities (e.g. CX1),<br /> documenting codes (Gaussian + dynamics; latest versions)<br /> and example input files.<br /> -[[User:Mjbear|Mjbear]] 16:16, 17 October 2008 (BST)<br /> <br /> Please amend and update this! Log in using your IC account.<br /> <br /> == Computing Resources ==<br /> === [[Resgrp:comp-photo-hpc|Using College HPC to run Gaussian: CX1]] ===<br /> ===== [[Resgrp:comp-photo-hpc-ax1|- AX1 / AX2 ]] =====<br /> === [[Resgrp:comp-photo-owncomp|Group-managed computers]] ===<br /> === [[Resgrp:utilities|Utilities]] ===<br /> <br /> HOLA<br /> <br /> == Codes ==<br /> === [[Resgrp:comp-photo-gaussian|Gaussian versions]] ===<br /> ===== [[Resgrp:comp-photo-gaussian_problems|- known problems ]] =====<br /> === [[Resgrp:comp-photo-dyn|MCTDH (DD-vMCG)]] ===<br /> === [[Resgrp:comp-photo-onthefly|Direct CAS/RAS]] ===<br /> <br /> == Example Calculations / Tutorials ==<br /> === [[Resgrp:comp-photo-benzene-tutorial|Benzene CASSCF tutorial (G03)]] ===<br /> === [[Resgrp:comp-photo-CHD|Seam calculations of CHD]] ===<br /> ===== [[Resgrp:comp-photo-seam|- Current Seam Frequency Code ]] =====<br /> === [[Resgrp:comp-photo/sh|Surface Hopping]] ===<br /> <br /> === [[Resgrp:comp-photo-visualise|GaussView, visualisation etc]] ===<br /> <br /> === [[ONIOM]] ===<br /> <br /> == Calculations ==<br /> === [[Resgrp:comp-photo-calculations|Examples]] ===</div>

Jjserran https://chemwiki.ch.ic.ac.uk/index.php?title=Resgrp:comp-photo&diff=181935 2011-05-09T17:25:23Z

<p>Jjserran: </p> <hr /> <div>= Computational Photochemistry Research Group Wiki, Imperial College London =<br /> <br /> A place to write something about computing facilities (e.g. CX1),<br /> documenting codes (Gaussian + dynamics; latest versions)<br /> and example input files.<br /> -[[User:Mjbear|Mjbear]] 16:16, 17 October 2008 (BST)<br /> <br /> Please amend and update this! Log in using your IC account.<br /> <br /> == Computing Resources ==<br /> === [[Resgrp:comp-photo-hpc|Using College HPC to run Gaussian: CX1]] ===<br /> ===== [[Resgrp:comp-photo-hpc-ax1|- AX1 / AX2 ]] =====<br /> === [[Resgrp:comp-photo-owncomp|Group-managed computers]] ===<br /> === [[Resgrp:utilities|Utilities]] ===<br /> <br /> <br /> == Codes ==<br /> === [[Resgrp:comp-photo-gaussian|Gaussian versions]] ===<br /> ===== [[Resgrp:comp-photo-gaussian_problems|- known problems ]] =====<br /> === [[Resgrp:comp-photo-dyn|MCTDH (DD-vMCG)]] ===<br /> === [[Resgrp:comp-photo-onthefly|Direct CAS/RAS]] ===<br /> <br /> == Example Calculations / Tutorials ==<br /> === [[Resgrp:comp-photo-benzene-tutorial|Benzene CASSCF tutorial (G03)]] ===<br /> === [[Resgrp:comp-photo-CHD|Seam calculations of CHD]] ===<br /> ===== [[Resgrp:comp-photo-seam|- Current Seam Frequency Code ]] =====<br /> === [[Resgrp:comp-photo/sh|Surface Hopping]] ===<br /> <br /> === [[Resgrp:comp-photo-visualise|GaussView, visualisation etc]] ===<br /> <br /> === [[ONIOM]] ===<br /> <br /> == Calculations ==<br /> === [[Resgrp:comp-photo-calculations|Examples]] ===</div>

Jjserran