Rep:Mod:hg408.1
The Basic Techniques of Molecular Mechanics and Semi-Empirical Molecular Orbital Methods for Structural and Spectroscopic Evaluations
Molecular Mechanics as a Modelling Technique
Application of Molecular Mechanics to certain simulated chemical environments can be shown to provide a hugely demonstrative representation of the system under study. The Molecular Mechanics method makes use of the Classical (Newtonian) Laws of dynamics to model a molecular system, with the potential energy described by a force field based on Hooke's Law. The molecular geometry is optimised with a view to providing a steric energy, from which the separate bond length, angular strain and Van de Waals contributions can be analysed.
Dimerisation of Cycolpentadiene
Cyclopentadiene dimerises to form exclusively the endo product by means of a [4+2] cycloaddition[1]. Both the exo and endo dimers have been modelled using ChemBio3D (MM2), and the results indicate the overall realtive stabilities (total energy) of each molecule, and explain in a quantatative manner, the opening experimental result. The total energy of the exo product is significantly lower; this would suggest that, based on thermodynamic considerations alone, it would be preferentially formed in the reaction (This has been confirmed by Baldwin et al[2], who observed that upon heating, the endo dimer isomerises to the exo dimer).
The experimental results contradict this theoretical basis (or at least indicate that it is incomplete), instead indicating that there is another factor which counts to make the endo product the only one formed[3]. Examination of the transition states involved in the dimerisation reaction would indicate that this result is due to the extent of steric interaction between constituent parts of the molecule during the chemical change. This energy difference comes from a repulsive 1,4 interaction incurred by the geometry of the endo-isomer Alders 'endo' rule states that the most stable (lowest energy) transition state is associated with the 'maximum accumulation of unsaturated centres', this in turn corresponds to the fastest formed product (or most rapid progress though the lower energy T.S.). This result can also be explained by considering the electronics involved, i.e. secondary orbital interactions (as predicted by Carmella et al), as well as through application of the Woodward-Hoffman rules.
The key to determining the nature of the product lies in the fact that the Diels-Alder Reaction is essentially irreversible; as the endo product predominates, the reaction can be understood to be under kinetic control.
| Energies (kcal/mol) | Molecule 1 | Molecule 2 |
|---|---|---|
| Total Energy | 31.8794 | 34.0133 |
The Hydrogenation of a Cyclopentadiene Dimer
Hydrogenation of the endo-dicyclopentadiene can be achieved through use of a catalyst with molecular hydrogen. Initially only one of the two double bonds on the molecule is saturated, through consideration of the relative energies of the mono-unsaturated dihydro products, the identity of this double bond can be theoretically predicted. Continued application of the hydrogenation conditions will eventually yield the tetrahydro product, but only after a significantly prolonged period.
The dihydro derivative labelled molecule 4 is seen to be the product that is formed. A comparison of the energy components shown in the table above shows that the dihydro molecule 4 has significantly lower bending strain than molecule 3. This is reasonably easily rationalised using only a slightly developed chemical intuition; the double bond in the norbornylene segment of the molecule experiences a higher strain due to the smaller bond angle, and is therefore relatively weaker (and necessarily longer) when compared to the cyclopentene double bond. This simple thermodynamic consideration demonstrates the relative ease of hydrogenation when it comes to the norbornylene and cyclopentene C=C bonds[4].
The subsequent hydrogenation of the endo dimer offers a new problem; that of a choice of two double bonds to saturate. The relative ease of saturation will not necessarily be governed by the the thermodynamic stability of each product, but rather by kinetic properties such as the ease of attack on the double bond in question. The two possible products have been analysed, and the results shown as below:
| Energies (kcal/mol) | Molecule 3 | Molecule 4 |
|---|---|---|
| Stretch | 1.2657 | 1.0973 |
| Bend | 19.8958 | 19.8958 |
| Torsion | 10.7752 | 12.4976 |
| 1,4 VDW | 5.6293 | 4.5124 |
| Total Energy | 35.6892 | 31.1539 |
| Molecule 1
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Molecule 2
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Molecule 3
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Molecule 4
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Stereochemistry of Nucleophilic Additions to Pyridinium Ring (NAD+ analogue)
This section concentrates on two related reactions, both of which involve the Nucleophilic attack by a reagent at the 4-position of a pyridine. Schultz et al[5]has proposed that the first of these reactions involves attack by the organometallic reagent, methylmagnesium iodide, on the optically active derivative of prolinol, while the second is another regiospecific reaction between anilene and N-methylquinolium, both are shown below in mechanistic terms.
Molecule 5
The highly selective nature of these reactions (both in terms of regiochemistry and stereochemistry) can possibly be explained mechanistically. In the first instance, a possible complexation or coordiantion of the carbonyl oxygen to the Magnesium centre (Grignard) will allow the conjugate addition at C4 direct access to the same face, resulting in the observed product stereochemistry. This same rational can be applied to the second reaction with a slight twist; without the metal centre to complex to, the carbonyl oxygen will prevent access to the same face (by electrostatic repulsion), and the nucleophilic lone pair on the Nitrogen will instead have to attack on the opposite ring face, again leading to the observed product.
The geometry of the pyridinium containing reagent was optimised with respect to the dihedral angle (highlighted in the molecule below). A number of different configurations were modelled and the results have been plotted below, with the most stable conformer represented by the lowest total energy of the molecule, the exact variance of energy with dihedral angle is not necessarily simple, and so the data was not connected in a line graph as this could potentially be misleading.
This energy minimum corresponds to a conformer with a dihedral angle of 22.6 degrees.
This dihedral angle is key to understanding the stereoselectivity of this reaction, as the mechanistic explanation given above relies on there being a differential in the angle of the oxygen to the ring in order to define the stereochemistry.
Molecule 7
In this analogous reaction between molecule 7 and aniline, the control of diasterofacial selectivity has again been attributed to the critical dihedral angle according to the brief mechanistic analysis offered above. The geometry has again been optimised with respect to the dihedral angle, this time offering an energy minimum corresponding to a conformer with angle of -20.1 degrees (i.e. below the ring). Attack on this diaseterofacial mode is prevented by a combination of electrostatic repulsion and steric hindrance, and is instead directed to C(4) from above the ring.
MeMgI cannot be used in the first example, as the screen shows that Mg is unknown to the program
Suggested Improvements
The computational calculations rely on a number of key approximations; when using molecular mechanics these are connected to the choice of force field. An optimisation based on MO theory would seem to be more appropriate to many of the cases being investigated, with MOPAC (employed later on) and DFT based simulations as good examples of such systems. It has been suggested in literature that making the molecule in question less conformationally flexible would be likely to increase the accuracy of the results; this can be achieved by adding bulky groups to prevent ring flipping and lock a particular conformation. Obviously this is useful only as a guideline, in many cases it would defeat the object of the study to change the molecular structure.
Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol
The total synthesis of Taxol involves an intermediate that has the potential to exist as a pair of atropisomers. An atropisomer is a stereoisomer in which the rotation about a single bond is sterically hindered. At reasonable temperatures, these form a pair of isomers that cannot interconvert.
The atropisomeric forms of the Taxol intermediate have been shown to convert from the molecule 10 form to that of molecule 11 when left to stand.
As in the earlier studies, a comparison of the relative contributions to the total energy from the bending and vibrational modes shows that the atropisomer 10 has a much higher bending strain than atropisomer 11. Again, the conformation of the molecule is the root cause of this energy difference; with the six membered ring in atropisomer 11 existing in a relatively lower energy chair formation with the carbonyl group pointing below the ring, compared with the the same ring in atropisomer 10, which is n the higher energy twist boat conformation, with the carbonyl group pointing above the ring. This is the origin of the relative stability of form 11 over that of 10, which explains the conversion of 10 when it is left to stand.
Hyperstable olefins have been definied as alkenes which are less strained than their correspondingly saturated form, and are characterised by a negative olefinic strain energy (OS), which is itself a direct measure of the imbalance in the strain experienced in an olefin and its saturated form (as its most stable conformer). A negative OS Energy indicates that the olefin in question will be resistant to hydrogenation, and as such these groups are often employed in total synthesis when there are other FG’s that may need to be reduced.
Modelling Using Semi-Empirical Molecular Orbital Theory
Regioselective Addition of Dichlorocarbene
The dichlorocarbene reagent can add to the double bond syn to the chloro-substituent of the molecule, only this mono-adduct has been detected experimentally:
Both the reactivity and the regiochemistry of a molecule are governed by the geometry of its electronic structure; this area has been thoroughly treated, and computer modeling is now used to predict the molecular orbitals corresponding to a certain LCAO. These modeled molecular orbitals can then be used to rationalise, or even to predict the site of attack and the resultant stereochemistry of the product. Investigations regarding the reactivity of a particular molecule generally focus on the MO's close to the crucial HOMO-LUMO gap. This method has been applied to the above reaction, yielding the following orbital sets:
| HOMO-1
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HOMO
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LUMO
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LUMO+1
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LUMO+2
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| Derivative | C-Cl stretch /cm-1 | syn C=C stretch /cm-1 | anti C=C stretch /cm-1 |
|---|---|---|---|
| Diene | 771.13 | 1756.87 | 1737 |
| Alkene (syn) | 774.94 | 1758.05 | - |
The HOMO shows a greater electron density at the syn-alkene relative to the anti-alkene, and as such would represent a better site of attack for an incoming electrophile.
The stretching frequencies gained from these simulations are reasonably uneven with regards to correlation to literature values. The C-Cl stretching frequency of 771.13cm-1 agrees reasonably well with the literature value of 760cm-1, while the values gained for the C=C bonds are not within the realms of experimental error, being far higher than those reported in literature (~1750cm-1 c.f. 1640-1680cm-1), this suggests a stronger bond than has been experimentally determined (with k being proportional to ϖ). This can be explained by the weakness of the model applied to the system; modeling a realistic bond on the physically ideal harmonic oscillator does not take into account a number of the specific interactions that force deviation from this model (the anharmonic approximations form the basis of the necessary corrections to the harmonic model). Modeling the system more accurately would require an expanded basis set, and to take into account these anharmonic deviations; together these would take up far more computation time and make the simulation very difficult to run and analyse in the time given.
The stretches corresponding to the anti-alkene are lower than those of the corresponding syn-alkenes, suggesting a lower bond energy, and hence weaker bond. This is however only a half truth as it does not take into account the relative contributions from the unequal pi and sigma bonds; the relative destabilization of the anti-alkene has been attributed by Rzepa et al. to the stabilizing antiperiplanar interactions between the anti-alkene π orbital (HOMO-1) and the C-Cl σ* orbital (LUMO+1). The aforementioned relatively high electron density in the syn-alkene is again connected to the local π orbital geometry.
An extension to the experiment was suggested, in which the compound effects on the C=C and C-Cl stretching frequencies of the addition of heteroatom groups onto the anti-alkene were measured.
| FG | Group | C-Cl stretch /cm-1 | anti C=C stretch /cm-1 | syn C=C stretch /cm-1 |
|---|---|---|---|---|
| Silyl | SiH3 | 763.8 | 1690.1 | 1757.2 |
| cyano | CN | 765.8 | 1706.4 | 1753.2 |
| Hydroxyl | OH | 762.9 | 1752.8, 1757.6 | 1752.8, 1757.6 |
The results were, unsurprisingly, a marked change in the bond structures and associated energy of many parts of the molecule. The Silyl group had the effect of lowering the C=C stretching frequency, perhaps due to a funneling of electron density from the double bond MOs to the low lying Silicon d orbitals. The same effect, albeit somewhat weaker, was noticed in the case of the cyano-substituted alkene; the inductive electron withdrawing nature of this substituent again removed electron density from the double bond. The hydroxy group exhibited equally expected behavior through resonance donation (in competition with inductive withdrawal) and therefore strengthening the bond.
Structure based Mini project using DFT-based Molecular orbital methods
The literature that I have decided to base my report on is:
Stereodivergent Synthesis of 1,3-syn- and -anti-Tetrahydropyrimidinones Michael Morgen, Sebastian Bretzke, Pengfei Li, and Dirk Menche* 2010 Vol. 12, No. 20 (4494-4497)
http://pubs.acs.org/doi/pdf/10.1021/ol101755m
The main aim of this project is to use the molecular modeling software to investigate the expected spectral assignments given to the products of a particular reaction.
This particular reaction is of potentially great interest as a synthetic tool in pharmaceutical chemistry as it allows for a simple and direct route to a strongly stereoselective synthesis of both 1,3-syn- and -anti-Tetrahydropyrimidinones, a key moiety in some notable alkaloids and HIV retrovirals. The reaction is based on the work of the work of the Tsuji research team, and developed by Trost
Data reported for both isomeric forms of the molecule are as follows:
(syn-isomer): 13C (75.48 MHz, CDCl3): δ = 21.7, 35.0, 57.0, 57.2, 69.1, 117.1, 125.7, 127.3, 128.2, 128.3, 128.4, 128.5, 129.2, 129.3, 134.7, 136.2, 136.3, 140.5, 144.7, 149.0, 153.1
(anti-isomer): 13C NMR (75.48 MHz, CDCl3): δ = 21.6, 38.1, 55.4, 57.2, 68.5, 118.0, 125.3, 127.7, 127.8, 128.1, 128.3, 128.9, 129.1, 129.2, 134.1, 135.0, 135.7, 141.0, 144.9, 148.9, 152.6
Mecahnistic Detail
The literature offers the suggestion that the pronounced solvent effect may be due to a reversal of the enantiofacial bias exhibited in a typical Tsuji-Trost mechanism. The extent of solvation of the nucleophilic amide is highlighted as a possible physical explanation for the selectivity demonstrated by the Palladium catalyst in the presence of different solvents. It is suggested that, in THF, a conventional attack on the side opposite to the π-allyl complex is expected, leading to an inversion of configuration at the chiral carbon. The opposite is proposed for the less solvated Nu/DCM system, in which the nucleophile may directly attack the π-allyl intermediate on the same side as the cationic complex – essentially an attractive electrostatic interaction, leading to retention of configuration.
The above offers only a brief mechanistic explanation describing the possible role of the solvent in this reaction; and further, offers no kinetic data on the reaction whatsoever. In order to elucidate the nature of the products, and therefore discover if solvent based stereodivergent strategy is based on the mechanistic interaction between solvent and reagent or whether it is based on the competition between thermodynamic and kinetic processes, a simple procedure can be proposed. Chemical intuition would suggest that the syn-isomer is the thermodynamic product (this is based on consideration of the relative stabilities of the heterocyclic ring conformers, with the 1,3-diequatorial interaction favoured over the 1,3-diaxial or 1-equatorial,3-axial), and is supported by MM2 calculations. If a dynamic equilibrium exists between the two isomers, the reaction will eventually favour the thermodynamic product; in order to see if this rational can be applied to these isomers, both products should be isolated and the conditions reversed (i.e., syn-product transferred to DCM and vice versa).
NMR Comparison between Calculated Spectra and Literature Values
Discussion of NMR data
The data seems to correspond surprisingly well with the experimental specta provided in the literature, and would seem to suggest a correct assignment by the authors. There do however, seem to be ranges in the spectra in which the differences are more pronounced - seen in the table above; these correspond to the regions closest to the heteroatoms. It would have been more appropriate to have found the closest conformer that corresponds to the global energy minimum for each isomer in order to gain the most realistic spectum - this would also prove to be a strong test of the approximations used in the process, instead a more rough effort was made to locate this conformer, giving a weaker representation of the drawn molecule.
Application of the Nuclear Overhauser Effect Spectroscopy (NOESY) would be sufficient to determine the stereochemistry of the diastereomers as it relies on the spacial relationship (through space interactions) of the two Nitrogen bearing substituents on the chiral carbons. This spectroscopic technique should be able to be used to determine the relative stereochemistry of the diastereomers.
Separation of a diastereomeric mix should not be a problem due to the stereodivergent synthesis methods used, however, varying types of chromatography could be used to further purify the products.
Mini Project Conclusion
The use of modeling software to predict the spectroscopic properties of the two isomeric products of this interesting reaction has proven the worth of the computational approach. The calculated NMR spectra was impressively close to the corresponding experimental spectra given in the literature. Potential methods of separation and characterisation of the diastereomeric pair have been offered, but will require further experimental work in order to determine their effectiveness.
References
- ↑ 1.0 1.1 1.2 N.L.J. Allinger, CJ. Am. Chem. Soc., 1977, 99, 8127: DOI:10.1021/ja00467a001
- ↑ J. Baldwin, J. Org. Chem., 1966, 2441
- ↑ K. Alder, G. Stein, Angew. Chem., 1937, 514
- ↑ D. Skála, J. Hanika, Pet. Coal, 2003, 45, 105
- ↑ A. Schultz, L. Flood, J. Springer, J. Org. Chem., 1986, 51, 838; DOI:10.1021/jo00356a016
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