Module One: Structure and Spectroscopy

Introduction

Computational modelling of molecular structure presents a modern approach to chemical research and support practical investigations in the lab. In principle, reactions can be simulated to predict quantitative properties and outcomes; therefore often time and resources are spared. The models often involve specifying nuclear geometries and applying theoretical knowledge such as sterics, stereoelectronics and interatomic forces as well as quantum mechanical wavefunctions to determine the approximate energies and spectroscopic data for many species along many possible reaction pathways. In conjunction with mechanistic rationale and consideration of the conditions set (i.e. whether thermodynamic or kinetic control exerts an influence), the identities of major and minor products as well as the route by which they are formed may be determined.

Modelling with Molecular Mechanics

Two molecular modelling methods are demonstrated on this page: molecular mechanics and semi-empirical molecular orbital theory. Molecular mechanics takes a non-quantum mechanical approach to estimate the total energy of a system based on summation of the following parameters:

Bond stretches
Bond angle deformations
Dihedral angles
Van der Waals repulsion forces
Dipolar electrostatic attraction forces

The corresponding equation assumes that each component is independent of all others:

$E_{s t e r i c} = \sum_{b o n d s} K_{r} (r - r_{e q})^{2} + \sum_{a n g l e s} K_{θ} (θ - θ_{e q})^{2} + \sum_{d i h e d r a l s} \frac{V_{n}}{2} [1 + c o s (n ϕ - γ)] + \sum_{n o n - b o n d e d} [\frac{A_{i j}}{R_{i j}^{12}} - \frac{B_{i j}}{R_{i j}^{6}} + \frac{q_{i} q_{j}}{ϵ R_{i j}}] + \sum_{H - b o n d e d} [\frac{C_{i j}}{R_{i j}^{12}} - \frac{D_{i j}}{R_{i j}^{10}}]$

The first three terms relate to the strain effects due to the defined configuration of the input structure. The equations required are Hooke's law potentials and a cosine function for the torsional strain along a bond. The final two components comprise the steric attractions and repulsions between non-bonded atoms and can be represented by a distance-potential energy function and summation of the hydrogen bonds present. Each contribution can be computed quickly since typical models (such as MM2) can compare the input structure with a large range of known force constants, torsion energies, potentials, charges and dipoles. Combination of the featured constants is known overall as the "force field". The Molecular Mechanics method avoids detailed considerations of electronic effects and this may be more convenient than a more complex quantum mechanical approach which takes much longer to compute even though greater accuracy may be expected. An obvious disadvantage of Molecular Mechanics also arises from its reliance on pre-defined data given that more complex molecules may have too many co-dependent parameters which are not predicted. The main feature of the model is finding the closest low energy conformation and hence the energy minima of a freely constructed structure. This is particularly useful when comparing isomeric intermediates or products as demonstrated in the next few examples. It is important to note that the MM2 model calculates absolute energies for molecules with identical atomic contents: only isomers and conformers may be compared. The steric energy is therefore not a comparable property for very different molecules such as reactants and products.

Hydrogenation of a Cyclopentadiene Dimer

The dimerisation of two cyclopentadiene rings has two theoretical stereochemical outcomes due to the pericyclic nature of the cycloaddition mechanism. The scheme below shows the exo and endo dimers:

The product isolated from the dimerisation has been identified experimentally as the endo isomer. Along with the exo isomer, this has been modelled using the MM2 method and the minimum energies have been calculated:

*MM2 calculated parameters for the hydro and dihydro products*
Energies (kcal/mol)	Exo	Endo	Product 3	Product 4
Stretch	1.2922	1.2615	1.2840	1.2615
Bend	20.5870	20.8507	19.8614	14.8507
Stretch-Bend	-0.8413	-0.8353	-0.8324	-0.8353
Torsion	7.6715	9.5055	10.8219	9.5055
Non-1,4 VDW	-1.4358	-1.5164	-1.2301	-1.5164
1,4 VDW	4.2320	4.3002	5.6275	4.3002
Dipole/Dipole	0.3778	0.4451	0.1621	0.4451
Total Energy	31.8834	34.0113	35.6944	31.0113

The results of the energy minimisation are tabulated along with a breakdown of the various contributions to the MM2 sum. Qualitatively, the exo isomer shows fewer areas of potential steric clash and so it is quantitatively the more stable product under thermodynamic conditions. Since the observed endo product has a higher total energy than the exo derivative, the reaction must be under kinetic rather than thermodynamic control.

Further reduction via hydrogenation can occur at one of the two remaining double bonds: the two possible products shown above have also been modelled:

The table to the right provides a breakdown of the relative contributions towards the total energy based on the MM2 method. This illustrates that the higher energy strain effects of stretching, bending and torsion as well as the fewer favourable van der Waals' forces and hydrogen bonding in product 3 make it less favourable thermodynamically and so 4 is the major product.

Nucleophilic Addition to a pyridinium ring

Similar analysis of steric energies may be applied to reactant conformations in order to rationalise the most likely geometries by which they may approach each other. The next two examples illustrate the addition of a nucleophile to a pyridinium ring and in both cases the product is stereospecifically determined. In the first example shown below, the nucleophile is a Grignard reagent: calculations had to be performed in the absence of this species since the chosen software cannot recognise the magnesium atom or tolerate more than one structure at once. This may impact the reliability of the results given that there is a known affinity between magnesium and the carbonyl oxygen.

For a single molecule such as reactant 5 there may be several low energy conformations; different structures may be obtained by altering the order in which the molecule is constructed and optimising the energy at many stages along the way. Two examples of this are displayed in three dimensions above. The energies of conformations a and b were 43.786 kcal/mol and 43.064 kcal/mol respectively- these are not substantially different but do demonstrate the possibility of optimising structures to false minima.
Further analysis of the geometry at the reaction centre is needed to rationalise the specificity of the mechanism. For example, the dihedral angles calculated for the carbonyl group with respect to the pyridinium ring were 23^o and 10^o. Since both are positive, as was the case for many tested structures of very similar energy, it can be seen that the more stable conformations for this molecule all prefer the carbonyl group facing up on the side of the ring shown. The fact that a great deal more steric bulk resides on the opposite face may significantly contribute to this although it is not directly adjacent to the reaction centre. This also has a large impact on the six-membered ring of the transition state; the oxygen atom coordinates to the magnesium centre of the Grignard reagent and the nucleophilic methyl attacks from the same side thus yielding a stereochemically pure product.

In the next example, the phenylamine nucleophile is much larger and steric control of the mechanism is consequently much more important. The lowest energy conformation for reactant 7 is given; this was obtained by the same variational treatment as for reactant 5.

As the 3D structure shows, there is a great deal more steric hindrance along the bottom face of the molecule (the "top" face being the one shown in the 2D figure). The carbonyl-pyridinium dihedral angle was 20^o on the opposite face this time to the approaching nucleophile; the oxygen atom has no cooperative effect on the reaction and so attacking on the same side would only result in higher steric clash.

The single product is also an atropisomer with the barrier to rotation occuring at the N-Ph bond. The 3D figure shows that full rotation of the phenyl ring would result in steric clash with one of the hydrogens on the quinoline benzoid ring.

The Stereochemistry of an Intermediate in the Synthesis of Taxol

A key intermediate in the synthesis of taxol also demonstrates atropisomerism; for this step a product mixture is obtained with an energy barrier to the rotation of the carbonyl group. Given enough time under normal conditions all of the molecules will convert to the more thermodynamically stable structure. Isomers 9 and 10 have been modelled using MM2 and MMFF94 with a breakdown of the contributions to the steric energy.

*MM2 calculated parameters for the taxol intermediate atropisomers*
Energies (kcal/mol)	9	10	Alkane
Stretch	2.6988	2.5513	4.1961
Bend	15.8846	10.6841	21.0517
Stretch-Bend	0.3981	0.3238	0.9432
Torsion	18.2322	19.7436	22.3730
Non-1,4 VDW	-1.1132	-1.4025	2.2353
1,4 VDW	12.6447	12.5581	16.7907
Dipole/Dipole	0.1462	-0.1791	0.0000
Total Energy	48.8914	44.2793	67.5900

By comparison of the total energies, it is clear that 10 is the more stable isomer. The MMFF94 total energies were in agreement with this: the results were 76.545 kcal/mol and 66.181 kcal/mol for 9 and 10 respectively. The most notable contribution to this difference in energy is the torsion strain about the carbonyl; when pointing up (as in 9) the geometry of the adjacent chiral centre deviates further from the ideal tetrahedral sp³ shape.

Another observation of the synthesis is that the alkene bond in the molecule will not readily undergo hydrogenation to the corresponding alkane. This appears to be an example of a "hyperstable alkene"; research has demonstrated that sometimes a C=C double bond adjacent to a bridgehead suffers less strain than the parent alkane^[1]. An MM2 calculation was performed on the reduced species (see table) and although absolute values cannot be compared, it is clear that bending strain contributes more substantially to the total energy of the alkane than it does for the alkene.

Semi-empirical Molecular Orbital Theory

The calculations required for semi-empirical orbital theory introduce some quantum mechanical considerations to the modelling of structures. Unlike Molecular Mechanics, this allows for the inclusion of stereoelectronic effects which may have a high impact on the accuracy of energy approximations. For example, Molecular Mechanics could only predict a kinetic effect on the outcome of the Diels Alder reaction of cyclopentadienes but no explanation for this was gained since the model ignores secondary orbital interactions. Although computing the results may be more complex, this theory is similar to Molecular Mechanics in that some typical known parameters are introduced to simplify the calculations with respect to an ab initio approach and therefore failures of the approximation occur when the structure tested deviates significantly from typical behaviour.

Regioselective Addition of Dichlorocarbene

MM2 calculates the total energy of dichlorocarbene to be 17.897 kcal/mol. The MOPAC/PM6 optimization yields 19.740 kcal/mol. Below are the results of the molecular orbital estimations. From left to right: The HOMO -1, HOMO, LUMO, LUMO +1 and LUMO +2 molecular orbital surfaces.

A common reason for the regioselective addition to alkenes is the Cieplak model^[2] but there are no especially electron rich σ orbitals and no discrimination between the σ* of the two featured double bonds. Instead, the hyperconjugation of σ* and the alkene π orbitals will be the focus of the investigation. The images above show that there is an anti-periplanar stabilising overlap of the exo π orbital (i.e. the bond which is anti to chlorine) in the HOMO -1 and the empty σ* C-Cl of the LUMO +1. This lowers the energy of the exo double bond relative to the endo C=C thus making it a poorer electron acceptor. In addition, the exo bond is more dispersed in the HOMO which makes it much less nucleophilic. These observations are supported by a physical bending of the exo bond towards the bridgehead group (also making it less geometrically acccessible to electrophiles) as seen in X-ray crystallographic studies^[3] of the structure. Therefore by considering frontier orbital and electrostatic reasoning, it can be demonstrated that the endo bond will be attacked by dichlorocarbene and other such electrophiles. This will occur on the face opposite the bridgehead to avoid steric clash.

*Key Results from the IR Spectra*
Bond stretch/cm^-1	dialkene	monoalkene	=C-CN	=C-OH	=C-SiH₃	=BH₂	Literature^[4]
C=C (syn)	1757	1758	1757	1757	1754	1758	1630-1680
C=C (anti)	1737	n/a	1670	1797	1633	1604	1630-1680
C-Cl	770	775	772	781	767	761	700-800

To demonstrate the effect of this stabilisation, the IR spectra of this reactant and an analogous structure with the exo double bond missing have been obtained using computational methods. In the dialkene, the C-Cl stretch is at a lower frequency hence the bond is weaker than that it would be in the monoalkene. This can be rationalised by the secondary orbital overlap described previously; electron density from the double bond contributes to increased anti-bonding character in the C-Cl bond.

The IR spectra of disubstituted reactants were also collected to compare this feature. The anti C=C stretches are at lower frequency for electron-donating substituents such as -SiH₃ and -BH₂, which is to be expected given that they enhance the ability of the double bond as a donor. In free alkenes the bond strength would be increased by such substituents leading to a contraction of bond length and a higher frequency stretch relative to =CH₂. The C-Cl bonds are also slightly lower due to enhanced donation to σ*. Further bending of the exo bond towards the bridgehead is likely to be observed in these cases to complement this. Conversely for -OH, which is electron-withdrawing, increases in the C=C and C-Cl stretching frequencies are seen to indicate a higher energy (shorter) bond. The donor interaction is lowered and this may be reflected in a relaxation of the exo bond bending towards the bridgehead. The case for -CN is more surprising in that it is known to be electron-withdrawing but shows a decrease in the C=C stretch and no noticeable changes in the C-Cl bond. It is possible that an additional positive resonance effect via conjugation with the multiple CN bond is taking place which strengthens the C=C bond.

Mini-Project: Diastereoselectivity in the Synthesis of Diketopiperazine-bis-α,β-epoxides

Diketopiperazines are found in a wide range of natural and pharmaceutical applications and their bis-epoxide derivatives are important intermediates in subsequent functionalisation reactions. Although the scheme above indicates that a theoretical mixture of six diastereomers is possible, either decomposition or mechanistic control results in the production of the two isomers shown. The crude mixture may be separated using flash chromatography to give one white (m.p. 140-142^oC) and one colourless product (m.p. 179-181^oC) in a 1:2 ratio. Ando and co-workers^[5] recently outlined a synthetic route and separated the racemic product; this was analysed using several techniques including carbon-13 NMR. These results will be reproduced electronically as well as other computational analyses in order to rationalise the selectivity of the reaction. In this case, techniques such as calculating ³J_HH couplings and emulating the Electronic Circular Dichroism of the sample would usually aid characterisation but unfortunately, in this example there are no H-H dihedral relationships about the critical chiral centres and the products do not exhibit strong colours.

MM2 Properties of the Six Diastereomers

It is interesting to note that each of these highly substituted cyclohexane prefers the boat conformation over the usually more stable chair (the MM2 calculated difference was about 4 kcal/mol). This is possibly due to the rigid, near-planarity of the peptide bonds and the steric clashing of the epoxide and methyl groups in the chair arrangement. The theoretical diastereomers were also modelled to compare their relative energies:

*MM2 calculated parameters for the six diastereomers*
Energies (kcal/mol)	Major SSSR	Minor SSSS	SRRS	SSRS	SRSR	SSRR
Stretch	17.8414	17.5312	18.1082	17.5365	17.7691	17.4778
Bend	61.3590	60.3839	60.1931	60.2416	60.6425	59.9848
Stretch-Bend	-0.1740	-0.8353	0.7403	0.3323	0.2060	0.3455
Torsion	1.0524	1.2936	-1.5671	-0.1814	0.3539	-0.1229
Non-1,4 VDW	-4.6774	-4.1184	-6.1109	-6.1593	-6.2999	-6.1568
1,4 VDW	20.4517	20.4390	20.9192	20.6886	20.6646	20.7229
Dipole/Dipole	-1.9694	-1.7773	0.6854	-1.5580	-1.8347	-1.5494
Total Energy	93.8071	93.5779	92.9683	90.9003	91.5015	90.7018

The results indicate kinetic control of the mechanism since the two least stable isomers are the observed products. Comparison of the various contributions to the total energies highlights that lower torsion and higher attractive van der Waals' forces are present in the four theoretical isomers accounts for the majority of this stabilisation. If kinetic control is a dominating factor in the product outcome, it may be more useful to look for possible stereoelectronic effects: this will be the next focus of the discussion.

Molecular Orbital Estimations

The literature proposes a mechanism involving bromohydration of one alkene bond at a time leading to mixture of syn and anti bromohydrins in preparation for the final intramolecular S_N2 epoxidations:

^[6]

MM2 and PM6 optimisation produces an interesting starting point: the most stable di-alkene has one trans and one cis bond (this was tested for several starting structures). Analysis of the HOMO (top) shows two very electron poor double bonds; the electron density is smeared across the molecule due to the proximity of several conjugating and strongly electron withdrawing groups. Hence the addition reaction is very facile. The regioselectivity may be explained with reference to the LUMO (bottom) in which there is now a slight differentiation between the two double bonds. The alkene on the right of the molecule shares less of its antibonding character with the surrounding groups and is therefore a higher energy acceptor. Reaction occurs at the lower energy π* orbital first. The phenyl groups lie on the same face of the molecule and so sterics will determine the syn nature of the first addition product: the Br⁺ electrophile favours addition at the less hindered face and the same is true for the following OH^- anion. Therefore overall there is complete diastereomeric control over this step; two chiral centres are formed with the same phase of optical rotation.

The structure of this intermediate was also optimised and the HOMO and LUMO were modelled (see images on the right). The remaining double bond of the LUMO has very little anti-bonding character unlike the MO of the first bromohydration. Further mechanistic analysis is required, but an initial suggestion to explain the new stereocontrol shown at this step would be that an alternative pathway to the conventional bromohydration may be followed. Observations^[7]^[8]^[9] of many diketopiperazines show a preference for the OH group to be syn with respect to the previously added groups but the bromine may add syn or anti to this. Thermodynamic control of these intermediates was investigated but the observed combination of stereocentres could not be found at the lowest energy conformations: kinetic control is still strongly supported.

A mixture of RRRR and RRRS diastereomers in a 1:2 ratio will then epoxidise via S_N2 which inherently leads to inversion of all chiral centres and the two products observed.

Carbon-13 NMR Analysis

¹³C NMR was used in the literature investigation to characterise the products. The following chemical shifts were reported for the simulated products as labelled in the diagrams below:

*¹³C NMR Data for the Major Isomer*^[10]
Carbon No.	Shift/ppm	Literature/ppm	Deviation
1	34.6	26.5	8.1
2	36.8	29.7	7.1
3	66.8	62.6	4.2
4	67.3	62.8	4.5
5	75.3	70.5	4.8
6	75.5	71.8	3.7
7	123.9	127.0	3.1
8	124.6	127.5	2.9
9	124.9	127.5	2.6
10	125.1	128.5	3.4
11	125.6	128.8	3.2
12	125.6	128.8	3.2
13	125.9	129.1	3.2
14	125.9	129.1	3.2
15	126.7	129.4	2.7
16	126.7	129.4	2.7
17	132.1	130.5	1.6
18	132.9	131.1	1.8
19	166.4	160.6	5.8
20	168.7	164.3	4.4

The model matches the literature assignments closely: most of the deviations are within 5 ppm, which may be the limit of the computational accuracy and its inherent conformational restrictions. The good agreement is of course particularly important for the four chiral carbons, which clearly differ in chemical shift for the major and minor isomers. More significant deviations are found for the phenyl carbons, which were difficult to assign and not defined clearly in the primary source. For the major isomer, the methyl groups on each nitrogen atom showed the largest error with respect to the experimental data; this is possible due to greater freedom of movement in the true molecule. The model is more accurate for the minor isomer which shows a great deal of equivalency due to its centrosymmetric nature. It was successfully characterised therefore by the smaller number of chemical shifts reported.

*¹³C NMR Data for the Minor Isomer*^[11]
Carbon No.	Shift/ppm	Literature/ppm	Deviation
1	29.0	26.3	2.7
2	63.8	63.0	0.8
3	70.7	71.4	0.7
4	123.3	126.8	3.5
5	123.5	128.4	4.9
6	123.9	128.4	4.5
7	124.20	129.1	4.9
8	124.24	129.1	4.86
9	130.4	130.4	0.0
10	160.8	160.7	0.1

References

↑ W. Maier and P. Schleyer, J. Am. Chem. Soc., 1981, 103, 1891-1893
↑ Cieplak, A. S., J. Am. Chem. Soc., 1981, 103, 4540-4552.
↑ B. Halton, R. Boese and H. S. Rzepa., J. Chem. Soc., Perkin Trans 2, 1992, 447.
↑ D. H. Williams, Spectroscopic Methods in Organic Chemistry (6th ed.), 2007, p38 and p52.
↑ S. Ando, A. L. Grote and K. Koide, J. Org. Chem., 2010, (articles ASAP).
↑ Image taken from: S. Ando, A. L. Grote and K. Koide, J. Org. Chem., 2010, (articles ASAP).
↑ E. Iwasa, Y. Hamashima et al, J. Am. Chem. Soc., 2010, 132, 4078–4079.
↑ E. Ohler, F. Tataruch and U. Schmidt, Chem. Ber., 1973, 106, 396-398.
↑ J. Kim, J. A. Ashenhurst, M. Movassaghi, Science, 2009, 324, 238-241.
↑ http://hdl.handle.net/10042/to-6403
↑ http://hdl.handle.net/10042/to-6463

[1] W. Maier and P. Schleyer, J. Am. Chem. Soc., 1981, 103, 1891-1893

[2] Cieplak, A. S., J. Am. Chem. Soc., 1981, 103, 4540-4552.

[3] B. Halton, R. Boese and H. S. Rzepa., J. Chem. Soc., Perkin Trans 2, 1992, 447.

[4] D. H. Williams, Spectroscopic Methods in Organic Chemistry (6th ed.), 2007, p38 and p52.

[5] S. Ando, A. L. Grote and K. Koide, J. Org. Chem., 2010, (articles ASAP).

[6] Image taken from: S. Ando, A. L. Grote and K. Koide, J. Org. Chem., 2010, (articles ASAP).

[7] E. Iwasa, Y. Hamashima et al, J. Am. Chem. Soc., 2010, 132, 4078–4079.

[8] E. Ohler, F. Tataruch and U. Schmidt, Chem. Ber., 1973, 106, 396-398.

[9] J. Kim, J. A. Ashenhurst, M. Movassaghi, Science, 2009, 324, 238-241.

[10] ttp://hdl.handle.net/10042/to-6403

[11] ttp://hdl.handle.net/10042/to-6463

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