The Basic Techniques of Molecular Mechanics and Semi Emperical Molecular Orbit Methods For Structual and Spectroscopic Evaluations
Modelling Using Molecular Mechanics
The Hydrogenation of the Cyclopentadiene Dimer
Cyclopentadiene will readily dimerise at room temperature. There are two possible distereoisomers that could be formed, but actually one isomer is produced almost exclusively over the other. The two possible isomers are shown below.
Exo
Endo
1
2
The endo isomer is formed almost exclusively during the dimerisation. However if the absolute energies of both these diastereoisomers are calculated, using a MM2 method, the Exo form is more thermodynamically stable.
Total Energy
Exo
31.8764 kcal/mol
Endo
33.9975 kcal/mol
This means that endo diastereoisomer can be thought of as being formed as the kinetic product of this dimerisation. This observation can be explained by looking at the frontier orbitals of two separate cyclopentadiene molecules as they come together during the dimerisation.[1]The diagram below shows the orbital overlap that forms the new C-C bonds and the other orbitals of correct symmetry that hold the two cyclopentadiene molecules in such a way that only the endo product is formed. For the exo product to be formed these interactions are completely lost, which is highly unfavoured.
Hydrogenation of the cyclopentadiene dimer initially forms one of following dihydro derivatives of the endo diastereoisomer, before hydrogenating both of the double bonds. The two possible forms of the singly hydrogenated dimer are shown below.
These structures were optimised using an MM2 energy minimisation to give the components of energy contribution tabulated below.
3
4
Stretch
1.2349
1.0965
All energies are in kcal/mol
Bend
18.9381
14.5243
Stretch-Bend
-0.7609
-0.5494
Torsion
12.1242
12.4974
Non-1,4 VDW
-1.5017
-1.0700
1,4 VDW
5.7289
4.5125
Dipole/Dipole
0.1631
0.1406
Total Energy
35.9266
31.1520
These values show that isomer 4 is the thermodynamically more stable singly hydrogenated product. It can also be seen the energy difference is almost all attributed to the differing bend energy contributions, with the total energy difference being 4.7746 kcal/mol and the difference in the bend contributions as 4.4138 kcal/mol. This difference in bending energies can be attributed to the differing environments of the remaining double bond. In isomer 3 the double bond is within a 6-membered ring with a bridging CH2, whereas in isomer 4 it is within a single 5-membered ring. In each case the carbons in the double bond are sp2 hybridised and would therefore have an optimal bond angle of 120°. The calculated bond angles of the optimised sp2 carbons are tabulated below.
Isomer 3
Isomer 4
Angle 1
107.6°
112.4°
Angle 2
107.6°
113.0°
Isomer 3, with the double bond contained within the 6-membered ring with the CH2 briding, has smaller bond angles on the sp2 carbons, which puts more strain on the molecule and causes it to have a higher energy. Isomer 4, with the double bond contained with the 5-membered ring, has bond angles that are clower to the optimal 120° resulting in a smaller contribution to the total energy by the bending energy and an overall thermodynamically more stable molecule. This would cause a high stereospecificity to isomer 4 as the mono-hydrogenated product.
Stereochemistry of Nucleophilic additions to a pyridinium ring (NAD+ analogue)
5
6
This derivative of proline(left) reacts with MeMgI to alkylate exclusively at the 4 position of the pyridine ring with the methyl group facing up as the structure on the right. The reason for this high level of stereoselectivity can be rationalised by producing a 3D model of the reactant and paying particular attention to the orientation of the carbonyl group with respect to the position of alkylation. The optimised structure, calculated by a MM2 energy minimisation, is shown below with a few key measurements. The MeMgI was first included in the calculation but the program returned an error message. This is probably because it would have tried to put the 2 molecules a distance of infinity apart in order to minimise the energy.
Molecule 5
Total Energy
26.3154 kcal/mol
Dihedral Angle C=O-C=C
24.3°
The most important value is the dihedral angle of the carbonyl oxygen. It is the preferred orientation of this carbonyl group to be pointing up that directs the attack of the grignard onto the same face of the pyridinium ring that the carbonyl is angling towards. This is due to a coordination of the Magnesium to the oxygen lone pairs and thus directing the methyl addition to the same face.[2]
7
8
This next example is interesting because it has an opposite stereochemical result. Molecule 7 on the left has the C=O group pointing downwards, opposite to the previous example. However upon reaction with phenylamine the bond is formed on the top face of the molecule, on the opposite side as the C=O angles toward.
Molecule 5
Total Energy
15.4440 kcal/mol
Dihedral Angle C=O-C=C
-43.1°
As the dihedral angle shows, in this case the C=O is below the pyridinium ring but the group still adds to the top face. This is because, in comparrison to the previous example, the carbonyl oxygen doesn't chelate to the attacking reagent. The phenylamine molecule would infact be repelled by lone pair interactions and therefore attack on the least hindered side of the pyridinium ring, to give the stereochemistry shown above.
Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol
10
11
Molecule 10
Molecule 11
A simple MM2 calculation was done to determine the lowest energy atropisomer. It is clear that with the C=O in a downward pointing geometry the molecule is of a lower energy. The main component that is changing the energies is the bend component. This is probably mostly due to the forcing of the C-(CO)-C angle to an angle of more than 120° in the higher energy case. In molecule 10 this angle is 126.2° and in the more stable 11 it is 120.1°.
Stretch
2.6790
2.5462
Bend
15.8365
10.6617
Stretch-bend
0.3949
0.3197
Torsion
18.2135
19.6973
Non-1,4 VDW
-1.0448
-1.3233
1,4 VDW
12.6481
12.5449
Dipole/Dipole
0.1476
-0.1813
Total Energy (kcal/mol)
48.8749
44.2651
The reason these alkenes are very unreactive is because hydrogenation of the double bond would result in a higher energy due to the strain of the ring that contains them. This only occurs for alkenes that are constrained in a ring and causes a negative value for the Olefin Strain energy.[3] In situations where this occurs the alkene is often referred to as hyperstable. The low rate of reactivity has relatively nothing to do with steric hinderance of carbonyls getting in the way of attack.
How One Might Induce Room Temperature Hydrolysis of a Peptide
The lowest energy conformers of molecules 13 and 14 with the N-Substituent in an axial and equatorial position are shown as JMols below with the total energies calculated using an MM2 energy minimisation.
13 Axial N-Substituent
13 Equatorial N-Substituent
14 Axial N-Substituent
14 Equatorial N-Substituent
Pentahelicene
Pentahelicene
Pentahelicene
Pentahelicene
Total Energy (kcal/mol)
19.3740
13.1030
11.9533
8.9878
Looking at both molecules it is the equatorial positioned N-Substituent that produces the lowest energy. The lowest energy conformers are found when the hydroxy hydrogen is orientated as facing the carbonyl lone pairs to gain stabilisation through hydrogen bonding. However studies in the literature[4] show that the required geometry for each molecule to undergo hydrolysis is different for each one. Molecule 13, with the hydroxy group down, requires the N-Substituent to be equatorial for the hydroysis to occur, and molecule 14, with the hydroxy up, requires the N-Substituent to be axial. This means that for molecule 13 the more stable geometry is also the one required for hydolysis, but for molecule 14 it needs to be in the higher energy arrangement with the N-Substituent axial. This requirement is obvious with the models of the products as the 6-membered ring that is being formed would be of a much higher energy if the opposite orientations than described were followed through into the products. Models of the products are shown below.
Product of 13
Product of 14
Pentahelicene
Pentahelicene
Modelling Using Semi-empirical Molecular Orbital Theory
Optimised Geometries
An MM2 optimisation was first done, followed by a Hartree-Fock/STO-3G and finally a B3LYP/6-31G(d). The optimised geometries of these 3 calculations are shown below.
MM2
HF/STO-3G
B3LYP/6-31G(d)
Molecule 13 MM2
Molecule 13 HF/STO-3G
Molecule 13 B3LYP/6-31G(d)
There is one visual difference between these 3 models, which is the orientation of the cyclohexene rings. In the first model the rings are of the same orientation and are mirror images of each other. However in the higher level B3LYP/6-31G(d) the ring endo to the Cl-C bond is flattened out and the exo ring remains in the same orientation as before. The Hartree-Fock/STO-3G shows an intermediate of these two.
Molecular Orbitals
These are the molecular orbitals for Molecule 13 and the exo-hydrogenated version.
Molecule 13
Exo bond hydrogenated
Orbital
HF/STO-3G
B3LYP/6-31G(d)
HF/STO-3G
B3LYP/6-31G(d)
HOMO
HOMO-1
LUMO
LUMO+1
LUMO+2
There are quite a few differences between the two methods of molecular orbital calculations. In molecule 13 the HOMO and HOMO-1 show the biggest difference, with the B3LYP/6-31G(d) model shows a lot more electron density on the C=Cπ orbitals. The LUMO orbitals of both are pretty similar. The two models are even more different in the exo-hydrogenated version.
Vibrations
Molecule 13
Bond
Frequency
IR Absorbance
C=C (Exo)
1740.74
4.1444
C=C (Endo)
1760.9
3.9035
Cl-C
772.632
25.2437
Molecule 13 With Exo-Double Bond Hydrogenated
Bond
Frequency
IR Absorbance
C=C
1761.7
4.2955
Cl-C
777.033
20.2435
The first observation of the vibrational energies is that the two double bonds in molecule 13 don't have the same energy as each other, they differ in frequency by 19.84Hz. Secondly, in the hydrogenated molecule the C-Cl bond vibrational frequency is higher in energy than in molecule 13 with both double bonds. A higher energy vibration means a stronger bond. Both these observations are accounted for in the bond lengths. In molecule 13 the exo-double bond is longer than the endo, suggesting is bond order has been reduced slightly. The trend also follows in the difference of the Cl-C bond length in the hydrogenated and non-hydrogenated, with bond lengths of 1.789Å and 1.791Å respectively. This can be explained by an overlap of the Cl-Cσ* orbital overlapping with the C=Cπ system.[5] This overlap partially delocalises electron density from the C=C and the Cl-C bonds, this weekens both these bonds and causes a lower frequency vibration. When the double bond in question is hydrogenated the effect is reversed and the Cl-C bond increases in energy due to the regaining of electron density. This loss of electron density suggests the stereoselectivity towards the endo double bond in molecule 13 being hydrogenated during reactions with electrophiles, such as dichlorocarbene. However this is not the same as the hydrogenated product given and calculated here. A different synthesis route would have to be taken in order to hydrogenate the exo bond.
Upon analysis of the molecular orbitals calculated there was a discrepancy between the previously stated rational and the literature.[5] The Cl-Cσ* MO is the LUMO+2 and the C=Cπ is the HOMO-1, however these calculated MOs do not show good overlap and are infact out of phase in both the HF/STO-3G and the B3LYP/6-31G(d). An investigation was then done on the PM3 model, as used in the previous literature.[5]
PM3 Calculation
A PM3 calculation was run on Molecule 13. The optimised geometry is shown below, along with the HOMO-1 and LUMO-2 calculated molecular orbitals.
Optimised Geometry
HOMO-1
LUMO+2
Molecule 13 PM3
The geometry obtained via this method is different again but follows then trend seen of the endo ring bending away from the Cl-C bond. The molecular orbitals obtained here also match very well with the theory above about the vibrational analysis. There is good in phase overlap between the Cl-Cσ* and the C=Cπ. The geometry and orbitals obtained are identical to the ones reported in the literature.[5]
Conclusion
It is very clear that very different sets of molecular orbitals can be obtained depending on the method of geometry optimisation performed. The highest level calculation (B3LYP/6-31G(d)) was used to predict accurate vibrational frequencies of a molecule, but the molecular orbitals obtained from this did not support the results returned. It was the lowest level calculation (PM3), apart from MM2, that returned the more agreeable molecular orbitals to support the vibrational analysis. The HF/STO-3G method seemed to be somewhere in the middle. This is evidence to suggest the perhaps a higher level geometry optimisation calculation is not the best method for obtaining molecular orbitals and that lower level approximations should be used in order to gain models to use for analysis.
Mini Project
Click Chemistry
When substituted alkynes and azides are used in a cycloaddition reaction there are two possible regioisomeric products. A model of each product was produced using ChemBio 3D and an MM2 optimisation was run. A mpw1pw91 optimisation was then run using the 6-31G(d,p) basis set followed by an NMR calculation. The calculated NMRs were then compared to literature values for both possible isomeric products.
Isomer A
Structure
Calculated 13C NMR
Click Isomer A
The Gaussian output file for this NMR can be found here.DOI:10042/to-1167
The calculated estimates for the 13C NMR are reasonably close to the experimentally observed spectra found in the literature,[6][7]all calcualted chemical shift values are within 5ppm of the experimental. There are a few key differences in the calculated NMRs than the observed spectra. Firstly the calculated spectra contain more observable peaks than the experimental ones. This is because Gaussian assigns an individual chemical shift value for each individual atom, which in reality are so close in chemical shift that with the currently used resolution they would be indistinguisable in a recoreded spectra and would look like a broader peak. This is certainly an advantage of this method as very intricate NMR spectra could be assigned by using a calculated approximation as an aid. One disadvantage of the NMR approximation used is that it doesn't predict splitting of the peaks. This is clear in both Isomer A and B as the peak due to the CH2 carbon is predicted as a singlet of same intensity as the other carbon peaks. The recorded spetrum shows a 1:1:1 due to the quadrupolar splitting caused by the adjacent nitrogen.
The calculated spectra were of good enough approximation to enable assigment of each isomer. The main differences in these structures spectroscopically is the position of the C-H group on the central 5-membered ring. This carbon can either lie in between the 2 aromatic groups or adjacent to just one of them. This causes a higher chemical shift value of this carbon, due a higher level of de-shielding, and makes this the easiest peak to distinguish these structures by. The literature values are given as 148.0 and 138.26ppm for isomers A and B respectively. The calculated chemical shift values were 145.064 and 139.102ppm. These are both reasonable estimates, enough to distinguish and categorise the compounds. Running an NMR prediction would be a very useful tool for checking that the spectra you have recorded is infact the product that was intended to be synthesised. In the case of the literature reference given[6] the product reported as being made agrees with enough accuracy to back up their report and also the same applies for the reference values found for Isomer B.[7]
References
↑Organic Chemistry; Clayden, Greeves, Warren and Wothers; Oxford University Press 2001; p916
↑A. G. Shultz, L. Flood and J. P. Springer, J. Org. Chemistry, 1986, 51, 838. DOI:10.1021/jo00356a016
↑Evaluation and prediction of the stability of bridgehead olefins; Wilhelm F. Maier, Paul Von Rague Schleyer; J. Am. Chem. Soc., 1981, 103 (8), pp 1891–1900 DOI:10.1021/ja00398a003
↑M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', J. Org. Chem.,2008, 73, 6413–6416 ASAP: DOI:10.1021/jo800706y
