The Basic Techniques of Molecular Mechanics and Semi-Empirical Molecular Orbital Methods for Structural and Spectroscopic Evaluations

Introduction

Computational chemical anaylysis has been greatly significant in these days as technology is becoming powerful enough to perform the theoretical calculations. In addition to this, there are many programmes which strongly rely on chemical data base that is now ample to provide accurate predictions even on spectroscopic data. In this experiment, a combination of programmes was used, including ChemBio3D and Gaussian. The purpose of this experiment is to familiarise the programmes in order to apply them in real organic laboratories. This includes the minimization of chemical conformation, prediction of major isomeric product and calculations of spectroscopic data. In the end of this expeiriment, the validity of computational chemistry will be examined.

The Hydrogenation of Cyclopentadiene Dimer

Exo Dimer (1)

Endo Dimer (2)

Hydrogenated Endo Dimer (3)

Hydrogenated Endo Dimer (4)

Energies (kcal/mol)	Exo Dimer (1)	Endo Dimer (2)	Hydrogenated Endo Dimer (3)	Hydrogenated Endo Dimer (4)
Stretch	1.30001	1.2502	1.2659	1.1000
Bend	20.5956	20.8555	19.8063	14.5121
Stretch-Bend	-0.8463	-0.8334	-0.8276	-0.5478
Torsion	7.6334	9.5050	10.8698	12.5072
Non 1,4 VdW	-1.3992	-1.5182	-1.2207	-1.0509
1,4 VdW	4.2246	4.3041	5.6394	4.5069
Dipole-Dipole	0.3771	0.4455	0.1621	0.1407
TOTAL	31.8853	34.0086	35.6953	31.1681

The table shows that exo product is more stable than endo product.

Hydrogenation of double bond in 6-membered ring results more thermomodynamically stable product than that of 5-membered ring.

Molecules 1 and 2

The above figure show the mechanism for the Diels-Alder raction for endo product.

The frontier orbitals are drawn to explain the for the endo product being the major product. As the two cyclopentadienes come together for the collision, we are able to see that symmetry is matched for bond formation. The two dashed lines indicate the formation of two sigma bonds. At the back of the diene, the symmetry of the orbitals is matched for bonding interactions. Although, these interactions do not directly lead to formations of any bonding, but these drive the transition state to resemble the endo product. The endo product is kinetically favoured over exo product.

The above digram highlights that the reaction pathway to endo product is kinetically more favoured.

There is an alternative explanation for endo rule other than of frontier orbital approach. The through-space attractive HOMO/LUMO interactions between the two components results the transition state to look like a sandwich where the electrons are holding them together whilst allowing them free to rotate until the formation of sigma bonds. This vertical rotation greatly drive the formation of endo products.

The hydrogenation of the double bonds

It is expected that hydrogenation would preceed firstly via the double bond of the 6-membered ring followed by the 5-membered ring. It can be deduced from the energy values that the hydrogenation of double bond first occur at the 6-membered ring and then followed by the 5-membered ring. The great energy change from Molecule 2 to Molecule 4 is the relief of bending energy while to Molecule 3 does not feature that large energy. The kinetic product cannot be directly concluded from these energies. This should be accompanied by a series of experiment with reaction rate constant against the temperatures.

Stereochemistry of Nucleophilic Additions to a pyridium ring (NAD+ analogue)

Molecules 5 and 6

The minimised energy for Molecule 5 was found to be 39.8642kcal/mol(by MM2) and 57.9231kcal/mol(MMFF94). The 7-membered ring was fairly rigid and only other fragments had significant effect on the total energy of the molecule.

After addition of the Grignard reagent (MeMgI), molecule 6 was formed. This reactions features a high steroselectivity where the Grignard reagent attacts from the top. This can be interpreted with the intermediate, in which the Mg chelates the oxygen atom (which always points up).Therefore, it is much easier for the methyl group to be added from top via a series of electron movement.

Molecules 7 and 8

The minimised energy for the ring was calculated by MM2, 62.4642kcal/mol with the carbonyl group pointing upwards (dihedral angle ~20 degrees). Therefore, the same mechanistical approach of the Mg metal is expected to happen here.

Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol

The total synthesis of Taxol proceeds via either intermediate 9 or 10.On standing, the compound isomerises into the alternative carbonyl isomer via atropisomerism. The stereochemistry of carbonyl addition is judged by which isomer is the most stable one. MM2 calculations reveals that Intermediate 9 has energy of 48.881kcal/mol and Intermediate has energy of 51.4286kcal/mol.On the other hand, MMFF94 calculations shows that Intermediate 9 has energy of 70.881kcal/mol and Intermediate has energy of 74.4286kcal/mol.

These are the details of energy compositions:

Intermediate 9

 Stretch:                2.7066
 Bend:                  15.8737
 Stretch-Bend:           0.4020
 Torsion:               18.1901
 Non-1,4 VDW:           -1.0134
 1,4 VDW:               12.5764
 Dipole/Dipole:          0.1486

Intermediate 10

 Stretch:                2.6887
 Bend:                  15.8369
 Stretch-Bend:           0.3966
 Torsion:               18.2591
 Non-1,4 VDW:           -1.1024
 1,4 VDW:               12.6636
 Dipole/Dipole:          0.1462

Scrutinisation of of the minimum energy conformations of intermediate 9 and 10 leads us to that cyclohexane ring possesses a boat conformation for intermediate 9 and a chair conformation of intermediate 10.

Modelling Using Semi-empirical Molecular Orbital Theory: Regioselective Addition of Dichlorocarbene

The HOMO-2, HOMO-1, HOMO, LUMO, LUMO+1, LUMO+2 MOs
HOMO-2	HOMO-1	HOMO
LUMO	LUMO+1	LUMO+2

Optimisation via HF method led to above molecular orbitals. Considering the orbital contribution to bond formation, as expected, the HOMO was concluded to be most amenable to attack of an electrophile. It can bee seen that the HOMO of the endo C=C double bond possesses a larger electron density in comparison to that of exo C=C double bond. This larger electron density imparts a greater nucleophilicity for endo C=C towards electrophiles. Another factor that enhances the reactivity of the endo c=c and stability of exo C=C is the interaction of the exo C=C pi orbitals with the antibonding orbitals of C-Cl bond. This lowers the total energy of exo C=C bond and make it less susceptible towards electrophilic reaction.

The addition of dichlorocarbone to this molecule 12 occurs on the endo C=C bond, even though there will be a greater steric repulsion of large chlorine atom. The following calculations reveal why this addition is still favoured.

Energy /kcalmol-1

Stretch 0.6156 Bend 4.7823 Stretch-Bend 0.0496 Torsion 7.6318 Non-1,4 VDW -1.1034 1,4 VDW 5.781 Dipole/Dipole 0.4125 Total Energy 18.2053 JMol

A disparity is observed between the hydrogen atom on the endo carbon double bond (2.8Å and 3.2Å). This contribute some effect to relieve the steric repulsion by the large chlorine atom. Therefore MM2 shows its ability to account for explaining this reaction.

It is observed that the anti-alkene shows a lower stretching frequency than that of the syn-alkene. Utilising the fact that the frequency of C=C bond represents the bond strength, it can be suggested that the exo C=C bond is weaker than the endon one.

C-Cl Stretch: 770.80cm−1 C=C Stretches: anti-alkene= 1740cm-1, syn-alkene= 1757cm-1

Structure based Mini project using DFT-based Molecular orbital methods

Space-Filling Model of Molecule 13

13C NMR Spectrum for Species 14 & 15 has the same chemical shifts NMR Calculated[ppm]:
25.8 (s), 27.3 (s), 54.5 (s), 58.6 (s), 79.3 (s), 79.4 (s), 112.6 (s), 127.3 (s), 132.4* (s).

NMR Experimental [ppm]:
25.2 (s), 27.1 (s), 50.2 (s), 54.5 (s), 73.9 (s), 76.8 (s), 108.7 (s), 125.5 (s), 130.0 (s).

(*132.4ppm is the corrected for spin-orbit coupling erros. C-Br by -12ppm)

The calculated NMR data were close to the experimental data from the literature. This shows that the molecular mechanics method is a reasonable way to predict NMR values.

Above is the calculated 13C NMR

Above is the calculated IR for molecule 14

Above is the calculated IR for molecule 15

IR spectra of the two compounds did not show a great difference.

In addition to NMR and IR, optical rotations were calculated:

For Molecule 14 = +103.34 degrees
For Molecule 15 = -84.35 degrees

The sign change shows that the modelled compounds were indeed stereoisomers of each other.

Reference

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