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The basic techniques of molecular mechanics and semi-empirical molecular orbital methods for structural and spectroscopic evaluations

Objectives

Computational chemistry enables chemists to accurately model many aspects of organic structure and reactivity. Such techniques are not only important for rationalisations of outcomes of reactions, but also extremely useful for predictions of modifications or even new types of reaction. Some of the diversity of such molecular modelling was attempted in the following experiments.

Modelling using Molecular Mechanics

The Hydrogenation of Cyclopentadiene Dimer

Dimerisation of Cyclopentadiene

The dimerisation of cyclopentadiene undergoes via Diels-Alder [2+4] cycloaddition, giving two products, the exo 1 and the endo 2 adducts. One molecule of cyclodiene acts as a 4π electron diene and the other one as a 2π electron dienophile. The reaction Scheme is shown in Scheme 1.

File:Cyclopentadiene dimerisation.svg
Scheme 1:Cyclopentadiene dimerisation[1]


The exo adduct is resulted from both σ bonds forming on the bottom face of the diene and both σ bonds forming on the top face of the dienophile, while the endo one is resulted from both σ bonds forming on the bottom faces on the diene and dienophile.[2] This is illustated in Figure 1. It can be seen that apart from the formations of two new σ bonds, at the back of endo dimer, there's also bonding interaction(shown in blue

arrow) since the symmetry of the orbitals are correct. Therefore, the endo 2 is more favoured due to this interaction between the space of the orbitals.[3]
Figure 1: Frontier Orbital Approach of the cycloaddition


Exo Dimer

Endo Dimer


However, the energies obtained by applying an MM2 force field to obtain the optimised geometries in Chembio3D suggest the exo dimer is more thermodynamically stable, having a lower total energy than that of the endo dimer. The endo dimer is thus the kinetic product. The results are summarised in Table 1.

Table 1:Minimised Energies in MM2 Force Field
Adducts Stretching

(kJ/mol)

Bending

(kJ/mol)

Stretch-Bending

(kJ/mol)

Torsion

(kJ/mol)

Non 1,4 Van der Waals

(kJ/mol)

1,4 Van der Waals

(kJ/mol)

Dipole/Dipole

(kJ/mol)

Total Energy

(kJ/mol)

Exo
5.3826 86.1606 -3.5081 32.0587 -5.9331 17.7198 1.5809 133.4609
Endo
5.2360 87.2856 -3.4993 39.8202 -6.4602 18.0845 1.8740 142.3407



As seen from the above table, the slight lower stretching energy of the endo dimer is due to the attractive interaction at the back of the diene, which is negative and resulted as a lower value of 6-12 potential.[4] The main difference of the energies between the two dimers generate from the torsional strain, with a difference of 7.6515 kJ/mol.


Although the exo dimer has a lower total energy than that of the endo dimer, it is reported in the literature[5] the endo dimer is the major product, with a yield of 95% while the exo is on of 5%, which agrees with the frontier molecular orbital approaches obtained. This means that the dimerisation of cyclopentadiene is kinetically controlled, with a lower energy barrier at the transition state.

Hydrogenation of Endo-Cyclopentadiene Dimer

The hydrogenation of the endo dimer of cyclopentadiene yields 3 and 4, which is shown below as Jmol files respectively. The optimised geometries of both are obtained using Chembio3D in MM2 force field. The results are summarised in Table 2.


Table 2: Minimised Energies in MM2 Force Field
Species 3
4
Stretching(kJ/mol) 5.1858 5.1493
Bending(kJ/mol) 78.6327 54.4841
Stretch-Bend(kJ/mol) -3.1481 -2.3651
Torsion(kJ/mol) 53.2548 51.9745
Non-1,4 Van der Waals(kJ/mol) -5.6204 -5.5537
1,4 Van der Waals(kJ/mol) 25.3385 18.5915
Dipole/Dipole (kJ/mol) 0.6833 0.5903
Total Energy(kJ/mol) 154.3267 122.4539


By comparing the total energies of 3 and 4, it can be seen that 4 is thermodynamically more stable with a much lower energy than that of 3. The main difference between the two is due to the bending energy, caused predominantly by the H-C=C bendings.[6] The torsion energies decrease in a small amount after hydrogenation. The bending energies of both 3 and 4 are lower than that of 2 as a result of the loss of one double bond. A comparison of the bond angles of the Endo-dimer and the hydrogenation products, 3 and 4 are shown in Table 3. The bond angle of H-C=C is 120 degree. [7] However, in all three cases, none of them are at 120 degree, the closer the angle to 120 degree, the less the binding energies required and less bond strain it has. Although both bond angles exhibited are closer than the others to the literature, the presence of two also results as a higher bending energy. Therefore, 4 is the one with the least strain and lowest binding energy. In addition, 1,4 Van der Waals energy also account for the energy difference between the two hydrogenation products.

3

4


Table 3:H-C=C Bond Angles
Molecules H-C=C angle 1 in blue

(degree)

H-C=C angle 2 in red

(degree)

Bending Energies (kJ/mol)
Endo-dimer
Endo dimer
113 108 87.2856
3
3
N/A 107 78.6327
4
4
112 N/A 54.4851





Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol

The most Stable Isomer

In the synthesis of Taxol proposed by Paquette, an intermediate 9 or 10 is initially prepared from the carbonyl group pointing either up or down, which are atropisomers of each other.[8]

9
10
Table 4: Minimised Energies in MM2 Force Field
Species 9 10
Stretching(kJ/mol) 11.6548 10.9694
Bending(kJ/mol) 69.2631 47.4905
Stretch-Bend(kJ/mol) 1.8016 -3.4993
Torsion(kJ/mol) 76.4305 82.3384
Non-1,4 Van der Waals(kJ/mol) -6.5155 -9.0393
1,4 Van der Waals(kJ/mol) 54.8827 53.8870
Dipole/Dipole (kJ/mol) -7.2222 -8.3824
Total Energy(kJ/mol) 200.2948 178.7056

The total energy of isomer 10 is lower than that of 9. The negative contribution from the stretch-bend energy indicates a stretch responding to a reduced angle between two bonds in order to alleviate the strain, which could possibly be due to the hydrogen bonding within the molecule. The much lower bending energy of 10 compared with 9 is a result of having the carbonyl group not pointing on the same side as the hydrogen, thus less hydrogen bonding and less energy is required to put in during optimisation to break the hydrogen bonding interaction.[9] This is illustrated in the Figure 2. The main atoms involved in the hydrogen bonding are highlighted with green. The ones with two pink balls on it are oxygen, and the other one represents for hydrogen. The Jmol files of both intermediates are also included.

Figure 2 (9)

Figure 2 (10)

Figure 3 (9 (cyclohexane:twist boat))

The results obtained from the optimisation of geometries in MM2 force field agree with the ones obtained in the MM2 force field as well as the literature. [10] Intermediate 9 is therefore the kinetic product with a lower transition state than that of intermediate 10. Both molecules are optimised by running on SCAN and the optimised intermediate 9 turns out to have a 'twist-boat' for the cyclohexane rather than the 'chair' used for the optimisation of geometries in MM2 force field and MMFF94 force field.

Table 5: Minimised Total Energies in different Force Fields
Intermediates MM2 Force Fields (kJ/mol) MMFF94 Force Fields (kJ/mol)
9 200.2948 195.3302
10 178.7056 253.5781
The slow reaction with alkene

OS, olefinic strain is the extra strain associated with the double bond.[11] It can be used to examine the stability of different species, and heats of hydrogenation is related to it.

In this case, the thermodynamic intermediate 10 is compared with its hydrogenation product. The results are summarised in Table 6. The hydrogenation product has a higher energy than that of the 10, which indicates the 10 is more stable, i.e. low reactivity, belonging to the hyperstable olefins, whose olefin strain energies are negative, less than that of their parent hydrocarbon. [12] The difference between the two is the olefin strain, which is -91.616kJ/mol. [13] The loss of the double bond during hydrogenation results as more strain in the molecule, which can be seen via the Jmol file. Therefore, the reaction with alkene is slow.

Table 6: Minimised Energies in MM2 Force Field
Species Hydrogenation product of 10 10
Stretching(kJ/mol) 3.3587 10.9694
Bending(kJ/mol) 74.4610 47.4905
Stretch-Bend(kJ/mol) 1.8016 -3.4993
Torsion(kJ/mol) 106.4753 82.3384
Non-1,4 Van der Waals(kJ/mol) -2.7779 -9.0393
1,4 Van der Waals(kJ/mol) 72.8759 53.8870
Dipole/Dipole (kJ/mol) 0 -8.3824
Total Energy(kJ/mol) 270.3216 178.7056
Figure 3 (10 (Parent hydrocarbon))


Modelling Using Semi-empirical Molecular Orbital Theory

Objectives

In this section, the electronic aspects of the molecular reactivity are studied and how they influence on bonds and spectra properties.

Regioselective Addition of Dichlorocarbene

Part 1

In this section, the energy minimisation of 12 is carried out in MM2 force field as well as using Mopac interface/PM6. The results of energies from geometry optimisation is shown in Table 7.

Table 7:Minimised Energies in MM2 Force Field
Molecule 12 Stretching

(kcal/mol)

Bending

(kcal/mol)

Stretch-Bending

(kcal/mol)

Torsion

(kcal/mol)

Non 1,4 Van der Waals

(kcal/mol)

1,4 Van der Waals

(kcal/mol)

Dipole/Dipole

(kcal/mol)

Total Energy

(kcal/mol)

Figure 3 (12)

0.6081 4.8064 0.0409 7.6112 -1.0760 5.7984 0.1117 17.9006

Molecular Orbital Diagrams of Molecule 12 obtained using Mopac/PM6

HOMO-1: π
LUMO
LUMO+1
LUMO+2: Cl-C σ*

[14]


Mopac Interface ------------

Model: molecule 12.mol

Mopac Job: AUX PM6 CHARGE=0 EF GNORM=0.100 GRAPH SHIFT=80 Finished @ RMS Gradient = 0.09310 (< 0.10000) Heat of Formation = 19.74008 Kcal/Mol


The molecule 12 has a symmetry of Cs. [15] Only LUMO+1 orbital is symmetrical, lying in the same mirror plane of the molecule. As seen from the above orbitals, most of the electron density is away from the green Cl atom as a result of electrostatic repulsion. The highest electron density is shown on HOMO -1, which implies that is more favoured as a site by electrophilic attack. Therefore, the monoalkene formed in such a way shown below.

Table 8:Minimised Energies in MM2 Force Field
Molecule 12 Stretching

(kcal/mol)

Bending

(kcal/mol)

Stretch-Bending

(kcal/mol)

Torsion

(kcal/mol)

Non 1,4 Van der Waals

(kcal/mol)

1,4 Van der Waals

(kcal/mol)

Dipole/Dipole

(kcal/mol)

Total Energy

(kcal/mol)

Monocarbene

1.2700 6.4155 0.1871 13.5592 0.0233 8.1906 0.1347 29.7804

The monocarbene has a higher energy, which may result from the torsion and strain due to the formation of the new bonding.

Part 2

Optisimised geometries and IR spectra are obtained after the submission of the gaussian file to SCAN.

Table 9:IR analysis
Molecules C=C stretch

(cm-1)

C=C stretch

(cm-1)

C-Cl stretch

(cm-1)

out of plane C-H stretch

(cm-1)

Molecule 12 1757 1736 770 686
Monocarbene 1757 n/a 805 672
IR of monocarbene
IR of 12


The peaks of monocarbene are generally higher than that of molecule 12. This is due to the C=Cl σ* orbital and the exo π-orbital overlap, which stabilises the whole molecule.

Monosaccharide chemistry: glycosidation

During the glycosidation, two sugars could be obtained due to the neighbouring group participation from the adjecent acetyl group. The reaction of glycosidation undergoes as follow: [16]

To keep the computational demand minimal, R group is taken as Me. The possible mechanism is shown in Figure 4.[17]

possible mechanism for glycosidation

[18]

For each structure of A and B a conformer is drawn for each with the acyl group pointing above or below the plane of the cation, A' and B'. The structures are optimised using MM2 force field and MOPAC/PM6 method. The results are shown in the Table 10.

Table 10:Energy minisation using MM2 force field
Molecules Stretch

(kcal/mol)

Bend

(kcal/mol)

Stretch-Bend

(kcal/mol)

Torsion

(kcal/mol)

Non-1,4 VDW

(kcal/mol)

1,4 VDW

(kcal/mol)

Charge/Dipole

(kcal/mol)

Dipole/Dipole

(kcal/mol)

Total Energy

(kcal/mol)

A 2.4246 10.9185 0.9823 3.4172 -1.3283 19.1468 -12.0693 6.0114 29.5031
A' 2.100 9.9046 0.8832 1.2707 -1.4837 18.8209 -9.8806 5.5435 27.3685
B 1.9643 10.2073 0.7349 3.5485 -2.3727 17.3133 -4.5471 1.5533 28.401
B' 2.4417 11.2226 0.9808 3.4136 -1.2465 19.2025 -12.8412 6.0172 29.1907
Table 11: Minimised Total Energies in different Force Fields
Intermediates MM2 Force Fields (kcal/mol) MMFF94 Force Fields (kcal/mol)
A 29.5031 -91.6541
A' 27.3685 -88.72873
B 28.401 -68.22976
B' 29.1907 -91.64555


The results obtained indicates that B is more thermodynamically stable. The same has applied to C and D by testing them together with the C' and D'. The results are shown below.


Table 12:Energy minisation using MM2 force field
Molecules Stretch

(kcal/mol)

Bend

(kcal/mol)

Stretch-Bend

(kcal/mol)

Torsion

(kcal/mol)

Non-1,4 VDW

(kcal/mol)

1,4 VDW

(kcal/mol)

Charge/Dipole

(kcal/mol)

Dipole/Dipole

(kcal/mol)

Total Energy

(kcal/mol)

C 2.0447 13.8824 0.7314 9.8701 -2.6194 17.9702 -10.2509 -2.2249 29.4036
C' 2.7918 18.0285 0.8580 9.4775 -2.3725 19.1867 5.5435 -1.6052 48.9186
D 1.9643 10.2073 0.7349 3.5485 -2.3727 17.3133 -4.5471 1.5533 28.401
D' 2.4417 11.2226 0.9808 3.4136 -1.2465 19.2025 -12.8412 6.0172 29.1907
Table 13: Minimised Total Energies in different Force Fields
Intermediates MM2 Force Fields (kcal/mol) MMFF94 Force Fields (kcal/mol)
C 29.4036 -91.6465
C' 48.9186 -66.8742
D 45.4998 -85.9359
D' 43.6590 -91.66175

Structure of A, B C, and D shown as Jmol files after energy optimisation.

Predicted IR spectrum of A
Predicted IR spectrum of B
Predicted IR spectrum of C
Predicted IR spectrum of D
A

B

C

C

Structure based MINI project using DFT-based Molecular orbital methods

The total synthesis of (-)-Cubebol

Cubebol was first discovered by the flavour company, Firmenich in 2001.[19] It is also known as FEMA 4497, its structure shown below together with the Jmol file. It can be prepared from (-)- menthone, following a series of reaction forming cubebol.[20]

Reaction Scheme

Following the reaction scheme, several molecules are tested and compared with the literature. The molecules are optimised and their IR and NMR spectra are predicted. [21]


(-)-Cubebol

Predicted IR spectrum of (-)-cubebol
Predicted NMR spectrum of (-)-cubebol
Table 14: (-)-Cubebol IR Analysis
Species predicted values(cm-1) literature values (cm-1) %Differences
O-H stretch 3168 3350 -5.4%
C-H stretch(nujol)(sym) 2992 2951 1.39%
C-H stretch(nujol)(asym) n/a 2860
C-O stretch 1520 1490 2.01%
CH2, CH3 deformation 1144 1142 0.18%
=C-H, =CH2 out of plane bending 968 910 6.37%
(-)-Menthol

Predicted IR spectrum of (-)-Menthol
Predicted NMR spectrum of (-)-Menthol
Table 15: (-)-menthone IR Analysis
Species predicted values(cm-1) literature values (cm-1) Differences(cm-1)
C-H stretch 3038 2961 2.6%
C-H stretch(nujol)(sym) n/a 2931
C-H stretch(nujol)(asym) n/a 2872
C=O stretch 1806 1712 5.5%
C-H out of plane bend 1512 1455 0.18%
=C-H, =CH2 1302 1369 6.37%
=C-H, =CH2 n/a 1315 3.9%
CH rocking 777 750 6.37%
Molecule 17

Predicted IR spectrum of Molecule 17
Predicted NMR spectrum of Molecule 17
Table 16: Molecule 17 IR Analysis
Species predicted values(cm-1) literature values (cm-1) Differences(cm-1)
C-H stretch (nujol)(sym) 2989 2955 0.91%
C-H stretch(nujol)(asym) 2982 2929 1.81%
C-H stretch 2905 2851 1.89%
CO stretch 1456 1463 0.48%
C-H out of plane bend 1512 1367 0.18%
=C-H, =CH2 stretch 910 918 6.37%
=C-H, =CH2 out of plane bending 875 836 3.9%
Molecule 39

Predicted IR spectrum of Molecule 39
Predicted NMR spectrum of Molecule 39
Table 17: Molecule 39 IR Analysis
Species predicted values(cm-1) literature values (cm-1) Differences(cm-1)
OH stretch n/a 3390
C-H stretch(nujol)(sym) 2976 2956 0.68%
n/a 2935
C-H stretch(nujol)(asym) n/a 2862
C-O stretch 1416 1447 -2.14%
=C-H, =CH2 stretch 1360 1368 0.58%
=C-H, =CH2 stretch 1328 1320 0.60%
CH2,CH3 deformation 1192 1193 0.08%
CH2,CH3 deformation 1144 1151 0.61%
=C-H, =CH2 out of plane bending 944 946 -0.21%
=C-H, =CH2 out of plane bending 936 931 0.54%


The molecular modelling techniques applied here generate reasonably good IR spectra as indicated by the difference percentage. However, the NMR obtained from the prediction is so much higher than the literature values. The results of the NMR spctra are attached at the end as txt files.

References

  1. Cycloaddition of Cyclopentadiene DOI:http://commons.wikimedia.org/wiki/File%3ACyclopentadiene_dimerisation.svg
  2. H. Rzepa, 2nd Year Conformation Analysis Lecture Notes,Imperial College London, 2011 DOI:http://www.ch.ic.ac.uk/local/organic/pericyclic/
  3. J. Clayden, N. Greeves, S. Warren and P. Wothers, Organic Chemistry, Oxford University Express, New York, USA, 2001, pp916-917 ISBN:978-0-19-850346-0
  4. J. E. Jones, Proceedings of the Royal Society of London. Series A, 1924, 106, 463-477 DOI:10.1098/rspa.1924.0082
  5. M. E. Jamróz, S. Gałka and J. C. Dobrowolski, Journal of Molecular Structure: THEOCHEM, 2003, 634, 225-233 DOI:10.1016/S0166-1280(03)00348-8
  6. DOI:http://en.wikipedia.org/wiki/Molecular_vibration
  7. S. E. Barrows and T. H. Eberlein, Journal of Chemical Education, 2005, 82, 9, 1329 DOI:http://pubs.acs.org/doi/abs/10.1021/ed082p1329#citing
  8. DOI:{{{1}}}
  9. DOI:http://mason.gmu.edu/~aphan6/projects/protein/PART%20III.htm
  10. S. W. Elmore and L. Paquette, Tetrahedron Letters, 1991, 319 DOI:http://dx.doi.org/10.1016/S0040-4039(00)92617-0
  11. W. F. Maier, P. Von Rague Schleyer, J. Am. Chem. Soc., 1981, 103, 1891. DOI:http://dx.doi.org/10.1021/ja00398a003
  12. A.B. McEwen, P. v. R. Schleyer, J. Am. Chem. Soc., 1986, 108, 14, pp 3951-3960 DOI:10.1021/ja00274a016
  13. W. F. Maier, P. Von Rague Schleyer, J. Am. Chem. Soc., 1981, 103, 1891. DOI:http://dx.doi.org/10.1021/ja00398a003
  14. DOI:http://dx.doi.org/10.1039/P29920000447
  15. http://symmetry.otterbein.edu/common/images/flowchart.pdf
  16. https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:organic#Monosaccharide_chemistry:_glycosidation
  17. https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:organic#Monosaccharide_chemistry:_glycosidation
  18. https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:organic#Monosaccharide_chemistry:_glycosidation
  19. J. C. Leffingwell, Cool without Menthol & Cooler than Menthol and Cooling Compounds as Insect Repellents DOI:http://www.leffingwell.com/cooler_than_menthol.htm
  20. K L. McPhail et al, Bioorganic & Medicinal Chemistry, 2011, 19, 6675–6701., DOI:10.1016/j.bmc.2011.06.011
  21. D.M. Hodgsont, S. Salik and D. J. Fox, J. Org. Chem., 2010, 75, 7, pp2157-2168 DOI:http://pubs.acs.org/doi/pdfplus/10.1021/jo9022974