Rep:Mod:bigbang007

Conformational analysis using Molecular Mechanics (Part 1)

The Hydrogenation of Cyclopentadiene Dimer

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition (Scheme 1). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 (Figure 1) before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. (Table 1)

Scheme 1. Dimerisation of cyclopentadiene via cycloaddition

Figure 1. Structures of Dihydro derivative 3 and 4 of dimer 2

Results and Discussions

Properties	dimer1	dimer2	dimer3	dimer4
Molecule label	Dimer 1	Dimer 2	Dihydro derivative 3	Dihydro derivative 4
Total bond stretching energy / (kcal/mol)	3.54283	3.46733	3.31126	2.82301
Total angle bending energy / (kcal/mol)	30.77281	33.19139	31.93650	24.68568
Total stretch bending energy / (kcal/mol)	-2.04133	-2.08213	-2.10212	-1.65715
Total torsional energy / (kcal/mol)	-2.73034	-2.94943	-1.47005	-0.37815
Total out-of-plane bending energy	0.01486	0.02196	0.01319	0.00028
Total van der Waals energy / (kcal/mol)	12.80095	12.35735	13.63736	10.63680
Total electrostatic energy / (kcal/mol)	13.01366	14.18423	5.11953	5.14702
Total energy / (kcal/mol)	55.37344	58.19070	50.44567	41.25749

Table 1. Molecule 1, 2, 3 and 4 optimized using MMFF94(s) force field with steepest descent

The total energy of dimer 1 (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer 2 (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer 2 rather than dimer 1 indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative 3 and 4, one can deduce that if the reaction is thermodynamically controlled, formation of molecule 4 is favored over molecule 3, and 4 is more stable than 3. Indeed, literature study shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer 2. Thus, molecule 4 is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of 4 over 3.

Atropisomerism in an Intermediate related to the Synthesis of Taxol

Molecule 9 and 10 (Figure 2) are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

Figure 2. Structures of atropisomers 9 and 10

Results and Discussions

The total energies of molecules 9 and 10 can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in Figure 2) as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules 9 and 10 lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. (Table 2)

Properties	molecule9	molecule10	parent9	parent10
Molecule label	Molecule 9	Molecule 10	Parent Hydrocarbon of 9	Parent Hydrocarbon of 10
Total bond stretching energy / (kcal/mol)	7.68872	7.59350	6.94420	6.42510
Total angle bending energy / (kcal/mol)	28.28780	18.79618	32.03408	22.28431
Total stretch bending energy / (kcal/mol)	-0.06988	-0.14163	0.30160	0.29425
Total torsional energy / (kcal/mol)	0.17522	0.20421	9.50507	9.19384
Total out-of-plane bending energy	0.96979	0.84520	0.25574	0.03607
Total van der Waals energy / (kcal/mol)	33.18616	33.31300	32.71128	31.30102
Total electrostatic energy / (kcal/mol)	0.29968	-0.05585	0.00000	0.00000
Total energy / (kcal/mol)	70.53750	60.55461	81.75198	69.53459

Table 2. Molecule 9, 10 and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent

From Table 2 one can see that intermediate 10 is more stable than molecule 9 since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer 9 to convert into atropisomer 10.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

Geometry	molecule9	molecule9	molecule9	molecule9	molecule9	molecule9
Description	9 with the alkene H pointing down and the cyclohexane ring adopting chair	9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat	9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat	10 with the alkene H pointing down and the cyclohexane ring adopting chair	10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat	10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
Energy / (kcal/mol)	77.63255	82.62521	77.90904	61.03452	77.83977	66.28665

Table 3. Other structures of Molecules 9, 10 and their corresponding energies after optimization with MMFF94(s) force field

Spectroscopic Simulation using Quantum Mechanics (Part 1)

A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol

The spectroscopic data have been reported in literature for molecules 17 and 18 (Figure 3), which are the derivatives of 9 and 10 respectively. The objective here is to simulate ¹H and ¹³C NMR spectra and compare them with the values given in literature to see whether the simulated spectra are consistent with the literature or not.

In this exercise, molecule 17 was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

px200

Figure 3. Structures of molecules 17 and 18

Results and Discussions

Just like its parent molecule 9, The total energy of 17 can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in Table 4 (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

Possible structures of molecule 17	molecule17	molecule17	molecule17
Energy / (kcal/mol)	104.31700	118.02981	120.10595

Table 4. Structures of molecule 17 after optimization using Avogadro with MMFF94(s) force field

molecule17

Figure 4. Geometry of molecule 17 after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC DOI:10042/27701

1H NMR Spectrum	13C NMR Spectrum

Table 5. Simulated NMR spectra of molecule 17 after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC DOI:10042/27701

1H NMR data from computational method	1H NMR data from literature
	1H NMR (300 MHz, CDCI3) δ 4.84(dd, J =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,J=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)

Table 6. Table of ¹H NMR data from computational method DOI:10042/27701 and literature

Figure 5. Comparison between computational ¹H NMR results and literature

Excel was used to draw comparisons between computational NMR data and literature . From Figure 5, one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From Figure 6 one can see that computational ¹³C NMR data matches with literature much better than that for ¹H NMR. This is due to each C environment is defined explicitly and unlike ¹H NMR, where an assumption was drawn in plotting the data.

To conclude, both ¹H and ¹³C NMR data have been successfully interpreted using computational method with ¹H NMR deviates more from literature than ¹³C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation; the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

13C NMR data from computational method	13C NMR data from literature
	13C NMR (75 MHz, CDCI3) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71

Table 7. Table of ¹³C NMR data from computational method DOI:10042/27701 and literature

Figure 6. Comparison between computational ¹³C NMR results and literature

In order to compare the relative energies of molecule 17 and 18, molecule 18 was optimized using exactly the same approach as that for molecule 17. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From Table 8, one can see that the free energies of 17 (-1651.459445 Hartrees) and 18 (-1651.463260 Hartrees) are very similar with 18 being slightly lower in the energy. This indicates that 18 is more stable and should be favored thermodynamically, which indeed is confirmed by literature.

molecule18

Figure 7. Geometry of molecule 18 (100.49578 kcal/mol) after optimization at MMFF94(s) level of theory using Avogadro

Types of Energies	Molecule 17	Molecule 18
Zero-point correction / (Hartree / Particle)	0.467967	0.467823
Thermal correction to Energy	0.489479	0.489248
Thermal correction to Enthalpy	0.490424	0.490192
Thermal correction to Gibbs Free Energy	0.420585	0.421083
Sum of electronic and zero-point Energies (E= Eelec + ZPE)	-1651.412064	-1651.416520
Sum of electronic and thermal Energies (E= E0 + Evib + Erot + Etrans)	-1651.390551	-1651.395096
Sum of electronic and thermal Enthalpies (H= E + RT)	-1651.389607	-1651.394151
Sum of electronic and thermal Free Energies (G= H - TS)	-1651.459445	-1651.463260

Table 8. Vibrational analysis of molecules 17 and 18 (energy unit is Hartree)

Analysis of the properties of the synthesized alkene epoxides (part 2)

The crystal structures of Shi and Jacobsen Catalysts

21 and 23 (Figure 8) are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the Conquest program, were exploited utilizing the Mercury program.

Figure 8. The stable precursors of the Shi and the Jacobsen catalysts

Results and Discussions

Vibration

Figure 9. Crystal structure of precursor 21 obtained from Cambridge Crystal database using the Conquest program

Atom C-O bond length/nm O5-C10 0.1409 O4-C10 0.1439 O6-C2 0.1403 O3-C2 0.1403 O3-C7 0.1441 O1-C7 0.1413

Table 9. C-O bond lengths of all anomeric centers within precursor 21

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from Table 9 most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule 21)

Vibration

Figure 10. Crystal structure of precursor 23 obtained from Cambridge Crystal database using the Conquest program

The metal center Mn in the Jacobsen catalyst precursor 23 has coordination number of five and it adopts square based pyramidal structure (Figure 10) with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

Calculated NMR properties of the Epoxide

The NMR spectra of epoxides (E1, E2) formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule 17. (Figure 11)

Figure 11. Epoxides of trans-Stilbene and 1,2-dihydronaphthalene

Results and Discussions

Geometry	E1RR	E1SS
Description	E1 RR	E1 SS
Energy / (kcal/mol)	39.45682	39.45704

Table 10. Structures of E1 after optimization using Avogadro at MMFF94(s) level of theory

Geometry	1s2r	1r2s	1r2r	1s2s
Description	E2 1S2R	E2 1R2S	E2 1R2R	E2 1S2S
Energy / (kcal/mol)	30.22440	30.68345	68.09538	68.09535

Table 11. Structures of E2 after optimization using Avogadro at MMFF94(s) level of theory

E1 RR 13C NMR DOI:10042/27801	E1 SS 13C NMR DOI:10042/27802	E1 RR 1H NMR DOI:10042/27801	E1 SS 1H NMR DOI:10042/27802

Table 12. Simulated NMR spectra of E1 after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory

E2 1S2R 13C NMR DOI:10042/27812	E2 1R2S 13C NMR DOI:10042/27814	E2 1S2R 1H NMR DOI:10042/27812	E2 1R2S 1H NMR DOI:10042/27814
E2 RR 13C NMR DOI:10042/27832	E2 SS 13C NMR DOI:10042/27833	E2 RR 1H NMR DOI:10042/27832	E2 SS 1H NMR DOI:10042/27833

Table 13. Simulated NMR spectra of E2 after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory

From Table 12 and 13, one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

Assigning the absolute configuration of the epoxides

Optical Rotatory Power (ORP)

	E1 RR DOI:10042/27838	Literature	E1 SS DOI:10042/27839	Literature
[α]d	297.93 deg (589nm)	239.2 deg (589nm, 25 oC, Chloroform)	-297.84 deg (589nm)	-205.2 deg (589nm, 20 oC, Chloroform)
	E2 1S2R DOI:10042/27840	Literature	E2 1R2S DOI:10042/27841	Literature
[α]d	35.86 deg (589nm)	-90.5 deg (589nm, 25 oC, Chloroform)	155.82 deg (589 nm)	129 deg (589nm, 20 oC, Chloroform)
	E2 1R2R DOI:10042/27843	Literature	E2 1S2S DOI:10042/27844	Literature
[α]d	-246.60 deg (589nm)	N/A	246.61 deg (589 nm)	N/A

Table 14. Comparison of ORPs between calculated values and literature

The [α]_d from literature shows -90.5 deg for E2 1S2R, whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]_d magnitude of greater than 100 deg.

Electronic Circular Dichroism (ECD)

E1 SS DOI:10042/27985	E1 RR DOI:10042/27986
E2 1S2S DOI:10042/27987	E2 1R2R DOI:10042/27988
E2 1S2R DOI:10042/27989	E2 1R2S DOI:10042/27990

Table 15. ECD analysis of E1 and E2

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

Vibrational Circular Dichroism (VCD)

E1 SS DOI:10042/27992	E1 RR DOI:10042/27994
E2 1S2S DOI:10042/27995	E2 1R2R DOI:10042/27996
E2 1S2R DOI:10042/27997	E2 1R2S DOI:10042/27998

Table 16. VCD analysis of E1 and E2

VCD is a much better option over ECD since as one can see from Table 16, within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

Using the (calculated) properties of transition state for the reaction

'	E1 R,R	E1 S,S	E2 R,S	E2 S,R
Free energy of Transition State 1 / Hartrees	-1534.687808	-1534.683440	-1381.120782	-1381.131343
Free energy of Transition State 2 / Hartrees	-1534.687252	-1534.685089	-1381.125886	-1381.116109
Free energy of Transition State 3 / Hartrees	-1534.700037	-1534.693818	-1381.134059	-1381.126039
Free energy of Transition State 4 / Hartrees	-1534.699901	-1534.691858	-1381.126722	-1381.136239
Average of free energies of 4 transition states / Hartrees	-1534.69375	-1534.688551	-1381.126862	-1381.127433
Difference in free energies / Hartress	-0.005198		0.00057025
Ratio of K	246		0.55
Enantiomeric excess	99.2% ee for RR		28.6% ee for S, R

Table 17. Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene

'	E1 R,R	E1 S,S	E2 R,S	E2 S,R
Free energy of Transition State 1 / Hartrees	-3574.921174	-3574.923087	-3421.359354	-3421.369033
Free energy of Transition State 2 / Hartrees	N/A	N/A	-3421.359499	-3421.361580
Average of free energies of 4 transition states / Hartrees	-3574.921174	-3574.923087	-3421.359427	-3421.365307
Difference in free energies / Hartrees	0.001913		0.00588
Ratio of K	0.13		0.002
Enantiomeric excess	77.0% ee for S,S		99.6% for S,R

Table 18. Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene

From Table 17 and 18, one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

Investigating the non-covalent interactions in the active site of the reaction transition state

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

R,S	S,R
Orbital	Orbital

Table 19. NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from Table 19.

Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state

R,S	S,R

Table 20. QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene

QTAIM analysis in this case is just supplementary to previous NCI analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

New candidates for investigations

Figure 12. Epoxides of R-(+)-pulegone

	Cis-R-pulegone oxide	Cis-S-pulegone oxide
[α]d	26 deg (589nm, CHCl3)	-17.3 deg (589nm, CHCl3)

Table 21. Literature optical rotation data for Pulegone oxides

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide (Figure 12) are the suggested new candidates for investigation. Their optical properties from literature are shown in Table 21. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

Limitations of Software and Future improvements

Limitations of Software

Avogadro: Avogadro is not good for drawing large complicated molecules, it is always better to draw them in Chemdraw first before importing them to Avogadro to make 3D structures.

Optical Rotation Analysis: only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

Future improvements

If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the QTAIM analysis, if had time, one could compute Extensions/QTAIM/Molecular graph with lone pairs in order to locate the positions of lone pairs within molecules.