Rep:Mod:yi111c

Cyclopentadiene dimer

Cyclopentadiene dimerises to afford two isomers; exo- and endo-dimer as shown in Isomer 1 and Isomer 2 respectively below.

Isomers of dicyclopentadiene

Table 1. Optimisation Energies of Cyclopentadiene dimers (MMFF94s)

Optimised Energies	Isomer 1 (exo)	Isomer 2 (endo)
	Isomer 1	Isomer 2
Total bond stretching energy /kcalmol-1	3.54301	3.46743
Total angle bending energy /kcalmol-1	30.77268	33.19131
Total torsional energy /kcalmol-1	-2.73103	-2.94945
Total van der Waals energy /kcalmol-1	12.80164	12.35726
Total electrostatic energy /kcalmol-1	13.01367	14.18431
Total Energy /kcalmol-1	55.37344	58.19070

Stabilising orbital interaction in the endo diastereomer of dicyclopentadiene.

As discovered by _____ [Ref], and as Table 1 shows, the lower energy exo-diastreomer is the more thermodynamically stable product however the kinetic endo-diastereomer is formed. This is due to kinetic control of the reaction where the endo form has a lower transition state according to Hammonds Postulate, otherwise the more thermodynamically favourable exo conformer would be seen. One can explain this phenomenon by considering frontier orbital theory. The HOMO of the cyclopentadiene acting as a the diene (Ψ2) is electron rich and the LUMO of the other acting as the dienophile (π* of one C=C double bond) is electron deficient, which leads to a smaller difference in energy and better overlap. As the two molecules approach each other, one can see that the "spare" double bond dienophile has the correct symmetry of the p-orbitals to align and interact with the empty p-orbitals at the "back" of the dieneophile. This through-space interaction stabilises the transition state of the endo form. This could also explain the lower bnd energy of the endo product being the greatest contributor to its lower total energy.

Hydrogenation of dicyclopentadiene

Mono-hydrogenation of the endo dimer (Isomer 2) gives Isomer 3 and Isomer 4 as shown below.

Cyclopentadiene hydrogenation scheme

Table 2. Optimisation Energies of Mono-hydrogenated Cyclopentadiene dimers (MMF94s)

Optimised Energies	Isomer 3	Isomer 4
	Isomer 3	Isomer 4
Total bond stretching energy /kcalmol-1	3.31190	2.82311
Total angle bending energy /kcalmol-1	31.93610	24.68539
Total torsional energy /kcalmol-1	-1.46985	-0.37833
Total van der Waals energy /kcalmol-1	13.63724	10.63721
Total electrostatic energy /kcalmol-1	5.11949	5.14702
Total Energy /kcalmol-1	50.44573 = 211.206 kJ/mol	41.25749 = 172.737 kJ/mol

All the relative contributions to the total energy are lower in Isomer 4 which is ~9kcalmol^-1 lower in energy than Isomer 3. The str energy is lower due to the lower ring strain on the 6-membered ring which does not possess a double bond in addition to a methyl bridge. The difference in bond angles at the unhydrogenated C=C double bond (Isomer 3) and the hydrogenated C-C bond (Isomer 4) can be seen here where it is 103 °as opposed to 107 °in the less strained conformer. The major contribution maybe the torsional energy difference where the -CH₂ hydrogens on the cyclopentane ring in Isomer 4 are gauche but are eclipsed in Isomer 3 which contributes again to the lowering of the total energy. It is also interesting to see that the ring junction C-C bond (joining the 6- and 5- membered rings) is 1.563 Â in Isomer 3 and 1.549 Â in Isomer 4, highlighting the relaxation of ring strain upon hydrogenation of the cyclopentene ring. Whilst the electrostatic energies are similar as the composition of both molecules are the same, the aforementioned differences allow Isomer 4 to be lower in energy, therefore the thermodynamic product.

As for the kinetic product, one must examine more transition states of this reaction and to determine which conformer proceeds via the lower.

Atropisomerism in an Intermediate related to the Synthesis of Taxol

Atropisomerism

Table 3. Atropisomers of Taxol (MMFF94s)

Optimised Energies	Isomer 9	Isomer 10
Total bond stretching energy /kcalmol-1	7.67191	7.58759
Total angle bending energy /kcalmol-1	28.27862	18.80989
Total torsional energy /kcalmol-1	0.24018	0.21960
Total van der Waals energy /kcalmol-1	33.15286	33.28941
Total electrostatic energy /kcalmol-1	0.30130	-0.05491
Total Energy /kcalmol-1	70.53753	60.55202

Isomer 10 is lower in energy by ～10　kcalmol-1 than Isomer 9. Initial examination of the structure may lead to attributing that to the decrease in transannular strain by orientation of the C=O carbonyl pointing down on the opposite face of the methyl bridge. However investigation into "hyperstable" alkenes by Maier has revealed such olefins containing less strain compared to their parent hydrocarbon are slow to react due to the twisted cage-like structure. From a molecular orbital point of view, this reduces the π overlap i.e. the HOMO-LUMO.

Spectroscopic Simulation using Quantum Mechanics

¹H and ¹³C NMR of one of the two isomers of an intermediate related to the synthesis of taxol; Isomer 17 and Isomer 18 were calculated. The energies were calculated first and the more stable form used to obtain spectroscopic values as the lower is more stable and observable to give experimental values in literature for comparison.

Table 4. Energies of Isomers 17 and 18 (MMFF94s)

Optimised Values	Isomer 17	Isomer 18
Total bond stretching energy /kcalmol-1	15.87430	15.01619
Total angle bending energy /kcalmol-1	31.46355	30.82548
Total torsional energy /kcalmol-1	11.24601	9.73773
Total van der Waals energy /kcalmol-1	51.96730	49.37303
Total electrostatic energy /kcalmol-1	-7.29917	-6.02965
Total Energy /kcalmol-1	104.75446	100.46580

Isomer 18 is the thermodynamic product of the two conformers, being lower in energy by 4.3 kcalmol^-1 than Isomer 17 which is consistent with reports in literature. Paquette has noted that the methyl substituent α to the C=O carbonly group is brought closer to the bridgehead methyl groups in this conformation which opposes what is expected in terms of a steric argument. The vdW energy is lower still due to the overiding factor of the C=O being tucked under the main ring.

¹H NMR calculation of Isomer 18

Table 5. ¹H NMR of Isomer 18 (TMS B3LYP/6-31(d,p) Chloroform)

Hydrogen number	Chemical shift /ppm		Splitting	Proton count	Spectrum (Click to enlarge)
	Molecular model	Literature	Literature	Literature
20	5.99	5.21	m	1
35, 32	3.13	3.00-2.00	m	6
34	3.00	2.70-2.35	m	4
33, 37	2.93	2.20-1.70	m	6
43	2.81	1.58	t, J = 5.4 Hz	1
23	2.55	1.50-2.00	m	3
41	2.47	1.10	s	3
28, 46	2.34	1.07	s	3
26	2.28	1.03	s	3
44, 40	2.00
27, 42	1.85
51	1.65
38	1.58
48, 30	1.51
29	1.36
47	1.30
31, 52	1.22
53, 50, 49	0.95
45	0.62

(Please note that the literature values do not correspond to the hydrogen number.) The ¹H NMR data shows that the assignments by Paquette are consistent at higher chemical shifts in terms upon inspection of the range covered and the number of atoms they have been assigned to. At the lower end, greater deviations are seen perhaps to the dimethyl protons on the methyl bridge. More information of splitting and spin-spin coupling constants is required to conclude whether the literature has correctly assigned the peaks.

¹³C NMR calculation of Isomer 18

The technique for comparing the calculated ¹³C chemical shifts to those in the literature was taken from Braddock and Rzepa's investigation.

Numbered atoms of Isomer 18 for NMR discussion.

¹³C NMR of Isomer 18 (TMS B3LYP/6-31(d,p) Chloroform)

Carbon number	δ /ppm		Δδ /ppm	Spectrum (Model values - Lit. values)
	Molecular model	Literature
25	22.59	19.83	-2.76
5	24.17	21.39	-2.78
15	24.57	22.21	-2.36
24	26.51	25.35	-1.16
16	28.42	25.56	-2.85
11	32.58	30.00	-2.58
22	33.72	35.47	1.75
13	38.73	36.78	-1.95
6	41.35	38.73	-2.62	Deviation of literature values from those calculated
8	44.16	40.82	-3.34
9	45.80	43.28	-2.52
4	48.11	45.53	-2.58
19	49.67	50.94	1.27
14,1	55.03	51.30	-3.73
2	65.94	60.53	-5.41
3	93.27	74.61	-18.66
18	120.22	120.90	0.68
17	148.01	148.72	0.71
12	213.05	211.49	-1.56

The deviation plot of the ¹³C NMR data shows that the chemical shifts have been assigned relatively closely to those calculated with a mean deviation of around -3 ppm. The experimental value of δ = 74.61 ppm at Carbon-3 is much lower than predicted, caused by the spin-orbit coupling of sulfur to which it is adjacent. No correction value is available at present however considering that for C-Cl it is -3 ppm and -12 ppm for C-Br a value theoretically between the two will not make up for the -18.66 ppm discrepancy.

Analysis of the Properties of Synthesised Alkene Epoxides

Crystal structures of the Shi and Jacobsen catalysts

Shi catalyst

The Shi catalyst has three anomeric centres. The C-O bond lengths come in pairs of one short, one longer as shown in Table 6. Taking C(10) as an example, C(10)-O(5) bond is shorter than the C(10)-O(4) as the O(5) acts as the electron donating group by lone pair donation into the empty σ^* orbital of C(10)-O(4), increasing the bond length. it is most interesting to see O(2) acting as both the electron donating and accepting counterparts of two anomeric centres without much differentiation particularly to C(9). C-O bond lengths at C(2) anomeric centre are much shorter due to the favoured anti-periplanar arrangement of the lone pair and σ^* creating a stronger interacting and shorter bond.

Table 6. C-O bond lengths

Anomeric centre	Bond length A	Bond length B
C(9)	1.423	1.454
C(2)	1.415	1.423
C(10)	1.428	1.456

Jacobsen catalyst

The adjacent t-butyl group on the Jacobsen catalyst are arranged in a staggered manner to minimise steric repulsion as they are so close. Its crystal structure suggests a through space separation of 2.421 Â at the shortest contact and 2.975 Â for the longest. The steric bulk not only helps to stabilise the catalyst but increases the enantioselectivity of epoxidation as discovered by Palucki et al

NMR properties of two synthesised epoxides

You can compute the expected 13C and 1H spectra (chemical shifts and coupling constants) of your epoxides to check the integrity of what you have made. The technique for doing this was illustrated for taxol above. This on its own however will not identify the absolute configuration of your product.

(R)-Styrene epoxide

NMR chemical shifts DOI:10042/26679 Spin-spin coupling DOI:10042/26680 gNMR http://books.google.co.uk/books?id=-pn8K53IUqgC&printsec=frontcover#v=onepage&q=gnmr&f=false

Numbered atoms of styrene epoxide corresponding to NMR dicussion

Table 7. ¹H NMR of (R)-Styrene epoxide

Hydrogen number	δ /ppm		Δδ /ppm	Splitting	Proton count		Spectrum (Click to enlarge)
	Calculated	Literature		Literature	Calculated	Literature
13	7.51	7.35	-0.16	m	4	5
10	7.51
12	7.48		-0.13
11	7.45		-0.10				Deviation of literature values from those calculated
14	7.30	7.35	-0.05	NA	1
15	3.66	3.87	-0.21			1
17	2.54	3.16	0.04
16	2.34	2.81	0.27

Table 8. ¹³C NMR of (R)-Styrene epoxide

Carbon number	δ /ppm		Δδ /ppm	Proton count	Spectrum (Click to enlarge)
	Calculated	Literature		Calculated
5	135.13	137.75	2.62	1
1	124.13	128.65	4.521	1
3	123.41		5.24	1
4	122.96	128.33	5.37	2	Deviation of literature values from those calculated
2	122.95	125.65	2.70	2
6	118.27	128.33	10.06	1
7	54.06	52.51	-1.55	1
8	53.47	51.33	-2.14	1

https://www.thieme-connect.de/ejournals/html/10.1055/s-2007-965877 ( R )-Styrene Oxide [( R )-7]

Colorless liquid; yield: 44 mg (37%); 87% ee [chiral GC analysis, chiral capillary column β-Hydrodex PM, 100 °C, isothermal, t R = 14.45 min (major), 15.13 min (minor)].

[α]D 20 +20.3 (c 0.3, CH2Cl2) {Lit. [8b] [α]D 23 +28.6 (neat)}. Schaus SE. Brandes BD. Larrow JF. Tokunada M. Hansen KB. Gould AE. Furrow ME. Jacobsen EN. J. Am. Chem. Soc. 2002, 124: 1307

1H NMR (400 MHz, CDCl3): δ = 2.81 (dd, J = 5.4, 2.5 Hz, 1 H, PhCHCHH), 3.16 (dd, J = 5.4, 4.0 Hz, 1 H, PhCHCHH), 3.87 (dd, J = 4.0, 2.5 Hz, 1 H, PhCHCH2), 7.30-7.40 (m, 5 H, Ph).

13C NMR (100 MHz, CDCl3): δ = 51.33, 52.51, 125.65, 128.33, 128.65, 137.75.

(1S,2R)-1,2-dihydronapthalene oxide

Numbered atoms of 1,2-dihydronapthalene oxide for NMR discussion.

DOI:10042/26641 TMS B3LYP/6-31G(d,p) Chloroform

Table 9. ¹H NMR of 1,2-dihydronapthalene oxide

Hydrogen number	δ /ppm		Δδ /ppm	Splitting	Proton count		Spectrum (Click to enlarge)
	Calculated	Literature		Literature	Calculated	Literature
15	7.62	7.44	-0.18	d, J = 7 Hz	1	1
12,13	7.39	7.33-7.21	-0.12	m	2	2
14	7.25	7.13	-0.12	d, J = 7 Hz	1	1
21	3.56	3.89	0.33	d, J = 4 Hz	1	1	Deviation of literature values from those calculated
20	3.48	3.77	0.29	t, J = 4 Hz	1	1
16	2.95	2.83-2.79	-0.18	m	1	1
17	2.27	2.59-2.55	0.30	m	1	1
18	2.21	2.49-2.41	0.24	m	1	1
19	1.87	1.18-1.76	-0.09	m	1	1

Table 10. ¹³C NMR of 1,2-dihydronapthalene oxide

Carbon number	δ /ppm		Δδ /ppm	Proton count	Spectrum (Click to enlarge)
	Calculated	Literature		Calculated
4	135.39	137.1	1.71	1
5	130.37	132.9	2.53	1
6	126.67	129.9	3.23	1
2	123.79	128.8	5.01	1
3	123.53	128.8	5.27	1	Deviation of literature values from those calculated
1	121.74	126.5	4.76	1
9	52.82	55.5	2.68	1
10	52.19	53.2	1.01	1
7	30.18	24.8	-5.38	1
8	29.06	22.2	-6.86	1

Assigning the absolute configuration of two epoxides

Assignment of the absolute configuration of the styrene epoxide and 1,2-dihydronapthalene oxide can be achieved in three different ways:

• investigation of literature

• calculation of chiroptical properties including

a) Optical Rotatory Dispersion, ORD

b) Electronic Circular Dichroism, ERD

c) Vibrational Circular Dichroism, VCD

• calculation of properties of the transition state for the reaction

Chiroptical properties of the product epoxides

a) Optical Rotatory Dispersion, ORD

ORD of styrene epoxide DOI:10042/26689

Method	[a]25D /°	Wave length /nm	Solvent
Mechanistic Model	-30.40	589	chloroform
Experimental	-33.3	589	neat

The calculated ORD of this enantiomer is very close to that of the literature where 5 have been reported but give different values. Other solvents were used which will affect the rotatory power as the light can be diffracted differently depending on the solvent.

ORD of 1,2-dihydronapthalene oxide

Method	(1S,2R)			(1R,2S)
	[a]25D /°	Wave length /nm	Solvent	[a]25D /°	Wave length /nm	Solvent
Mechanistic Model	35.86	589	chloroform	155.82	589	chloroform
Experimental	-38.8	589	chloroform	152.5	589	chloroform

The S,R ORD of was calculated to give the opposite rotation of the same magnitude however upon calculation of the R,S, a positive rotation matched that in literature.

c) Vibrational Circular Dichroism, VCD

styrene epoxide DOI:10042/26685 :

1,2-dihydronapthalene oxide DOI:10042/26672 :

Transition state properties of epoxidation

Styrene epoxide

Calculation of enantiomeric excess of R-styrene epoxide

Energy	Diastereoisomer
	R	S
G /Hartree/particle	-3343.962162	-3343.969197
G /kJmol-1	-8779572.656	-8779591.127
ΔG /kJmol-1 R-S	18.471
K	1728.973
ee /%	99.94	Lit. 99

cis-β-methyl styrene epoxide

Calculation of enantiomeric excess of R,S-cis-β-methyl styrene epoxide

Energy	Diastereoisomer
	R,S	S,R
G /Hartree/particle	-3383.251060	-3383.259559
G /kJmol-1	-8882725.658	-8882747.972
ΔG /kJmol-1 R-S	22.314
K	8155.095287
ee /%	99.98	Lit. 82

Non-covalent interactions (NCI) in the active-site of the reaction transition state

Transition state in R,R Jacobsen epoxidation of styrene

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

Conclusion

It was found that many programs can be used to predict properties of compounds using computer modelling to further understand reactions that we may not have otherwise been able to using other methods. Some still have drawbacks such as the QTAIM analysis only providing quantitative visual analysis however it will be exciting to see future developments leading it to perhaps widespread use.