Rep:Mod:sdaw6262

Module 1: Structure and Spectroscopy (Molecular Mechanics and Molecular Orbital)

Introduction

Molecular mechanics can be used to predict the likely products from a reaction through thermodynamic reasoning. By examining the relative stabilities of the possible products and reactants, the thermodynamically controlled reaction products are revealed. The process of modelling molecular structures is highly useful in research chemistry, for instance it is commonplace for a reaction to give mixtures of isomers, e.g. diastereoisomers, and by knowing the relative energies of the two diastereomers one may engineer the reaction conditions in such a way as to produce exclusively the isomer of interest. Another use of molecular mechanics is that the stereoselectivity of a reaction can often be determined by observation of steric interactions within the starting material, so it is possible to apply this technique not only quantitatively but qualitatively as well.

The program used here is ChemBioUltra3D. Within ChemBioUltra3D can be found MM2, a molecular mechanics program that has been used here for geometry optimisations. MM2 accomplishes this by considering bond stretching, bending and torsion as well as Van der Waals' forces, dihedral angles, dipole interactions, and then altering the molecule's shape in small iterative steps until its energy reaches a minimum. All of the 'Jmols' shown in this section are the result of the molecule in question having undergone an MM2 optimisation.

The Hydrogenation of Cyclopentadiene Dimer

Endo Dimer

Endo

Exo Dimer

Exo

Minimised Energies

Interaction	Energy of endo	Energy of exo
Stretch:	1.2454	1.2923
Bend:	20.8603	20.5870
Stretch-Bend:	-0.8320	-0.8413
Torsion:	9.5039	7.6715
Non-1,4 VDW:	-1.5083	-1.4358
1,4 VDW:	4.3012	4.2320
Dipole/Dipole:	0.4448	0.3778
Total Energy:	34.0153 kcal/mol	31.8834 kcal/mol
Total Energy:	0.0542 Hartree	0.05081 Hartree

The exo conformation of cyclopentadiende is found to be the lowest in energy. The difference in total energy is mostly down to the torsion energy difference indicating less torsional strain in the exo conformer. The higher torsional strain of the endo conformer can be observed on account of its shape as the two rings are locked into a c-shape, which entails a certain degree of strain to maintain such a shape. Whereas the exo bicyclic system takes a z-shape. Since the endo dimer is produced on dimerisation of cyclopentadiene and this is the thermodynamically less stable product then the reaction must be kinetically controlled, i.e. the reaction pathway leading to the endo dimer must have a lower energy transition state. See A. Kumar and S. S. Pawar, for more information. A limitation of molecular mechanics presents itself here in that the energy of the transition state cannot be calculated rendering it impossible to predict the outcome of a kinetically controlled reaction with just the knowledge of the energies of the products.

The endo dimer can be hydrogenated at two different positions to yield the molecules shown below.

Product 3

Product3

Product 4

Product4

Minimised Energies

Interaction	Energy of Product 3	Energy of Product 4
Stretch:	1.2067	1.0963
Bend:	18.8637	14.5075
Stretch-Bend:	-0.7528	-0.5493
Torsion:	12.2396	12.4972
Non-1,4 VDW:	-1.5532	-1.0507
1,4 VDW:	5.7649	4.5124
Dipole/Dipole:	0.1632	0.1407
Total Energy:	35.9322 kcal/mol	31.154 kcal/mol
Total Energy:	0.0573 Hartree	0.0496 Hartree

Hydrogenation of the endo dimer yields two structural isomers 3 and 4. Isomer 4 is the thermodynamically most stable isomer indicating that the double bond in the bridged 5-membered ring is the most readily hydrogenated out of the two. The difference in total energy between 3 and 4 is mostly down to the bending energies, all other energy components are very similar. The difference in stability is due to the postion of the bridge in relation to the alkene. The conversion of an sp3 hybridised centre to an sp2 centre restricts the ring's movement. The presence of the bridge already makes the ring which it bridges quite strained so the reduction in rotational freedom and a constriction of the C-C bond that becomes the alkene accentuates this. It can be seen that the bond angles in product 3 are 107.2 degrees, closer to that expected at an sp3 centre rather than the 120 degree bond angle typical for alkenes. This small bond angle results in a large strain and is a consequence of the bridging carbons, which pull the tertiary carbons that it is connected to closer together, locking the alkene into an elongated 5-membered ring. Whereas in isomer 4, the carbon-carbon alkene bond angle is larger at 112 degrees with a resultant reduction in strain.

Stereochemistry of Nucleophilic Additions to a Pyridinium Ring

Product 5 (first optimisation)

Product5

Product 5 (second optimisation)

Product5

Product 7 (first optimisation)

Product7

Product 7 (second optimisation)

Product7

Minimised Energies

Interaction	Energy of 5 (1st opt)	Energy of 5 (2nd opt	Energy of 7 (1st opt)	Energy of 7 (2nd opt)
Stretch:	1.2030	1.1901	1.7248	1.7727
Bend:	11.7259	11.6255	10.6239	9.5401
Stretch-Bend:	0.0538	0.0568	0.4006	0.4024
Torsion:	4.8237	4.8511	-5.9913	-6.2463
Non-1,4 VDW:	-1.7957	-1.9572	-0.9981	-1.2728
1,4 VDW:	11.9745	11.8778	18.0644	17.8667
Charge/Dipole:	2.6213	2.6734	2.5839	2.5455
Dipole/Dipole:	-4.0134	-3.9753	-4.8116	-4.7855
Total Energy:	26.5931 kcal/mol	26.3422 kcal/mol	21.5966 kcal/mol	19.8228 kcal/mol
Total Energy:	0.0424 Hartree	0.0420 Hartree	0.0344 Hartree	0.0316 Hartree

Methylmagnesium iodide cannot be computed using ChemBio3DUltra because it is an inorganic molecule. The parameters used in MM2 cover elements typical of organic molecules.

In both of compounds 5 and 7 the carbonyl oxygen points slightly above the plane of the aromatic ring. By doing so the oxygen maintains a slightly staggered position relative to the hydrogen para to the nitrogen of the pyridinyl ring, minimising the Van der Waals' repulsion. The second optimisation of both compounds corresponds to an increase in the degree of staggering and is reflected by the lower total energies. For compound 5 there is an increase in the dihedral angle from the oxygen to the the carbon in the para position in the pyridinyl ring from 22.8 after the first optimisation to 23.5 after the second. The second optimisation of compound 7 reveals a significant reduction in the bending energy as the major stabilising effect which appears to relate to a twisting in conformation of the two methyl groups connected to the nitrogen of the amide..

In the reaction of compound 5 with methylmagnesium iodide there are two possible diastereomeric products. The diastereomer with the methyl up is major (product 6). This can be explained by the mechanism of reaction. The methylmagnesium iodide chelates the carbonyl oxygen via magnesium, since the carbonyl points above the pyridine ring then the chelation also occurs above the ring. The reaction proceeds “via a six-centred transition state” resulting in methylation above the ring. In the reaction of compound 7 with aniline there are once again two possible diastereomers produced, the aniline can be up or down in the product. The major diastereomer is the one with the aniline substituent up. This is most likely due to repulsion between the lone pair of nitrogen and those on the carbonyl oxygen and could be regarded as a type of atrop-diastereoselectivity. Another diastereoselective mechanism consquent of the position of this carbonyl is shown in the reaction of sodium borohydride with a quinolinium salt in which diborane complexes the salt leading to attack of the face that is not sterically hindered by the complexation. The explanations proposed for this diasteroselection does not take into account molecular orbital theory. The interaction of frontier molecular orbitals in particular may provide an alternative way of understanding the mechanisms of these reactions.

Stereochemistry and Reactivity of an Intermediiate in the Synthesis of Taxol

Product 10

Product10

Saturated product 10

Satproduct10

Product 11

Product11

Saturated product 11

Satproduct11

Minimised Energies

Interaction	Energy of 10	Energy of saturated 10	Energy of 11	Energy of saturated 11
Stretch:	3.0370	5.0084	2.5429	4.5744
Bend:	18.4779	27.0850	11.7052	23.4356
Stretch-Bend:	0.4010	1.0859	0.3898	1.1318
Torsion:	19.9647	19.9946	19.0373	19.5626
Non-1,4 VDW:	-0.5443	2.1428	-0.8732	2.4104
1,4 VDW:	13.6181	17.8323	12.4412	16.8445
Dipole/Dipole:	0.0054	0.0000	0.1432	0.0000
Total Energy:	54.9599 kcal/mol	73.1489 kcal/mol	45.3864 kcal/mol	67.9595 kcal/mol
Total Energy:	0.0876 Hartree	0.1166 Hartree	0.0723 Hartree	0.1083 Hartree

Compound 11 has a much lower energy than compound 10 and is therefore the most stable conformation. The bending energy is the most significant factor here and is much higher for 10 because the up position of the carbonyl forces the cyclohexyl substituent downwards. The saturated versions of 10 and 11 are much higher in energy due to the greater number of conformations possible with the absence of the C=C double bond to restrict rotation. The alkene in both 10 and 11 will likely react slowly because of the steric hindrance from the methyl group on the bottom face and the vicinal CH2’s on the top face. In addition to this, in isomer 11 the carbonyl oxygen is pointing downwards so attack from the bottom face may be disrupted due to attraction to the lone pairs on oxygen by an attacking electrophile.

Room Temperature Hydrolysis of a Peptide

OH down, axial

OHdownaxial

OH down, equatorial

OHdownequatorial

OH up, axial

OHupxaial

OH up, equatorial

OHupequatorial

Minimised Energies

Interaction	Energy of OH down, axial	Energy of OH down, equatorial	Energy of OH up, axial	Energy of OH up, equatorial
Stretch:	1.6364	1.7146	1.5273	1.4839
Bend:	8.1989	5.1912	5.0643	3.8106
Stretch-Bend:	0.6428	0.5290	0.5487	0.5073
Torsion:	11.9830	9.3527	9.0035	7.6762
Non-1,4 VDW:	-8.0034	-7.3803	-7.1003	-7.1007
1,4 VDW:	10.2222	10.0244	9.6219	9.9019
Dipole/Dipole:	-4.8540	-6.3006	-6.5910	-6.5819
Total Energy:	19.8258 kcal/mol	13.1311 kcal/mol	12.0744 kcal/mol	9.6972 kcal/mol
Total Energy:	0.0316 Hartree	0.0209 Hartree	0.0192 Hartree	0.0155 Hartree

In all cases the conformers where the amide group is axial, the total energy is higher due to the large size of the group causing in a large 1,3 repulsion. In the cases where the conformer’s OH group hydrogen bonds with the oxygen of the amide, the nucleophilic oxygen of the hydroxyl group is tied up by the hydrogen bonding so is unlikely to attack the carbonyl carbon because the electron density of the nucleophilic oxygen is concentrated away from the amide group as the hydrogen bond occurs via donation of electron density from the amide nitrogen so that the hydrogen of the OH group points towards the amide rather than the lone pairs, these conformations will therefore not be considered here. The isomer with the hydroxyl group down reacts most quickly to form the ester because in this position it can react with the equatorially positioned amide. However if the hydroxyl group is up then the amide group must be axial for reaction to occur, whereby a simple rotation of the C- (ring)N bond yields a reactive conformation. An addition to the activation energy in rearrangement from the equatorial conformer (11.9980 kcal/mol) to the thermodynamically less stable axial isomer conformer (17.1367 kcal/mol) is thus required so the rate of reaction is lower. The half-lives of both reactions are relatively short for a few reasons. The nucleophilic and electrophilic centres are already close together compared to straight chain molecules where the reacting centres may be at opposite ends of the molecule. The close proximity of the reacting centres allows for hydrogen bonding to occur which brings these centres even closer together. The most stable hydrogen bonded conformation is always the one with an oxygen-oxygen hydrogen bond wherein the hydroxyl shares its hydrogen with the carbonyl oxygen, lowering the energy of the pi* orbital making it accept the lone pair from the hydroxyl more readily (or the carbonyl carbon is more acidic); furthermore the lone pair on the hydroxyl oxygen is more basic due to the partially ‘donated’ hydrogen making the hydroxyl more nucleophilic.

Modelling using semi-empirical molecular orbital theory

Dichlorocarbene

Dichlorocarbene

Hydrogenated Product

chlorocarbene

IR Vibrational Frequencies

Dicarbene/Carbene	Vibration No.	Frequency/(1/cm)	Intensity	Functional Group/Bond
Dicarbene	19	772.545	25.28	C-Cl
Dicarbene	55	1740.9	4.155	C=C (Anti to C-Cl))
Dicarbene	56	1762.01	3.8961	C=C ('Syn' to C-Cl)
Carbene	19	776.881	20.278	C-Cl
Carbene	60	1761.67	4.289	C=C ('Syn' to C-Cl)

These results make it possible to see which of the alkenes has been hydrogenated. Clearly the one anti to C-Cl has been hydrogenated since the alkene stretch remaining in the hydrogenated product is almost identical (1761.67 per cm versus 1762.01 per cm) to the alkene in the 'syn' position in dichlorocarbene.

MO's of Dichlorocarbene

HOMO

HOMO-1

LUMO

LUMO+1

LUMO+2

Mini project using DFT MO Methods

Introduction

Whereas molecular mechanics took a more classical approach, density functional theory (DFT) utilises quantum theory. The calculations are more complex and consequently take significantly longer to carry out. The calculation method generally used here is mPW1PW91 with a 6-31G basis set, which is a low basis set and one of the simpler calculation methods.

NMR Spectroscopy can be a highly useful analytival tool to distinguish one isomer of a acompound from another. However, the chemical shifts present in the spectra of some isomers may be almost identical, which is where coupling constant data come into play. A coupling constant depends on a dihedral angle in a molecule and by using the Karplus equation such an angle can be determined allowing isomeric identification.

The reaction below can yield two diastereoisomers, but predominantly the alpha-anomer which is illustrated below where the cyclopropyl ring is syn to the acetate para relative to it. The beta-anomer shows an anti relationship between the aforementioned acetate and cyclopropyl ring.

13C NMR Chemical Shift Calculation

The geometries of both diastereomers were first optimised to yield the molecules shown below before the NMR predictions were made.

(Alpha anomer: Geometry optimisation and vibrational frequencies DOI:10042/to-1035 , NMR calculation DOI:10042/to-1037 ) (Beta anomer: Geometry optimisation and vibrational frequencies DOI:10042/to-1036 , NMR calculation DOI:10042/to-103? )

Alpha Anomer

Alphaanomer

Beta Anomer

Betaanomer

Minimised Energies

Interaction	Energy of Alpha Anomer	Energy of Beta Anomer
Stretch:	1.4361	1.4310
Bend:	5.7114	6.3965
Stretch-Bend:	0.5580	0.6680
Torsion:	-1.2160	-1.0534
Non-1,4 VDW:	-3.6785	-3.0442
1,4 VDW:	11.3570	14.0219
Dipole/Dipole:	2.7946	7.9763
Total Energy:	24.8092 kcal/mol	27.7899 kcal/mol
Total Energy:	0.0395 Hartree	0.0443 Hartree

Generally, the alpha anomer of compounds with a heteroatom attached to the anomeric carbon are thermodynamically more stable than the corresponding beta anomer due to the anomeric effect whereby there is donation of the lone pair on the ring oxygen into the σ* orbital of the C-Het bond, which can only occur when the heteroatom occupies an axial position. This electronic stabilising effect counters the increased steric hindrance due to 1,3-compression.

The alpha anomer is the most stable in this case too, however this time there can be no anomeric stabilisation due to the lack of a heteroatom. But this is not surprising since the 1,3-compression is probably similar for both isomers as although carbon is larger than hydrogen, the C-C bond (1.476A) in the alpha anomer is longer than the C-H bond (1.115A) in the beta anomer in the at the axial position on the anomeric carbon. The carbon attached to the anomeric carbon in the alpha anomer is also more staggered relative to the nearest hydrogen in the 1,3 position than the corresponding hydrogen in the beta anomer. The energy difference is primarily due to diope-dipole and 1,4-Van Der Waals' interactions.

Literature Chemical Shifts for NMR of Alpha Anomer

13C NMR (75 MHz, CDCl3) δ 8.4, 20.8, 21.0, 24.8, 63.1, 64.2, 64.8, 67.9, 69.6, 71.0, 90.8, 124.8, 129.9, 170.3, 170.9

Calculated Chemical Shifts for NMR of Alpha Anomer

13C NMR, reference= TMS mPW1PW91/6-31G(d,p) CDCl3 GIAO, δ 2.5, 11.7, 12.1, 20.9, 22.1, 63.8, 66.9, 67.1, 67.2, 68.8, 89.8, 124.3, 128.1, 165.6(171.2), 166.6(172.1)

Note: the calculated values for the chemical shifts of the carbonyl carbons were corrected by applying the formula, δcorr = 0.96δcalc + 12.2. The corrected results are given in brackets next to the raw data.

Literature:δ 8.4, 20.8, 21.0, 24.8, 63.1, 64.2, 64.8, 67.9, 69.6, 71.0, 90.8, 124.8, 129.9, 170.3, 170.9

Calculated:δ 2.5, 11.7, 12.1, 20.9, 22.1, 63.8 66.9, 67.1, 67.2, 68.8, 89.8, 124.3, 128.1, 171.2, 172.1

The experimental shift at 8.4, which corresponds to the carbon connecting the cyclopropyl to the alkyne has a much lower calculated shift. Thisd indicates that the anisotropic effect of the pi-electrons which will cause this carbon to experience increased deshielding has not been fully accounted for by the calculation method, a possible limitation of the software. The same situation applies to the shifts at 20.8 and 21.0 which are the other two cyclopropyl carbons. Although there are other possibilities for the orientation of the cyclopropyl ring, it is very unlikely that the chemical shifts of its carbons would change by much because the anisotropic effect of the alkyne would be unchanged as the cyclopropyl can only rotate about the C-C alkyne axis so the angle that the effect is dependent upon would be unchanged. The other possibility is in the ring being slightly closer to some of the oxygens, but they are too far away to have any observable effect. The emboldened chemical shift appears to be wrongly reported since the two calculated values of 20.9 and 22.1 are of the carbons of the two acetate methyl groups and as such one would expect these two shifts to be almost identical as calculated, however the two respective literature values are 24.8 and 63.1. The remainder of the chemical shifts are in good agreement.

Dihedral Angles

There is only one dihedral angle which differs in the two isomers and that is between the hydrogen on the carbon that the alkyne is joined to on the 5-membered ring and the hydrogen on the adjacent carbon of the alkene. As the dihedral angle increases from 0 degrees to 90 degrees the coupling constant decreases, reaching a minimum at 90 degrees and a maximum when the hydrogens are eclipsed and anti-periplanar. Since this angle is larger in the beta anomer then the (closer to 90 dgrees) then coupling constant will be smaller.

Anomer	Dihedral Angle/degrees	3-J Coupling constant/Hz
Alpha	-52.18631	2.9158
Beta	73.98297	0.3674

The literature value for the alpha anomer coupling constant is 3.27Hz which is quite close to the theoretical value. The difference may be due to a slighlty inaccurate conformation. However, the difference between the two predicted coupling constants is large enough that even if the conformations are not quite right the isomers should still be distinguishable by this particular coupling constant. Some of the other coupling constants will vary slightly, but this one is the most reliable for identification purposes.

IR Vibrational Frequencies

Alpha/Beta	Vibration No.	Frequency/(1/cm)	Literaure frequency/(1/cm)	Intensity	Functional Group/Bond
Alpha	87	1738.83	1740	0.5632	Alkene C=C stretch
Alpha	90	2344.85	2359	56.7794	Alkyne stretch
Alpha	62	1211.31	1207	37.0683	Alkene C-H scissoring
Alpha	91	3027.22	2957	14.7184	H-COC stretch, cyclic ether, furthest from alkyne
Alpha	92	3037.96	3032	17.4525	H-COC stretch, cyclic ether, closest to alkyne
Beta	87	1737.33	1740	3.282	Alkene C=C stretch
Beta	90	2359.33	2359	64.6695	Alkyne stretch
Beta	64	1210.25	1207	29.4019	Alkene C-H scissoring
Beta	92	2999,82	2957	13.5556	H-COC stretch, cyclic ether, furthest from alkyne
Beta	91	2931.72	3032	35.4397	H-COC stretch, cyclic ether, closest to alkyne

The IR results do vary a little. Surprisingly, the alkyne stretch of the beta anomer matches more closely the literature value for the alpha anomer. A possoble way of distinguishing the isomers could be by the cyclic ether C-H stretches since one is lower than the other and which is lower depends on the isomer according to the results of the calculation. However I think that as an analytical means of conclusively characterising one isomer with respect to the other, the results are not sufficient since IR stretches can have too large a fluctuation to afford reliability in this example.