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

In this module MM2 Allinger calculations were used to not only model molecules, but also to examine more closely properties such as molecular strain, steric effects or stereoselectivity quantitively by defining bond stretches, bond angle distortions, bond torsions, non-bonding VdW repulsions and bond dipoles. MM2 then optimises the model geometry by minimising the total energy by changing these individual bond parameters, i.e. bond lengths, angles and torsion angles.

This computationally relatively simple approach is used in the following exercises to analyse the most stable reaction intermediate or reactivity of a compound. MM2 determines the total energy of a compound as a sum of the above individual non-interacting parameters noted above upon application of a so-called MM" force field. However, during these exercises the limitations of these simplified calculations will be encountered and further analysed.

The Hydrogenation of Cyclopentadiene Dimer

In this exercise Allinger MM2 molecular mechanics calculations were carried out to examine thermodynamic versus kinetic control of a reaction. This was illustrated using the example of cyclopentadiene dimerisation and subsequent hydrogenation of the dimer.

Formation of the Cyclopentadiene dimer

Cyclopentadiene dimerises via a Diels-Alder cycloaddition. This reaction involves 6 pi electrons and hence proceeds via Hueckel topology with suprafacial components only with the 2 hydrogens at the ring linkage remaining cis to each other. There are 2 possible outcomes of this reaction, which are shown in Table 1: the endo- and the exo-product.

**Table 1: summary of the 2 potential products of Cyclopentadiene Diels-Alder addition**
Product	Structure	Total Energy
endo		34.0029 kcal/mol
exo		31.8849 kcal/mol

As can be seen from the total energies calculated, the exo-product has a lower energy. It is therefore the thermodynamic, i.e. the more stable product of this reaction. Compared to the endo-conformation the eclipsed ring in this exo-compound causes less steric hindrance and the dimer is less strained. Therefore, under reversible conditions, i.e. under thermodynamic control, the exo-product would be formed.

However, it was found that in fact the higher energy, less stable kinetic endo-product of the reaction is formed. This indicates that the reaction must be under kinetic control. In short, rather than the total energy, i.e. stability of the final product, the energy of the transition state controls the reaction outcome. The rate of the reaction, i.e. the activation energy barrier leading to the transition state determine the major product of this reaction. This explains, why the endo-conformation is preferred.

Transition state stabilisation in the endo-conformation

In addition to the primary HOMO-LUMO overlap that essentially leads to the formation of the 2 new ~~sigma~~ bonds the transition state leading to the endo-conformer is stablised by secondary orbital overlap. This pseudo ~~pi???~~ bond at the back of the diene means additional stabilising bonding interaction, which cannot be found in the transition state giving the exo-product. The endo-transition state is therefore lower in energy and since under kinetic control the endo-conformer is the predominately formed product. This is also referred to as the endo-rule ^[1].

Hydrogenation of the Cyclopentadiene dimer

INCLUDE DIPOLE IN TABLE = H-bonding!!!!!!!!!!!!!!!!! The endo-cyclopentadiene dimer 2 can then be hydrogenated to give either the dihydro derivatives 3, 4 or the tetrahydroderivative 5*, which are summarised in the following Table 2.

Table 2: Summary of relative energies of the hydrogenation products 3, 4 and 5*
	Compound 3	Compound 4	Compound 5*
bend (kcal/mol)	19.8063	14.5224	14.7153
stretch (kcal/mol)	1.2659	1.0944	1.2187
torsion (kcal/mol)	10.8698	12.5071	15.3750
VdW (kcal/mol)	5.6394	4.5046	6.0156
Total Energy (kcal/mol)	35.6953	31.1617	36.1269

In contrast to its formation the hydrogenation of the cyclopentadiene dimer is assumed to proceed under thermodynamic control since we know that compound 5, the tetrahydro derivate is not readily formed. Compound 5 has - compared to compound 4 and 5 - the highest total energy.

In the face of the thermodynamic control of the hydrogenation, it is therefore assumed that compound 4 is the major product, since is has the lowest total energy and hence offers the greatest dG driving force for this reaction. Furthermore, the endo-compound (34.0 kcal/mol) must readily hydrogenate to compound 4 (31.2 kcal/mol) since the total energy upon this reaction is reduced and dG=-ve, which would not be the case for hydrogenation to compound 3 (increase in total energy to 35.7 kcal/mol).

The following images show the bond angle of the alkene to account for the relative energies calculated.

For all 4 compounds bending > torsion > VdW > stretching. The of the energy contributions of bend (3>4), stretch (3~4), torsion (3<4) and VdW (3>4) to the total energy give compound 4 as the major product.

The bond angles measured above further confirm compound 4 as the major hydrogenation product. In compound 4 the more strained double bond next to the bridging-unit in compound 2 is hydrogenated. In the endo-dimer both double bonds experience significant strain since the angle at the sp²-hybridised C is ~~108&deg and 112&deg respectively and hence deviates significantly from the ideal 120&deg.~~ Therefore, between compound 3 and 4 reaction to compound 4 achieves the greater relief of strain since the doublebond next to the bridging-unit in compound 2 is most contrained (12&deg vs 8&deg deviation). Compound 3 still contains a highly constrained doublebond. For the hydrogenated single bonds the sp³-C has a bond angle of 103&deg, which is in agreement with the ideal tetrahedral bondangle of 109&deg.

The bend energy term accounts for this increase in energy due to deviations from ideal bond angle conformation and is therefore as expected largest for compound 3 with the 108&deg doublebond. The bending energy shows the largest contribution to the total energy. As the total energy of the compound increases, the VdW contributions increase. This is due to the increasing number of hydorgens and hence the increase in steric clash between hydrogens in the 1,4 positon. The stretching of bond lengths stays constant for all hydrogenation products. The torsion, the deviation from dihedral angle at the ring linkage is slightly increased in compound 4 relative to 3 due to the presence of the strained alkene on the RHS of the dimer. Additional torsion is one of the reasons why tetrahydro derivates are unlikely.

The formation and hydrogenation of a cyclopentadiene dimer is also an example for the limitations of MM2 calculations. MM2 only consider the ground state and hence only the thermodynamic stability of a reaction. However, to get a full picture of the chemical reactivity, more information about the energy gap between the starting ground state and the transition state is needed. MM2 calculations are therefore not sufficient to draw conclusions about the kinetic aspect of the reaction. MM2 calculations focus on the position of the individual atoms, however when breaking bonds in a reaction as above more complex calculations have to include the full wavefunction of the structure to be able to model the transition state of a reaction. For MM2 bonding needs to be exactly assigned in the form of single or double bonds.

Stereochemistry of Nucleophilic additions to a pyridinium ring (NAD⁺analogue)

In this exercise the geometry of the products of the reaction of 2 prolinol derivatives was analysed and subsequently linked to the mechanism of the reaction and the carbonyl-position in the starting derivatives.

Conformation of the starting proline compounds 5 and 7

The conformation of the molecule computed was analysed in terms of its total energy and the dihedral of the carbonyl group relative to the plane of the pyridine ring. Table 3 shows a summary of the total energies found for varying geometry of the starting compounds. Since the pyridine ring and the 5-membered ring are relatively rigid, mainly the position of the carbonyl-oxygen relative to the plane of the molecule and the alignment of the oxygen and the adjacent carbond to the right in the 7-membered ring was changed manually.

**Table 3: summary of trial geometries for compound 5 and 7**
	Compound 5							Compound 7
dihedral angle / ~~&deg~~	7	8	9	10	11	12	22	-20	-22	-124
Torsion / kcal/mol	5.0991	5.0174	5.0319	5.0433	5.1347	5.2081	13.5354	9.6850	9.6941	28.5384
Total Energy / kcal/mol	43.2403	43.1653	43.1229	43.1247	43.1274	43.1488	44.7937	62.6487	63.3840	161.3115

Upon trying to change the geometry of compound 5 it was found that due to the inflexible 7-membered ring the carbonyl group can be arranged either in plane or slightly above the plane of the pyridine. Conformations with the carbonyl group below the plane of the molecule were hard to optimise and had energies of ~~== 161.41 kcal/mol~~. Furthermore, from Table 3 above, it can be seen that for compound 3 the lowest energy conformation is where the carbonyl is slightly above the plane of the compound by ~~9degrees !!! symbols!!!~~. In this conformation the balance between steric clash between the carbonyl and adjacent Hs and torsion energy contributions is most favourable. The torsional strain increases, as the carbonyl group moves significantly out of the plane of the molecule due to the deviation in the dihedral angle. To achieve further energy minimisation the position of the oxygen and the carbon to its RHS in the 7-membered ring was manipulated. The most stable configuration with least steric strain was found to be where the oxygen is in the plane of the molecule and the carbon slightly above the plane. Also, the Me-group on the pyridine ring was found to be in the plane of the molecule.

For compound 7 the structure was manipulated in a similar way with the difference that the most stable configuration is with the carbonyl-group below the plane at an angle of -20&deg to keep strain of the inflexible ring-components in compound 7 to a minimum.

Both compounds 5 and 7 are an example where the position of the carbonyl group is restricted and cannot be freely rotated due to steric inhibition. Ready rotation would require high steric demand, which cannot be fulfilled by the highly substituted and rigid 7-membered ring in both compounds.

IMAGE TO SHOW WORKING!!!!!!!!!!!!!! !!!!!!!!! write on general method!!!!!!!!!!!! how MM2 is not sufficient, and how it depends on what u put in

Stereocontrol of the nucleophilic attack on compound 5 and 7

The reaction of compound 5 with a Grignard reagent is highly regioselective to the 4-position as well as stereoselective wrt the orientation of the Me-group added. This is due to the coordination between the Grignard reagent and the amide-O in the course of the reaction. This is also referred to as the Chelation control.

Key steps in this reaction showing the conjugate delivery of Me and the resulting Mg-enolate

As can be seen from the Transition State this mechanism essentially mirrors an intramolecular addition of Me, which as a result has to be added on the same face as the Carbonyl-group the Grignard is coordinated to, i.e. above the plane of the pyridine ring. In the product the Me-group is anti to the H on the chiral centre.

The selectivity of MeMgI is relatively high, however higher regio-stereoselectivity could be achieved by using bulkier R groups. PhMgBr for instance has a selectivity of >99:1 compared to MeMgBr with 19:1 ^[2] .

The reaction of compound 7 is also a nucleophilic attack of the 4 position. In this case the nucleophile is added on the opposite face of the Carbonyl to reduce electronic repulsion between the electronegative carbonyl-O and the sterically large elecron-rich Ph-group of the incoming nucleophile.

Since as established above the carbonyl group in compound 7 is orientated below the plane of the molecule, in the opposite face of the Me-group on the RHS, in the product NHPh is syn to this Me-group. Applying MM2 calculations on the anti-conformer product, the molecule automatically reverts back with the NHPh group coming out of the plane. As indicated in the image to the left nucleophilic reactions are determined and controlled by high e^--density of the attacking nucleophile, which leads to electronic repulsion and in this case explains the stereocontrol of the product 8.

Note that for all calculations the lowest global energy minima conformation was tried to isolate via a trial-and-error process. However, it is impossible to ensure that the lowest energy conformation was found, especially as the compounds get larger and more complex such as compound 5 or 7 (and in the next section 9 and 10 in particular). For larger ring systems, the trial-and-error approach becomes increasingly insufficient due to infinite number of different conformations. Also, they cannot be parameterised accurately against standard diatomic models, which is what is essentially done when running MM2 models.

As molecules become more complex, the simplifications made in the MM2 calculations no longer hold. For instance for aromotic rings, or highly substituted structures as above, individual bonds cannot be isolated and individual energies cannot be simply added up. To obtain an accurate quantitive estimate of the model the quantum-mechanical aspect in form of the Schroedinger wave fucntion of the molecule has to be taken into account. Furthermore, as established in the example of the Cyclopentadiene dimer, using MM2 one can only make limited assumptions about the reactivity of a modelled structure. To getter a better idea about the electronic aspect of a reaction MOPAC/PM6 could be used (as later in part 1.4).

Another way to solve this problem could be the Monte Carlo method to examine conformations of e.g. bicyclic ring systems as e.g. Taxol intermediates in the following exercise.

References

↑ Clayden, Greeves, Warren, Worthers, "Organic Chemistry", pp.912-916, Oxford University Press, 2001
↑ A.G.Shultz, L.Flood and J.P.Springer, J.Org.Chemistry, 1986, 51, 838 DOI:10.1021/jo00356a016

~~# Leleu, Stephane; Papamicael, Cyril; Marsais, Franci~~s; Dupas, Georges; Levacher, Vincent. Tetrahedron: Asymmetry, 2004, 15, 3919-3928. DOI:10.1016/j.tetasy.2004.11.004

Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol

Structure of the Intermediate

Due to the sterically inhibited and hence restricted rotation of the highly substituted and hence rigid ring structure the intermediate in the synthesis of Taxol isomerises between 2 main structures 9 and 10, shown below. The isolation of 2 isomers due to an energy barrier of rotation is referred to as atropisomerism.

Isomer 9	Isomer 10

**Table 4: Energies of isomers 9 and 10**
	compound 9	compound 10
Bend / kcal/mol	16.5552	10.7550
Stretch / kcal/mol	2.7704	2.5682
Torsion / kcal/mol	20.5854	19.6040
1,4-VdW / kcal/mol	13.9136	12.5222
Total Energy / kcal/mol	54.1027	44.2878

Based on the total energy calculations and individual energy contributions for compound 9 and 10 the most stable isomer is assumed to be compound 10, with the carbonyl group pointing down. It was also found that in order to achieve an energy minima for compound 9 the cyclohexane-ring has to be in a twisted boat conformation. In contrast to this compound 10 was foudn to be most stable with the cyclohexane-component in a stable chair conformation. This twist in compound 9 also contributes towards its higher VdW energy (14.1 kcal/mol) compared to compound 10 (12.5 kcal/mol) as in the twisted conformation the ring-hydrogens come within the VdW radius of each other causing repusive interaction and raising the energy in form if increased transannular strain across the ring. Furthermore, upon trying to optimise compound 9 with the cyclohexane in chair-conformation, the structure always reverts back to a twist-boat, which indicates that in structure 9 the twist-boat conformation is more stable than the chair-conformation due to relief of torsional strain. It was then tried to minimise the a boat conformation. This repuslion of the cyclohexane-ring hydrogens across the ring (transannular strain), however, is assumed to be too large in the boat-conformer

It was also tried to change the orientation of the ring at the alkene and the Carbonyl-attachment, however the most stable configuration is as shown in the images above with the bridgehead alkene and the other, opposite bridgehead C-C pointing away from each other to increase the distance between the 2 hydrogens and avoid destabilising transannular strain.

Since the structural difference between the 2 isomers is small, the energy difference between compound 9 and 10 was not expected to be very large. The 1,4-VdW interaction is large for both compounds as it is primarily due to steric clash between hyrogens adjacent to each other or across the ring (transannular strain). The higher VdW in compound 9 have been explained above. The stretching distortion from ideal bond length is similar as both structures are based on a complex, highly substituted, rigid ring structure. Torsional strain is high in both compounds due to large twisting about single bonds. It is higher for compound 9 as there is higher repulsion between the pointing-up carbonyl and the adjacent hydrogens at the cyclohexane-ring-linkage.

The main difference between 9 and 10 is the bending energy caused by large angle strain. This summarises the stability of compound 10 where the cyclohexane-ring is in a stable chair and the carbonyl is pointing down and therefore less distorted by adjacent H on the ring-linkage, which are pointing up.

Reactivity of the Intermediate-Olefin

The alkene in bridgehead position in this intermediate is unusually stable und subsequently very unreactive, contrary to what would be expected based on Bredt's rule for small rings (focuses on the twisting distortion of pi-bonds in bridgehead alkenes). Normally, the ring and angle strain make the bridgehead position unfavourable for alkenes. However, Bredt's rule can be violated in large enough ring molecules. Isomer 10 is such an example for a hyperstable alkene in bridgeposition. This hyperstability is quantitively defined by the -ve olefin strain OS relative to the parent hydrocarbon ^[1] As can be seen from Table 4 the main contributions towards the total energy in comopund 10 is the bending component, VdW interactions and Torsion. These contributions are expected to increase even further upon changing the hybridisation from the sp²-hybridised C in compound 10 to sp³ due to functionalisation of the alkene. Due to the larger angle for sp²-hybridised C (120^o vs 109^o) and the more planar geometry relief the large angular strain in isomer 10 relative to a parenthydrocarbon. Also, space is less congested due to a reduced number of hydrogens present for an sp² alkene and destabising transannular interactions reduced.

References

↑ Maier, schleyer

Modelling using semi-empirical molecular orbital theory

In the following exercise the reactivity of Dichlorocarbene was studied. However, it was established from the previous exercises that one of the limitations of the MM2 calculations is its purely mechanical, i.e. classical approach. Therefore, in the following exercise the MM2 method was extended by using MOPAC/PM6. This means the extension of a purely classical model to a molecular modelling calculation that includes quantum-mechanical aspects, i.e. the wave description of the electrons. The information obtained was then used to explain the reactivity of Dichlorocarbene more accurately.

Reactivity of Dichlorocarbene

MOPAC/PM6 geometry optimization parameters were used to examine the reactivity and regioselective addition of Dichlorocarene. MOPAC extends the MM2 optimization and produces approximate molecular wavefunctions of the valence electrons. Table 6 shows a summary of these Molecular Orbitals. ROTATING PICTURES!!! with MOS