Methods

 

Calculations were performed using the techniques described in Chapter . A cut off energy of 650eV was used for the plane wave basis set and the molecule was embedded in a cubic supercell with a side of length 8Å. As acetylcholine has a net charge of +1e, the post-hoc correction described in Section was applied to the total energy. Due to constraints on time and computing resources available, it was found that absolute convergence of the energy with respect to supercell size could not be obtained. However, convergence of energy differences between conformations was found to be practical to within kcal .

We have used the crystal structure of acetylcholine chloride [67] as the initial geometry of the acetylcholine molecule. This data does not define the positions of the three terminal hydrogen atoms of the acetyl group containing . Some previous studies have defined the positions of these atoms such that the dihedral angle , while others have defined . Total energy calculations were performed for these two possibilities and these showed that the arrangement with was energetically favourable. This arrangement was therefore used for the remaining calculations, with the hydrogen atoms arranged relative to in the usual tetrahedral geometry for a methyl group.

Three sets of calculations were performed:

• Static calculations

  The total energy of the molecule was calculated for a number of different values of D2 and D3 on a regular grid over half of the phase plane defined by these angles. The set of points for which the energies were calculated consisted of two interpenetrating, regular 60 degree grids with origins at , and , . The ions were not relaxed during these calculations.

• Relaxed calculations

  The total energy of the molecule was recalculated for each grid point on the conformational energy map, allowing the structure of the molecule to relax towards its minimum energy conformation while the dihedral angles D2 and D3 were constrained to remain fixed. The constraints used to achieve this are described in Appendix .

  A full relaxation to the ground state conformation for each point was not possible due to constraints on the computing resources available. However, relaxations were carried out to reduce the large steric forces and the relaxation was continued until the energy differences between conformations remained constant.

• Calculation of the ground state structure

  Unconstrained relaxations were performed with a set of initial geometries chosen to lie close to the minima found on the relaxed conformational energy map. Thus, the structure corresponding to the global minimum was believed to have been determined.