Due to the coarse nature of the grid used in the calculations described in the previous subsection, the location of the absolute minimum on the energy surface is uncertain. In order to identify this minimum, a series of unconstrained relaxations were performed. In each case, the starting point was chosen to lie within one of the minima identified on the relaxed conformational energy map. The starting conformations, the final relaxed conformations and the relative energies of the minima are given in Table .
|Starting Geometry||Relaxed Geometry||Relative Energy (kcal )|
From these data we can see that the most stable conformation of acetylcholine is the trans, gauche conformation of the dihedral angles D2 and D3 (see Figure ). This is in agreement with studies by Pullman and Port  and Edvardsen and Dahl . In the fully relaxed geometry the angles D1 and D4 are found to be and respectively.
Figure: The calculated ground state conformation of acetylcholine showing isosurfaces of charge density at 0.5 , 1.2 and 1.8 .
If we examine the Mulliken populations of the atoms in the ground state conformation, as shown in Figure , we find that the cationic alkyl ammonium head has a net charge of +0.63e. This is in good agreement with calculations by Pullman and Port . Similarly, in agreement with Pullman and Port, this positive charge is found to be distributed among the hydrogen atoms of the three methyl groups bound to the nitrogen. Thus, the positive charge is spread over the exterior of the cationic head. This contrasts with the results of Beveridge and Radna  who find that the majority of the positive charge resides on the N and C atoms. The distribution of this charge is relevant to the interaction of the molecule with a nucleophile such as water or a cationic receptor cite. The Mulliken populations do not differ significantly between the three minima we have investigated. This is because all of the minima correspond to a trans arrangement of the D2 bond which results in an extended geometry for the molecule. Thus, there is little interaction between the alkyl ammonium head and the methylene group in any of the conformations examined. A more compact form of the molecule would result in greater interactions between the different sections of the molecule and hence would probably lead to a significant rearrangement of the atomic charges.
Figure: The Mulliken charges of the acetylcholine molecule in its ground state. Oxygen atoms are shown as red, nitrogen as light blue, carbon as grey and hydrogen as white. Charges are in electronic units and are labeled in the colour corresponding to the species with the exception of hydrogen atoms which are labeled in black.