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  ) |
 |  | 0 |
 |  | 16 |
 |  | 6 |
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 [65] and
Edvardsen and Dahl [66]. 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 [65]. 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
[63] 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.
