This chapter has demonstrated the use of *ab initio* methods for
the study of a biological system, namely the molecule
acetylcholine. It was shown that the results obtained from the
calculations agree well with experiment. In particular, the two
lowest energy minima identified for the isolated molecule agree well
with the biologically active conformations identified. Some small
deviations from the calculated minima would be expected due to
environmental effects such as solvation in water.

The significant difference in the characters of the static and relaxed
energy surfaces demonstrates the importance of relaxation in the
investigation of the energetics of a system. This highlights one
advantage of the *ab initio* approach used within this thesis,
which permits efficient calculation of forces.

It should be noted that only the internal energy of the molecule was calculated, there was no consideration of entropy. It is possible to calculate entropies and hence free energies by calculating the electronic, translational, rotational and vibrational partition functions. However, the full vibrational spectrum must be obtained and even within the harmonic approximation, this would require at least three additional total energy calculations for each atom in the system, at each point sampled on the energy surface. This arises from the need to calculate the second derivative of the energy with respect to each degree of freedom of the system. In comparison to the large differences in internal energy between conformations, the contribution of the entropy to differences in the free energy are expected to be small and, as has been shown, useful results may be obtained through consideration of the internal energy alone.

This study has provided the validation of the methods used for application to biological systems and the confidence required to move forward to the study of more challenging systems which are not as well understood as acetylcholine.

Wed Sep 24 12:24:18 BST 1997