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.