Calculation of the vibrational states of small biomolecules

The present thesis documents the development of a general method for calculating the vibrational energies of small biomolecules. Starting with the general time-dependent molecular Hamiltonian, assumptions allowing the separation of coordinates are outlined. The variational Configuration Interaction technique for calculating ab initio electronic eigenstates is adapted for vibrational systems, and a general method for solving the Hamiltonian in normal coordinate space is described. A computer program is developed, implementing this formulation of the quantum problem. The code is tested against benchmark systems including the Morse Oscillator, the Henon-Heiles 3D potential and water monomer. It is seen that the results agree well with those of DVR and variational calculations. The vibrational CI method is applied to tryptamine and its water clusters, systems of great biological importance. Results are used to test the assignment of experimental IR spectra for the monomer and are compared with ab initio results to probe the accuracy of anhar- monic terms in the molecular modelling potential. An attempt is made to assign the conformational isomers found in the solvated spectra. The results of CI calculations are found to be an improvement on harmonic calculations, agreeing well with experimental spectra in some cases. High order terms in the potential are found to model the anharmonicity of the system accurately. The results demonstrate that anharmonic effects in widely-used potential functions for biomolecules are large and need to be treated accurately in interpreting vibrational spectra