Electronic Structure of Proteins: Exciton Hamiltonian for a Dipeptide

Abstract

Protein folding has attracted a great deal of interest alongside the increased amount of structural information on proteins. Different spectroscopies, for example, X-ray crystallography and Nuclear Magnetic Resonance (NMR), are often used to study protein structure. Optical spectroscopy despite limited spatial resolution, for example, circular dichroism (CD), has considerable interest, arising from the ability to derive information about secondary structures of a protein from its CD spectrum. The aim of the present work is to explore whether fully ab initio Complete Active Space Self-Consistent Field (CASSCF) calculations of the electronic excited states of dipeptides can help to construct the exciton Hamiltonian for a dipeptide. Exciton theory is an approximate approach allowing the calculation of the CD of proteins. We have treated the problem of finding the exciton Hamiltonian matrix elements as an optimization problem in which the ab initio energies represent the “true” solutions and are used to compute the “error” that will be minimized. We use a Monte Carlo algorithm to conduct optimization. We find many possible solutions, all of which upon diagonalizing the exciton Hamiltonian give energies close to the ab initio energies. Some of the off-diagonal elements are also well-defined, while other distributions of some elements are more variable. More work will be needed to reduce the number of solutions