A Coupled Local Mode Method for the Analysis of Molecular Vibrations: Theory and Applications

A considerable amount of theoretical and experimental work has focused on the application of vibrational infrared spectroscopy to questions of molecular structure and dynamics of aqueous systems. This is due to both the uniqueness of molecular vibrations for a given structure and the exquisite sensitivity of molecular vibrations to changes in environment. Thus, a strong understanding of molecular vibrations and spectroscopy gives chemists the ability to directly probe chemical structure and environment of aqueous systems.

An accurate quantum mechanical description of the microscopic chemical details which give rise to observed spectral responses leads to a variety of unique differential equations which need to be solved. In Chapter 1, a general discrete variable represen- tation method is developed which allows the solution of arbitrary linear differential equations. Because this theory applies to the solution and representation of arbitrary differential equations and operators, this chapter is a stand-alone mathematical work.

In Chapter 2, the origin of spectroscopic transitions from the interaction of the electromagnetic field of light with the charged particles that constitute molecules is shown. An explicit treatment of the theory of molecular vibrations in the harmonic approximation and coupled local mode theory are given, along with commentary on extensions of harmonic theory into post-harmonic methods. A generalization of the coupled local mode theory to include dynamical lineshapes and a treatment of Pipek’s inverse participation ratio for vibrational non-locality are also given.

In Chapter 3, numerous results of the applications of the coupled local mode theory to protonated water clusters are given. These simulation results are validated against experimental results. The coupled local mode approach produces accurate results and gives a fully microscopic picture of the molecular vibrations in terms of the contributions of the individual internal coordinates. Analysis of methods for cost- reduction and the dependence of coupled local mode results upon choices in electronic structure methods, basis sets, and the derivative truncation of the potential energy for couplings is given. It is concluded that the coupled local mode method offers hope for accurately dissecting the complicated infrared spectra which arise in condensed- phase systems.