# Optimizing Vibrational Coordinates To Modulate Intermode Coupling

journal contribution

posted on 2016-02-25, 00:00 authored by Paul M. Zimmerman, Peter SmerekaThe
choice of coordinate system strongly affects the convergence
properties of vibrational structure computations. Two methods for
efficient generation of improved vibrational coordinates are presented
and justified by analysis of a model anharmonic two-mode Hessian and
numerical computations on polyatomic molecules. To produce optimal
coordinates, metrics which quantify off-diagonal couplings over a
grid of Hessian matrices are minimized through unitary rotations of
the vibrational basis. The first proposed metric minimizes the total
squared off-diagonal coupling, and the second minimizes the total
squared

*change*in off-diagonal coupling. In this procedure certain anharmonic modes tend to localize, for example X–H stretches. The proposed methods do not rely on prior fitting of the potential energy, vibrational structure computations, or localization metrics, so they are unique from previous vibrational coordinate generation algorithms and are generally applicable to polyatomic molecules. Fitting the potential to the approximate*n*-mode representation in the optimized bases for all-trans polyenes shows that off-diagonal anharmonic couplings are substantially reduced by the new choices of coordinate system. Convergence of vibrational energies is examined in detail for ethylene, and it is shown that coupling-optimized modes converge in vibrational configuration interaction computations to within 1 cm^{–1}using only 3-mode couplings, where normal modes require 4-mode couplings for convergence. Comparison of the vibrational configuration interaction convergence with respect to excitation level for the two proposed metrics shows that minimization of the total off-diagonal coupling is most effective for low-cost vibrational structure computations.