A general expression for vibrational Hamiltonians expressed in oblique coordinates

Mark A Boyer; Edwin L Sibert 3rd

doi:10.1063/5.0181135

A general expression for vibrational Hamiltonians expressed in oblique coordinates

J Chem Phys. 2023 Dec 21;159(23):234108. doi: 10.1063/5.0181135.

Authors

Mark A Boyer¹, Edwin L Sibert 3rd¹

Affiliation

¹ Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.

PMID: 38108478
DOI: 10.1063/5.0181135

Abstract

We examine the properties of oblique coordinates. The coordinates, introduced by Zúñiga et al. [J. Phys. B: At., Mol. Opt. Phys. 52, 055101, (2019)], reduce vibrational mode-mixing and enhance the quality of vibrational assignments in quantum mechanical investigations of two-dimensional model Hamiltonians. Oblique coordinates are obtained by making non-orthogonal rotations of the original coordinates that convert the matrix representation of the quadratic Hamiltonian operator into a block-diagonal matrix where the blocks are distinguished by the total quanta of vibrational excitation. Using techniques for the polar decomposition of matrices, we present a scheme for finding these coordinates for systems of arbitrary dimensions. Several molecular examples are presented that highlight the advantages of these coordinates.