Investigating optimal coordinates for describing vibrational motion

A general expression for vibrational Hamiltonians expressed in oblique coordinates

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.

Determination of a Potential Energy Surface for CO2 Using Generalized Internal Vibrational Coordinates

A potential energy surface for CO2 is determined from experimental data using generalized internal vibrational coordinates. These coordinates are defined as two arbitrary distances and the angle between them and depend on two external parameters, which can be properly optimized. An optimal generalized internal coordinate system is obtained for CO2 by minimizing unconverged vibrational energies with respect to the external parameters. The optimal coordinates are shown to be superior to previously derived normal hyperspherical coordinates for this molecule. A nonlinear least-squares fit of the potential energy surface of CO2 to observed vibrational frequencies is made by using the optimal internal coordinates and fully variational calculations. The potential function is represented by a fourth-order Morse-cosine expansion and its quality is checked by computing highly excited vibrational transition frequencies which were not included in the fit. Copyright 1999 Academic Press.