A quartic force field coordinate substitution scheme using hyperbolic sine coordinates

Abstract

Quartic force fields (QFF) are currently the most cost-effective method for the approximation of potential energy surfaces for the calculation of anharmonic vibrational energies. It is known, although, that its performance can be less than satisfactory due to limitations related to slow convergence of the series. In this article, we present a coordinate substitution scheme using a combination of Morse and sinh coordinates, well adapted for its use with cartesian normal coordinates. We derive expressions for analytical integrals for use in VSCF and VCI calculations and show that the simultaneous substitution of symmetric and antisymmetric normal coordinates by Morse and sinh coordinates, respectively, significantly improves the vibrational transition frequencies for these modes in a well-balanced fashion. The accuracy of this substitution scheme is demonstrated by comparing one and two-dimensional sections of substituted and unsubstituted QFF with ab initio potential energy grids, as well as with vibrational energy calculations using as test cases two well-studied benchmark molecules: water and formaldehyde. We conclude that the coordinate substitution scheme presented constitutes a very attractive alternative to simple QFFs in the context of cartesian normal coordinates.