Variational vibrational calculations using high-order anharmonic force fields

Abstract

A simple variational procedure, termed DOPI for discrete variable representation—Hamiltonian in orthogonal coordinates—direct product basis–iterative diagonalization, is described and applied to compute low-lying vibrational band origins (VBOs) of the triatomic systems H₂O, CO₂, and N₂O, employing published empirical and theoretical sextic force fields. While in these cases no difficulties arise when quartic potentials are used, the limited range of applicability of 6th-order potentials presents difficulties for the variational determination of VBOs, in particular for the higher-lying bending states. For H₂O, transformation of quadratic and quartic force fields from simple bond stretching to Simons–Parr–Finlan (SPF) coordinates results in computed VBOs deviating less from experiment. This, however, does not hold for the VBOs computed from the transformed sextic force fields where the two representations provide highly similar results. While use of empirical quartic and sextic force fields result in a much better reproduction of experimental VBOs than that of ab initio force fields, especially at higher (fifth- and sixth-) order the empirical force constants, obtained through different refinement procedures, do not correspond to the associated derivatives of the potential energy surface (PES). Rotational constants characterizing low-lying vibrational states have been evaluated as expectation values using inertia tensor formulas in the Eckart and principal axis frames. Only the Eckart axes should be used for these computations and they yield accurate vibrationally averaged rotational constants.

Notes

This paper is dedicated to Professor Nicholas C. Handy on the occasions of his retirement from the Department of Chemistry of Cambridge University, Cambridge, UK, and the conference in his honour entitled ‘Molecular quantum mechanics: a no nonsense path to progress’. Professor Handy has been instrumental in many of the original developments related to anharmonic force fields, including their determination through analytic derivative techniques of electronic structure theory, and the variational computation of rovibrational energy levels.

Additional information

Notes on contributors

Viktor Szalay

This paper is dedicated to Professor Nicholas C. Handy on the occasions of his retirement from the Department of Chemistry of Cambridge University, Cambridge, UK, and the conference in his honour entitled ‘Molecular quantum mechanics: a no nonsense path to progress’. Professor Handy has been instrumental in many of the original developments related to anharmonic force fields, including their determination through analytic derivative techniques of electronic structure theory, and the variational computation of rovibrational energy levels.