A two-step quadrature-based variational calculation of ro-vibrational levels and wavefunctions of CO2 using a bisector-x molecule-fixed frame

Abstract

In this paper, we propose a new two-step strategy for computing ro-vibrational energy levels and wavefunctions of a triatomic molecule and apply it to CO₂. A two-step method [J. Tennyson and B. T. Sutcliffe, Mol. Phys., 1986, 58, 1067] uses a basis whose functions are products of K-dependent “vibrational” functions and symmetric top functions. K is the quantum number for the molecule-fixed z component of the angular momentum. For a linear molecule, a two-step method is efficient because the Hamiltonian used to compute the basis functions includes the largest coupling term. The most important distinguishing feature of the two-step method we propose is that it uses an associated Legendre basis and quadrature rather than a K-dependent discrete variable representation. This reduces the cost of the calculation and simplifies the method. We have computed ro-vibrational energy levels with J up to 100 for CO₂, on an accurate available potential energy surface which is known as the AMES-2 PES and present a subset of those levels. We have converged most levels up to 20 000 cm⁻¹ to 0.0001 cm⁻¹.