Calculating rovibrational energy levels of a triatomic molecule with a simple Lanczos method

Abstract

We present a simple Lanczos method for calculating rovibrational energy levels of a triatomic molecule from a kinetic energy operator (KEO) with the z axis perpendicular to the molecular plane. We use rotational basis functions which are linear combinations of symmetric top functions so that all matrix elements are real. For some molecules, coupling between rotation and vibration is less important if the z axis is chosen perpendicular to the molecular plane, but the singularities of the z-axis operator are more difficult to deal with than those of the commonly used y-axis operator. The KEO with z axis perpendicular to the plane also reduces the number of sums over vibrational indices required to evaluate Hamiltonian matrix-vector products. Using a new symmetry-adapted basis and the z-axis KEO we calculate rovibrational energy levels of H2O for high J values. Even at J=40 we do not observe the formation of fourfold clusters. © 1999 American Institute of Physics.