Computing rovibrational levels of polyatomic molecules with polyspherical coordinates and a contracted basis built with a K-independent vibrational primitive basis

Abstract

To compute the rovibrational spectrum of a molecule undergoing large amplitude motion it is important to use geometrically defined internal coordinates. In this paper, we use polar-type coordinates and a contracted basis of products of vibrational wavefunctions and symmetric top functions: |v〉|JKM〉. To facilitate computing matrix elements of the kinetic energy operator obtained when the molecule-fixed axes are attached to two of the vectors used to define the coordinates, it is common to use vibrational basis functions that depend on K, the quantum number for the molecule-fixed z component of the angular momentum. In this paper, we show that it is possible to use a |v〉|JKM〉 basis and forgo the K-dependent primitive vibrational functions. Instead, we use a K-independent primitive basis that is an extension of the one employed in Mol. Phys. 110, 825, (2012) for triatomics. Using a K-independent primitive basis obviates the need to compute and store contracted vibrational bases for each K. First, we demonstrate that rovibrational levels of H2O2 computed with the primitive basis, and no contraction, are accurate. Second, using the contracted |v〉|JKM〉 basis we compute J > 0 levels of CH3D. In both cases, we compute rovibrational levels with J values higher than those of levels calculated heretofore and for lower J there is satisfying agreement with previous calculations using K-dependent vibrational basis functions.