K-independent vibrational bases for systems with large amplitude motion

For J > 0 calculations it would be advantageous to have a vibrational basis independent of rotational quantum numbers, but which can be applied to molecules or systems with large amplitude motion. Several authors have explored the possibility of using as bend functions (m = 0) Legendre polynomials. Their most obvious disadvantage is the existence of infinite matrix elements. Their behaviour near the theta = 0 and pi singularities will also be inappropriate for some wavefunctions. In this paper, we test and analyse several rotational-index-independent vibrational bases and compare them to the standard basis of associated Legendre polynomials, Theta(m)(l), where m depends on K, the quantum number for the molecule-fixed z component of the angular momentum. We find that for three-atom systems with wavefunctions having both significant amplitude at linearity and important Theta(m=odd) components a Legendre basis is poor, despite the repulsive singularity at linear geometries. Similar problems occur for systems with more than three atoms.