On intervector angle descriptions and their numerical implementation for solving molecular problems

Abstract

The angular parametrization comprising only bending angles is considered in detail. For tetratomic and pentatomic molecules, we first study the volume element, coordinate ranges, and parity-adapted basis functions. In contrast to the common belief, we show that the intervector angle description allows to uniquely specify the internal molecular geometry and to model tunneling through planarity. The redundant intervector angle and coordinate interdependences are explained by simple geometrical means. Principal difficulties arising from the interdependent coordinate ranges obstruct the numerical implementation of the description studied, since the angular basis functions are nonorthogonal and the overlap matrix may easily become ill-conditioned. For the symmetry-adapted representation, the origin of multiple solutions for the redundant coordinate is discussed. We additionally show that the redundant coordinate plays an important role by the characterization of the internal molecular geometry of pentatomic molecules described in terms of the cosines of the intervector angles.