A complete list of symmetry adapted expressions to the fourth power for compact bending potentials in molecules with and symmetry from a general symbolic algebra program

Abstract

An algorithm is proposed to perform the reduction of direct product representations of finite groups and, in particular, to perform the complete symmetry adaption of power representations, which may be used to obtain compact analytical representations of potential energy surfaces following an idea described in Marquardt and Quack [J. Chem. Phys. 109, 10628 (1998)]. The algorithm is general in the sense that it can be applied to any finite group being characterized by its set of irreducible representations. It is automatic in the sense that, in case the reduction yields multiple degenerate irreducible subspaces of the same species, all degenerate irreducible subspaces are obtained with a coherent phase relation. The algorithm is based on the standard reduction rule of traditional representation theory. A symbolic algebra computer program based on MAPLE is presented and applied here to obtain the complete list of symmetry adapted expressions of bond angle coordinates up to the fourth power in all irreducible representations of the C3v and Td point groups.