A general method to obtain vibrational symmetry adapted bases in a local scheme

A general approach to obtain symmetry adapted bases from a local set of states is presented. The approach is based on the identification of the invariant subspaces which, when projected by means of the eigenfunction method developed by Chen (1989, Group Representation Theory for Physicists Singapore, World Scientific), allow the generation of a symmetry adapted basis. The symmetrized functions so obtained are further taken as a basis to diagonalize simultaneously a set of normal number operators, which provides a set of normal states expanded in terms of the symmetry adapted local basis. In this approach the normal number operators are generated implicitly from the one quantum space through a tensorial formalism. Although the normal operators are defined in a harmonic basis, the locality of the basis allows the approach to be extended to anharmonic functions. This approach has the additional advantage of allowing the elimination of the spurious states, a common problem in a local coordinate representation. An important advantage of this symmetrization method is that it allows generation of a code to analyse any molecular system with a minimum set of input data.