The theory of the canonical force field revisited

In a previous Letter, Kuczera’s theory of the canonical force field was generalized to the case of redundant curvilinear internal coordinates related by non-linear constraints. A central issue in this theory is the projection from the space of internal coordinates onto the pure vibrational manifold. In this Letter we present a new mathematical treatment of the projection that solves some problems of inconsistency that have arisen when applying the theory to molecules with a central atom. In addition to solving these problems, this treatment greatly simplifies the attainment of the projection and, consequently, the calculation of canonical force constants.