Tensor formalism in anharmonic calculations

A new method is presented to compute cartesian tensors in the expansion of curvilinear internal coordinates. Second- and higher-order coefficients are related to the metrics of the space of displacements. Components of the metric tensor are taken from existing tables of inverse kinetic energy matrix elements or, when rotations are involved, derived from general invariance conditions of scalars within a molecule. This leads to a tensor formalism particularly convenient in dealing with curvilinear coordinates in anharmonic calculations of vibrational frequencies. Formulae are given for elements of the potential energy matrix, related to quadratic and cubic force constants in terms of Christoffel symbols. The latter quantities are also used in the expansion of redundancy relations, with explicit coefficients given up to the third order.