Dynamics of complex molecular systems with numerical kinetic energy operators in generalized coordinates

Dynamics of complex molecular systems in generalized coordinates (q,p) using numerical kinetic energy operators is investigated. The kinematical tools necessary for quantum, classical or semiclassical dynamics with or without constraints mainly come from the covariant and contravariant components of the metric tensor and their derivatives up to the second ones. These quantities are computed numerically but without any other approximation than the numerical precision by the code TNUM. This code generates kinetic energy operators in the internal coordinates of the Z-matrix describing the molecular frame geometry in the ab initio quantum chemistry step or in symmetry adapted coordinates [D. Lauvergnat, A. Nauts, J. Chem. Phys. 116 (2002) 8560]. Various reduced dimensionality models can be used in the upgraded code. The interface with an ab initio code is calibrated on a 22-atom system for which a two-dimensional quantum treatment with a constrained Hamiltonian has been carried out previously. The test application concerns the spreading properties of a wave packet in an unstable flat region around a valley ridge inflexion point between two transition states in the Endo-dimerization of cyclopentadiene. We perform here on-the-fly classical or semiclassical dynamics in full or reduced dimensionality.