METHOD FOR QUASI-CLASSICAL TRAJECTORY CALCULATIONS ON POTENTIAL-ENERGY SURFACES DEFINED FROM GRADIENTS AND HESSIANS, AND MODEL TO CONSTRAINTHE ENERGY IN VIBRATIONAL-MODES

A method for calculating quasiclassical trajectories on potential ener gy surfaces defined using a sequence of model quadratic surfaces (QCT/ GH) is suggested, and tested for atom-diatom collisions against the tr aditional quasiclassical trajectory approach. A simple model is also s uggested to constrain the classical energy of a bound vibrational mode to be greater than a specified amount, namely, its zero-point energy value. Essentially the model consists of assuming that the sum of the energies in the nonrelevant vibrational modes (typically unbound modes ) of the supermolecular complex acts as a pool from which energy may b e taken to compensate any leak of vibrational energy in the relevant b ound modes, hence preventing the latter from falling below zero-point value. Extensive QCT/GH trajectory calculations carried out for the HH-2 exchange reaction, which occurs over an energy barrier, as well as exploratory trajectories for the reaction O + OH --> O-2 + H, which o ccurs on a potential energy surface with a deep chemical well, have sh own that the total energy and total angular momentum are conserved wit hin a small numerical tolerance. Correcting for the leak of zero-point vibrational energy still leaves the total energy rigorously conserved but the total angular momentum is then only approximately kept consta nt. For H + H-2 (upsilon = O, j = O) --> H-2 (upsilon', j') + H, the c alculated state-to-state QCT/GH cross sections show reasonably good ag reement with those of converged quantum results reported in the litera ture for the same Hg potential energy surface. This agreement does not deteriorate after correction of zero-point energy leak. For both H-3 and HO2, accurate global analytical potential energy surfaces based on the double many-body expansion method have been utilized. Using these prototype systems, an assessment is made of the difficulties encounte red on direct reaction dynamics using the novel QCT/GH method.