Semiclassical treatment of molecular vibrational energy transfer in collision between vibrationally excited O3 and Ar Original Research Article

A semiclassical (classical path) collision model has been used to calculate cross sections and rate constants for vibrational transitions in collision involving vibrationally excited O3 and Ar. In the semiclassical model the motion of Ar relative to O3 and the rotation of O3 have been solved using classical trajectory method. The vibrational degree of freedom of O3 has been treated quantum mechanically by solving the time-dependent Schrödinger equation using a state expansion method. Local modes are used to describe the interatomic positions in O3. Therefore two Hamiltonian operators have been derived. First, the Hamiltonian operator for an N-atomic molecule in Cartesian coordinates. This Hamiltonian operator is then used to derive the Hamiltonian operator for a triatomic molecule in local mode coordinates.