ℒ2 Calculations of accurate quantal-dynamical reactive scattering transition probabilities and their use to test semiclassical applications

Abstract

We discuss the calculation of quantum-mechanical amplitudes for reactive scattering based on the Fock scheme for coupling arrangement channels and expansion of the coupled amplitude densities in terms of square-integrable (ℒ²) basis functions. First, we provide a derivation of the coupled equations for the amplitude densities from the Fock-scheme integrodifferential equations for wavefunction components. Then we discuss the solution of these equations by ℒ² techniques. The methods are applied to calculate the thresholds and tunnelling probabilities for the reactions O + H₂(v= 0, 1)→ OH + H and H + OH(v= 0, 1)→ O + H₂, where v denotes the vibrational quantum number. The results, which represent accurate quantal dynamics for a given potential-energy surface, are used to test the predictions of variational transition-state theory for threshold energies and the least-action semiclassical method for tunnelling probabilities.