ℒ²Calculations of accurate quantal-dynamical reactive scattering transition probabilities and their use to test semiclassical applications

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.