Use of semiclassical collision theory to compare analytic fits to the interaction potential for vibrational excitation of H2by Hethinsp;

摘要

Vibrational transition probabilities for strongly classically forbidden singlehyphen;quantum and twohyphen;quantum transitions calculated by two semiclassical methods involving realhyphen;valued trajectories are compared to quantum mechanical close coupling for various analytic fits to theabinitiointeraction potential for the Hendash;H2system. The finalhyphen;valuehyphen;representation integral expression from classicalSmatrix theory and the classicalhyphen;trajectory forcedhyphen;quantumhyphen;oscillator method are found to be in semiquantitative agreement with the quantum mechanical calculation even for transition probabilities as small as about 10minus;6. Further, the semiclassical methods reproduce the important trends in the results as functions of the interaction potential. The reliability of these semiclassical calculations allows one to determine the region of the potential energy surface which is sufficient for calculation of vibrational excitation probabilities. The important region for the present calculations is in the classically allowed region of the potential energy surface and at the fairly high total energy of 0.14 hartree includes the range of H2distances 1.195ndash;1.467 bohr for the forced quantum oscillator methods and the wider range 0.927ndash;2.000 bohr for the more accurate final value representation. The region which must be known for an accurate calculation is more restricted than previous discussions had suggested. At lower energies, an even more restricted range of the potential energy surface contributed to the semiclassical calculations.