A test of the semiclassical energy conserving trajectory technique for low energy electron transfer reactions

A semiclassical procedure, quantum internal states plus classical translational path, is detailed. Enforcing conservation of total energy leads to a coupling of the time-dependent Schrödinger equation and Hamilton’s equations through the use of an instantaneous expectation value of the interaction potential in the latter. A general computer program was written to solve the resulting set of coupled first order differential equations. We present two detailed tests of the numerical accuracy. Applications to electron transfer in the symmetric O+2+O2 reaction are presented using two interaction potentials. The first is identical to that used in previous semiclassical calculations. Comparison of state-to-state cross sections from the present and previous semiclassical calculations shows essentially no agreement, even though the dynamical equations, basis set, and interaction potential are identical in both studies. The second interaction potential is identical to that used in a previous exact quantal calculation. Comparison of state-to-state transition probabilites at 1 eV kinetic energy from the present semiclassical and previous quantal calculations shows good agreement for the resonant and near-resonant channels only. At 8 and 36 eV kinetic energies, the present semiclassical state-to-state cross sections are in excellent agreement with the quantal ones for all channels. These results demonstrate the quantitative accuracy of the semiclassical energy conserving trajectory approach to charge transfer even at low kinetic energies.