The Journal of Chemical Physics · 1970 · 616 citations · 15 references
Numerical AnalysisSpectral TheoryQuantum DynamicEngineeringComputational MechanicsSemiclassical TheoryQuantum Mechanical PropertyQuantum TheoryMatrix MethodQuantum MatterClassical S MatrixQuantum ScienceStatistical MechanicsPhysicsQuantum Statistical MechanicsAtomic PhysicsQuantum ChemistryMatrix AnalysisCondensed Matter TheoryMolecular CollisionsInterference EffectsNatural SciencesQuantum SystemCollision Detection
A semiclassical theory of molecular collisions grounded in exact classical mechanics has been developed for linear atom–diatom vibrational excitation. The authors derive an integral representation of the S‑matrix elements using only classical quantities, extending beyond the validity of semiclassical or uniform semiclassical approximations. Classical, semiclassical, and uniform semiclassical transition probabilities for H₂+He vibrational transitions were compared to exact quantum results; classical predictions are accurate only on average, while semiclassical and uniform semiclassical methods agree within a few percent, indicating that inelastic collision dynamics are essentially classical with simple quantum interference.
A previously developed semiclassical theory of molecular collisions based on exact classical mechanics is applied to the linear atom–diatom collision (vibrational excitation). Classical, semiclassical, and uniform semiclassical results for individual vibrational transition probabilities corresponding to the H2+He system are presented and compared to the exact quantum mechanical results of Secrest and Johnson. The purely classical results (the classical limit of the exact quantum mechanical transition probability) are seen to be accurate only in an average sense; the semiclassical and uniform semiclassical results, which contain interference effects omitted by the classical treatment, are in excellent agreement (within a few percent) with the exact quantum transition probabilities. An integral representation for the S-matrix elements is also developed which, although it involves only classical quantities, appears to have a region of validity beyond that of the semiclassical or uniform semiclassical expressions themselves. The general conclusion seems to be that the dynamics of these inelastic collisions is basically classical, with all quantum mechanical structure being of a rather simple interference nature.
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