Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations

• Published in: The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory Vol. 117; no. 32; pp. 7190 - 7194
• Main Authors: Cotton, Stephen J, Miller, William H
• Format: Journal Article
• Language: English
• Published: Washington, DC American Chemical Society 15.08.2013
• Subjects: Atomic and molecular collision processes and interactions; Atomic and molecular physics; Computation; Computer simulation; Exact sciences and technology; General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.); Grounds; Mathematical analysis; Physics; Trajectories; Vibrational states; Wigner distribution; Window functions; Reactive collision; Ground states; Diatomic molecules; eV range; Wigner function; Inelastic scattering; Distribution function; Potential energy surfaces; Classical trajectory; Hydrogen molecules; Vibrational states; Atom-molecule collisions; Distribution functions
• ISSN: 1089-5639; 1520-5215
• DOI: 10.1021/jp401078u

A microscopically reversible approach toward computing reaction probabilities via classical trajectory simulation has been developed that bins trajectories symmetrically on the basis of their initial and final classical actions. The symmetrical quasi-classical (SQC) approach involves defining a classical action window function centered at integer quantum values of the action, choosing a width parameter that is less than unit quantum width, and applying the window function to both initial reactant and final product vibrational states. Calculations were performed using flat histogram windows and Gaussian windows over a range of width parameters. Use of the Wigner distribution function was also investigated as a possible choice. It was demonstrated for collinear H + H2 reactive scattering on the BKMP2 potential energy surface that reaction probabilities computed via the SQC methodology using a Gaussian window function of 1/2 unit width produces good agreement with quantum mechanical results over the 0.4–0.6 eV energy range relevant to the ground vibrational state to the ground vibrational state reactive transition.