Generalized Langevin theory for many-body problems in chemical dynamics: Gas-surface collisions, vibrational energy relaxation in solids, and recombination reactions in liquids

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Abstract
Model classical trajectory simulations of gas‐solid inelastic collisions, vibrational energy relaxation of a diatom in a solid, and atomic recombination reactions in a liquid are presented. These simulations are first applications of the molecular timescale generalized Langevin equation (MTGLE) theory [S. A. Adelman, Adv, Chem. Phys. 44, 143 (1980)] for condensed phase energy transfer and chemical reaction processes. The main conclusions of these model studies are as follows: (i) The MTGLE theory often provides computationally practical methods for condensed phase chemical problems. These methods are applicable with equal ease to both solid and liquid state processes. (ii) The equivalent harmonic chain heatbath modeling for reducing many‐body chemical problems to effective few‐body problems often converges rapidly. This rapid convergence is found for both short (subpicosecond) timescale processes (gas–solid collisions) and long (nanosecond) timescale processes (vibrational energy relaxation). (iii) The simplest harmonic chain model (heatbath replaced by a single fictitious atom) is often found to yield a qualitatively correct description of heatbath influence on both solid and liquid state processes. (iv) The MTGLE parameters ω e0 (chemical system Einstein frequency) and ω2 c1 (chemical system/heatbath coupling constant) are the quantities which often determine the gross magnitude of heatbath influence on condensed phase chemical processes. For both solid and liquid state processes ω e0 determines the effective vibrational frequencies (normal modes) of the chemical system and ω2 c1 determines the gross efficiency of chemical system/heatbath energy transfer. For liquid state processes ω e0 also determines the frequency of oscillations in the solvent cage, and ω2 c1 also determines rigidity of the solvent cage. (ω2 c1=0 means the cage is perfectly rigid).