Configuration-specific kinetic theory applied to the elastic collisions of hard spherical molecules

Classical trajectory simulations can be used to glean a wealth of information on the geometric details of gas-phase molecular collision events for which the standard theoretical treatment lacks the ability to predict. For instance, the standard treatment gives no information on configuration-specific collision parameters. A configuration-specific parameter is defined here as the average value for a collision parameter that is exclusive to either an ensemble of front-end or an ensemble of rear-end molecular collisions. This paper presents statistical results of simulation "measurements" on several configuration-specific parameters, including the configuration-specific collision frequencies. The simulations use single-component systems of hard spherical molecules confined within a spherical boundary. To complement the simulation effort, a systematic mathematical analysis for the configuration-specific parameters is presented. This analysis uses the Maxwell-Boltzmann distribution of molecular speeds as usual, but exploits the distinction between front-end and rear-end collision space, and uses the line-of-centers speed rather than the relative speed. The configuration-specific expressions derived from this analysis are in very good agreement with the simulation measurements for every molecular collision parameter studied in this work.