Exact classical scaling formalism for nonreactive processes

Publisher Website
Google Scholar
Abstract
A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, ϑ) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T̄, the result is T̄−T̄(0) = α+βp(0)+γI(0), where the superscripted ’’0’’ indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom–collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively.