Generalized Langevin theory for many-body problems in chemical dynamics: Modelling of solid and liquid state response functions

Abstract

The equivalent harmonic chain heatbath modelling method [S. A. Adelman, J. Chem. Phys. 71, 4471 (1979)] for reducing problems in condensed phase chemical dynamics to effective few‐body trajectory problems is tested via the calculation of typical solid and liquid state velocity response (correlation) functions χ̇ (t). Finite nearest neighbor harmonic chain models for condensed phase atomic dynamics which may be used in trajectory simulations, are constructed from moments of the spectral density of χ̇ (t) and from additional information about the small z behavior of e.g., diffusion coefficients. Model response functions are then generated numerically as specified trajectories of the chain equations of motion. The convergence of chain model response functions is investigated for the bulk elastic model (isotropic continuum elastic treatment) of a solid and for the Gaussian approximation to the Levesque–Verlet molecular dynamics results for a Lennard‐Jones liquid. For both cases, the chain model heatbaths are found to give response functions which: (i) converge rapidly and systematically; (ii) exactly reproduce the chemically crucial short‐time response and thus account for caging (in liquids) and initial chemical system/heatbath energy transfer; (iii) reproduce the chemically less important long time response in a qualitatively correct manner. It is thus concluded that the chain modelling techniques yield a chemically and calculationally useful reduction of condensed phase dynamics.