The harmonic mean field model for molecular solvents: A liquid state analog of the harmonic oscillator-rigid top approximation

Abstract

A liquid state analog of the gas phase harmonic oscillator-rigid top model is developed. This analog, which we call the harmonic mean field model, permits one to compute the equilibrium and dynamic properties of real, i.e., vibrating, molecular solvents from the structure and dynamics of the corresponding rigid solvents. The harmonic mean field model is based on: (i) A mean field harmonic model for the solvent vibrational (V) force field. (ii) A rigid solvent model treatment of translational–rotational (TR) fluctuations. (iii) Complete neglect of explicit coupling between V and TR fluctuations. (Implicit coupling is included in the vibrational force field.) The model is developed for statics via a sequence of physically motivated approximations to the exact canonical ensemble phase space distribution function of the solvent, fCA[S]. This yields a model distribution function f(0)CA[S] =f(0)CA[pyy]fCA[pww; v0], where f(0)CA[pyy] is an effective harmonic vibrational phase space distribution function which describes mean field harmonic V fluctuations and where f(0)CA[pww; v0] is the rigid solvent canonical ensemble distribution function. The nonequilibrium version of the model is defined as the solvent dynamics generated by a model Liouville operator L(0). This is defined via the model equilibrium Liouville equation L(0)f(0)CA [S]=0. Explicit results for equilibrium averages and time correlation functions of molecular solvents are obtained. The frequency spectra of the time correlation functions contain a low frequency ‘‘acoustic’’ branch arising from solvent TR motions and high frequency ‘‘optical’’ branches arising from collective solvent V motions. A detailed analysis of the frequency spectra of autocorrelation functions of diatomic solvents is presented.