The statistical mechanics of vibration-rotation spectra in dense phases

Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 

The time-dependent classical statistical mechanics of systems of simple molecules is reviewed. The Liouville equation is derived the relationship between the generalized susceptibility and time-correlation function of molecular variables is obtained and a derivation of the generalized Langevin equation from the Liouville equation is given. The G.L.E. is then simplified and/or approximated by introducing physical assumptions that are appropriate to the problem of rotational motion in a dense fluid. Finally, the well-known expressions for spectral intensity of infrared and Raman vibration-rotation bands are reformulated in terms of time correlation functions. As an illustration, a brief discussion of the application of these results to the analysis of spectral data for liquid benzene is presented. 

We will first show how one can obtain the time-correlation function expression for the susceptibility in a classical statistical ensemble of particles which exhibits a linear response to an externally applied perturbation. This will be followed by an outline of the argument that leads to the generalized Langevin equation for the time-dependence of an arbitrary function of the molecular canonical coordinates. In both cases, derivations with minor modifications have been presented previously in numerous reviews, monographs, etc. However, the results are employed in a large fraction of current descriptions of dynamical processes in dense phases and thus, it seems worthwhile to again show the basic ideas underlying the formalism. 

Barnes et al (eds.). Molecular Liquids - Dynamics and Interactions, 111-150. 1984 by D. Reidel Publishing Company. 

Consider an isolated system of N interacting particles with coordinates. . Qjj and momenta jp, The equations of motion for this system can be derived fTom the Hamiltonian H, Thus 

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THE STATISTICAL MECHANICS OF VIBRATION-ROTATION SPECTRA IN DENSE PHASES... 

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