Langevin equations, vibrational modes

This paper describes some new developments and applications based on the reaction path model. In section II the original form of the reaction path Hamiltonian [of. equation (1) below] is transformed to a new representation that has a more desirable structure for some applications. Section III shows how the reaction path model makes application of the unified statistical model for chemical reactions especially simple, and a generalized version of the unified statistical model is also developed there. Finally, in section IV the fact that the reaction path model consists of one special degree of freedom — i.e., the reaction coordinate — coupled to a number of harmonic oscillators is exploited to derive a generalized Langevin equation (GLE) for motion along the reaction path. This is a reduced equation of motion for only the reaction coordinate, but it experiences friction" and a "random force" because of coupling to the transverse vibrational modes. 

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