# A generalized Langevin approach to vibrational relaxation in fluids

#### Abstract

A new, first-principles theory of vibrational energy relaxation (VER) of a solute normal mode infinitely diluted in a monatomic solvent is presented, and numerical applications, including molecular dynamics computer simulation results, are reported. The molecular-level analysis begins with a physically realistic generalized Langevin equation of motion that reflects the basic physics of the ultra-short time-scale and distance-scale motions characterizing typical chemical processes at liquid densities. The central result of the theory is a rigorous, computationally practical expression for the VER time $T\sb1$ in terms of the friction kernel of the relaxing normal mode evaluated at the liquid-phase frequency of the solute. The friction kernel is obtained as the cosine Fourier transform of the autocorrelation function of the fluctuating force exerted by the solvent on the solute normal mode given that this coordinate is fixed at its equilibrium value. A Gaussian approximation to the force autocorrelation function allows $T\sb1$ to be evaluated from the equilibrium properties of the solution.^ The theory is implemented for dihalogen and hydrogen-isotope solutes relaxing in monatomic solvents. These studies investigate the temperature, density, and isotope dependencies of $T\sb1$. Molecular dynamics simulations are also performed to test the validity of the Gaussian model to the force autocorrelation function. ^

#### Degree

Ph.D.

#### Advisors

Major Professor: Steven A. Adelman, Purdue University.

#### Subject Area

Chemistry, Physical|Physics, Molecular|Physics, Fluid and Plasma

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