Molecular theory of electronic spectroscopy in nonpolar fluids: Ultrafast solvation dynamics and absorption and emission line shapes

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Abstract
We present a theory of time- and frequency-domain spectroscopy of a dilute nonpolar solute in a nonpolar liquid or supercritical fluid solvent. The solute and solvent molecules are assumed to interact with isotropic pair potentials. These potentials, together with the solute and solvent masses, are the only input in the theory. We arrive at expressions for the absorption and emission line shapes, which include the possibility of motional narrowing, and for the time-resolved fluorescence and transient hole-burning observables, by assuming that the solute’s fluctuating transition frequency describes a Gaussian process. These expressions depend only on the average and variance of the transition frequency distributions in absorption and emission and on the normalized frequency fluctuation time-correlation functions. Within our formalism the former are obtained from the solute-solvent and solvent-solvent radial distribution functions, which are calculated using integral equations. The time-correlation functions involve the time-dependent solute-solvent Green’s function. Its solution depends upon the solute and solvent diffusion constants, which in turn are determined from the radial distribution functions. The theory compares favorably with computer simulation results of the same model. We then investigate the dependence of the various spectroscopic observables on the solvent density, the temperature, and the difference between the ground- and excited-state solute’s pair interaction with the solvent molecules. For example, since our theory for the time-correlation functions captures both their short- and long-time behavior, we can see how the crossover from inertial to diffusive dynamics depends on these variables. Our results are similar to a variety of experiments on solutes in both nonpolar and polar solvents.

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