We propose a method for treating equation of motions for atoms taking into account the inertial term with an interaction site model for capturing solvent dynamics attributed to solvent motions in a short-time regime, t < 100 fs. We show a prescription for solving the equation which governs the development of the fluctuation of solvent number density with the inertial term, and the results of the van Hove space-time correlation function of water are compared with those by a molecular dynamics simulation. Also, the procedure is applied to the study of solvation dynamics of the simplest betaine dye molecule pyridinium N-phenoxide in water in the excited state. It is shown that the coupling between solvation and a fast intramolecular reaction such as charge transfer is likely to play an important role in solvation dynamics of the simplest betaine, and the importance of tracking solvation process associated with electronic reorganization in the solute molecule in the short-time region is indicated.
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