Instantaneous normal mode analysis of hydrated electron solvation dynamics

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Abstract
The instantaneous normal mode (INM) method is implemented in the context of mixed quantum-classical molecular dynamics (MD) simulations and applied to the analysis of the short-time solvation dynamics of the hydrated electron. Numerically suitable equations for computing the solvent dynamical matrix (Hessian) for both ground and excited adiabatic electronic states are derived using analytical derivative methods of quantum chemistry. Standard diagonalization of the Hessian leads to the sets of eigenfrequencies and eigenvectors that underlie the INM theory. Comparison of the hydrated electron and pure water INM spectra and the corresponding mode participation ratios shows that the quantum solute enhances the participation of collective low-frequency unstable modes (imaginary frequencies) at the expenses of stable ones. Distinct differential INM spectra, involving distinct solvent configurational averages, are introduced to describe the changes experienced by the solvent INMs upon the vertical excitation of the electron. The overall picture is that the INMs associated with lower frequency translational and rotational motions, as well as fast librational reorientations are markedly affected by the photoexcitation, as opposed to the localized internal vibrations of the individual water molecules. The INM solvation response for the upward transition calculated from the real modes agrees with the response obtained directly from the energy gap time correlation up to approximately 100 fs. The agreement extends over much longer times for downward transitions. The INM analysis of the solvation responses following vertical upward and downward transitions reveals that diffusive translational and librational motions are both important mechanisms for the early stages (≲50 fs) of the solvent response, with the latter dominating the first half of this time period. It is also shown that the short-time solvent relaxation involves the combined motion of molecules from the first and second hydration shells. In addition, the linearized INM solvation response calculated for D2O indicates a significant (∼36%) solvent isotope effect in the first 25 fs of the response, where the decay is Gaussian. These results are compared with previous studies of the hydrated electron solvation dynamics.