Molecular dynamics study of vibrational energy relaxation of CN− in H2O and D2O solutions: An application of path integral influence functional theory to multiphonon processes

Vibrational energy relaxation of a cyanide ion in the aqueous solutions has been investigated. Both the solute $({\mathrm{CN}}^{-})$ and the solvent $({\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ or ${\mathrm{D}}_{\mathrm{2}}\mathrm{O})$ were treated quantum mechanically based upon the path integral influence functional formalism assuming a harmonic oscillator bath. Single and multiphonon spectral densities were evaluated numerically from the normal modes of the solvent, i.e., the bath phonons, and the linear and nonlinear coupling constants between the C–N stretching coordinate and the phonons for 30 different quenched and instantaneous solvation structures generated by molecular dynamics calculations. The method combined with the normal mode analysis successfully presented not only the time constant of the relaxation but also information about what sorts of the solvent bath modes are responsible for the relaxation process. We show that two-phonon process caused by the nonlinear coupling between the C–N stretching mode and two bath phonons are shown to be mostly responsible for the present system. It is found, too, that the coupling of the system with two bath rotational libration modes and the coupling with a bath bending mode and a bath rotational libration mode are dominant in the relaxation process in an ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ solution, while, in a ${\mathrm{D}}_{\mathrm{2}}\mathrm{O}$ solution, the coupling with the bath bending mode and bath rotational libration mode is most important. The normal modes that represent large motion of the water molecules inside the first and second solvation shells of the cyanide ion are particularly significant for the relaxation.