A molecular analysis of the vibrational energy relaxation mechanism of the CN− ion in water based upon path integral influence functional theory combined with a dipole expansion of the solute-solvent interaction

The molecular mechanism of vibrational energy relaxation of the CN− ion in water has been investigated using path integral influence functional theory combined with a dipole expansion of the solute-solvent interaction. First, in order to find out which solvent water molecules contribute most to the absorbtion of the solute excess vibrational energy, the normal modes of the solution, adopted for the harmonic oscillators bath approximation in the influence functional theory, have been back-transferred to the molecular coordinates and a contribution to the relaxation has been assigned to each water molecule according to the transformation matrix. Then, the coupling intensity C(i)2 between solute and solvent molecules playing a major role in the relaxation, has been analyzed by dipole expansion of the solute-solvent interaction, where bending, rotational and translational degrees of freedom were all represented by the standard variables μ1, μ2, R, θ1, θ2, and ϕ for the dipole expansion. From these analyses, it is clarified that (1) the contribution of the solvent water to the relaxation decreases rapidly in proportion to 1 / R6, such that only water molecules in the first hydration shell take part in the relaxation, (2) water molecules located in the direction of C-N bond contribute much to the relaxation, and (3) the excess energy is transferred to the bending of the relevant water molecule and its rotational libration represented by the variable θ2.