Vibrational energy relaxation of the cyanide ion in water

The vibrational relaxation time of the cyanide ion in ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ and in ${\mathrm{D}}_{\mathrm{2}}\mathrm{O}$ was measured by IR-pump–IR-probe experiments. The isotopic composition of the ion was varied in order vary the oscillation frequency of the ${\mathrm{CN}}^{\mathrm{-}}$ vibrational mode. In ${\mathrm{D}}_{\mathrm{2}}\mathrm{O},$ the vibrational relaxation rate is accelerated from 120 to 71 ps when increasing the vibrational frequency from $\text{2004\hspace{0.17em}}{\mathrm{cm}}^{\mathrm{-1}}$ ${(}^{\mathrm{13}}{\mathrm{C}}^{\mathrm{15}}\mathrm{N})$ to $\text{2079\hspace{0.17em}}{\mathrm{cm}}^{\mathrm{-1}}$ ${(}^{\mathrm{12}}{\mathrm{C}}^{\mathrm{14}}{\mathrm{N}}^{\mathrm{-}}\mathrm{).}$ In ${\mathrm{H}}_{\mathrm{2}}\mathrm{O},$ time constants between 31 and 28 ps were observed. The systematic dependence of the relaxation rates on the vibrational frequency provides a small portion of the friction spectrum. A significant correlation between vibrational relaxation time of the solute and the IR absorption cross section of the solvent was found, providing experimental evidences for a dominating contribution to vibrational relaxation of Coulomb interactions and the importance of coupling to internal solvent modes. In addition, the infrared bandwidths and the orientational diffusion times are reported. All experimental observables $T_1,$ $T_2,$ and ${\tau }_{\text{2R}}$ related to the vibrational transitions of ${\mathrm{CN}}^{\mathrm{-}}$ are now experimentally available and can be compared with model theoretical calculations.