Vibrational lifetimes of cyanide ion in aqueous solution from molecular dynamics simulations: intermolecular vs intramolecular accepting modes.

The lifetimes of the first vibrational state of (12)C(14)N(-) and (13)C(15)N(-) dissolved in H2O or D2O were calculated. The calculations were based on the Landau-Teller formula that puts the vibrational lifetimes in terms of the autocorrelation function of the force exerted on the C-N stretch by the remaining degrees of freedom. The force autocorrelation functions were calculated from classical molecular dynamics simulations of the four cyanide/water isotopomer combinations ((12)C(14)N(-)/H2O, (12)C(14)N(-)/D2O, (13)C(15)N(-)/H2O, (13)C(15)N(-)/D2O). The cyanide ion was described by a polarizable force field, and the water was described by either the rigid SPC/E model or the flexible SPC/Fw model, in order to compare two different types of accepting modes, namely, (1) intermolecular (translational and rotational) solvent accepting modes (rigid SPC/E water) and (2) intramolecular (vibrational) solvent accepting modes (flexible SPC/Fw water). Since quantum effects are expected to increase in size with increasing frequency mismatch between relaxing and accepting modes, different quantum correction factors were employed depending on the identity of the accepting modes, more specifically, the harmonic/Schofield quantum correction factor in the case of intermolecular accepting modes and the standard quantum correction factor in the case of intramolecular accepting modes. The lifetimes with either the rigid SPC/E or flexible SPC/Fw water models were found to be in good quantitative agreement with the experimentally measured values for all isotopomer combinations. Our results suggest that taking into account quantum effects on the vibrational energy relaxation of cyanide in aqueous solution can make the intermolecular pathway at least as likely as the intramolecular pathway.