Vibrational Energy Relaxation in Liquid HCl and DCl via the Linearized Semiclassical Method: Electrostriction versus Quantum Delocalization

Abstract

The rate constant for vibrational energy relaxation of the H-Cl stretch in liquid HCl (T = 188K, ρ = 19.671 nm(-3)) is calculated within the framework of the Landau-Teller formula. The force-force correlation function is calculated via the recently introduced force-derivative-free linearized semiclassical method [Vázquez et al. J. Phys. Chem. A2010, 114, 5682]. The calculated vibrational energy relaxation rate constant is found to be in excellent agreement with experiment, and the electrostatic force is found to contribute significantly to the high frequency component of the force-force correlation function. In contrast, the corresponding classical vibrational energy relaxation rate constant is found to be 2 orders of magnitude slower than the experimental value, and the classical force-force correlation function is found to be dominated by the Lennard-Jones forces. These observations suggest that quantum delocalization, enhanced by the light mass of hydrogen, amplifies the contribution of repulsive Coulombic forces to the force-force correlation function, thereby making electrostriction an unlikely mechanism for vibrational energy relaxation in the case of hydrogen stretches. This interpretation is reinforced by the results of a similar calculation in the case of the D-Cl stretch in liquid DCl under the same conditions. In this case, the quantum enhancement of the vibrational energy relaxation rate constant is observed to be greatly diminished in comparison to HCl, thereby giving rise to a reversal of the isotope effect in comparison to that predicted by the corresponding classical treatment (i.e., whereas the classical vibrational energy relaxation rate of DCl is faster than that of HCl, the opposite trend is predicted by the linearized semiclassical treatment). It is also shown that the vibrational energy relaxation of DCl is completely dominated by the Lennard-Jones forces within either classical and semiclassical treatments, thereby suggesting that electrostriction is the underlying mechanism in this case.