Vibrational Energy Relaxation of a Hydrogen-Bonded Complex Dissolved in a Polar Liquid via the Mixed Quantum−Classical Liouville Method

Abstract

The vibrational energy relaxation (VER) of the hydrogen stretch in a linear hydrogen-bonded complex dissolved in a polar solvent is studied. The study is based on the Azzouz-Borgis model [Azzouz, H.; Borgis, D. J. Chem. Phys. 1993, 98, 7361], which is known to account for many important features of real hydrogen-bonded systems, including ionic-to-covalent tautomerism and a broad distribution of hydrogen stretch frequencies. A description of VER in this strongly coupled system is considered, which consists of the following three consecutive steps: (1) solvation on the adiabatic excited vibrational surface; (2) nonadiabatic transition from the excited to the ground adiabatic vibrational surface; and (3) solvation on the adiabatic ground vibrational surface. The relaxation dynamics during those three steps were simulated via the mixed quantum-classical Liouville method, where the hydrogen is treated quantum-mechanically, while the other particles are treated in a classical-like manner. The solvation on the excited-state surface was found to occur rapidly ( approximately 0.5 ps) and to involve energy exchange with both the intramolecular and intermolecular degrees of freedom. It was also found that, while energy is released to the solvent during the solvation of the covalent tautomer, the solvation of the ionic tautomer involves absorption of energy from the solvent. The decrease in the transition frequency during the solvation process also facilitates the nonadiabatic transitions, which occur rapidly ( approximately 0.8 ps) thereafter. The nonadiabatic transitions were shown to be induced by interactions with a large number of solvent molecules and to be relatively insensitive to their location relative to the complex. Finally, solvation on the ground-state surface was seen to occur on a time scale of approximately 1.0 ps and leads to nonequilibrium ionic and covalent subpopulations. Equilibration on the ground-state surface occurs on a significantly slower time scale ( approximately 7.6 ps). Our results shed new light on the problem of VER in strongly coupled condensed phase systems that lie outside the range of validity of the Landau-Teller formula.

Analysis of the quantum-classical Liouville equation in the mapping basis

“…While the QCLE has a number of attractive features and has been shown to provide an accurate description of the dynamics in many instances [9][10][11][12][13][14][15][16][17][18][19][20][21] , it is difficult to solve. A direct numerical integration of Eq.…”

Heat transfer statistics in mixed quantum-classical systems

“…We also anticipate applications of the method to multi-level (i.e., beyond two levels) subsystems with more complex environments. Finally, one could consider applying other mixed quantum-classical and semiclassical methods, such as those previously used in the study of vibrational energy transfer in condensed phases [67][68][69], to nonequilibrium heat transfer problems.…”

Correlation Functions in Open Quantum-Classical Systems

“…For the more general bath and coupling potentials, the QCLE provides an approximate description of the quantum dynamics. In this case, comparisons of simulations of QCL dynamics with exact quantum results have indicated that it is quantitatively accurate for a wide range of systems [36,[39][40][41][42][43][44][45][46][47][48] The QCLE equation can be simulated using ensembles of trajectories, which, in combination with the quantum initial condition sampling discussed above, provides a way to compute quantum correlation functions. As we shall see, the nature of the trajectories that enter in the simulations depends on the algorithm and should not be ascribed physical significance.…”

“…C AB (t) = 1 Z Q n 1 ,n 2 ,n 3 dX n 1 |ρ W (X) |n 3 n 3 |Â |n 2 n 2 |B W (X, t) |n 1 (43) whereρ W (X) and Z Q are given by Equations (40) and (42), respectively.…”