Multidimensional Spectra via the Mixed Quantum-Classical Liouville Method: Signatures of Nonequilibrium Dynamics

Abstract

Multidimensional optical spectra are often expressed in terms of optical response functions. These optical response functions consist of contributions from a number of Liouville pathways that differ with respect to the chromophore's quantum state during the time intervals between light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals are dictated by potential energy surfaces that are explicitly dependent on the chromophore's quantum state. One therefore expects the system to hop between potential surfaces in a manner dictated by the Liouville pathways and the spectra to reflect the dynamics during the resulting nonequilibrium process. However, the approach commonly used to model spectra of complex condensed-phase systems is based on the ad hoc assumption that the photoinactive degrees of freedom undergo equilibrium dynamics on the potential surface that corresponds to the chromophore's ground state. In this paper, we formulate optical response in terms of mixed quantum-classical Liouville dynamics, which inherently accounts for the underlying nonequilibrium dynamics. It is shown that, when nonadiabatic transitions are neglected, the resulting formulation is equivalent to that obtained via the linearized semiclassical approximation. We demonstrate the feasibility and utility of the approach by using it to calculate the one- and two-dimensional infrared spectra of the hydrogen stretch of a moderately strong hydrogen-bonded complex dissolved in a dipolar liquid. The results are compared with previously reported spectra that were calculated within the framework of the standard equilibrium ground-state dynamical approach [ J. Phys. Chem. B 2008 , 112 , 12991. ], thereby shedding light on the spectral signatures of nonequilibrium dynamics in systems of this type.