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The Journal of Chemical Physics

Homogeneity and Markovity of electronic dephasing in liquid solutions

Being J. Ka, Ming-Liang Zhang, Eitan Geva

Published Sep 28, 2006• 11 citations
Publisher

Abstract

The electronic dephasing dynamics of a solvated chromophore is formulated in terms of a non-Markovian master equation. Within this formulation, one describes the effect of the nuclear degrees of freedom on the electronic degrees of freedom in terms of a memory kernel function, which is explicitly dependent on the initial solvent configuration. In the case of homogeneous dynamics, this memory kernel becomes independent of the initial configuration. The Markovity of the dephasing process is also the most conveniently explored by comparing the results obtained via the non-Markovian master equation to these obtained via its Markovian counterpart. The homogeneous memory kernel is calculated for a two-state chromophore in liquid solution, and used to explore the sensitivity of photon echo signals to the heterogeneity and non-Markovity of the underlying solvation dynamics.

DOI
10.1063/1.2354155

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The electronic dephasing dynamics of a solvated chromophore is formulated in terms of a non-Markovian master equation. Within this formulation, one describes the effect of the nuclear degrees of freedom on the electronic degrees of freedom in terms of a memory kernel function, which is explicitly dependent on the initial solvent configuration. In the case of homogeneous dynamics, this memory kernel becomes independent of the initial configuration. The Markovity of the dephasing process is also the most conveniently explored by comparing the results obtained via the non-Markovian master equation to these obtained via its Markovian counterpart. The homogeneous memory kernel is calculated for a two-state chromophore in liquid solution, and used to explore the sensitivity of photon echo signals to the heterogeneity and non-Markovity of the underlying solvation dynamics.
Two- and three-pulse photon echo signals are calculated for various model systems. The use of an experimental solvation correlation function as the solvent fluctuation correlation function leads to two conclusions. First, inertial solvent motion plays a major role in the electronic dephasing process. Second, simple models such as Markovian or exponential models for the solvent fluctuation correlation function may not provide an adequate description of the echo signal. The real and imaginary parts of the echo response, which may be measured via heterodyne detected stimulated photon echoes, are compared with conventional photon echo signals.
We calculate the signal in a time-resolved, coherent light scattering experiment on a dilute solution of a nonpolar solute dissolved in a nonpolar solvent. We model the solute and solvent molecules as electronic two level systems, and assume that only the solute interacts with radiation. The electronic degree of freedom is treated perturbatively within the Born–Oppenheimer approximation. The nuclear degrees of freedom are treated classically, and their effects are modeled by a molecular dynamics simulation. We assume the electronic absorption spectrum is dominated by inhomogeneous broadening. The validity of this assumption for our model is verified through the calculation of the absorption line shape with and without the inhomogeneous broadening assumption. A quantitative measure of the homogeneous dephasing time is obtained from a calculation of the photon echo signal for our model. The time dependence of the light scattering signal is shown to reflect both dynamics of the fluid in its electronic ground state and in its electronic excited state. We analyze the relative importance of contributions to the signal from these two types of dynamics as a function of experimental time scale and laser frequency.
We calculate the photon echo signal for a nonpolar chromophore dissolved in a nonpolar solvent. Results of molecular dynamics simulations are compared to calculations in which molecular motions are taken to be ballistic, to assess the contribution of such motions to the echo decay. The validity of the conventional assumption that fluctuations in the electronic transition frequency obey Gaussian statistics is investigated for this model. We consider the role of fluctuations in the repulsive portion of the intermolecular potential in determining the echo decay. The calculations suggest that electronic dephasing in liquids may arise primarily from a slight rearrangement of the first solvation shell about the chromophore.
Photons are useful quantum systems for investigating the fundamental and practical aspects of dephasing, decoherence, and other types of open quantum dynamics. However, descriptions of open dynamics of photonic systems are usually in terms of decoherence functions and in many cases an explicit master-equation-based description is not available. This is particularly true when considering multipartite photonic open systems having possibly correlated environments. We obtain generic master equations for the reduced dephasing dynamics of a two-photon polarization state coupled to respective frequency degrees of freedom when the frequency degrees of freedom that form the environment are initially correlated. Our results show the explicit dependence of the operator form of the master equation and the decay rates on these correlations as well as on various types of frequency distributions. Furthermore, we use the recently developed bath-positive decomposition method to treat an initially correlated polarization-frequency state of a photon and demonstrate how this allows us to gain new insight and detailed information on how the contributions of different origins influence the photonic dephasing.
A rigorous theoretical connection between the polarizability spectral density obtained from optical Kerr effect (OKE) measurement with the correlation function describing solvent-induced optical dephasing detected in photon echo measurements is given. The experimentally obtained spectral density has a more reasonable physical basis than model correlation function descriptions of solvent fluctuations. The experimental OKE spectrum is demonstrated to provide a natural description of solvent motions that modulate the chromophore electronic states in the case of weak induced-dipolar interactions. The chromophore optically active vibrational modes are obtained from pump-probe spectra and are employed in the calculation of echo signals. It is found that the fast decays of the two-pulse echo signals result from both solvent and solute intramolecular motions while the echo peak shifts are dominated by the solvent intermolecular modes.
The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of nonequilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.