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The Journal of Chemical Physics

Determining the solvation correlation function from three-pulse photon echoes in liquids

K. F. Everitt, Eitan Geva, James L. Skinner

Published Jan 15, 2001• 72 citations
Publisher

Abstract

The decay of three-pulse photon echo signals from a solute in a liquid solvent is sensitive to the solute’s transition frequency fluctuations, as characterized by its two-point time correlation function, otherwise known as the solvation correlation function. The most widely used method for determining this solvation correlation function from photon echo data involves the three-pulse photon echo peak shift (3PEPS) method. Using this method the long-time decay of the solvation correlation function can be obtained directly, but the determination of the short-time decay requires a difficult numerical fitting procedure. In this study we propose several alternative approaches to determining the solvation correlation function from echo data, the most promising and straightforward of which we call the S3PE (short-time slope of the three-pulse photon echo) method. The accuracy and efficacy of this approach is illustrated by extracting the solvation correlation function from “experimental” data obtained from classical molecular dynamics computer simulations.

DOI
10.1063/1.1332811

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The decay of three-pulse photon echo signals from a solute in a liquid solvent is sensitive to the solute’s transition frequency fluctuations, as characterized by its two-point time correlation function, otherwise known as the solvation correlation function. The most widely used method for determining this solvation correlation function from photon echo data involves the three-pulse photon echo peak shift (3PEPS) method. Using this method the long-time decay of the solvation correlation function can be obtained directly, but the determination of the short-time decay requires a difficult numerical fitting procedure. In this study we propose several alternative approaches to determining the solvation correlation function from echo data, the most promising and straightforward of which we call the S3PE (short-time slope of the three-pulse photon echo) method. The accuracy and efficacy of this approach is illustrated by extracting the solvation correlation function from “experimental” data obtained from classical molecular dynamics computer simulations.
Abstract This account summarizes our recent work on measurements of the correlation function of the transition frequency fluctuations by a three-pulse photon echo method. The correlation function of the transition frequency fluctuations is a sensitive measure for the magnitudes and time scales of dynamical interactions between solute and solvent. We describe the results of the solvation dynamics of small ions in protic solvents such as methanol and water obtained by an infrared photon echo method.
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.
The time-integrated three-pulse photon echo is discussed in terms of the line-shape functions which are shown to be directly related to the solvation dynamics. By using the short-time approximation to the line-shape function, an algebraic form of the three-pulse photon echo signal S PE (τ, T ) is obtained as a function of two delay times, τ and T, between pulses. On the basis of the approximate form of the photon echo signal, the echo peak shift with respect to the second delay time (population evolution period) is derived and found to be linearly proportional to the time-dependent fluorescence Stokes shift function for times greater than the bath correlation time, τ c . In the case of intermediate inhomogeneous broadening, the asymptotic echo peak shift magnitude is found to be useful in estimating the static inhomogeneous width. To illustrate the theoretical results, an analysis of the echo peak shift measurement of IR144 in a room temperature glass, PMMA, is presented.
We explore how the width of the three-pulse photon echo signal at long population times can be used to determine the strength of the system-bath interaction. Using simulation with finite pulses we show that a simple relation exist between the width of the echo signal, the coupling strength, and the pulse autocorrelation. The derived model is applied to Rhodamine 6G in alcoholic solution, a paradigm system for the study of solvation dynamics, and the results are compared to conventional methods. The independently determined coupling strength forms the basis for a computationally inexpensive route to determine the entire spectral density, the key parameter when considering system-bath interactions. Our method allows us to accurately estimate the relative amplitude of fast and slow components in the correlation function using only impulsive limit simulations. We show that the peak shift significantly overestimates the amplitude of the fastest decay component for our experimental data. Changing solvent from methanol to 1-hexanol we observe a narrowing of the width of the echo profile. The changes in the echo width allow us to estimate the changes of the coupling strength in various solvents.
An understanding of chemical reactivity begins with an understanding of the dynamics involved regarding system-bath interactions. Spectroscopic studies of these interactions in condensed-phase multichromophoric systems are intricate and contain much information. Photon-echo spectroscopy has proven to be a useful tool for probing these interactions. A description of three-pulse photon-echo peak shift spectroscopy (3PEPS)--theory, experiment, and application--for the study of solvation and dynamics of nanoscale excitons is presented. Also, we discuss how two-dimensional photon-echo spectroscopy (2DPE) relates to 3PEPS and show how 3PEPS data can be extracted from 2D photon-echo data.
Two-color three pulse photon echo peak shift spectroscopy (2C3PEPS) has been used to probe correlation in electronic transitions in two different regions of the electronic spectrum of a chromophore in the condensed phase. The 2C3PEPS can be done in an “uphill” or a “downhill” sense, where the first two interactions are of lower (higher) frequency than the final interaction with the radiation field. In both cases no correlation between the two spectral regions is observed at very short times. Different parts of the spectrum gain correlation owing to ultrafast solvent motion and the accompanying Stokes shift. We propose a model for the spectral shift that incorporates a conditional probability distribution for transition frequencies in the two spectral regions. The model qualitatively reproduces all the features of complete numerical simulations. Our results show that memory is partially conserved during the spectral diffusion process from the pump to the probe region. The downhill difference peak shift is very sensitive to the time scale of the inertial component of solvation and seems very promising for an accurate determination of this time scale.