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The Journal of Chemical Physics

Time resolved stimulated light scattering from a solvated chromophore: A molecular dynamics study

Alan M. Walsh, Roger F. Loring

Published Jun 15, 1991• 21 citations
Publisher

Abstract

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.

DOI
10.1063/1.460144

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Physical Review Letters•Jan 30, 1995•118 citations
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.
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.
Light scattering by isolated small and intermediate-size molecules is studied theoretically. A quantum-mechanical model is developed that treats the molecule and the radiation field on equal terms and allows a nonperturbative solution for arbitrary wave forms and field strengths. The molecular states are described in terms of a basis set of zeroth-order states chosen so as to minimize the number of excited molecular states in the laser frequency range that combines radiatively with the initial (ground) state, i.e., that act as doorways for the field. Detailed calculations are restricted to the case of a single doorway. Closed-form expressions are obtained for the frequency-resolved scattering rates and time-resolved scattering spectra, including fluorescence and Rayleigh–Raman components, for a variety of conditions, including δ(t) excitation, excitation by a Lorentzian light pulse, by a coherent train of pulses and stationary excitation. The case of nonlinear scattering by very intense pulses is also investigated. Model calculations are reported for systems of 1–3 molecular levels. It is found that in general phase relations are maintained so that the coherence survives as long as the signal.
The connection between dephasing of optical coherence and the measured spectral density of the pure solvent is made through measurements and calculations of photon echo signals. 2-pulse photon echo measurements of a cyanine dye in polar solvents are presented. Signals are recorded for both phase matched directions enabling accurate determination of the echo signal time shift. Echo signals are calculated by two approaches that employ the response function description of nonlinear spectroscopy; (i) a single Brownian oscillator line shape model, and (ii) the line shape obtained using the solvent spectral density. The strongly overdamped Brownian oscillator model incorporates only a single adjustable parameter while the experimental data present two fitting constraints. The second model incorporates the measured solvent spectral density. Both give very good agreement with the experimental results. The significance of the second method lies in this being a new approach to calculate nonlinear spectroscopic signals, for comparison with experimental data, that uses directly the measured spectrum of equilibrium fluctuations of the solvent. This approach also provides a better conceptual perspective for deriving insight into the nature of the solute–solvent coupling mechanism. Comparing the parameters for the strength of interaction in a variety of polar solvents it is found that the coupling involves the solvent polarizability and not the solvent polarity. The interaction mechanism cannot be deduced from the Brownian oscillator calculations.
The vibrational photon echo measurement employs short pulses of coherent infrared radiation to discriminate among line broadening processes of different time scales. The measurement has been analyzed with the optical Bloch equations, in which the coupling of a quantum three-level system to a bath is represented by dephasing times. A detailed treatment of vibrational dynamics in a molecular liquid requires a Hamiltonian model. As such models are more readily treated in classical than in quantum mechanics, we consider the calculation of the vibrational echo in classical mechanics. Vibrational echoes are calculated for a solvated anharmonic oscillator. The classical mechanical echo is shown to share attributes of a quantum mechanical calculation.