Time-dependent fluorescence in nanoconfined solvents: Linear-response approximations and Gaussian statistics

Laird, Brian B.; Thompson, Ward H.

doi:10.1063/1.3626825

Cited by 20 publications

(53 citation statements)

References 38 publications

(69 reference statements)

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“…For a more detailed description the reader is referred to the literature. 30,37,38 Generally, the energy of the system can be written as the Hamiltonian corresponding to the ground state, H g , as well as a perturbation that is turned on at the moment of excitation: [37][38][39]…”

Section: Theorymentioning

confidence: 99%

On the validity of linear response approximations regarding the solvation dynamics of polyatomic solutes

Heid

Moser

Schröder

2017

Phys. Chem. Chem. Phys.

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The time-dependent fluorescence of a chromophore can be calculated from either nonequilibrium simulations, or, as long as linear response theory holds true, from equilibrium solvent fluctuations in the ground or excited state if the perturbation inflicted by the chromophore is small. The assumption of Gaussian statistics, in contrast, links the nonequilibrium dynamics to solvent fluctuations solely in the excited state, as long as the energy gap distribution is Gaussian throughout the process. The validity of linear response theories on the ground and excited state surface as well as Gaussian statistics is thoroughly tested in this study by calculating the time-dependent Stokes shift of different benzene-like solutes. The effect of the size of change in partial charges of the solute, the multipolar order of charge distribution, the direction of change, as well as the influence of different solvents on the validity of linear response theory is examined by simulating 54 different systems. Calculation of the Gaussian character of the energy distribution in equilibrium, as well as the time-evolution of the peak width in the nonequilibrium simulation sheds light on the validity of Gaussian statistics in a nonstationary regime. We observed that a large intermediate broadening of the width of the energy distribution correlates with a failure of correlation functions to describe the nonequilibrium event. These results are accompanied by analysis of higher order correlation functions, as well as the structure of the solvents water, acetonitrile and methanol around the solute, to yield a comprehensive view, as well as general guidelines, on when and why equilibrium solvent fluctuations can correctly depict solvation dynamics.

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Section: Theorymentioning

confidence: 99%

On the validity of linear response approximations regarding the solvation dynamics of polyatomic solutes

Heid

Moser

Schröder

2017

Phys. Chem. Chem. Phys.

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“…All these predictions go beyond the standard expectations of L-models, 40,41,43 implying that the dynamics are nonlinear. We find all these predictions to hold when tested against MD simulations: all correlation functions depend on the electronic state of the chromophore (cf.…”

Section: Dynamicsmentioning

confidence: 99%

“…It is commonly assumed that the correlation function C 2,i (t) in eq (13) does not depend on the electronic state, 40,41 C 2,g (t, 0) = C 2,e (t, 0) = C 2 (t, 0), which is true for the L-models. Further, the linear response approximation 42 in Ω(q) relates non-equilibrium dynamics of the spectral maximum to the equilibrium two-point correlation function, 41,43,45 as is also derived in the Supporting Information (SI)…”

Section: Time-resolved Lineshapesmentioning

confidence: 99%

“…Equation (14) holds for either of the two states 40,41,43 and, therefore, the index indicating the state has been dropped on its right-hand side. Since the secondcumulant approximation in eq (13) and the linear relation in eq (14) are not necessarily equivalent, we will reserve the term "Gaussian dynamics" for the former 44 and "linear dynamics" for the latter.…”

Section: Time-resolved Lineshapesmentioning

confidence: 99%

“…Since the secondcumulant approximation in eq (13) and the linear relation in eq (14) are not necessarily equivalent, we will reserve the term "Gaussian dynamics" for the former 44 and "linear dynamics" for the latter. 40,41,43,45 The linear response approximation also allows one to calculate S σ (t) in eq (12), which yields (see SI)…”

Section: Time-resolved Lineshapesmentioning

confidence: 99%

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Non-Gaussian Lineshapes and Dynamics of Time-Resolved Linear and Nonlinear (Correlation) Spectra

Dinpajooh

Matyushov

2014

J. Phys. Chem. B

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Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

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Computational solvation dynamics: Implementation, application, and validation

Schröder

Heid

2020

Annual Reports in Computational Chemistry

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Time-dependent fluorescence in nanoconfined solvents: Linear-response approximations and Gaussian statistics

Cited by 20 publications

References 38 publications

On the validity of linear response approximations regarding the solvation dynamics of polyatomic solutes

On the validity of linear response approximations regarding the solvation dynamics of polyatomic solutes

Non-Gaussian Lineshapes and Dynamics of Time-Resolved Linear and Nonlinear (Correlation) Spectra

Computational solvation dynamics: Implementation, application, and validation

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