Molecular Dynamics Simulation of Solvation Dynamics in Methanol−Water Mixtures

Skaf, Munir S.; Ladanyi, Branka M.

doi:10.1021/jp961634o

Cited by 114 publications

(110 citation statements)

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“…At the same time, solvation dynamics are an important testing ground for these approximations and violations of linear response have been observed. [14][15][16][17][18][19] We recently showed 20 that if one assumes E is a Gaussian random variable, then S(t) is equal to the equilibrium excited-state correlation function, C e (t) ≡ δ E(t)δ E(0) e / δ E(0) 2 e ; see Eq. (33).…”

Section: S(t) = E(t) − E(∞) E(0) − E(∞) mentioning

confidence: 99%

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

Laird

Thompson

2011

The Journal of Chemical Physics

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The time-dependent fluorescence of a model dye molecule in a nanoconfined solvent is used to test approximations based on the dynamic and static linear-response theories and the assumption of Gaussian statistics. Specifically, the results of nonequilibrium molecular-dynamics simulations are compared to approximate expressions involving time correlation functions obtained from equilibrium simulations. Solvation dynamics of a model diatomic dye molecule dissolved in acetonitrile confined in a spherical hydrophobic cavity of radius 12, 15, and 20 Å is used as the test case. Both the timedependent fluorescence energy, expressed as the normalized dynamic Stokes shift, and the timedependent position of the dye molecule after excitation are examined. While the dynamic linearresponse approximation fails to describe key aspects of the solvation dynamics, assuming Gaussian statistics reproduces the full nonequilibrium simulations well. The implications of these results are discussed.

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Section: S(t) = E(t) − E(∞) E(0) − E(∞) mentioning

confidence: 99%

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

Laird

Thompson

2011

The Journal of Chemical Physics

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“…13 Skaf and Ladanyi found that the linear-response approximation can be unsatisfactory even when the ground-and excited-state correlation functions are the same. 14 Since the derivation of the excitedstate correlation function from Eq. ͑8͒ relies on the linearresponse approximation, it is useful to consider a different approach to the derivation based instead on the second approximation described above.…”

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confidence: 99%

On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence

Laird

Thompson

2007

The Journal of Chemical Physics

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Time-dependent fluorescence ͑TDF͒ of a chromophore in a polar or nonpolar solvent is frequently simulated using linear-response approximations. It is shown that one such linear-response-type approximation for the TDF Stokes shift derived by Carter and Hynes ͓J. Chem. Phys. 94, 5961 ͑1991͔͒ that is based on excited-state dynamics gives the same result as that obtained by assuming Gaussian statistics for the energy gap. The derivation provides insight into the much discussed relationship between linear response and Gaussian statistics. In particular, subtle but important differences between the two approximations are illuminated that suggest that the result is likely more generally applicable than suggested by the usual linearization procedure. In addition, the assumption of Gaussian statistics directly points to straightforward checks of the validity of the approximation with essentially no additional computational effort. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2747237͔A common experimental approach for probing solvation dynamics relevant to charge-transfer processes is the measurement of the time-dependent fluorescence Stokes shift. [1][2][3][4] In these experiments a probe dye molecule-generally with a charge-transfer electronic transition that is accompanied by a significant change in dipole moment-is excited and the fluorescence energy ⌬E͑t͒ is measured as a function of the time after excitation. Typically, the results are plotted as the normalized dynamic Stokes shift S͑t͒,where ⌬E͑ϱ͒ is the relaxed Stokes shift. The decay of S͑t͒ with time provides information about time scales for solvent reorganization, time scales that are relevant, for example, to electron and proton transfer reactions. The normalized dynamic Stokes shift can be simulated using nonequilibrium molecular dynamics. In this approach, an equilibrium molecular-dynamics trajectory of the groundstate dye molecule in solution is run to generate a representative set of initial conditions for excitation. Each of these initial configurations of the solute and solvent nuclei is used as the starting point of a nonequilibrium trajectory with the dye electronic state changed to the excited one; this creates an excited-state dye molecule in a nonequilibrium solvation configuration. The fluorescence energy ⌬E͑t͒ is then followed during the subsequent nonequilibrium trajectory and is used to compute S͑t͒. Thus, this simulation is quite analogous to the experiment.Another approach to simulating the results of timedependent fluorescence measurements is to invoke the linearresponse approximation. In this case, the dynamic Stokes shift can be approximated by results from equilibrium molecular-dynamics simulations. The general approach is to write the Hamiltonian for the system as a zeroth-order Hamiltonian and a "perturbation" that is turned on at time t =0 ͑the moment of excitation͒,where ͑t͒ is the Heaviside step function and H g and H e are the Hamiltonians for the ground-and excited-state dye molecule, respectively. The perturbation, howeve...

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“…468,483,[522][523][524][525][526] Thus, calculations of both S(t) and C ν (t) are useful for elucidating the mechanism of solvent dynamics. Fig.…”

Section: Solvation Dynamicsmentioning

confidence: 99%

Reactivity and Dynamics at Liquid Interfaces

Benjamin¹

2015

Reviews in Computational Chemistry

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Molecular Dynamics Simulation of Solvation Dynamics in Methanol−Water Mixtures

Cited by 114 publications

References 50 publications

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

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

On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence

Reactivity and Dynamics at Liquid Interfaces

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