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. 2018 Feb 14;20(7):5246-5255.
doi: 10.1039/c7cp07052g.

Solvation Dynamics in Polar Solvents and Imidazolium Ionic Liquids: Failure of Linear Response Approximations

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Solvation Dynamics in Polar Solvents and Imidazolium Ionic Liquids: Failure of Linear Response Approximations

Esther Heid et al. Phys Chem Chem Phys. .
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Abstract

This study presents the large scale computer simulations of two common fluorophores, N-methyl-6-oxyquinolinium betaine and coumarin 153, in five polar or ionic solvents. The validity of linear response approximations to calculate the time-dependent Stokes shift is evaluated in each system. In most studied systems linear response theory fails. In ionic liquids the magnitude of the overall response is largely overestimated, and linear response theory is not able to capture the individual contributions of cations and anions. In polar liquids, the timescales of solvation dynamics are often not correctly reproduced. These observations are complemented by a detailed analysis of Gaussian statistics including higher order correlation functions, variance of the energy gap distribution and its time evolution. The analysis of higher order correlation functions was found to be not suitable to predict a failure of linear response theory. Further analysis of radial distribution functions and hydrogen bonds in the ground and excited state, as well as the time evolution of the number of hydrogen bonds after solute excitation reveal an influence of solvent structure in some of the studied systems.

Figures

Fig. 1
Fig. 1. Stokes shift relaxation function after excitation, S(t), after deexcitation, SR(t), and time correlation functions Cg(t) and Ce(t) in ground and excited state in acetonitrile (top), methanol (middle) and 2-propanol (bottom) for MQ (left) and C153 (right). The colored area corresponds to a 95% confidence interval. Experimental data (labeled EXP) are taken from ref. 14 and 68.
Fig. 2
Fig. 2. Stokes shift relaxation function S(t) and time correlation functions Cg(t) and Ce(t) in ground and excited state in [Im21][DCA] (top) and [Im21][OTf] (bottom) for MQ (left) and C153 (right). The colored area corresponds to a 95% confidence interval. Experimental data (labeled EXP) are taken from ref. 69.
Fig. 3
Fig. 3. Scaling of the relaxation time τ from nonequilibrium (S(t), left) and equilibrium simulations in the ground (Cg(t), middle) and excited state (Ce(t), right) with solvent viscosity ηexp (see Table 2).
Fig. 4
Fig. 4. Absolute change in energy ΔU(t) calculated from the Stokes shift relaxation function S(t) and time correlation functions Cg(t) and Ce(t) in ground and excited state in MeOH (left) and [Im21][OTf] (right) for C153. Experimental data (labeled EXP) are taken from ref. 14 and 69.
Fig. 5
Fig. 5. Time-evolution of the spectral width W(t) of the interaction energy between MQ (left) or C153 (right) and different solvents. The circles at the edges of the curves represent the corresponding widths of the equilibrium simulations.
Fig. 6
Fig. 6. Contributions from cations and anions to the Stokes shift relaxation function S(t) (top panel) and time correlation functions Cg(t) (middle panel) and Ce(t) (bottom panel) in ground and excited state in [Im21][OTf] for MQ (left) and C153 (right). The colored area corresponds to a 95% confidence interval.
Fig. 7
Fig. 7. Higher order correlation functions Cn, where and a1 = 1, a2 = 1.6, a3 = 3, a4 = 6.4 and a5 = 15 according to eqn (5) after rearrangement. System: 2-PrOH for MQ (left) and C153 (right). The colored area corresponds to a 95% confidence interval.
Fig. 8
Fig. 8. Normalized correction Ccorre to the time correlation function Ce(t) according to eqn (11) in 2-PrOH for MQ (left) and C153 (right). The colored area corresponds to a 95% confidence interval.
Fig. 9
Fig. 9. Top: Radial distribution functions of solvent molecules around the central solute MQ (left), or C153 (right) in [Im21][OTf]. Bottom: Change in number of first shell ions around the central solute for the same system. The colored area corresponds to a 95% confidence interval.
Fig. 10
Fig. 10. Time evolution of normalized number of hydrogen bonds compared to the normalized Stokes shift. Inset: Normalization at 0.1 ps.

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