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Reorientational time correlation functions Cl(t)(≡≤Pl[cos θ(t)]>) for a diatomic solute in 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI+PF6-) are analyzed via molecular dynamics computer simulations, where ≤...≥ denotes an equilibrium ensemble average, Pl the lth order Legendre polynomial and θ(t) the angle between the solute orientation at time t and its initial direction. Overall results are indicative of heterogeneous dynamics in EMI+PF6-. For a small nondipolar solute, Cl(t) are well-described as stretched exponential functions in wide time ranges. One striking feature is that after rapid initial relaxation, C2(t) decays more slowly than C1(t). As a result, the correlation time associated with the former is considerably longer than that with the latter. This is ascribed to solvent structural fluctuations, which allow large-amplitude solute rotations. As the solute size grows, relaxation of Cl(t) approaches exponential decay. [ABSTRACT FROM AUTHOR]

The Jarzynski identity can be applied to instances when a microscopic system is pulled repeatedly but quickly along some coordinate, allowing the calculation of an equilibrium free energy profile along the pulling coordinate from a set of independent non-equilibrium trajectories. Using the formalism of Wiener stochastic path integrals in which we assign temperature-dependent weights to Langevin trajectories, we derive exact formulae for the temperature derivatives of the free energy profile. This leads naturally to analytical expressions for decomposing a free energy profile into equilibrium entropy and internal energy profiles from non-equilibrium pulling. This decomposition can be done from trajectories evolved at a unique temperature without repeating the measurement as done in finite-difference decompositions. Three distinct analytical expressions for the entropy-energy decomposition are derived: using a time-dependent generalization of the weighted histogram analysis method, a quasi-harmonic spring limit, and a Feynman-Kac formula. The three novel formulae of reconstructing the pair of entropy-energy profiles are exemplified by Langevin simulations of a two-dimensional model system prototypical for force-induced biomolecular conformational changes. Connections to single-molecule experimental means to probe the functionals needed in the decomposition are suggested. [ABSTRACT FROM AUTHOR]

To understand the nonexponential relaxation associated with solvation dynamics in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate, we study power spectra of the fluctuating Franck-Condon energy gap of a diatomic probe solute via molecular dynamics simulations. Results show 1f dependence in a wide frequency range over 2-3 decades, indicating distributed relaxation times. We analyze the memory function and solvation time in the framework of the generalized Langevin equation using a simple model description for the power spectrum. It is found that the crossover frequency toward the white-noise plateau is directly related to the time scale for the memory function and thus the solvation time. Specifically, the low crossover frequency observed in the ionic liquid leads to a slowly decaying tail in its memory function and long solvation time. By contrast, acetonitrile characterized by a high crossover frequency and (near) absence of 1f behavior in its power spectra shows fast relaxation of the memory function and single exponential decay of solvation dynamics in the long-time regime.