**Decompositions of Solvent Response Functions in Ionic Liquids: A Direct
Comparison of Equilibrium and Nonequilibrium Methodologies**

ZL Terranova and SA Corcelli, JOURNAL OF PHYSICAL CHEMISTRY B, 122, 6823-6828 (2018).

DOI: 10.1021/acs.jpcb.8b04235

Time-dependent Stokes shift (TDSS) measurements provide crucial insights
into the dynamics of liquids. The interpretation of TDSS measurements is
often aided by molecular dynamics simulations, where solvent response
functions are computed either with an equilibrium or nonequilibrium
approach. In the nonequilibrium approach, the solvent is at equilibrium
with the ground electronic state of the solute and its charge
distribution is instantaneously changed to that of the first excited
state. The solvation response function is then calculated as a
nonequilibrium average of the subsequent evolution of the solvent
influence on the electronic energy gap. In the equilibrium approach, the
normalized time correlation function of the fluctuations of the solvent-
perturbed electronic energy gap is calculated. If the linear response
approximation is valid, then the nonequilibrium solvation response
function is identical to the equilibrium time correlation function. The
nonequilibrium methodology conceptually mimics the experiment, but it is
significantly more computationally expensive than the equilibrium
approach. In multicomponent systems such as ionic liquids, it is natural
to inquire how the various components affect the observed relaxation
dynamics. When utilizing the nonequilibrium methodology, the solvation
response naturally decomposes into a sum of responses for each component
present in the system. However, the equilibrium time correlation
function does not decompose unambiguously. Here, we have evaluated a
decomposition strategy that is consistent with the linear response
approximation for the study of solvation dynamics of coumann 153 (C153)
in the 1-ethyl-3-methyl imidazolium tetrafluoroborate, **emim****BF4**,
ionic liquid. The agreement of the equilibrium and nonequilibnum
solvation response functions demonstrates the validity of the linear
response approximation for the C153/**emim** **BF4** system. Moreover,
decompositions of the equilibrium time correlation function into
contributions of the translational and rovibrational motions of the
anions and cations are essentially identical to the same decompositions
of the nonlinear solvation response.

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