Hidden Breakdown of Linear Response:  Projections of Molecular Motions in Nonequilibrium Simulations of Solvation Dynamics

The linear response (LR) approximation forms the cornerstone of nonequilibrium statistical mechanics and has found special utility in studies of solvation dynamics, in which LR implies that nonequilibrium relaxation dynamics is governed by the same molecular motions responsible for fluctuations at equilibrium. When the motions at and away from equilibrium fall in the LR regime, the equilibrium and nonequilibrium response functions are identical. However, similarity of the equilibrium and nonequilibrium solvent response functions does not guarantee that LR holds and that the underlying molecular motions are the same. In this paper, we present computer simulation studies of the removal of charge from an atomic solute in liquid tetrahydrofuran, a system for which the equilibrium and nonequilibrium solvation responses appear quite similar. We then introduce a method for projecting nonequilibrium response functions onto specific molecular motions. We find that the equilibrium relaxation is dominated by solvent rotations, whereas the nonequilibrium relaxation is much more complex, having translations dominating at early times and a delayed onset of rotations. The results imply that LR may not hold as often as is widely believed and that care should be taken when using equilibrium response functions to understand nonequilibrium solvation dynamics.