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Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium–nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium–nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

Fluoride ion batteries are potential “next-generation” electrochemical storage devices that offer high energy density. At present, such batteries are limited to operation at high temperatures because suitable fluoride ion–conducting electrolytes are known only in the solid state. We report a liquid fluoride ion–conducting electrolyte with high ionic conductivity, wide operating voltage, and robust chemical stability based on dry tetraalkylammonium fluoride salts in ether solvents. Pairing this liquid electrolyte with a copper–lanthanum trifluoride (Cu@LaF₃) core-shell cathode, we demonstrate reversible fluorination and defluorination reactions in a fluoride ion electrochemical cell cycled at room temperature. Fluoride ion–mediated electrochemistry offers a pathway toward developing capacities beyond that of lithium ion technology.