Equilibrium–nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

Abstract

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.

Two-dimensional infrared-Raman spectroscopy as a probe of water’s tetrahedrality

“…For sufficiently small ε , the thermal average of Eq. ( 2 ) is linear in ε , meaning that the time-dependent response function R MD ( t 1 , t 2 ) is, as expected, independent of its exact value 63 , 65 . The two-dimensional spectra are computed through a double sine transform 42 , 55 …”

Quantitative molecular simulations

“…166 Also, non-equilibrium RPMD and CMD simulations may provide effective routes to improved spectroscopic characterizations of systems in the condensed phase. 167,168…”

Two-dimensional infrared-Raman spectroscopy as a probe of water's tetrahedrality

“…55 Although such nuclear quantum effects on one-dimensional IR and Raman spectra have been well studied using approximate but reliable classical-like methods, no tools similar to the equilibriumnonequilibrium MD have been available to study nuclear quantum effects on the twodimensional IR-Raman spectra. [58][59][60] Recently, we have developed a new RPMD approach, 61 which reproduces correctly the quantum-mechanical thermal distribution and preserves it during approximate classical dynamics. In this way, the equilibrium-nonequilibrium RPMD method can simulate, at least approximately, the nuclear quantum effects on the twodimensional IIR spectra.…”