On the “Matsubara heating” of overtone intensities and Fermi splittings

Abstract

Classical molecular dynamics (MD) and imaginary-time path-integral dynamics methods underestimate the infrared absorption intensities of overtone and combination bands by typically an order of magnitude. Plé et al. [J. Chem. Phys. xx, xxx (2021)] have shown that this is because such methods fail to describe the coupling of the centroid to the Matsubara dynamics of the fluctuation modes; classical first-order perturbation theory (PT) applied to the Matsubara dynamics is sufficient to recover most of the lost intensity in simple models, and gives identical results to quantum (Rayleigh-Schrödinger) PT. Here, we show numerically that the results of this analysis can be used as post-processing correction factors, which can be applied to realistic (classical MD or path-integral dynamics) simulations of infared spectra. We find that the correction factors recover most of the lost intensity in the overtone and combination bands of gas-phase water and ammonia, and much of it for liquid water. We then re-derive and confirm the earlier PT analysis by applying canonical PT to Matsubara dynamics, which has the advantage of avoiding secular terms, and gives a simple picture of the perturbed Matsubara dynamics in terms of action-angle variables. Collectively, these variables 'Matsubara heat' the amplitudes of the overtone and combination vibrations of the centroid to what they would be in a classical system with the oscillators (of frequency Ω i ) held at their quantum effective temperatures (of Ω i coth(β Ω i /2)/2k B ). Numerical calculations show that a similar neglect of 'Matsubara heating' causes path-integral methods to underestimate Fermi resonance splittings.

Equilibrium–nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

“…50 Because two-dimensional Raman and hybrid THz-Raman spectra vanish for harmonic potentials with linear dipole moment or polarizability operators, 74 adequate computational approaches must capture the effect of electrical and mechanical anharmonicities, which poses a challenge for RPMD and the above-mentioned methods. 77,85 To derive the equilibrium-nonequilibrium RPMD, we did not invoke the concept of the Kubo transformation, which is traditionally done for one-time correlation functions, 40 but instead combined nonequilibrium RPMD with classical response theory. This new way of deriving real-time path-integral methods will be of special interest for simulating timeresolved spectroscopic experiments, but also in other contexts where multi-time correlation or response functions appear, or if a derivation of the appropriate Kubo transformed correlation function is not obvious.…”

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

“…45 Because two-dimensional Raman and hybrid THz-Raman spectra vanish for harmonic potentials with linear dipole moment or polarizability operators, 56 adequate computational approaches must capture the effect of electrical and mechanical anharmonicities, which poses a challenge for RPMD and the above-mentioned methods. 59,64 To derive the equilibrium-nonequilibrium RPMD, we did not invoke the concept of the Kubo transformation, which is done traditionally for one-time correlation functions, 35…”

Improved torque estimator for condensed-phase quasicentroid molecular dynamics

“…[1][2][3][4] The positions and intensities of the fundamental bands are in excellent agreement with the exact quantum results, and the positions of the overtone and combination bands are in reasonable agreement. However, the intensities of the latter are an order of magnitude too small, which was shown recently 19,20 to be because QCMD neglects coupling between the Matsubara dynamics 9,[21][22][23][24] of the centroid and the fluctuation modes [as also do CMD, RPMD and classical molecular dynamics (MD)]. 25 In the condensed phase, QCMD has been tested on the qTIP4P/F water model, for the liquid at 300 K and for ice I h at 150 K. 1,2 Detailed comparisons with experiment are not possible for such a simple potential, 26 but the QCMD results are promising: the spectra appear to inherit the advantages of the gas-phase QCMD calculations, with the stretch bands showing none of the artefacts that appear in the corresponding CMD and (T)RPMD spectra at low temperatures 27 and lining up well with the results of other simulation methods.…”