Anharmonic spectral features via trajectory-based quantum dynamics: A perturbative analysis of the interplay between dynamics and sampling

Abstract

The performance of different approximate algorithms for computing anharmonic features in vibrational spectra is analysed and compared on model and more realistic systems that present relevant nuclear quantum effects. The methods considered combine approximate sampling of the quantum thermal distribution with classical time propagation and include Matsubara dynamics, path integral dynamics approaches, linearized initial value representation and the recently introduced adaptive quantum thermal bath. A perturbative analysis of these different methods enables to account for the observed numerical performance on prototypes for overtones and combination bands and to draw qualitatively correct trends for the numerical results obtained for Fermi resonances. Our results prove that the unequal performances of these approaches often derive from the method employed to sample initial conditions and not, as usually assumed, from the lack of coherence in the time propagation. Furthermore, as confirmed by the analysis reported in J. Chem. Phys. 130, 194510 (2021), we demonstrate, both via the perturbative approach and numerically, that path integral dynamics methods fail to reproduce the intensities of these anharmonic features and follow purely classical trends with respect to their temperature behaviour. Finally, the remarkably accurate performance of the adaptive quantum thermal bath approach is documented and motivated.

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…”

Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths

“…It can be shown that the overtone intensity is underestimated by approximately a factor of two due to the absence of position-momentum correlation in the QTB phase space sampling [43,44]. This error on the overtone intensity can be detected (and potentially corrected) using the first-kind fluctuation-dissipation theorem criterion defined in Section 7, and it remains limited compared to that of path integral methods (see Section 6), which yield a much lower overtone intensity, similar to that of classical simulations [16].…”

“…Similar shifts are observed between the classical, QTB and exact quantum results as for the main resonance. The detailed perturbation analysis performed in [16] shows that an analogy can be drawn between the QTB and linearized semiclassical initial value representation (LSC-IVR) methods, that combine quantum phase space sampling with classical molecular dynamics for the evaluation of time correlation functions [41,42]. Indeed, in QTB simulations, the short-term dynamics is essentially classical, whereas the coupling with the bath introduces quantum statistics in the phase space sampling.…”

“…Another more fundamental limitation concerns dynamical observables such as vibrational spectra: PIMD is based on an imaginary-time path integral mapping of the quantum equilibrium density to that of the classical equivalent system described by Equation ( 29), but this mapping does not capture the quantum dynamics (even in the large P limit). PIMD is nontheless at the basis of different approximations to the quantum dynamics among which, in particular, centroid MD and ring-polymer MD as well as other more computationally demanding methods [10,16,30].…”

“…In Section 5, we review the capabilities of quantum bath methods by summarizing some significant applications to realistic models of condensed matter systems. Remarkably, these techniques prove useful not only in the simulation of static equilibrium properties of quantum nuclei, but also in the calculation of vibrational spectra [15], including subtle anharmonic features that elude other trajectory-based approximations to quantum dynamics [16]. In Section 6, we complete the overview of important applications of thermal baths by showing how they can be used to improve the convergence of calculations based on the path integral formalism.…”