Fermi resonance in CO2: Mode assignment and quantum nuclear effects from first principles molecular dynamics

Abstract

Vibrational spectroscopy is a fundamental tool to investigate local atomic arrangements and the effect of the environment, provided that the spectral features can be correctly assigned. This can be challenging in experiments and simulations when double peaks are present because they can have different origins. Fermi dyads are a common class of such doublets, stemming from the resonance of the fundamental excitation of a mode with the overtone of another. We present a new, efficient approach to unambiguously characterize Fermi resonances in density functional theory (DFT) based simulations of condensed phase systems. With it, the spectral features can be assigned and the two resonating modes identified. We also show how data from DFT simulations employing classical nuclear dynamics can be post-processed and combined with a perturbative quantum treatment at a finite temperature to include analytically thermal quantum nuclear effects. The inclusion of these effects is crucial to correct some of the qualitative failures of the Newtonian dynamics simulations at a low temperature such as, in particular, the behavior of the frequency splitting of the Fermi dyad. We show, by comparing with experimental data for the paradigmatic case of supercritical CO, that these thermal quantum effects can be substantial even at ambient conditions and that our scheme provides an accurate and computationally convenient approach to account for them.

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

“…Our simulations are compared to the perturbative expressions derived by Basire et al in Ref. 52 for the amplitude of the Fermi splitting in the classical (dashed line) and in the quantum (continuous line) frameworks. As in ref.…”

“…In ref. 52, Basire et al developed a different perturbative approach and showed that the temperature-dependence of this splitting is qualitatively different if the system is treated classically or quantummechanically, accounting for zero-point motion. Indeed, the classical Fermi splitting goes to zero as T 1/2 at low temperature while the quantum one saturates at a non-zero value.…”

“…As in ref. 52, to compare the analytical trends and the simulations, in the latter, the splitting is measured as the distance between the center of mass of each of the two peaks that constitute the Fermi dyad. The perturbative result is in close agreement with the splitting obtained from the numerical solution of Schrödinger equation (black diamond shapes in Figure 3).…”

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

“…Fermi resonances occur when a stretch mode of frequency Ω 1 splits by coming into resonance with a bend overtone of frequency 2Ω 2 ≃ Ω 1 . A simple model of a Fermi resonance, which is sufficient to demonstrate the failure of classical and path-integral methods to predict the splitting, is 32,54 H =Ĥ (0) +V (1) ,…”

“…Tests on simple models have shown that path-integral methods essentially reproduce the classical splittings, 6,32 which agree with the quantum splittings at high temperatures, but underestimate them at low temperatures, predicting an erroneous T 1/2 dependence. 54 In Section IV, we show numerically that this failing is also caused by the neglect of 'Matsubara heating', whereby the coupling of the fluctuation modes increases the amplitudes of the perturbed centroid vibrations. Further possible examples of dynamics which could be affected by coupling between the centroid and fluctuation modes are discussed briefly in Section V, which concludes the article.…”