Vibrational Spectra of Materials and Molecules from Partially-Adiabatic Elevated-Temperature Centroid Molecular Dynamics

TL;DR

This work introduces PA-$T_e$-CMD, a partially-adiabatic, elevated-temperature centroid MD approach that computes the centroid PMF on the fly using a two-temperature Langevin thermostat to separate centroid and internal ring-polymer mode temperatures. By selecting an elevated temperature $T_e$ that minimizes curvature artifacts while preserving quantum statistics, PA-$T_e$-CMD produces vibrational spectra that closely match reference quantum results and $T_e$-PIGS benchmarks across molecular and condensed-phase systems, including water, CAF, and MAPI across multiple phases. Compared with $T_e$-PIGS, PA-$T_e$-CMD avoids the need for pre-trained PMFs, enabling a single-shot setup with modest computational cost and broad transferability, though it can suffer from energy leakage at very low temperatures. The method, implemented in i-PI, provides a flexible and user-friendly route to accurate vibrational spectra under nuclear quantum effects, particularly for systems where strong anharmonicity or phase transitions complicate PMF training.

Abstract

Centroid molecular dynamics (CMD) incorporates nuclear quantum statistics into the calculation of vibrational spectra. However, when performed in Cartesian coordinates, CMD shows unphysical artifacts in certain vibrational bands, known as the curvature problem. Recent work showed that CMD spectra can be freed from the curvature problem by evolving the ring-polymer centroid on a potential of mean force (PMF) calculated at an elevated temperature ($T_e$-CMD). Here we present a partially-adiabatic implementation of $T_e$-CMD (PA-$T_e$-CMD), which eliminates the need for precomputed PMFs and instead yields the centroid force 'on the fly'. We introduce a two-temperature path-integral Langevin thermostat to achieve a temperature separation between centroid and internal modes of the ring polymer. Because it is paramount that the elevated temperature be chosen as low as possible for a given physical temperature in this formulation, we present a general scheme for its determination. We benchmark PA-$T_e$-CMD against exact vibrational spectra for the isolated water monomer and discuss its performance for challenging anharmonic systems: the carbonic acid fluoride molecule (CAF) and the methylammonium lead iodide perovskite (MAPI). We conclude that PA-$T_e$-CMD mitigates the curvature problem and the steep increase in computational cost with decreasing temperature of conventional path-integral methods. We observe energy leakage from the hot internal modes to high-frequency centroid modes in some cases, which, nevertheless, only compromises the spectral lineshapes at lower temperatures. While an adiabatic setup based on a coarse-grained centroid PMF is still preferable when a good pre-trained PMF can be easily obtained, PA-$T_e$-CMD presents a low-barrier single-shot setup for any system.

Figures (6)

• Figure 1: Elevated temperature $T_e$ as a function of the physical temperature $T_{\mathrm{phys}}$ for the analytical radial OH Morse potential with the same parameters as in Ref. Trenins2019 (blue) and for a numerically evaluated O–H bond-stretching potential of the carbonic acid fluoride (CAF) molecule (green). The CAF potential was obtained by displacing the hydrogen atom along the O–H bond direction.
• Figure 2: Time evolution of the temperatures of the centroid mode (nm $=0$, blue line) and the second internal normal mode of the ring polymer (nm $=2$, green line) during a PA-$T_e$-CMD simulation of an isolated water monomer at $T_{\mathrm{phys}} = 300$ K and $T_e = 600$ K. Solid lines show centered moving averages, and shaded areas indicate the 95% confidence intervals computed from a moving window. Both modes exhibit stable and distinct temperatures throughout the simulation, as expected from the 2T-PILE thermostat.
• Figure 3: Bending (1100--2000 cm$^{-1}$) and O--H stretching (3500--4200 cm$^{-1}$) infra-red vibrational bands of a water monomer obtained via PA-T$_e$-CMD with five parameter sets compared to the DVR reference Tennyson2004 at (a) 600 K, (b) 300 K, and (c) 50 K.
• Figure 4: Comparison between PA-T$_e$-CMD (Set E), T$_e$-PIGS, standard CMD, TRPMD, and classical MD against the DVR reference Tennyson2004 for bending (1100--2000 cm$^{-1}$) and O--H stretching (3500--4200 cm$^{-1}$) IR vibrational bands of a water monomer at (a) 600 K, (b) 300 K, and (c) 50 K.
• Figure 5: Vibrational density of states (VDOS) of carbonic acid fluoride (CAF) at 100 K, computed using (from top to bottom) $T_e$-PIGS, PA-$T_e$-CMD, TRPMD-GLE, TRPMD, CMD, and classical MD. $T_e = 350~\text{K}$ for $T_e$-PIGS and PA-$T_e$-CMD. Experimental IR bands are shown as gray dashed lines. The molecular structure of CAF is shown on the right. Atom color code: oxygen (red), hydrogen (white), carbon (brown), and fluorine (light blue).