Quantum dynamics using path integral coarse-graining

Abstract

Vibrational spectra of condensed and gas-phase systems containing light nuclei are influenced by their quantum-mechanical behaviour. The quantum dynamics of light nuclei can be approximated by the imaginary time path integral (PI) formulation, but still at a large computational cost that increases sharply with decreasing temperature. By leveraging advances in machine-learned coarse-graining, we develop a PI method with the reduced computational cost of a classical simulation. We also propose a simple temperature elevation scheme to significantly attenuate the artefacts of standard PI approaches and also eliminate the unfavourable temperature scaling of the computational cost. We illustrate the approach, by calculating vibrational spectra using standard models of water molecules and bulk water, demonstrating significant computational savings and dramatically improved accuracy compared to more expensive reference approaches. We believe that our simple, efficient and accurate method could enable routine calculations of vibrational spectra including nuclear quantum effects for a wide range of molecular systems.

Fast Quasi-Centroid Molecular Dynamics for Water and Ice

“…The final panel of Figure compares the f-QCMD spectrum with the Te PIGS spectrum obtained using a centroid potential of mean force calculated at 600 K . The bending bands of the two spectra are the same, but the Te PIGS librational band is slightly blue-shifted, and the Te PIGS O–H stretching band is slightly red-shifted relative to the f-QCMD spectrum.…”

“…Figure compares the resulting f-QCMD spectrum for liquid water at 300 K with the spectra obtained from classical molecular dynamics, the adiabatic QCMD method, and the Te PIGS method . (The adiabatic QCMD results were obtained using the new torque estimator described in ref , and were provided to us by George Trenins).…”

“…Since this stops changing at around 600 K, where the curvature problem is not yet an issue, a centroid potential of mean force constructed at this temperature can be used in simulations of the vibrational spectrum at lower temperatures. Kapil and coworkers employed machine learning techniques to construct the 600 K centroid potential of mean force and demonstrated that the resulting ‘elevated temperature path integral ground state’ (Te PIGS) method avoids the curvature problem in liquid water at 300 K and in ice at lower temperatures . We shall compare our f-QCMD results with theirs for both of these systems in Section 3.…”

Fully First-Principles Surface Spectroscopy with Machine Learning

“…However, the curvilinear motion of dangling O–D in D 2 O shows an extremely broad feature, , which calls for the use of other approaches which do not suffer from the curvature problem of CMD nor the broadening problem of TRPMD. The recent method proposed by Musil et al seems a promising approach to tackle this issue . We note, however, that none of these can describe accurately the Fermi resonance contributions. ,,, …”

“…The recent method proposed by Musil et al seems a promising approach to tackle this issue. 70 We note, however, that none of these can describe accurately the Fermi resonance contributions. 44,53,71,72 In summary, the work presented here sets a new standard for atomistic simulation of nonlinear spectroscopies of condensed phases.…”