Nuclear Quantum Effects in Liquid Water at Near Classical Computational Cost Using the Adaptive Quantum Thermal Bath

Abstract

We demonstrate the accuracy and efficiency of a recently introduced approach to account for nuclear quantum effects (NQEs) in molecular simulations: the adaptive quantum thermal bath (adQTB). In this method, zero-point energy is introduced through a generalized Langevin thermostat designed to precisely enforce the quantum fluctuation−dissipation theorem. We propose a refined adQTB algorithm with improved accuracy and report adQTB simulations of liquid water. Through extensive comparison with reference path integral calculations, we demonstrate that it provides excellent accuracy for a broad range of structural and thermodynamic observables as well as infrared vibrational spectra. The adQTB has a computational cost comparable to that of classical molecular dynamics, enabling simulations of up to millions of degrees of freedom.

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

“…In Appendix A, the practical noise generation as well as the choice of the algorithms to integrate the Langevin equation is briefly discussed. With this precaution, in the limit of small values of γ, the Lorentzian factors in Equations ( 20) and ( 21) tend to Dirac δ-functions and both the kinetic and the potential energy equal θ(ω 0 , T)/2 as expected for the quantum harmonic oscillator (for nonzero γ, the average energies are slightly different from θ(ω 0 , T)/2, although this difference can be corrected using spectral deconvolution techniques [18,40]). The position and the momentum probability distributions obtained in QTB simulations of the harmonic oscillator are Gaussian, with widths fixed by Equations ( 20) and ( 21), therefore the method provides exact estimates (at least in the γ → 0 limit) for the quantum average of any static observable depending only on position or momentum, including zero-point energy effects.…”

“…The following results show that the performances of quantum baths are rather system-and property-dependent, although in most cases the introduction of NQEs via the quantum baths improves the description of vibrational properties, even in very anharmonic systems. Although the coupling with the bath tends to distort vibrational spectra, particularly in the context of the QT method, this effects can be efficiently corrected a posteriori using spectral deconvolution techniques [18,40]. Moreover, quantum baths have been employed to study intrinsically nonequilibrium properties, such as thermal conductivity in crystals (see Section 5.3.3).…”

“…As observed in Section 4, QTB simulations provide direct access to vibrational spectra, accounting consistently (though approximately) for anharmonic and quantum effects. This property has been exploited in different studies to confront QTB results with other, more established simulation methods [15,18], or with experimental data. In particular, the phonon spectrum of ice was extracted from QTB simulations at various pressures, computed from the Fourier transform of the velocity-velocity autocorrelation function [1].…”

“…We then introduce in Section 7 a recent development that, by exploiting the quantum fluctuation-dissipation theorem, enables to monitor and efficiently compensate ZPE leakage. This approach, known as the adaptive quantum thermal bath [17] (adQTB) extends considerably the domain of application of the QTB, leading, for example, to the successful simulation of liquid water [18]. The review ends with a discussion of remaining limitations, open questions and possible future developments of quantum baths as effective and accurate tools for the simulation of condensed phase systems.…”

A Hessian free method to prevent zero-point energy leakage in classical trajectory simulation

“…Recently, an adaptive QTB model (adQTB) has been proposed 16,17 to suppress the ZPE leakage phenomenon, where quantum fluctuation-dissipation criterion is actively enforced by adjusting the system-bath coupling parameter all along the simulation. In other words, instead of a constant coupling, an "on-the-fly" tuned frequency-dependent coupling parameter is used to construct the Langevin equation of motion.…”