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.
Quantum thermal bath (QTB) simulations reproduce statistical nuclear quantum effects via a Langevin equation with a colored random force. Although this approach has proven efficient for a variety of chemical and condensed-matter problems, the QTB, as many other semiclassical methods, suffers from zero-point energy leakage (ZPEL). The absence of a reliable criterion to quantify the ZPEL without resorting to demanding comparisons with path integral based calculations has so far hindered the use of the QTB for the simulation of real systems. In this work, we establish a quantitative connection between ZPEL in the QTB framework and deviations from the quantum fluctuation-dissipation theorem (FDT) that can be monitored along the simulation. This provides a rigorous general criterion to detect and quantify the ZPEL without any a priori knowledge of the system under study. We then use this criterion to build an adaptive QTB method that strictly enforces the quantum FDT at all frequencies via an on-the-fly, spectrally resolved fine tuning of the system-bath coupling coefficients. The validity of the adaptive approach is first demonstrated on a simple two-oscillator model. It is then applied to two more realistic problems: the description of the vibrational properties of a model aluminium crystal at low temperature and the simulation of the liquid-solid phase transition in a 13-atom neon cluster. In both systems, the standard QTB results are strongly altered by the ZPEL, which can be essentially eliminated using the adaptive approach.
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