Quantum Effects in Electric-Field–Driven Dissociation of Liquid Hydrogen Fluoride

The inclusion of Nuclear Quantum Effects (NQEs) in molecular dynamics simulations is increasingly recognized as essential for accurately modeling systems involving light nuclei, particularly hydrogen. Classical approaches, such as standard \emph{ab initio} molecular dynamics (AIMD), is not suited to predict key quantum-mechanical phenomena such as zero-point motion and proton tunneling, which can critically influence both structural and dynamical behavior. This is especially true in H-bonded systems, where the strength and directionality of interactions are highly sensitive to quantum delocalization. In this work, we investigate the impact of NQEs on liquid hydrogen fluoride (HF) at standard conditions and subjected to strong external electric fields by comparing classical nuclei AIMD and path-integral AIMD (PI-AIMD) simulations. Hydrogen fluoride presents a rich H-bonding network and strong molecular dipole moments leading to the manifestation of important NQEs even in the absence of the field. Furthermore, our results demonstrate that quantum effects significantly alter the response of bulk liquid HF to applied electric fields, leading to enhanced proton delocalizations favoring the protolysis reaction \(2\,\mathrm{HF} \rightleftharpoons \mathrm{H_{2}F^+} + \mathrm{F^-}\). Similarly to water, indeed, inclusion of NQEs lowers by one-third the field threshold necessary for dissociating HF molecules [\emph{i.e.}, $0.15$~V/{\AA} (classical) vs. $0.05$~V/{\AA} (quantum)] and increased proton mobility. These differences become particularly evident under moderate-to-strong field strengths, where quantum simulations predict molecular dissociation and Grotthuss diffusion processes that are either absent or underestimated in classical AIMD simulations, though the general mechanism for proton migration is unaltered by the inclusion of quantum effects.