Nuclear Quantum Effects on Hydrogen Diffusion via Langevin-based Molecular Dynamics

In the contest of condensed-matter physics and chemistry, light nuclei, mainly hydrogen, exhibit the so called Nuclear Quantum Effects (NQEs), such as zero-point energy motion and tunneling, due to their intrinsic quantum delocalization. NQEs have a large impact on the structure and the dynamics of materials. Any approximated method that treats light nuclei as classical objects cannot reproduce correctly their physical properties. Real application of this problem are, for example, solid fuel cells, which are relevant for energy harvesting. The most used approach to study the NQEs is the Feynman’s Path Integral (PI) formalism, which conserves the concept of trajectories in the quantum picture, hence the use of Molecular Dynamics simulation techniques, such as Ring Polymer Molecular Dynamics. However, PI-based methods present high computational costs, urging the development of simpler alternative techniques. A promising method is the Quantum Thermal Bath (QTB). Its main idea is to maintain the classical equations of motion and trajectories, but to use a generalized Langevin equation with colored noise to mimic quantum delocalization of light nuclei. Although QTB has proven efficient for a variety of problems, it suffers from a major drawback, namely the Zero-Point Energy Leakage. There fore, the method is refined into the Adaptive Quantum Thermal Bath (adQTB), thanks to the Quantum Fluctuation-Dissipation theorem, which allows to recover the correct quantum energy distribution during the simulation. This work is a comparative study of these methods on a simple model of a 2D solid material, in which protons or hydrogen can diffuse. Both QTB and adQTB simulation methods are discussed, using classical results as a reference. The main result is that physical properties of diffusion emerge even at this level of simple model systems and it is possible to highlight how NQEs play a major role in the study of light nuclei.