Hydrogen Transport Between Layers of Transition Metal-Dichalcogenides

Abstract
Hydrogen is a crucial source of green energy and has been extensively studied for its potential usage in fuel cells. The advent of two-dimensional crystals (2DCs) has taken hydrogen research to new heights, enabling it to tunnel through layers of 2DCs or be transported within voids between the layers, as demonstrated in recent experiments by Geim's group. In this study, we investigate how the composition and stacking of transition-metal dichalcogenide (TMDC) layers influence the transport and self-diffusion coefficients (D) of hydrogen atoms using well-tempered metadynamics simulations. Our findings show that modifying either the transition metal or the chalcogen atoms significantly affects the free energy barriers (∆F) and, consequently, the self-diffusion of hydrogen atoms between the 2DC layers. In the H^h_h polytype (2H stacking), MoSe2 exhibits the lowest ∆F, while WS2 has the highest, resulting in the largest D for the former system. Additionally, hydrogen atoms inside the R^M_h (or 3R) polytype encounter more than twice lower energy barriers and, thus, much higher diffusivity compared to those within the most stable H^h_h stacking. These findings are particularly significant when investigating twisted layers or homo- or heterostructures, as different stacking areas may dominate over others, potentially leading to directional transport and interesting materials for ion or atom sieving.
https://doi.org/10.48550/arXiv.2308.03418

Overview
This repository contains calculation files, optimized structures, plots, and Excel files for studies of H diffusion within vdW crystals. A general guide is written here and also in the README.txt file. The repository classifies based on material type and each material has a specific README.txt file that contains more detailed information. Calculation towards self-diffusion coefficients for each step of each material follows: 

Cell optimization of the pristine material: To optimize lattice constants and structural parameters.
Single H atom site tests. To find a favorable H location within vdW crystals to initialize dynamic calculations.
Molecular dynamics. Pre-optimization of thermal equilibrium before performing metadynamics calculations.
Well-tempered Metadynamics simulations: to get a free-energy surface and ultimately; to get a ∆F to calculate D.
The final FES is plotted, and the calculation of the self-diffusion coefficients is noted down in the Excel file.

Acknowledgment
This research was supported by the Deutsche Forschungsgemeinschaft (projects GRK 2721/1 and SFB 1415). The authors acknowledge the high-performance computing center of ZIH Dresden, the Leipzig University Computing Centre, and the Paderborn Center for Parallel Computing (PC2 ) for computational resources. The authors thank  Prof. Thomas Heine for fruitful discussions.