Three-dimensional free-energy landscape of hydrogen and oxygen molecules in polymer electrolyte membranes: Insight into diffusion paths

An exa-scale high-performance molecular dynamics simulation program: MODYLAS

A new version of the highly parallelized general-purpose molecular dynamics (MD) simulation program MODYLAS with high performance on the Fugaku computer was developed. A benchmark test using Fugaku indicated highly efficient communication, single instruction, multiple data (SIMD) processing, and on-cache arithmetic operations. The system's performance deteriorated only slightly, even under high parallelization. In particular, a newly developed minimum transferred data method, requiring a significantly lower amount of data transfer compared to conventional communications, showed significantly high performance. The coordinates and forces of 101 810 176 atoms and the multipole coefficients of the subcells could be distributed to the 32 768 nodes (1 572 864 cores) in 2.3 ms during one MD step calculation. The SIMD effective instruction rates for floating-point arithmetic operations in direct force and fast multipole method (FMM) calculations measured on Fugaku were 78.7% and 31.5%, respectively. The development of a data reuse algorithm enhanced the on-cache processing; the cache miss rate for direct force and FMM calculations was only 2.74% and 1.43%, respectively, on the L1 cache and 0.08% and 0.60%, respectively, on the L2 cache. The modified MODYLAS could complete one MD single time-step calculation within 8.5 ms for the aforementioned large system. Additionally, the program contains numerous functions for material research that enable free energy calculations, along with the generation of various ensembles and molecular constraints.

Global diffusion of hydrogen molecules in the heterogeneous structure of polymer electrolytes for fuel cells: Dynamic Monte Carlo combined with molecular dynamics calculations

Using our recently developed dynamic Monte Carlo (MC) method [Nagai et al., J. Chem Phys. 156, 154506 (2022)], we investigated global diffusion of hydrogen molecules over structural heterogeneities of polymer electrolyte membranes in fuel cells. The three-dimensional position-dependent free energies and the diffusion constants of the hydrogen molecules, required by the present dynamic MC calculations, were taken from our previous study [Nagai et al., J. Chem. Phys. 156, 044507 (2022)] and newly evaluated in this work, respectively. The calculations enabled evaluating the hydrogen dynamics over long-time scales, including global diffusion constants. Based on the calculated global diffusion constants and free energies, the permeability of hydrogen molecules was estimated via the solubility-diffusion model. The estimated values were in good agreement with reported experimental data, thus validating the present methodology. The analysis of the Monte Carlo trajectories indicated that the main permeation paths are located in the polymer and interfacial phases, although the water phase may make a non-negligible contribution to mass transport.

Dynamic Monte Carlo calculation generating particle trajectories that satisfy the diffusion equation for heterogeneous systems with a position-dependent diffusion coefficient and free energy

A series of new Monte Carlo (MC) transition probabilities was investigated that could produce molecular trajectories statistically satisfying the diffusion equation with a position-dependent diffusion coefficient and potential energy. The MC trajectories were compared with the numerical solution of the diffusion equation by calculating the time evolution of the probability distribution and the mean first passage time, which exhibited excellent agreement. The method is powerful when investigating, for example, the long-distance and long-time global transportation of a molecule in heterogeneous systems by coarse-graining them into one-particle diffusive molecular motion with a position-dependent diffusion coefficient and free energy. The method can also be applied to many-particle dynamics.