Artificial neural network-based path integral simulations of hydrogen isotope diffusion in palladium

Abstract

The contribution of nuclear quantum effects (NQEs) to the kinetics and dynamics of interstitial H isotopes in face-centered cubic Pd was intensively investigated using several path-integral techniques, along with a newly developed machine-learning interatomic potential based on artificial neural networks for Pd–H alloys. The diffusion coefficients (D) of protium, deuterium, and tritium in Pd were predicted over a wide temperature range (50–1500 K) based on quantum transition-state theory (QTST) combined with path-integral molecular-dynamics simulations. The importance of NQEs even at high temperatures was illustrated in terms of the characteristic temperature dependence of the activation free energies for H-isotope migration in Pd. This illuminates the overall picture of anomalous D crossovers among the three H isotopes in Pd. In addition, the D of protium in Pd was directly computed using two approximate quantum-dynamics methods based on Feynman’s path-integral theory, i.e. centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), in the temperature range 370–1500 K. The D values obtained from the CMD and RPMD simulations were very similar and agreed better with the reported experimental values than the QTST results in this temperature range. Our machine learning-based path-integral calculations elucidate the underlying quantum nature of the ‘reversed S’-type nonlinear behavior of D for the three H isotopes in Pd on the Arrhenius plots.

Theoretical Study of the Thermal Rate Coefficients of the H3+ + C2H4 Reaction: Dynamics Study on a Full-Dimensional Potential Energy Surface

“…The integration of the equations of the motion of the ring polymer Hamiltonian was carried out using the velocity–Verlet method with a time step of Δ t = 0.10 fs, totaling 10 4 –10 6 simulation steps. Subsequently, RPMD simulations were performed, extending the PIMD method to enable real-time dynamics simulations, which are particularly adept at capturing nuclear quantum effects, such as zero-point energy and tunneling [ 30 , 36 , 44 , 45 , 46 , 47 , 48 , 49 ]. The impact parameter ( b ) for collisional simulations was set below b = b max ζ 1/2 , where b max represents the maximum impact parameter, and ζ is a random number within the range of [0, 1].…”

Hydrogen Embrittlement as a Conspicuous Material Challenge─Comprehensive Review and Future Directions

“…Except for Fe−H binary system, there exist ML potentials for other metallic materials in the presence of H. For instance, Kimizuka et al 935 developed an ML potential for Pd-H system within the framework of Neural Network. Based on this ML potential, they delved into the pivotal role of nuclear quantum effects (NQEs) on the diffusion of H isotopes within palladium.…”

“…Based on this ML potential, they delved into the pivotal role of nuclear quantum effects (NQEs) on the diffusion of H isotopes within palladium. With the help of path integral techniques, Kimizuka et al 935 accurately forecast H diffusivity in protium, deuterium, and tritium in palladium across a broad temperature range, which shed light on the significance of NQEs in governing the diffusion of H isotopes and provided valuable insights into the temperature-dependent activation free energies associated with H-isotope migration.…”

ænet-PyTorch: a GPU-supported implementation for machine learning atomic potentials training

“…aenet also includes the utilities to employ the MLPs in real applications, for example, in molecular dynamics simulations 6 (using the interface with LAMMPS 54 or TINKER 55 ), in path integral molecular dynamics 56 , or in any of the capabilities provided in the Atomic Simulation Environment 57 Python package. Our new program has been designed as an extension to the original aenet code, and all of these utilities that aenet provides can be readily used with the potentials generated by aenet-PyTorch.…”