Nuclear quantum effects, such as zero-point motion and tunneling, play an important role in hydrogen dynamics in bulk and surface metals. We have studied hydrogen-isotope diffusion using path-integral-based methods, including quantum transition-state theory (QTST), ring-polymer molecular dynamics (RPMD), and centroid molecular dynamics (CMD) [1-3]. Combined with first-principles calculations and machine-learning potentials, these approaches have enabled the quantitative evaluation of isotope effects and have shown good agreement with experiments.
While RPMD and CMD are useful for describing diffusion dynamics, they have intrinsic difficulties in vibrational dynamics. To overcome this limitation, Brownian chain molecular dynamics (BCMD) was proposed as an approximate quantum dynamics method, in which Newtonian dynamics of the centroid mode is combined with overdamped Brownian dynamics of the non-centroid modes [4]. BCMD has been shown to reproduce hydrogen inelastic neutron scattering (INS) spectra, which are difficult to describe by classical dynamics because they reflect local anharmonic hydrogen vibrations and coupling with metal phonons [5].
Recently, path-integral simulations with machine-learning potentials have been accelerated to the nanosecond time scale [6], opening the way to longer-time simulations of quantum molecular systems. We are also developing a theoretical foundation and an improved numerical algorithm for BCMD, particularly through a quasi-density-operator (QDO) formulation and a multiple-time-step scheme designed to enhance numerical stability.

References
[1] Kwon, H., Shiga, M., Kimizuka, H., Oda, T., Acta Mater., 2023, 247, 118739.
[2] Kataoka, Y. Haruyama, J., Sugino, O., Shiga, M., Phys. Rev. Res, 2024, 6, 043224.
[3] Kimizuka, H., Ogata, S., Thomsen, B., Shiga. M., J. Phys. Condens. Matter, 2025, 37, 193001.
[4] Shiga, M., J. Comput. Chem., 2022, 43, 1864.
[5] Shiga, M., Thomsen, B., Kimizuka, H., Phys. Rev. B, 2024, 109, 054303.
[6] Shiga. M., Elsner, J., Behler, J., Thomsen, B., J. Chem. Phys., 2025, 163, 134119.