Highly efficient path-integral molecular dynamics simulations with GPUMD using neuroevolution potentials: Case studies on thermal properties of materials.

Path-integral molecular dynamics (PIMD) simulations are crucial for accurately capturing nuclear quantum effects in materials. However, their computational intensity often makes it challenging to address potential finite-size effects. Here, we present a specialized graphics processing units (GPUs) implementation of PIMD methods, including ring-polymer molecular dynamics (RPMD) and thermostatted ring-polymer molecular dynamics (TRPMD), into the open-source Graphics Processing Units Molecular Dynamics (GPUMD) package, combined with highly accurate and efficient machine-learned neuroevolution potential (NEP) models. This approach achieves almost the accuracy of first-principles calculations with the computational efficiency of empirical potentials, enabling large-scale atomistic simulations that incorporate nuclear quantum effects, effectively overcoming finite-size limitations at a relatively affordable computational cost. We validate and demonstrate the efficacy of the combined NEP-PIMD approach by examining various thermal properties of diverse materials, including lithium hydride (LiH), three porous metal-organic frameworks (MOFs), liquid water, and elemental aluminum. For LiH, our NEP-PIMD simulations successfully capture the isotope effect, reproducing the experimentally observed dependence of the lattice parameter on the reduced mass. For MOFs, our results reveal that achieving good agreement with experimental data requires consideration of both nuclear quantum effects and dispersive interactions. For water, our PIMD simulations capture the significant impact of nuclear quantum effects on its microscopic structure. For aluminum, the TRPMD method effectively captures thermal expansion and phonon properties, aligning well with quantum mechanical predictions. This efficient GPU-accelerated NEP-PIMD implementation in the GPUMD package provides an alternative, accessible, accurate, and scalable tool for exploring complex material properties influenced by nuclear quantum effects, with potential applications across a broad range of materials.