Modelling complex proton transport phenomena -- Exploring the limits of fine-tuning and transferability of foundational machine-learned force fields

The solid acids CsH$_2$PO$_4$ and Cs$_7$(H$_4$PO$_4$)(H$_2$PO$_4$)$_8$ pose significant challenges for the simulation of proton transport phenomena. In this work, we use the recently developed machine-learned force field (MLFF) MACE to model the proton dynamics on nanosecond time scales for these systems and compare its performance with long-term ab initio molecular dynamics (AIMD) simulations. The MACE-MP-0 foundation model shows remarkable performance for all observables derived from molecular dynamics (MD) simulations, but minor quantitative discrepancies remain compared to the AIMD reference data. However, we show that minimal fine-tuning -- fitting to as little as 1 ps of AIMD data -- leads to full quantitative agreement between the radial distribution functions of MACE force field and AIMD simulations. In addition, we show that traditional long-term AIMD simulations fail to capture the correct qualitative trends in diffusion coefficients and activation energies for these solid acids due to the limited accessible time scale. In contrast, accurate and convergent diffusion coefficients can be reliably obtained through multi-nanosecond long MD simulations using machine-learned force fields. The obtained qualitative and quantitative behavior of the converged diffusion coefficients and activation energies now matches the experimental trends for both solid acids, in contrast to previous AIMD simulations that yielded a qualitatively wrong picture.