Proton transport in liquid phosphoric acid: the role of nuclear quantum effects revealed by neural network potential†

Pure phosphoric acid exhibits high proton conductivity and is widely used in modern industry. However, its proton transport mechanism remains less understood compared to that of water, which presents a significant challenge for advancing technologies like phosphoric acid fuel cells. In this study, we utilize machine learning potentials and molecular dynamics (MD) simulations to investigate the proton diffusion mechanisms in liquid phosphoric acid systems. The neural network potentials we developed demonstrate quantum chemical accuracy and stability across a range of temperatures. Our simulations reveal continuous proton hopping between phosphoric acid anions. Moreover, the radial distribution functions and diffusion coefficients obtained from ring polymer MD—a variant of path-integral MD—exhibit improved alignment with experimental values compared to classical MD results, as ring polymer MD inherently accounts for nuclear quantum effects on proton behavior. Additionally, we employed neural networks combined with the charge equilibration method to predict the charge distribution in liquid phosphoric acid, examining the proton transport mechanism through vibrational spectra analysis.