pGM5P-26: A Polarizable Gaussian Multipole Water Model with Transferable Temperature-Dependent Thermodynamics

Water belongs to a small family of liquids whose density maximum lies above the melting point, a signature of their preference for open, tetrahedral networks. Reproducing this anomalous density–temperature curve, together with ambient thermodynamics, remains a demanding test for water force fields: fixed-charge models trade 298 K accuracy for large errors in ρ(T), while point-multipole polarizable models must exclude the 1–2 and 1–3 intramolecular contributions that govern molecular anisotropy and, through nonadditive coupling, shape the long-range field. We present pGM5P-26, a five-point polarizable Gaussian Multipole (pGM) water model whose Gaussian-distributed charges and dipoles remain finite at all distances, giving a unified treatment of short- and long-range electrostatics that retains these intramolecular contributions in a fully self-consistent induction. Its 14 independent parameters were optimized exclusively at 298 K against the liquid density, oxygen–oxygen radial distribution function, and uncorrected finite-box self-diffusion coefficient using SMAC Bayesian optimization with Hyperband scheduling. Despite this single-temperature training, pGM5P-26 gives the lowest absolute density RMSE and the second-lowest 298 K-anchored density-shape RMSE among the ten simulated models over the out-of-training temperatures from 245 to 380 K. Its thermal-expansion curve ranks second by both metrics, and its approximate finite-size-corrected self-diffusion curve ranks third, placing all three temperature dependences among the closest to experiment in the benchmark set. Its temperature of maximum density is 280.3 K (experiment: 277.1 K), the second closest after TIP4P/2005. The second virial coefficient reaches near-quantitative agreement with experiment above 773 K. These results show that Gaussian multipole polarization combined with automated optimization captures water’s density anomaly without explicit temperature-dependent training.