Modelling phosphate hydration with a polarizable bond-dipole framework: parameter optimization and benchmark testing

Abstract

A polarizable interaction model based on bond-centered dipoles (PBFF) has previously been applied to model a range of molecular systems. In this study, the model is extended to hydrated phosphate species, where accurate representation of polarization and many-body effects remains a significant challenge. Parameters were determined by fitting to high-level quantum mechanical reference data, including conformational energies and dipole moments of six representative phosphate monomers, as well as interaction energies of phosphate–water dimers and trimers. The resulting model was evaluated against DLPNO-CCSD(T)/CBS benchmarks, with root-mean-square errors below 0.81 kcal mol⁻¹ for conformational energies, 0.40 Debye for dipole moments, and 2.06 kcal mol⁻¹ for many-body interaction energies. These results indicate that key interaction patterns in small hydrated clusters can be reasonably captured. Compared to established polarizable models, a similar level of accuracy was achieved with a reduced number of electrostatic parameters. It should be noted that validation was carried out exclusively against quantum chemical data, and no comparison with experimental observables has yet been performed. This work represents a step toward adapting the bond-dipole-based framework to phosphate-containing systems, and provides a foundation for further development aimed at improving transferability and performance in condensed-phase environments.