A Status Report on "Gold Standard" Machine-Learned Potentials for Water

Abstract

Owing to the central importance of water to life as well as its unusual properties, potentials for water have been the subject of extensive research over the past 50 years. Recently, five potentials based on different machine learning approaches have been reported that are at or near the "gold standard" CCSD(T) level of theory. The development of such high-level potentials enables efficient and accurate simulations of water systems using classical and quantum dynamical approaches. This Perspective serves as a status report of these potentials, focusing on their methodology and applications to water systems across different phases. Their performances on the energies of gas phase water clusters, as well as condensed phase structural and dynamical properties, are discussed.

Figure 1

Comparison of the 2-body fit (black line) and direct CCSD(T) energies (red circles) for an attractive cut. The isolated monomer dipole–dipole interaction is also indicated (green diamonds).

Figure 2

Comparison of 3-b (top) and 4-b (bottom) q-AQUA potentials with direct CCSD(T) energies for an attractive cut.

Figure 3

OO radial distribution function from classical (blue) and path integral (red) molecular dynamics simulations at 298 K using q-AQUA (panel A) and q-AQUA-pol potentials (panel B). The experimental data are from refs ( and 46). Simulation data are from refs ( and 41).

Figure 4

Oxygen–oxygen–oxygen triplet angular distribution functions from classical and path integral molecular dynamics simulations at 298 K and 1 atm using the q-AQUA-pol potential. The experimental data are taken from ref (48). Reproduced from ref (41). Copyright 2023 American Chemical Society.

Figure 5

Temperature-dependence of the density of liquid water at 1 atm. The experimental data are taken from refs (50) and (51). Reproduced from ref (41). Copyright 2023 American Chemical Society.

Figure 6

Probability distribution of the tetrahedral order parameter q at different temperatures from classical MD simulations. Reproduced from ref (41). Copyright 2023 American Chemical Society.

Figure 7

Binding energies (A), 2-body energies (B), 3-body energies (C), and 4-body energies (D) for water hexamer isomers from TTM3-F, q-AQUA (panel A), q-AQUA-pol, and benchmark CCSD(T) calculations (data taken from ref (52)).

Figure 8

Effects of 2-b, 3-b, and 4-b corrections on the OO radial distribution function of liquid water at 298 K from classical MD simulations. The experimental data are taken from refs ( and 46).

Figure 9

Probability distribution of the tetrahedral order parameter q at room temperature from q-AQUA-pol, q-AQUA, and recent NN-transfer-learned potential with CCSD(T) accuracy. Reproduced from ref (41). Copyright 2023 American Chemical Society.

Figure 10

OO radial distribution function from classical MD simulations at 298 K using q-AQUA-pol potential for three range parameters indicated (Å) for the 3-b interaction.

Figure 11

Oxygen–oxygen–oxygen triplet angular distribution functions of liquid water at 298 K from classical MD simulations for three range parameters indicated (in Å) for the 3-b interaction.

Figure 12

Probability distribution of the tetrahedral order parameter q at 298 K from classical MD simulations for three range parameters indicated (in Å) for the 3-b interaction.