Elevating density functional theory to chemical accuracy for water simulations through a density-corrected many-body formalism

Abstract

Density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of "gold standard" coupled-cluster theory. Building upon the accuracy of DC-SCAN within a many-body formalism, we introduce a data-driven many-body potential energy function, MB-SCAN(DC), that quantitatively reproduces coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, molecular dynamics simulations carried out with MB-SCAN(DC) also reproduce the properties of liquid water, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the liquid phase.

Fig. 1. 2B energies of the water hexamer isomers.

Two-body energies calculated for the first eight low-energy isomers of the water hexamer using SCAN, DC-SCAN, SCAN0 (with 25% exact exchange), and DC-SCAN0, along with the corresponding CCSD(T)/CBS reference values from ref. . The 2-body energy, on average, contributes ~80−85% to the total interaction energy in water. The errors associated with a given functional relative to the CCSD(T)/CBS values are roughly the same for each isomer.

Fig. 2. Comparison of dimer interaction energies.

a Errors in 2-body energies calculated with SCAN and DC-SCAN relative to CCSD(T)-F12b values for dimers with an oxygen−oxygen distance shorter than 5.5 Å which were extracted from an NPT simulation of liquid water carried out with MB-pol⁻ at ambient conditions. b CCSD(T)-F12b, SCAN and DC-SCAN interaction energies calculated for an unrelaxed scan of the water dimer along the O ⋯ H distance. The inset of panel (b) shows the errors associated with DC-SCAN and SCAN relative to the CCSD(T)-F12b reference values as a function of r(O ⋯ H).

Fig. 3. Errors in nB interaction energy of water octamers.

Errors relative to CCSD(T)-F12b reference values for each nB energy contribution to the interaction energies calculated for the two isoenergetic isomers, a D_2d and b S₄, of the water octamer using the SCAN and DC-SCAN functionals.

Fig. 4. Many-body and interaction energies for the isomers of the water hexamer.

a 2-body (2B), b 3-body (3B), c 4-body (4B) and d total interaction energies of the first eight isomers of the water hexamer calculated using SCAN, DC-SCAN, MB-SCAN, MB-SCAN(DC), along with the CCSD(T)/CBS reference values of ref. .

Fig. 5. Density of liquid water.

Temperature-dependence of the density of liquid water at 1 atm calculated from classical NPT simulations carried out with MB-SCAN(DC) along with the results from SCAN-AIMD, SCAN-NNP, and SCAN0-NNP (with 10% HF exchange) simulations. The MB-pol results are from ref. , while the experimental data are from the NIST Chemistry WebBook. Error bars for the MB-SCAN(DC) results represent 95% confidence intervals.

Fig. 6. Structure of liquid water.

Oxygen−oxygen (g_OO) radial distribution function (RDF) calculated from NPT simulations carried out with the MB-SCAN(DC) PEF at 298 K and 1 atm. The MB-pol RDF is from ref. , while the experimental RDF at 295 K is from ref. .

Fig. 7. Self-diffusion of liquid water.

Temperature-dependence of the self-diffusion coefficient of liquid water calculated from NVE simulations carried out with the MB-SCAN(DC) PEF. The SCAN-NNP data are from ref. , the MB-pol results are from ref. , while the experimental data are from refs. ^,,. Error bars for the MB-SCAN(DC) results represent 95% confidence intervals.