Assessing the Interplay between Functional-Driven and Density-Driven Errors in DFT Models of Water

Abstract

We investigate the interplay between functional-driven and density-driven errors in different density functional approximations within density functional theory (DFT) and the implications of these errors for simulations of water with DFT-based data-driven potentials. Specifically, we quantify density-driven errors in two widely used dispersion-corrected functionals derived within the generalized gradient approximation (GGA), namely BLYP-D3 and revPBE-D3, and two modern meta-GGA functionals, namely strongly constrained and appropriately normed (SCAN) and B97M-rV. The effects of functional-driven and density-driven errors on the interaction energies are first assessed for the water clusters of the BEGDB dataset. Further insights into the nature of functional-driven errors are gained from applying the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) to the interaction energies, which demonstrates that functional-driven errors are strongly correlated with the nature of the interactions. We discuss cases where density-corrected DFT (DC-DFT) models display higher accuracy than the original DFT models and cases where reducing the density-driven errors leads to larger deviations from the reference energies due to the presence of large functional-driven errors. Finally, molecular dynamics simulations are performed with data-driven many-body potentials derived from DFT and DC-DFT data to determine the effect that minimizing density-driven errors has on the description of liquid water. Besides rationalizing the performance of widely used DFT models of water, we believe that our findings unveil fundamental relations between the shortcomings of some common DFT approximations and the requirements for accurate descriptions of molecular interactions, which will aid the development of a consistent, DFT-based framework for the development of data-driven and machine-learned potentials for simulations of condensed-phase systems.

How Good Is the Density-Corrected SCAN Functional for Neutral and Ionic Aqueous Systems, and What Is So Right about the Hartree–Fock Density?

“…As expected, the addition of the D3 dispersion correction results in significant overbinding for all clusters, with SCAN-D3 and DC-SCAN-D3 being associated with MUEs of 10.10 and 2.34 kcal/mol, respectively. Overall, the analysis of the binding energies of the WATER27 data set indicates that, by largely reducing density-driven errors, DC-SCAN is a highly accurate functional not only for neutral water, as demonstrated in refs , , and , but also for protonated and deprotonated water.…”

Hydration Structure of Na+ and K+ Ions in Solution Predicted by Data-Driven Many-Body Potentials

“…In contrast, DRSLL-opt88, which was optimized for van der Waals and hydrogen-bonding interactions, and SCAN, which is a nonempirical functional that satisfies all 17 constraints known for meta-GGA functionals, predict a more structured first hydration shell that is shifted toward shorter distances, in better agreement with the (2B+3B+NB)-MB-nrg results. In this context it should be noted that recent studies demonstrated that several density functionals suffer from both functional- and density-driven errors, which significantly affect their performance when applied to aqueous systems. − In particular, large density-driven errors were found in SCAN calculations for pure water systems as well as for ions in water, ,, which suggests that the apparent agreement between the RDFs calculated from MD simulations with the SCAN functional and the (2B+3B+NB)-MB-nrg PEF may result from error cancellation in the SCAN representation of water–water and ion–water interactions.…”

“…Recent AIMD simulations carried out with the SCAN functional were found to accurately describe the hydration structure of Na + and K + in solution, although SCAN provided a relatively poorer description of liquid water . Recent analyses have shown that the different performance of a given density functional in describing pure water and ions in water can be rationalized by considering the interplay between functional- and density-driven errors. − …”

Detection and Correction of Delocalization Errors for Electron and Hole Polarons Using Density-Corrected DFT

“…The same is true for the hybrid SCAN0 functional . The DC-SCAN procedure has been recommended in some recent work, − but in this particular application the quality of SCAN energetics is somewhat degraded by density correction.…”

“…DC-DFT is a simple procedure whereby a self-consistent Hartree–Fock (HF) density, ρ HF , is used to evaluate the XC energy. This procedure incorporates electron correlation effects but avoids self-consistent iterations at the DFT level, which would introduce SIE into the density, and has been shown to afford reasonable reaction barrier heights even when GGA functionals are used. , Although this basic idea is an old one, − it has been revived and championed by Burke and Sim and their co-workers, ,− and more recently by others, − as an ad hoc correction for problems where DFT errors are “density-driven” rather than “functional-driven”. − In such cases, errors may be ameliorated through the use of an SIE-free density, namely, ρ HF . The usefulness of DC-DFT therefore hinges on identifying cases where the error is density-driven because otherwise it is probably not advantageous to sacrifice self-consistency. , Delocalization error in systems with one or more unpaired electrons represents a clear case where the error is density-driven, thus we expect such problems to benefit from DC-DFT.…”