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

Abstract

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree–Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H*, covalently bound to the donor oxygen atom) from the acceptor (OA) and donor (OD) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.

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.…”

“…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. 47−52 In particular, large density-driven errors were found in SCAN calculations for pure water systems as well as for ions in water, 48,51,52 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.…”

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

“…46 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. [47][48][49][50][51][52] Despite much progress in characterizing the hydration properties of ions in water, a transferable molecular model capable of correctly predicting structural, thermodynamic, and dynamical properties of hydrated ions from small aqueous clusters in the gas phase to aqueous solutions and interfaces is still missing. In the past years, we introduced the many-body energy (MB-nrg) theoretical/computational framework for data-driven manybody potential energy functions (PEFs).…”

“…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. [47][48][49][50][51][52] In particular, large density-driven errors were found in SCAN calculations for pure water systems as well as for ions in water, 48,51,52 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.…”

Towards predictive design of electrolyte solutions by accelerating ab initio simulation with neural networks.

“…The first and perhaps most significant problem is that the DFT functionals used to generate the training data can have significant inaccuracies associated with them. [90][91][92][93] One potential solution to this problem is to add correction potentials adjusted to minimise this error using either higher level calculations on small clusters 39,42,94 or experimental information. Using machine learning to determine the corrections is also a possibility.…”