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Reducing Self-Interaction Error in Transition-Metal Oxides with Different Exact-Exchange Fractions for Energy and Density

Harshan Reddy Gopidi, Ruiqi Zhang, Yanyong Wang, Abhirup Patra, Jianwei Sun, Adrienn Ruzsinszky, John P. Perdew, Pieremanuele Canepa

Abstract

Density functional theory (DFT) in chemistry and materials science aims for "chemical accuracy," but this goal is challenged by the need to approximate the exact exchange-correlation (XC) energy functional. The r$^2$SCAN, meta-generalized gradient approximation to the XC functional fulfills 17 exact constraints of the XC energy, and has significantly boosted prediction accuracy for molecules and materials. However, r$^2$SCAN remains inadequate at predicting properties of open \textit{d} and \textit{f} transition-metal strongly correlated compounds, such as band gaps, magnetic moments, and oxidation energies. Prediction inaccuracies of r$^2$SCAN energies arise from functional and density-driven errors, mainly resulting from the DFT self-interaction error. We propose the r$^2$SCANY@r$^2$SCANX method to mitigate the self-interaction error of XC functionals for the accurate simulations of electronic, magnetic, and thermochemical properties of transition metal oxides. r$^2$SCANY@r$^2$SCANX uses different fractions of exact Hartree-Fock exchange: X for the electronic density and Y for the density functional approximation of the total energy, thereby simultaneously addressing functional-driven and density-driven inaccuracies. Building just on 1 (or maximum 2) parameters that apply unchanged to \emph{s-p}-bonded systems, we demonstrate that, r$^2$SCANY@r$^2$SCANX improves upon the r$^2$SCAN predictions for 20 highly correlated oxides and even outperforms the highly parameterized DFT(r$^2$SCAN)+\emph{U} method -- the state-of-the-art approach to predict strongly correlated materials. Prediction uncertainties for oxidation energies and magnetic moments of transition metal oxides are significantly reduced by r$^2$SCAN10@r$^2$SCAN50 and band gaps with r$^2$SCAN10@r$^2$SCAN. r$^2$SCAN10@r$^2$SCAN50 diminishes the density-driven error of the energy in r$^2$SCAN and r$^2$SCAN10.

Reducing Self-Interaction Error in Transition-Metal Oxides with Different Exact-Exchange Fractions for Energy and Density

Abstract

Density functional theory (DFT) in chemistry and materials science aims for "chemical accuracy," but this goal is challenged by the need to approximate the exact exchange-correlation (XC) energy functional. The rSCAN, meta-generalized gradient approximation to the XC functional fulfills 17 exact constraints of the XC energy, and has significantly boosted prediction accuracy for molecules and materials. However, rSCAN remains inadequate at predicting properties of open \textit{d} and \textit{f} transition-metal strongly correlated compounds, such as band gaps, magnetic moments, and oxidation energies. Prediction inaccuracies of rSCAN energies arise from functional and density-driven errors, mainly resulting from the DFT self-interaction error. We propose the rSCANY@rSCANX method to mitigate the self-interaction error of XC functionals for the accurate simulations of electronic, magnetic, and thermochemical properties of transition metal oxides. rSCANY@rSCANX uses different fractions of exact Hartree-Fock exchange: X for the electronic density and Y for the density functional approximation of the total energy, thereby simultaneously addressing functional-driven and density-driven inaccuracies. Building just on 1 (or maximum 2) parameters that apply unchanged to \emph{s-p}-bonded systems, we demonstrate that, rSCANY@rSCANX improves upon the rSCAN predictions for 20 highly correlated oxides and even outperforms the highly parameterized DFT(rSCAN)+\emph{U} method -- the state-of-the-art approach to predict strongly correlated materials. Prediction uncertainties for oxidation energies and magnetic moments of transition metal oxides are significantly reduced by rSCAN10@rSCAN50 and band gaps with rSCAN10@rSCAN. rSCAN10@rSCAN50 diminishes the density-driven error of the energy in rSCAN and rSCAN10.

Paper Structure

This paper contains 18 sections, 4 equations, 21 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Improving ab initio Predictions of meta-GGA-type r2SCAN Functionals
  4. r2SCAN Predictions of Transition-metal Oxides Properties
  5. Benchmarking Oxidation Enthalpies of MiOjs with r2SCANY@r2SCANX Functionals
  6. Achieving Optimal Fractions of Exact Exchange in the r2SCANY@r2SCANX Formulations
  7. Effects of Exact-exchange Fractions X and Y on the Binding Energy of the Oxygen Molecule
  8. Effects of Exact-Exchange Fractions X and Y on On-site Magnetic Moments
  9. Effects of Exact-exchange Fractions X and Y on the Prediction of Fundamental Band Gaps
  10. Relative Stability of MnO, NiO and ZnO Polymorphs with r2SCANY@r2SCANX Approaches
  11. Discussion
  12. Electron Densities from Hartree-Fock, Hybrids, and DFT+U Approaches
  13. Sources of Uncertainty and Error
  14. r2SCANY@r2SCANX as a Generalization of Single-Shot and Density-Corrected Approaches
  15. False Metals and Structure Symmetry Breaking
  16. ...and 3 more sections

Figures (21)

  • Figure 1: Schematically connecting the self-consistent and non-self-consistent (non-SCF) approaches required in the r2SCANY@r2SCANX methods. Self-consistent functionals used in this work are LSDA, PBE, r2SCAN, r2SCAN10, and LAK. Non-self-consistent hybrid functionals, including a fraction of exact HF exchange, such as r2SCAN@HF, r2SCAN10@r2SCAN, r2SCAN@r2SCAN50, r2SCAN10@r2SCAN50, r2SCAN@LAK, r2SCAN10@LAK, require a self-consistent step to generate orbitals on which the energy is evaluated non-self-consistently.
  • Figure 1: Stabiltiy of various magnetic configurations in dimerized (a) Ti$_2$O$_3$ and (b) VO$_2$ using r$^{2}$SCANY@r$^{2}$SCANX approaches. Here as elsewhere, we use the r$^{2}$SCAN geometries. In Table 1 of the manuscript, we have used the magnetic state that achieves the lowest energy in our best hybrid, r$^{2}$SCAN10@r$^{2}$SCAN50: NM for Ti$_2$O$_3$ and AFM for VO$_2$.
  • Figure 2: Prediction error of 3d MiOj oxidation energies of reactions in Table \ref{['tab:2']} (except for CeiOj compounds) with several XC functionals, including r2SCANY@r2SCANX and r2SCANY@LAK as defined in Fig. \ref{['fig:1']}. (a) Error in oxidation energies of 18 reactions considered. (b) Violin representation of error distributions. (c) The mean absolute errors. Errors in predicting oxidation energies of all DFT functionals except r2SCAN+U are evaluated at r2SCAN geometries. The mean experimental oxidation energy is --3.82 eV/O2.
  • Figure 2: Error in oxidation enthalpy of oxidation reaction of Cerium oxides with r$^2$SCANY@r$^2$SCANX method. Oxidation reaction is indicated.
  • Figure 3: Identification of optimal values of X and Y in r2SCANY@r2SCANX functionals, by locating minima in mean absolute and root mean square errors of oxidation energies of all possible oxidation reactions of MiOjs. Panel a shows that the mean absolute error minimizes at 55.0% exact exchange in orbitals and 9.6% exact exchange in the functional, forming r2SCAN10@r2SCAN55, which produces an error of $\sim$0.38 eV/O2. Panel b shows that the root mean square error minimizes, with an error value of $\sim$0.53 eV at 46.3% exact exchange in orbital and 7.7% exact exchange in functional, thus r2SCAN8@r2SCAN46. See Sec. \ref{['sec:DFTmethod']} for details on the interpolation scheme to coarse-grain values of X and Y.
  • ...and 16 more figures