Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals

Abstract

The SCAN meta-GGA exchange-correlation functional [Phys. Rev. Lett. 115, 036402 (2015)] is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single orbital electron densities accurately, and another describes slowly-varying densities accurately. To conserve constraints known for the exact exchange-correlation functional, the derivatives of this interpolation vanish in the slowly-varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional's efficiency. We have recently reported a modification to the SCAN functional, termed r${}^2$SCAN [J. Phys. Chem. Lett. 11, 8208 (2020)] that introduces two regularizations into SCAN which improve its numerical performance at the expense of not recovering the fourth order term of the slowly-varying density gradient expansion for exchange. Here we show the derivation of a progression of functionals (rSCAN, r++SCAN, r${}^2$SCAN, and r${}^4$SCAN) with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r${}^2$SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r${}^4$SCAN does.

References in corpus (26)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Ab initio theory and modeling of water
• Regularized SCAN functional
• Fractional spins and static correlation error in density functional theory
• Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA
• Rungs 1 to 4 of DFT Jacob's ladder: extensive test on the lattice constant, bulk modulus, and cohesive energy of solids
• More-Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme
• Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality
• Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
• Evaluating transition-metal oxides within DFT-SCAN and SCAN+U frameworks for solar thermochemical applications
• r2SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications
• Antiferromagnetic Ground State of La${}_2$CuO${}_4$: A Parameter-free Ab Initio Description
• Gedanken Densities and Exact Constraints in Density Functional Theory
• Landscape of competing stripe and magnetic phases in cuprates
• Meta-GGA Performance in Solids at Almost GGA Cost
• What types of chemical problems benefit from density-corrected DFT? A probe using an extensive and chemically diverse test suite
• Symmetry-Breaking Polymorphous Descriptions for Complex Materials without Interelectronic U
• High-Level Correlated Approach to the Jellium Surface Energy, Without Uniform-Electron-Gas Input
• Jellium surface energy beyond the local-density approximation: Self-consistent-field calculations
• Characterization of Thin Film Materials using SCAN meta-GGA, an Accurate Nonempirical Density Functional
• Enhancing the efficiency of density functionals with a novel iso-orbital indicator
• Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations
• Correlation in noncollinear antiferromagnetic $\alpha$-Mn
• Spin-Crossover From a Well-Behaved, Low-Cost meta-GGA Density Functional
• Examining the order-of-limits problem and lattice constant performance of the Tao--Mo Functional
• The Tin Pest Problem as a Test of Density Functionals Using High-Throughput Calculations

Cited by in corpus (7)

• Workhorse minimally-empirical dispersion-corrected density functional, with tests for weakly-bound systems: r${}^2$SCAN+rVV10
• Predictive Power of the Exact Constraints and Appropriate Norms in Density Functional Theory
• Many recent density functionals are numerically ill-behaved
• Performance of the r${}^2$SCAN functional in transition metal oxides
• A simple and efficient route towards improved energetics within the framework of density-corrected density functional theory
• Comparing first-principles density functionals plus corrections for the lattice dynamics of YBa${}_2$Cu${}_3$O${}_6$
• How Semilocal Are Semilocal Density Functional Approximations? -Tackling Self-Interaction Error in One-Electron Systems