[Paper Review] Accurate and numerically efficient r$^2$SCAN meta-generalized gradient approximation

James W. Furness, Aaron D. Kaplan+3 more|arXiv (Cornell University)|Aug 7, 2020

Advanced NMR Techniques and Applications87 citations

TL;DR

The paper introduces r2SCAN, a regularized-restored meta-GGA that keeps SCAN’s accuracy while achieving rSCAN-like numerical efficiency by restoring exact constraint adherence through a new regularized iso-orbital indicator. It analyzes improvements in grid convergence and potential smoothness for large-scale DFT calculations.

ABSTRACT

The recently proposed rSCAN functional [J. Chem. Phys. 150, 161101 (2019)] is a regularized form of the SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.

Motivation & Objective

• Motivate the need for a meta-GGA that combines SCAN accuracy with computational efficiency for large-scale materials and molecular studies.
• Restore exact constraint adherence in a regularized meta-GGA to maintain SCAN-level accuracy.
• Ensure numerical stability and grid convergence comparable to rSCAN while retaining SCAN’s transferability.
• Provide a functional form and implementation details that enable better pseudopotential generation and smoother XC potentials.

Proposed method

• Review limitations of SCAN and rSCAN, focusing on constraint adherence and numerical stability.
• Introduce a regularized iso-orbital indicator bar{\alpha} = (\tau - \tau_W)/(\tau_{unif} + \eta \tau_W) with \eta = 10^-3 to restore uniform-density behavior.
• Adopt rSCAN interpolation with the regularized indicator to form r2SCAN, and modify exchange and correlation components to recover GE2X and approximate GE2C.
• Replace the SCAN/rSCAN exchange function with a tailored form x(p) to recover the gradient expansion for exchange under the new indicator (Eq. 8).
• Modify the correlation gradient expansion by introducing a new term (\Delta y) and a revised g(At^2, \Delta y) function to approximately recover GE2C.
• Demonstrate that r2SCAN preserves numerical efficiency similar to rSCAN and improves energy-density smoothness and potential behavior compared to SCAN.

Experimental results

Research questions

• RQ1 Can exact constraint adherence be restored in rSCAN-like functionals without sacrificing numerical efficiency?
• RQ2 Does r2SCAN recover the key gradient expansions (GE2X and GE2C) and the uniform-density limit that SCAN satisfies?
• RQ3 Does r2SCAN offer improved grid convergence and smoother XC potentials relative to SCAN and rSCAN across diverse test sets?
• RQ4 Is r2SCAN transferable across molecular, barrier, weak interaction, and lattice-constant benchmarks as compared to SCAN and rSCAN?

Key findings

• r2SCAN restores important exact constraints (Uniform Density, GE2X, and approximate GE2C) while maintaining rSCAN-like numerical efficiency.
• On the G3 atomization-energy set, r2SCAN achieves accuracy similar to SCAN and significantly better grid-convergence behavior than SCAN; rSCAN shows degraded transferability.
• Across 76 reaction barriers, 22 weak interactions, and 20 lattice constants, r2SCAN shows competitive performance with SCAN and rSCAN, with G3 being the notable exception where r2SCAN matches SCAN.
• The XC potential and energy-density derivatives in r2SCAN are smoother than in SCAN, potentially aiding pseudopotential generation and applications requiring a stable potential.
• The study suggests r2SCAN as a practical meta-GGA for large-scale computations due to its combination of transferability (constraint adherence) and grid efficiency.