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Performance Improvement of Deorbitalized Exchange-Correlation Functionals

H. Francisco, B. Thapa, S. B. Trickey, A. C. Cancio

TL;DR

This paper tackles the computational and numerical challenges of deorbitalizing meta-GGA exchange-correlation functionals by replacing $\tau_{\rm S}$ with a Laplacian-inclusive semi-local description, producing a local KS potential. It introduces smooth, constraint-respecting deorbitalizers (CR-based, RPP-derived, notably SRPP and SRPP2) and applies them to $r^2$SCAN to assess accuracy and solid-state timing, finding substantial per-cycle speedups and improved potential smoothness for solids, with competitive molecular performance. The study demonstrates that smoothing mitigates the latently problematic oscillations tied to $\nabla^2 n$ while preserving many key constraints, leading to faster and more reliable solid-state calculations, though AIMD presents remaining stability challenges. Overall, the work provides a practical path toward efficient deorbitalized meta-GGAs, offering guidance on when and how to pursue Laplacian-based functionals and highlighting areas for further optimization in switching schemes and MD-enabled workflows.

Abstract

Deorbitalization of a conventional meta-generalized-gradient exchange-correlation approximation replaces its dependence upon the Kohn-Sham kinetic energy density with a dependence on the density gradient and Laplacian. In principle, that simplification should provide improved computational performance relative to the original meta-GGA form because of the shift from an orbital-dependent generalized Kohn-Sham potential to a true KS local potential. Often that prospective gain is lost because of problematic roughness in the density caused by the density Laplacian and consequent roughness in the exchange-correlation potential from the resulting higher-order spatial derivatives of the density in it. We address the problem by constructing a deorbitalizer based on the RPP deorbitalizer [Phys. Rev. Mater. 6, 083803 (2022)] with comparative smoothness of the potential along with retention of constraint satisfaction as design goals. Applied to the r^2SCAN exchange-correlation functional [J. Phys. Chem. Lett. 11, 8208 (2020)], we find substantial timing improvements for solid-state calculations over both r^2SCAN and its earlier deorbitalization for high precision calculations of structural properties, while improving upon the accuracy of RPP deorbitalization for both solids and molecules.

Performance Improvement of Deorbitalized Exchange-Correlation Functionals

TL;DR

This paper tackles the computational and numerical challenges of deorbitalizing meta-GGA exchange-correlation functionals by replacing with a Laplacian-inclusive semi-local description, producing a local KS potential. It introduces smooth, constraint-respecting deorbitalizers (CR-based, RPP-derived, notably SRPP and SRPP2) and applies them to SCAN to assess accuracy and solid-state timing, finding substantial per-cycle speedups and improved potential smoothness for solids, with competitive molecular performance. The study demonstrates that smoothing mitigates the latently problematic oscillations tied to while preserving many key constraints, leading to faster and more reliable solid-state calculations, though AIMD presents remaining stability challenges. Overall, the work provides a practical path toward efficient deorbitalized meta-GGAs, offering guidance on when and how to pursue Laplacian-based functionals and highlighting areas for further optimization in switching schemes and MD-enabled workflows.

Abstract

Deorbitalization of a conventional meta-generalized-gradient exchange-correlation approximation replaces its dependence upon the Kohn-Sham kinetic energy density with a dependence on the density gradient and Laplacian. In principle, that simplification should provide improved computational performance relative to the original meta-GGA form because of the shift from an orbital-dependent generalized Kohn-Sham potential to a true KS local potential. Often that prospective gain is lost because of problematic roughness in the density caused by the density Laplacian and consequent roughness in the exchange-correlation potential from the resulting higher-order spatial derivatives of the density in it. We address the problem by constructing a deorbitalizer based on the RPP deorbitalizer [Phys. Rev. Mater. 6, 083803 (2022)] with comparative smoothness of the potential along with retention of constraint satisfaction as design goals. Applied to the r^2SCAN exchange-correlation functional [J. Phys. Chem. Lett. 11, 8208 (2020)], we find substantial timing improvements for solid-state calculations over both r^2SCAN and its earlier deorbitalization for high precision calculations of structural properties, while improving upon the accuracy of RPP deorbitalization for both solids and molecules.

Paper Structure

This paper contains 14 sections, 36 equations, 8 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Background
  3. MetaGGA Structure
  4. Deorbitalization models
  5. Kinetic and exchange potentials
  6. Noise problem quantification
  7. Computational methods
  8. Results
  9. Atoms
  10. Structural properties
  11. Timing results
  12. Detailed analysis of computational parameter dependence
  13. Molecular dynamics of Aluminum
  14. Discussion and Concluding remarks

Figures (8)

  • Figure 1: Pauli enhancement factor $F_{\theta} (\equiv \alpha)$ for various KED functionals as a function of reduced density gradient $p$ with reduced Laplacian $q=0$. Models used are: GEA ($=1+\Delta F_\theta^{(2)}$), PC [Eqs. (\ref{['FthetaMGE4']}-\ref{['eq:PCform']})], PC$_\mathrm{opt}$ (same form, altered coefficients), CR [Eqs. (\ref{['eq:alphacsk']}-\ref{['eq:theta']})], RPP [Eqs. (\ref{['eq:RPPform']}-\ref{['eq:RPPswitch']})] and SRPP [Eq. (\ref{['eq:SRPP']})]. $\alpha^{vW} = 0$ by construction.
  • Figure 2: Pauli kinetic potential $v_\theta = v_{\tau} - v_{\rm W}$ for various Laplacian-level KED functionals for the hydrogen atom, evaluated at the exact atomic density. The exact value for the H atom, $v_\theta=0$, is at the solid black line.
  • Figure 3: Local part of the r$^2$SCAN exchange potential for the H and Si atoms (scaled by radius $r$) compared to the exchange potentials of several deorbitalized versions of r$^2$SCAN for the same atoms.
  • Figure 4: The local part of the r$^2$SCAN X potential for atomic H compared to deorbitalized X potentials, plotted over a much larger range in length and energy.
  • Figure 5: Bar charts showing timing performance for r$^2$SCAN, and r$^2$SCAN-L with the PC$_\mathrm{opt}$, RPP, and SRPP deorbitalizers for the entries in the 55-solid test set. Indexing of materials: 1-4 elemental semiconductors; 5-16: compound semiconductors; 17-22: ionic compounds; 23-31: simple metals; 32-55 transition metals.
  • ...and 3 more figures