Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Kinetic energy constructed from exact gradient expansion of second order in uniform gas limit

Abhishek Bhattacharjee, Hemanadhan Myneni, Manoj K. Harbola, Prasanjit Samal

TL;DR

The paper tackles the transferability and efficiency gap in orbital-free DFT by introducing KGE2, a parameter-free semilocal KEDF at the GGA level that exactly recovers the GE2 in the small-$s$ limit while balancing TF and vW contributions. By enforcing a Pauli-enhancement factor $F_ heta(s)=1/(1+ ext{$\\alpha$s$^2$})$ with $ ext{$\\alpha$}=1.481$, and using $T_s^{GGA}= au_{TF}( ho)[F_ heta(s)+ rac{5}{3}s^2]$ with $ ext{$\\lambda$}=1$, KGE2 achieves comparable accuracy to nonlocal and meta-GGA KEDFs across metals and semiconductors, without parameter fitting. The work also derives the GGA linear-response behavior and Pauli-potential constraints, showing GE2-consistent semilocals can capture short-range response and density features while preserving positivity and correct scaling. Benchmarking on bulk solids and finite clusters demonstrates that KGE2 provides balanced performance, outperforming several semilocal functionals in many cases and offering a scalable, general-purpose KEDF for large-scale OFDFT applications.

Abstract

Orbital-Free Density Functional Theory (OFDFT) has re-emerged as a viable alternative to Kohn-Sham DFT, driven by recent advances in kinetic energy density functionals (KEDFs). Nonlocal (NL) KEDFs have significantly extended OFDFT's applicability, particularly for bulk solids, but their high computational cost and dependence of system-specific parameters limit their universality. In this work, we propose a semilocal KEDF at the Generalized Gradient Approximation (GGA) level that achieves accuracy comparable to state-of-the-art NL and meta-GGA functionals, while remaining entirely parameter-free. Our construction revives the Thomas-Fermi-von Weizsacker (TFvW) framework by modulating the relative contributions of TF and vW terms through physically motivated constraints and preserving the exact second-order gradient expansion. Despite its simple form, the proposed functional (KGE2) performs remarkably well across both extended systems (metals and semiconductors) and finite systems (clusters), without any need for parameter tuning. These results mark a step toward a transferable, computationally efficient, and general-purpose KEDF suitable for large-scale OFDFT simulations.

Kinetic energy constructed from exact gradient expansion of second order in uniform gas limit

TL;DR

The paper tackles the transferability and efficiency gap in orbital-free DFT by introducing KGE2, a parameter-free semilocal KEDF at the GGA level that exactly recovers the GE2 in the small- limit while balancing TF and vW contributions. By enforcing a Pauli-enhancement factor \\alpha^2 with \\alpha, and using with \\lambda, KGE2 achieves comparable accuracy to nonlocal and meta-GGA KEDFs across metals and semiconductors, without parameter fitting. The work also derives the GGA linear-response behavior and Pauli-potential constraints, showing GE2-consistent semilocals can capture short-range response and density features while preserving positivity and correct scaling. Benchmarking on bulk solids and finite clusters demonstrates that KGE2 provides balanced performance, outperforming several semilocal functionals in many cases and offering a scalable, general-purpose KEDF for large-scale OFDFT applications.

Abstract

Orbital-Free Density Functional Theory (OFDFT) has re-emerged as a viable alternative to Kohn-Sham DFT, driven by recent advances in kinetic energy density functionals (KEDFs). Nonlocal (NL) KEDFs have significantly extended OFDFT's applicability, particularly for bulk solids, but their high computational cost and dependence of system-specific parameters limit their universality. In this work, we propose a semilocal KEDF at the Generalized Gradient Approximation (GGA) level that achieves accuracy comparable to state-of-the-art NL and meta-GGA functionals, while remaining entirely parameter-free. Our construction revives the Thomas-Fermi-von Weizsacker (TFvW) framework by modulating the relative contributions of TF and vW terms through physically motivated constraints and preserving the exact second-order gradient expansion. Despite its simple form, the proposed functional (KGE2) performs remarkably well across both extended systems (metals and semiconductors) and finite systems (clusters), without any need for parameter tuning. These results mark a step toward a transferable, computationally efficient, and general-purpose KEDF suitable for large-scale OFDFT simulations.
Paper Structure (19 sections, 38 equations, 9 figures, 3 tables)

This paper contains 19 sections, 38 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Functional construction
  4. Response function analysis of semilocals
  5. Pauli potential and exact constrains
  6. Results and discussions
  7. Computational Details and Materials
  8. Analysis of density
  9. Assessment of Bulk Properties Using RMARE
  10. Elastic Properties
  11. Application of KGE2 on finite systems: Clusters
  12. Conclusion
  13. Pauli Potential of semilocals:
  14. Exact conditions of $v_{\theta}$
  15. Scaling conditions
  16. ...and 4 more sections

Figures (9)

  • Figure 1: Plot of Pauli enhancement factors of various functionals as a function of variable $s$.
  • Figure 2: Here we compare the response function of non-local part of various semilocal KEDFs with exact Lindhard function. The plots are dimentionless as they are normalised with TF response as per Eq.\ref{['eq:Chi_GGA']}.
  • Figure 3: Density plotting of Si CD along [111] direction for various available KEDFs. The blue line is KS-density; see legend for other labels. The inset plot is density difference $\rho^{KS}-\rho^{OF}$ along [111] direction. The density is in atomic units, and on the x-axis, we have grid points.
  • Figure 4: Density difference of Al-FCC (KS-OF) in 3D in the order: TFvW, PG , KGE2 and LKT. We have chosen this view to display how the density improves with increasing functional quality. Isoscale is set at 100% yellow saturation for density difference of 0.02 $a.u$ and 100% blue saturation for density difference -0.02 $a.u.$.
  • Figure 5: Density difference of Si-CD (KS-OF) in 3D in the order: WT, TFvW, LKT, PG, KGE2 and HC. We have chosen this view to display how the density improves with increasing functional quality. Isoscale is set at 100% yellow saturation for density difference of 0.035 $a.u$ and 100% blue saturation for density difference -0.035 $a.u.$.
  • ...and 4 more figures