Pseudopotentials for Orbital-Free DFT: Capturing Nonlocality and Correcting Functional Approximants

TL;DR

This work addresses the difficulty of creating reliable local pseudopotentials for orbital-free DFT (OF-DFT), especially for transition metals. The authors develop a KS-to-OF-DFT inversion framework that uses an optimized effective potential (OEP) to construct local pseudopotentials (LPPs) by targeting existing nonlocal NLPPs, and they generate four LPP sets (PGBRV1.0, PGBRV0.2, PPSL1.0, PPSL0.2). By incorporating approximate kinetic-energy functionals $\tilde{T}_s$ and enforcing short-range, spherically symmetric corrections $\Delta v_{LPP}(r)$, they demonstrate substantial improvements in pseudodensity accuracy, equation-of-state trends, and phonon spectra relative to the local parts of NLPPs, with PGBRV0.2 typically offering the best performance. The results indicate meaningful progress toward practical OF-DFT simulations of transition metals, though they also underscore the ongoing need to refine KEDFs, cutoff radii, and element-specific pseudization strategies. Overall, the work provides a rigorous framework for developing transferable LPPs compatible with approximate OF-DFT functionals and highlights avenues for future methodological refinements and broader applicability.

Abstract

Developing reliable pseudopotentials for orbital-free density functional theory (OF-DFT), especially for transition metals, remains a significant challenge. In this study, we provide a theoretical framework for analyzing pseudization strategies for OF-DFT calculations. From the analysis arises a proposed pseudization method which involves constructing local pseudopotentials by targeting existing Kohn-Sham DFT pseudopotentials through an optimized effective potential procedure. We produce four distinct sets of local pseudopotentials and evaluate their accuracy and transferability on the transition metal elements. Our results indicate a substantial improvement over previously available pseudopotentials. Although current OF-DFT functionals still only reach a qualitative accuracy for transition metals, our newly developed pseudopotentials provide a rigorous framework for further methodological advancements.

Figures (6)

• Figure 1: Depiction of the maps in Eqs. (\ref{['revised:map:nlpp']},\ref{['revised:map:lpp']}) and the concept of NLPP representation (set of nonlocal PPs on the left-hand side) mapping to a target pseudodensity, $n({\mathbf{r}})$. The bijectivity of the map connecting the pseudodensity with the associated local KS potential, $v_{LPP}({\mathbf{r}})$ is indicated by a left-right arrow.
• Figure 2: Percent density deviation, $\Delta_v$, for the atoms in the most stable phase of all transition metals. Green regions are elements with $\Delta_v \leq 5\%$; red $5 < \Delta_v \leq 8\%$ and blue $\Delta_v >8\%$. The four panels are each devoted to one set of pseudopotentials (PGBRV0.2, PGBRV1.0, PPSL0.2, PPSL1.0, see text for more details).
• Figure 3: Density deviation per $d$ electron, $\Delta_d$. The panels compare pseudopotentials constructed using the TF0.2vW functional (left) and the TFvW functional (right) for transition metals. Red circles represent GBRV pseudopotentials, green triangles PSL.
• Figure 4: Phonon spectra of Cu, Ag, Au, and Pd calculated with OF-DFT using TF0.2vW with PGBRV0.2 LPPs (black lines) and the local part of the GBRV NLPPs (blue lines). Reference KS-DFT are also included (red line).
• Figure 5: Left-most panel: enhancement factor, $F_\tau(s)$, of several GGA functionals. Right two panels: electron density deviation, $\Delta n_{iso}$, against TF0.2vW and TFvW functionals for several GGA KEDF (LKT, revAPBEk, TFvW) and nonlocal functionals (revHC and LMGP).