[Paper Review] Reformulation of DFT+U as a pseudo-hybrid Hubbard density functional

Luis A. Agapito, Stefano Curtarolo+1 more|arXiv (Cornell University)|Jun 12, 2014

Inorganic Fluorides and Related Compounds86 references3 citations

TL;DR

This paper reformulates DFT+U as a pseudo-hybrid Hubbard density functional—ACBN0—that improves band gap predictions in insulators like TiO₂, MnO, NiO, and ZnO with minimal computational overhead. By combining DFT with exact exchange-like corrections via a self-consistent, orbital-dependent approach, it achieves accuracy comparable to hybrid functionals while retaining the efficiency of DFT+U.

ABSTRACT

The accurate prediction of the electronic properties of materials at a low computational expense is a necessary conditions for the development of effective high-throughput quantum-mechanics (HTQM) frameworks for accelerated materials discovery. HTQM infrastructures rely on the predictive capability of Density Functional Theory (DFT), the method of choice for the first principles study of materials properties. However, DFT suffers of approximations that result in a somewhat inaccurate description of the electronic band structure of semiconductors and insulators. In this article we introduce ACBN0, a pseudo-hybrid Hubbard density functional that yields an improved prediction of the band structure of insulators such as transition-metal oxides, as shown for TiO2, MnO, NiO and ZnO, with only a negligible increase in computational cost.

Motivation & Objective

• Address the persistent failure of standard DFT to accurately describe electronic band structures in insulators and semiconductors.
• Overcome the limitations of LDA and GGA approximations, which severely underestimate band gaps due to self-interaction error.
• Develop a computationally efficient method that improves band gap prediction without the high cost of GW or DMFT methods.
• Integrate exact exchange-like corrections into DFT+U via a self-consistent, orbital-dependent functional to enhance accuracy for strongly correlated systems.
• Enable reliable high-throughput materials screening by combining predictive accuracy with low computational overhead.

Proposed method

• Reformulate DFT+U as a pseudo-hybrid functional by introducing a self-consistent, orbital-dependent correction based on exact exchange-like terms.
• Use a Hubbard-like potential derived from electron repulsion integrals (ERIs) and a screened Coulomb interaction to correct for self-interaction error.
• Express maximally localized Wannier functions (MLWFs) as linear combinations of Gaussian-type orbitals (GTOs) to enable analytical computation of two-electron integrals.
• Project plane-wave Kohn-Sham states onto atomic-orbital basis sets using a filtering and shifting procedure to construct real-space Hamiltonian and density matrices.
• Compute electron repulsion integrals (ERIs) analytically using Cartesian Gaussian expansions, enabling efficient and accurate evaluation of the Hubbard U term.
• Integrate the resulting functional into a high-throughput DFT framework to enable scalable materials screening with improved band gap accuracy.

Experimental results

Research questions

• RQ1 Can a DFT+U approach be reformulated to achieve hybrid-functional-like accuracy in band gap prediction without the associated computational cost?
• RQ2 How can the self-interaction error in standard DFT be corrected in a way that preserves the efficiency required for high-throughput materials discovery?
• RQ3 To what extent can a pseudo-hybrid functional based on DFT+U improve band gap predictions for transition metal oxides compared to standard DFT+U and hybrid functionals?
• RQ4 Can the use of Gaussian-type orbitals and real-space projection techniques enable accurate and efficient evaluation of electron repulsion integrals in periodic systems?
• RQ5 What is the trade-off between accuracy and computational cost when applying this reformulated functional to a diverse set of insulators?

Key findings

• The ACBN0 functional significantly improves band gap predictions for transition metal oxides such as TiO₂, MnO, NiO, and ZnO compared to standard DFT+U.
• The method achieves accuracy comparable to hybrid functionals like HSE06, with a negligible increase in computational cost, making it suitable for high-throughput screening.
• The reformulated functional successfully captures the derivative discontinuity in the exchange-correlation functional, correcting the underestimation of band gaps inherent in LDA and GGA.
• The use of Gaussian-type orbitals and real-space projection enables analytical and efficient computation of electron repulsion integrals, crucial for the functional's performance.
• The functional is robust across diverse insulating materials, demonstrating consistent improvement in band gap prediction without requiring system-specific tuning.
• The method maintains charge conservation and is compatible with norm-conserving pseudopotentials, ensuring reliability in periodic DFT calculations.