Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations (1707.00856v2)

Abstract: The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC-DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra.

• The paper introduces the LOSC framework to correct delocalization errors in DFT by merging global and local scaling corrections into a unified methodology.
• It demonstrates significant improvements in energy predictions and electron density consistency across diverse systems from small molecules to polymers.
• The LOSC method offers computational efficiency with minimal additional cost, making it practical for large-scale electronic structure calculations.

Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations

The paper under discussion presents a framework aimed at systematically rectifying the delocalization errors prevalent in Density Functional Approximations (DFAs) by introducing the Localized Orbital Scaling Correction (LOSC). Delocalization error within density functional theory (DFT) is a long-standing issue that undermines predictive accuracy by violating the Perdew–Parr–Levy–Balduz (PPLB) condition, resulting in inaccuracies across various properties including system energies, electron densities, and the prediction of band gaps.

The LOSC framework unifies previously established methodologies of global and local scaling corrections, providing a comprehensive approach to address these inaccuracies across both global fractions (full electrons) and local fractions (partial electrons). By focusing on the accurate characterization of these fractions, the paper asserts that the LOSC can correct energy derivatives and electron densities in a manner that is both self-consistent and size-consistent. This results in improved outcomes across a variety of calculations, such as the dissociation of cationic species, molecular and polymer chain band gaps, and photoemission spectra.

Key Contributions and Results

1. Unified Correction Framework: The LOSC framework effectively combines the strengths of global and local scaling approaches, addressing the limitations of each when used in isolation. It leverages a newly defined concept of localized orbitals, termed "orbitallets", to explicitly deal with fractional electron distributions and related errors.
2. Energy and Density Corrections: The LOSC framework is designed to correct inaccuracies in system energies and electron densities resulting from delocalization errors, as demonstrated in a variety of systems from small molecules to large polymers. The approach offers systematic improvement in the prediction of fundamental gaps, achieving size-consistency that was previously unattainable.
3. Scalability: The methodology developed extends well beyond small molecular systems to polymers, potentially addressing delocalization errors in both molecules and solids, offering improved predictions for dissociation processes and band gap energies.
4. Implementation and Computational Efficiency: The authors have implemented LOSC self-consistently within the generalized Kohn-Sham framework. The additional computational cost is minimal compared to the overall calculation, enhancing practicality for large-scale applications.

Implications and Future Directions

The implications of this work are significant, providing a robust framework for improving DFA calculations in both finite and infinite systems. The ability of LOSC to effectively handle delocalization errors supports a wide range of potential applications, from chemical reaction studies to materials science investigations, dealing with large molecular systems and solid-state band structures.

Looking forward, future research might focus on refining the LOSC framework further, possibly integrating machine learning techniques for parameter optimization or extending the framework for more accurate handling of spin-polarized systems. Additionally, the successful application of LOSC could potentially pave the way for advancements in other areas of electronic structure theory that suffer from similar fundamental challenges, pushing the boundaries of what can be accurately predicted using DFT.

In conclusion, by addressing the systematic failures associated with delocalization errors, the LOSC framework offers an enhanced method for DFT calculations, setting a new standard for accuracy and reliability in electronic structure computations.