Crystal Orbital Guided Iteration to Atomic Orbitals: A Pathway to Chemically Adaptive Atomic Orbitals from DFT

TL;DR

The paper introduces COGITO, a novel framework for constructing adaptable, localized atomic orbitals from DFT that improve tight-binding models while maintaining chemical interpretability.

Contribution

It develops a method to create optimal atomic orbitals that overcome mathematical challenges in nonorthogonal bases, enhancing electronic structure modeling.

Findings

COGITO achieves tight-binding accuracy comparable to MLWF-based methods.

It preserves the interpretability of atomic orbitals in electronic structure analysis.

The method reveals orbital-resolved covalent bonds and charge transfer.

Abstract

Atomic orbitals underpin our understanding of electronic structure, providing intuitive descriptions of bonding, charge transfer, magnetism, and correlation effects. Despite their utility, an atomic basis that is adaptable, strictly localized on atomic centers, and enables accurate tight-binding interpolation has remained elusive. Here, we introduce Crystal Orbital Guided Iteration To atomic-Orbitals (COGITO), a framework that constructs an optimal atomic orbital basis by identifying and resolving key mathematical obstacles inherent to nonorthogonal bases -- particularly uncontrolled orbital mixing, and the fixed-overlap constraint between orbitals. We demonstrate that COGITO enables tight-binding models as accurate as MLWF-based approaches, while preserving the ability of tight-binding parameters to represent the projected atomic basis -- an essential feature lost in schemes that enforce orbital orthogonality or maximal localization. By creating accurate and chemically interpretable models of electronic structure, COGITO reveals the orbital-resolved covalent bonds and charge transfer that is encoded in the Kohn-Sham wavefunctions of DFT. Our method thus offers a powerful tool for any physics- or chemistry-based application that relies on a faithful description of local electronic structure.