Self-Consistent Equations for Nonempirical Tight Binding Theory

TL;DR

This paper introduces a new reference state for density functional theory called the independent atom ansatz, enabling exact electron density representation and deriving self-consistent equations with tight binding-like total energy functional.

Contribution

It presents a novel independent atom ansatz that simplifies electron interactions and provides analytical Hamiltonian matrix elements, enhancing DFT accuracy and interpretability.

Findings

Exact electron density representation with the ansatz

Derivation of self-consistent localized state equations

Analytical Hamiltonian matrix elements in weak interaction limit

Abstract

A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals. Self-consistent equations for localized states are derived. Total energy functional is found to closely resemble tight binding theory. The independent atom ansatz facilitates partial cancellation of inter-atomic electron-electron and electron-nuclear interactions, which allows for the derivation of analytical Hamiltonian matrix elements in a weak interaction limit. The formalism provides charge and energy decomposition analyses at no additional cost. It also includes mechanisms to remove self-interaction and static correlation errors. Initial numerical results for simple model systems have been previously reported [Mironenko, J. Phys. Chem. A 127, 7836 (2023)].