Environment-dependent tight-binding models from ab initio pseudo-atomic orbital Hamiltonians

TL;DR

This paper introduces an environment-dependent tight-binding model derived from ab initio pseudo-atomic orbital Hamiltonians, enabling accurate, transferable simulations of complex materials with a compact basis.

Contribution

The authors develop a novel environment-dependent tight-binding framework fitted to ab initio spectra, improving transferability and accuracy for large systems.

Findings

Accurately models electronic structure of diverse systems like platinum, silicon, and graphene.

Demonstrates transferability and efficiency on systems with thousands of atoms.

Implemented in the exttt{PAOFLOW} code for broad property evaluations.

Abstract

\textit{Ab initio} pseudo-atomic orbital (PAO) Hamiltonians express the electronic structure of a solid in a compact, localized basis that spans the same Hilbert space as a conventional Slater--Koster tight-binding model, thereby providing an exact \textit{ab initio} representation without any loss of accuracy. Building on this correspondence, we develop an environment-dependent tight-binding (EDTB) framework in which Slater--Koster hopping integrals are augmented with bond-screening functions that capture the local coordination environment. All parameters are determined by fitting to the PAO eigenvalue spectrum across multiple atomic configurations simultaneously, which breaks the degeneracy between screening and hopping parameters and yields physically meaningful, transferable models capable of generating Hamiltonians for large systems with \textit{ab initio} precision. We demonstrate the efficiency and accuracy of the approach on four prototypical systems: bulk platinum, silicon surfaces, Si/Ge~[001] superlattices, and twisted bilayer graphene with up to $4{,}324$ atoms. The method is implemented in the \paoflow{} code and integrates seamlessly with its full post-processing suite, enabling the evaluation of a broad range of electronic, optical, and transport properties.