Optimization of Ab-Initio Based Tight-Binding Models

TL;DR

This paper introduces a machine-learning inspired method to optimize tight-binding models, achieving high accuracy with fewer parameters and smaller ranges, facilitating automated large-scale electronic structure calculations.

Contribution

It presents a novel optimization procedure for tight-binding models that improves accuracy while reducing complexity compared to traditional Wannier-based methods.

Findings

Models have smaller ranges and fewer orbitals.

Achieve equal or better accuracy than Wannier functions.

Suitable for automated large-scale calculations.

Abstract

The electronic structure of solids can routinely be calculated by standard methods like density functional theory. However, in complicated situations like interfaces, grain boundaries or contact geometries one needs to resort to more simplified models of the electronic structure. Tight-binding models are using a reduced set of orbitals and aim to approximate the electronic structure by short range hopping processes. For example, maximally localized Wannier functions are often used for that purpose. However, their accuracy is limited by the need to disentangle the electronic bands. Here, we develop and investigate a different procedure to obtain tight-binding models inspired by machine-learning techniques. The model parameters are optimized in such a way as to reproduce ab-initio band structure data as accurately as possible using an as small as possible number of model parameters. The procedure is shown to result in models with smaller ranges and fewer orbitals than maximally localized Wannier functions but same or even better accuracy. We argue that such a procedure is more useful for automated construction of tight-binding models particularly for large-scale materials calculations.