Optimization of Ab-Initio Based Tight-Binding Models

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.