Choosing Tight-Binding Models for Accurate Optoelectronic Responses

Tight-binding models provide great insight and are a low-cost alternative to \emph{ab initio} methods for calculation of a material's electronic structure. These models are used to calculate optical responses, including nonlinear optical effects such as the shift current bulk photovoltaic effect. The validity of tight-binding models is often evaluated by comparing their band structures to those calculated with Density Functional Theory. However, we find that band structure agreement is a necessary but not sufficient condition for accurate optical response calculations. In this Letter, we compute the shift current response and dielectric tensor using a variety of tight-binding models of {MoS$_2$}, including both Slater-Koster and Wannier tight-binding models that treat the Mo $4d$ orbitals and/or S $3p$ orbitals. We also truncate hoppings in the Wannier function models to next-nearest neighbor, as is common in tight-binding methods, in order to gauge the effect on optical response. By examining discrepancies in energies and optical matrix elements, we determine the interpolation quality of the different tight-binding models and establish that agreement in both band structure and wavefunctions is required to accurately model optical response,