Assessing the role of interatomic position matrix elements in tight-binding calculations of optical properties

We study the role of hopping matrix elements of the position operator \hat{r} r ̂ in tight-binding calculations of linear and nonlinear optical properties of solids. Our analysis relies on a Wannier-interpolation scheme based on calculations, which automatically includes matrix elements of \hat{r} r ̂ between different Wannier orbitals. A common approximation, both in empirical tight-binding and in Wannier-interpolation calculations, is to discard those matrix elements, in which case the optical response only depends on the on-site energies, Hamiltonian hoppings, and orbital centers. We find that interatomic \hat{r} r ̂ -hopping terms make a sizeable contribution to the shift photocurrent in monolayer BC _2 2 N, a covalent acentric crystal. If a minimal basis of p_z p z orbitals on the carbon atoms is used to model the band-edge response, even the dielectric function becomes strongly dependent on those terms.