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

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