  We study the role of hopping matrix elements of the position operator
$\mathbf{\hat{r}}$ in tight-binding calculations of linear and nonlinear
optical properties of solids. Our analysis relies on a Wannier-interpolation
scheme based on \textit{ab initio} calculations, which automatically includes
matrix elements of $\mathbf{\hat{r}}$ 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
$\mathbf{\hat{r}}$-hopping terms make a sizeable contribution to the shift
photocurrent in monolayer BC$_2$N, a covalent acentric crystal. If a minimal
basis of $p_z$ orbitals on the carbon atoms is used to model the band-edge
response, even the dielectric function becomes strongly dependent on those
terms.
