  The linear combination of atomic orbitals (LCAO) is a standard method for
studying solids and molecules, it is also known as the tight$-$binding (TB)
method. In most of the implementations only the basis set and the coupling
constants are provided, without the explicit definition of kinetic and
potential energy operators. The tight$-$binding scheme is, nonetheless, capable
of providing an accurate description of properties such as the electronic bands
and elastic constants for many materials. However, for some applications, the
knowledge of the underlying electronic potential associated with the
tight$-$binding hamiltonian might be important to guarantee that the actual
physics is preserved by the semiempirical scheme. In this work the electronic
potentials that arise from the use of tight$-$binding effective hamiltonians it
is explored. The formalism is applied to the extended H\"{u}ckel
tight$-$binding (EHTB) hamiltonian, which is a two$-$center Slater$-$Koster
approach that makes explicit use of the overlap matrix.
