Abstract
We have investigated the basis dependence of calculated energy eigenvalues of gap states, introduced by ideal vacancies and surfaces, in the tight binding (orbital removal) method by employing a Green’s function analysis. We find that (a) if Wannier functions are employed there are no ideal vacancy or surface gap states; (b) if atomic orbitals are used, no ideal vacancy gap states exist in the limit as the number of orbitals on the atom to be removed approaches infinity, although (c) spurious solutions for finite band models can exist. We find the reason for these results is that the orbital removal method is not equivalent to removing the potential of the removed atom. We show that if the size of the basis set is allowed to increase without limit, the orbital removal method yields the same energy eigenvalues as the Hamiltonian of the unperturbed system. This result is independent of the method used to solve the eigenvalue equation. Finally, employing a Green’s function technique, we show how these states may be calculated within the framework of the orbital removal method by incorporating the change in potential into the matrix elements. However, we note with Pena and Mattis that if the true vacancy state is not orthogonal to the orbitals on the removed atom, then the application of the orbital removal method is not justified.
Published Version
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