Transition state method and Wannier functions

We propose a computational scheme for materials where standard local density approximation (LDA) fails to produce a satisfactory description of excitation energies. The method uses Slater's ``transition state'' approximation and Wannier functions basis set. We define a correction to LDA functional in such a way that its variation produces one-electron energies for Wannier functions equal to the energies obtained in transition state constrained LDA calculations. In the result eigenvalues of the proposed functional could be interpreted as excitation energies of the system under consideration. The method was applied to MgO, Si, NiO, and $\mathrm{Ba}\mathrm{Bi}{\mathrm{O}}_{3}$ and gave an improved agreement with experimental data of energy gap values comparing with LDA.