Lowdin-Mattheis transformation to obtain orthonormal wave functions

A Lowdin-Mattheiss transformation is done in order to obtain orthonormal and localized basis sets.
Then the Hamiltonian can be written in terms of these new basis functions, and serve as input to tight-binding models.
It can be compared with a Wannierization, but we keep the symmetry of the localized basis sets (at the expenses of the maximum localization).
It is based on the information given by J. Íñiguez and T. Yildirim, cond-mat/0407677