Localized non-orthogonal orbitals in silicon

A comparison of orthogonal and non-orthogonal localized wavefunctions for S i in the diamond structure is carried out. We have used a real-space grid f ormulation of density functional theory in combination with the local densi ty approximation for exchange and correlation to describe the energetics. M aximally localized wavefunctions, obtained from the extended Kohn-Sham stat es with and without an orthogonality constraint, are calculated and it is f ound that the wavefunctions calculated without any orthogonality constraint are the most localized. When solving directly for localized states, by app lying a localization constraint to each electronic state, we find that ther e is a large difference between orthogonal and non-orthogonal states: when the localization region is a sphere with a radius of 3.0 Angstrom, we get a n error in the total energy due to the localization constraint of 0.2 and 2 .7 eV/atom for non-orthogonal and orthogonal wavefunctions respectively.