Localization in an occupied-subspace-optimization approach to electronic structure: application to yttria-stabilized zirconia

The constraint of localization on Wannier orbitals is the central approximation in many linear scaling methods. We investigate the effects of localization constraints on non-orthogonal Wannier-like orbitals (resulting from an occupied-subspace-optimization in our Gaussian representation) in determining the accuracy of forces acting on the atoms, the relaxed geometries and the relative energies to determine the formation enthalpies of defects. We use yttria-stabilized zirconia as a testing system because it has been thoroughly studied and can serve as reference for comparison. A minimum of 5.0 Bohr for the localization range is required to determine reasonably accurate forces and a relaxed atomic configuration. We comment on the versatility of using localization constraints with optimization approaches and compare the computational effort to diagonalization.