Optimally localized Wannier functions within the Vanderbilt ultrasoft pseudo-potential formalism

We generalize the approach proposed by Silvestrelli et al. (Solid State Commun., 107 (1998) 7; Phys. Rev. B, 59 (1999) 9703) for the calculation of the optimally localized Wannier functions (OLWF) in the F-point approximation to the non-norm-conserving ultrasoft pseudo-potential scheme devised by Vanderbilt. The scheme described in this paper can be easily implemented in conventional ab initio band-structure codes whenever a plane-wave basis set is employed, e.g. in density functional theory (DFT) calculations on periodic or disordered systems. In addition, we show how to compute the single-point Berry, phase (SPBP) and hence the polarization in a periodic system adopting the same formalism. We test our procedure by performing DFT calculations of the electronic properties of molecular NH3, which are compared to analogous calculations carried out using norm-conserving pseudo-potentials, and we apply it to the investigation of the interactions responsible for the bonding properties of Be-2 and Mg-2. (C) 2001 Elsevier Science B.V. All rights reserved.