Well localized crystalline orbitals obtained from Bloch functions: The case of KNbO 3

The crystalline orbitals of KNbO3 are localized according to an iterative mixed Wannier-Boys scheme. The transformed orbitals turn out to be extremely localized; their features and degree of localization are described in terms of various indices. The spontaneous polarization and the effective Born charges of the various atoms are evaluated starting from the localized Wannier function ~LWF! centroids and from delocalized Bloch functions through the Berry phase ~BP! scheme. It turns out that the results provided by both approaches agree very well ~for example, the spontaneous polarization is 0.3361 and 0.3347 C/m from the LWF and BP methods, respectively!.