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Best Localized Symmetry-Adapted Wannier Functions of the Diamond Structure

✍ Scribed by H. Teichler

Publisher: John Wiley and Sons
Year: 1971
Tongue: English
Weight: 630 KB
Volume: 43
Category: Article
ISSN: 0370-1972
DOI: 10.1002/pssb.2220430132

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✦ Synopsis

Abstract

By application of proper unitary matrices the four Bloch functions of each bandgroup with equal wave vector k are transformed into modified Bloch functions in such a way that the resulting four sets of Wannier functions are adapted to the tetrahedral symmetry of the lattice. The Wannier functions behave like the “equivalent MO's” of the tight‐binding approximation (but with vanishing non‐orthogonality integrals). Furthermore, we give explicitely those phases of the Bloch functions that lead to best localized Wannier functions. Values of energy matrix elements between these functions are determined for Ge and Si.

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The electronic structure of the cubic perovskites SrTiO 3 , BaTiO 3 and PbTiO 3 is calculated by Hartree -Fock and density functional theory methods. Wannier-type atomic orbitals (WTAOs) are obtained from symmetrized combinations of Bloch states of some occupied and vacant bands by a variational met