Localization of Wannier functions for entangled energy bands

A new method for the localization of crystalline orbitals for entangled energy bands is proposed. It is an extension of the Wannier-Boys algorithm [C. M. Zicovich-Wilson, R. Dovesi, and V. R. Saunders, J. Chem. Phys. 115, 9708 (2001)] which is particularly well-suited for linear combination of atomic orbital representations of the Bloch waves. It allows the inclusion of additional bands during the optimization of the unitary hybridization matrix used in the multi-band Wannier transformation. By a projection technique, the proper chemical character is extracted from the Bloch waves and compact localized orbitals are obtained even for entangled bands. The performance of the new projective Wannier-Boys localization is demonstrated on the low-lying unoccupied bands of trans-polyacetylene, diamond and silicon.