  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.
