  Maximally localized Wannier functions are widely used in electronic structure
theory for analyses of bonding, electric polarization, orbital magnetization,
and for interpolation. The state of the art method for their construction is
based on the method of Marzari and Vanderbilt. One of the practical
difficulties of this method is guessing functions (initial projections) that
approximate the final Wannier functions. Here we present an approach based on
optimized projection functions that can construct maximally localized Wannier
functions without a guess. We describe and demonstrate this approach on several
realistic examples.
