General and efficient algorithms for obtaining maximally localized Wannierfunctions

Recent advances in the theory of polarization and the development of linear -scaling methods have revitalized interest in the use of Wannier functions for obtaining a localized orbital picture within a periodic supercell. To e xamine complex chemical systems it is imperative for the localization proce dure to be efficient; on the other hand, the method should also be simple a nd general. Motivated to meet these requirements we derive in this paper a spread functional to be minimized as a starting point for obtaining maximal ly localized Wannier functions through a unitary transformation. The functi onal turn out to be equivalent to others discussed in the literature with t he difference of being valid in simulation supercells of arbitrary symmetry in the Gamma-point approximation. To minimize the spread an iterative sche me is developed and very efficient optimization methods, such as conjugate gradient, direct inversion in the iterative subspace, and preconditioning a re applied to accelerate the convergence. The iterative scheme is quite gen eral and is shown to work also for methods first developed for finite syste ms (e.g., Pipek-Mezey, Boys-Foster). The applications discussed range from crystal structures such as Si to isolated complex molecules and are compare d to previous investigations on this subject.