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We describe a robust method for determining Pipek-Mezey (PM) Wannierfunctions (WF), recently introduced by J\'onsson et al. (J. Chem. Theor. Chem.2017, 13, 460), which provide some formal advantages over the more common Boys(also known as maximally-localized) Wannier functions. TheBroyden-Fletcher-Goldfarb-Shanno (BFGS) based PMWF solver is demonstrated toyield dramatically faster convergence compared to the alternatives (steepestascent and conjugate gradient) in a variety of 1-, 2-, and 3-dimensional solids(including some with vanishing gaps), and can be used to obtain Wannierfunctions robustly in supercells with thousands of atoms. Evaluation of the PMfunctional and its gradient in periodic LCAO representation used a particularlysimple definition of atomic charges obtained by Moore-Penrose pseudoinverseprojection onto the minimal atomic orbital basis. An automated "CanonicalizePhase then Randomize" (CPR) method for generating the initial guess for WFscontributes significantly to the robustness of the solver.

Robust Pipek-Mezey Orbital Localization in Periodic Solids