k-CIAH enables efficient second-order optimization of Pipek-Mezey Wannier functions with O(N_k² n³) scaling, yielding 2-3x speedup over first-order k-space methods.
(37) Throughout this section, − kkk is understood as − kkk mod GGG for an appropriate reciprocal lattice vector GGG that maps − kkk back into the first Brillouin zone
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Fast Generation of Pipek-Mezey Wannier Functions via the Co-Iterative Augmented Hessian Method
k-CIAH enables efficient second-order optimization of Pipek-Mezey Wannier functions with O(N_k² n³) scaling, yielding 2-3x speedup over first-order k-space methods.