(1)] gives Σ kkk = ˜Σ kkk − ˜Σ † kkk, ˜Σ kkkmn = − 2p∑ TTT A Qp− 1 TTT A,000n ∑ kkk′ ( PTTT A,kkkkkk′vkkk′ ) mn (19)

Connected symmetric term Σ X kkkmn = − p ∑ TTT A,i Qp− 1 TTT A,000iℜ   ∂ U † kkk ∂ Xkkkmn PTTT A,kkkkkk′ ∑ kkk′pq ( ∂ Ukkk′ ∂ Xkkk′pq vX kkk′pq + ∂ Ukkk′ ∂ Ykkk′pq vY kkk′pq ) 

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Fast Generation of Pipek-Mezey Wannier Functions via the Co-Iterative Augmented Hessian Method

physics.chem-ph · 2026-02-12 · unverdicted · novelty 7.0

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.

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Fast Generation of Pipek-Mezey Wannier Functions via the Co-Iterative Augmented Hessian Method physics.chem-ph · 2026-02-12 · unverdicted · none · ref 25
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.

(1)] gives Σ kkk = ˜Σ kkk − ˜Σ † kkk, ˜Σ kkkmn = − 2p∑ TTT A Qp− 1 TTT A,000n ∑ kkk′ ( PTTT A,kkkkkk′vkkk′ ) mn (19)

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