Fully Automated Wannier Disentanglement via Projectability Selection in Gaussian and Augmented Plane-Wave Frameworks

Abstract

Constructing the frozen manifold for entangled bands requires balancing exact reproduction of the target bands with sufficient variational freedom to build a well-localized subspace from the broader Bloch pool. We present a workflow that systematically determines the energy ceiling for a target number of selected Wannier projections, freezing every Bloch state below this threshold across the sampled k-mesh. By measuring projectability, the spectral weight of each Bloch state projected onto the target localized basis, the workflow detects missing conduction channels and quantifies discrepancies between orbital character and energy-based freezing. In comparisons where we controlled the extent of the energy ceiling, freezing all sub-ceiling states is generally favored over projectability-based frozen states. Of the seven materials we tested, freezing all sub-ceiling states lowers the band error on four from between 11 meV and 1.2 eV to 18 meV or less, and matches the projectability-based choice to within about 2 meV on the remaining three. In each of the four, projectability-based frozen states give the lower spread, showing that spread alone cannot identify the better model. With the frozen states held fixed, the workflow minimizes the gauge-invariant spread, constructs the gauge from density-matrix columns on atomic orbitals, and passes an isolated set of bands to Wannier90 for localization. The workflow is implemented in two programs for seamless high-throughput Wannierization with WIEN2k (wien2wannier) and CRYSTAL (LCAO2Wannier). Using a single set of calibrated defaults, the CRYSTAL implementation with analytic overlaps produces models that reproduce the reference bands of five cells, from bulk h-BN in a joint valence-and-conduction model to a magnetic framework with 1424 orbitals. The WIEN2k implementation produces eight such models from seven calculations.