Data for "A Scalable Translationally Invariant Variational Theory of Ab Initio Polarons"

Polaron extent — atomic displacement fields Each polaron_extent_<N>.npy and polaron_extent_<N>_<NK-1>_<PATH>.npy stores the real part of the lattice-distortion eigenvector of an ab initio self-trapped polaron, on an N × N × N Born–von Karman supercell of the primitive cell. Each extent corresponds to a crystal momentum of K=0, unless NK is specified. If NK is provided, the extent is evaluated from a dD2 state at crystal momentum K=(NK/N, NK/N, NK/N) for PATH=lg, and K=(NK/N, 0, NK/N) for PATH=gx. Files File System N K Shape Atoms / cell Band channels lif_hole_extent_121.npy LiF hole 121 0 (6, 3, 1 771 561) 2 (Li, F) 3 (F-2p, degenerate) lif_elec_extent_121.npy LiF electron 121 0 (6, 1, 1 771 561) 2 (Li, F) 1 lif_elec_extent_121_30_gx.npy LiF electron (dD2) 121 (31/121, 0, 31/121) (6, 1, 1 771 561) 2 (Li, F) 1 lif_elec_extent_121_30_lg.npy LiF electron (dD2) 121 (31/121, 31/121, 31/121) (6, 1, 1 771 561) 2 (Li, F) 1 rutile_extent_69.npy Rutile TiO₂ electron 69 0 (18, 10, 328 509) 6 (2 Ti + 4 O) 10 (Ti-3d) anatase_extent_57.npy Anatase TiO₂ electron 57 0 (18, 10, 185 193) 6 (2 Ti + 4 O) 10 dtype float64. Arrays are not pre-centered. Indexing — shape (3·N_at, N_b, N³) Axis 0: cartesian × atom-in-primitive-cell, packed as (atom 0: x,y,z; atom 1: x,y,z; …). Axis 1: polaron band channels; sum to get the total density-displacement correlation. Axis 2: unit cell in the supercell, FFT-linear order lin = ix·N² + iy·N + iz. Reshape to (…, N, N, N) and roll each spatial axis by -N/2 to center the polaron. Use Loaded and rendered in selected_four_panel_row.ipynb via center_extent and build_supercell_data / vectors6Nk_to_supercell_vectors. Values are the upstream solver's eigenvector amplitudes — the absolute scale is not physically normalized; the notebooks apply per-system display scaling for visualization only.