-------------------------------------------------------------------- NaCl Pm-3m (a = 4.0 bohr) — 48 operations -------------------------------------------------------------------- First three rotations (fractional basis): op 0: [[1, 0, 0], [0, 1, 0], [0, 0, 1]] op 1: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]] op 2: [[0, -1, 0], [1, 0, 0], [0, 0, 1]] -------------------------------------------------------------------- SYM2c — overlap LatticeMatrixSet (515 cells, 18 AOs) -------------------------------------------------------------------- n_triples = 2060 (cells × atom-pairs) n_orbits = 108 compression = 19.07× orbit sizes = min 1, max 48, mean 19.1 max block error = 4.441e-16 (S = reconstruct(compress(S)) to machine precision) -------------------------------------------------------------------- SYM2b — single-atom Mg primitive cubic (origin-fixed path) -------------------------------------------------------------------- n_cells = 515 n_orbits = 27 compression = 19.07× max block error = 4.441e-16 (SYM2b's compression equals SYM2c on this cell because the single-atom primitive has only the trivial atom-pair.) -------------------------------------------------------------------- SYM1 — real-basis Wigner-D at l=2, 90°-about-z rotation -------------------------------------------------------------------- Cartesian rotation matrix: [+0.00 -1.00 +0.00] [+1.00 +0.00 +0.00] [+0.00 +0.00 +1.00] D (real d-basis, rows/cols in order d_{-2}, d_{-1}, d_0, d_{+1}, d_{+2}): [-1.0000 +0.0000 +0.0000 +0.0000 +0.0000] [+0.0000 +0.0000 +0.0000 +1.0000 +0.0000] [+0.0000 +0.0000 +1.0000 +0.0000 +0.0000] [+0.0000 -1.0000 +0.0000 +0.0000 +0.0000] [-0.0000 +0.0000 +0.0000 +0.0000 -1.0000] orthogonality ‖D Dᵀ − I‖_∞ = 4.441e-16