GPAW plane-wave Si
Unfold pristine GPAW pseudo plane-wave coefficients by reciprocal cosets with the backend-free plane-wave engine. The 8-atom conventional cubic Si supercell is sampled on the exact 305-point primitive fcc path recorded in the fixture restart and compared with independently computed primitive-cell plane-wave bands. This does not reconstruct PAW all-electron weights.
The Si:P plane-wave restart is Γ-only: it provides one supercell momentum, not a sampled band path. Its sparse doped output is suppressed. The sparse restart remains in the repository’s test fixtures; the public bundle and this page present the adequately sampled pristine path only. This does not affect the GPAW LCAO Si:P example, whose supercell uses an 8×8×8 k-grid.
Run parameters and shared options (mode, spin, resolve_degenerate, method, supercell-matrix row convention, k-path coordinates, and energy references) are explained in the method and k-path guide.
Configuration
The bundle config supplies the exact kpoints, xcoords, xticks, and names generated for the GPAW plane-wave fixture. The PW route requires exact matching to the stored supercell k-point grid; special_points and npts do not reproduce this per-segment grid. It writes a separate CLI figure (gpaw_si_pw_cli.png); the Python reproducer writes gpaw_si_pw_unfolded.png with the primitive-cell reference overlay.
# Generate data/si8_pw.gpw with `python generate_restart.py` first.
# A GPAW PW restart must contain these mapped supercell k-points.
route = "gpaw"
[input]
supercell = "data/si8_pw.gpw"
[structure]
supercell_matrix = [[-1, 1, 1], [1, -1, 1], [1, 1, -1]]
[path]
kpoints = [
[0, 0, 0],
[0.0076923076923076927, 0, 0.0076923076923076927],
[0.015384615384615385, 0, 0.015384615384615385],
[0.023076923076923078, 0, 0.023076923076923078],
[0.030769230769230771, 0, 0.030769230769230771],
[0.038461538461538464, 0, 0.038461538461538464],
[0.046153846153846156, 0, 0.046153846153846156],
[0.053846153846153849, 0, 0.053846153846153849],
[0.061538461538461542, 0, 0.061538461538461542],
[0.069230769230769235, 0, 0.069230769230769235],
[0.076923076923076927, 0, 0.076923076923076927],
[0.08461538461538462, 0, 0.08461538461538462],
[0.092307692307692313, 0, 0.092307692307692313],
[0.10000000000000001, 0, 0.10000000000000001],
[0.1076923076923077, 0, 0.1076923076923077],
[0.11538461538461539, 0, 0.11538461538461539],
[0.12307692307692308, 0, 0.12307692307692308],
[0.13076923076923078, 0, 0.13076923076923078],
[0.13846153846153847, 0, 0.13846153846153847],
[0.14615384615384616, 0, 0.14615384615384616],
[0.15384615384615385, 0, 0.15384615384615385],
[0.16153846153846155, 0, 0.16153846153846155],
[0.16923076923076924, 0, 0.16923076923076924],
[0.17692307692307693, 0, 0.17692307692307693],
[0.18461538461538463, 0, 0.18461538461538463],
[0.19230769230769232, 0, 0.19230769230769232],
[0.20000000000000001, 0, 0.20000000000000001],
[0.2076923076923077, 0, 0.2076923076923077],
[0.2153846153846154, 0, 0.2153846153846154],
[0.22307692307692309, 0, 0.22307692307692309],
[0.23076923076923078, 0, 0.23076923076923078],
[0.23846153846153847, 0, 0.23846153846153847],
[0.24615384615384617, 0, 0.24615384615384617],
[0.25384615384615383, 0, 0.25384615384615383],
[0.26153846153846155, 0, 0.26153846153846155],
[0.26923076923076927, 0, 0.26923076923076927],
[0.27692307692307694, 0, 0.27692307692307694],
[0.2846153846153846, 0, 0.2846153846153846],
[0.29230769230769232, 0, 0.29230769230769232],
[0.30000000000000004, 0, 0.30000000000000004],
[0.30769230769230771, 0, 0.30769230769230771],
[0.31538461538461537, 0, 0.31538461538461537],
[0.32307692307692309, 0, 0.32307692307692309],
[0.33076923076923082, 0, 0.33076923076923082],
[0.33846153846153848, 0, 0.33846153846153848],
[0.34615384615384615, 0, 0.34615384615384615],
[0.35384615384615387, 0, 0.35384615384615387],
[0.36153846153846159, 0, 0.36153846153846159],
[0.36923076923076925, 0, 0.36923076923076925],
[0.37692307692307692, 0, 0.37692307692307692],
[0.38461538461538464, 0, 0.38461538461538464],
[0.39230769230769236, 0, 0.39230769230769236],
[0.40000000000000002, 0, 0.40000000000000002],
[0.40769230769230769, 0, 0.40769230769230769],
[0.41538461538461541, 0, 0.41538461538461541],
[0.42307692307692313, 0, 0.42307692307692313],
[0.43076923076923079, 0, 0.43076923076923079],
[0.43846153846153846, 0, 0.43846153846153846],
[0.44615384615384618, 0, 0.44615384615384618],
[0.4538461538461539, 0, 0.4538461538461539],
[0.46153846153846156, 0, 0.46153846153846156],
[0.46923076923076923, 0, 0.46923076923076923],
[0.47692307692307695, 0, 0.47692307692307695],
[0.48461538461538467, 0, 0.48461538461538467],
[0.49230769230769234, 0, 0.49230769230769234],
[0.5, 0, 0.5],
[0.5, 0.007575757575757576, 0.50757575757575757],
[0.5, 0.015151515151515152, 0.51515151515151514],
[0.5, 0.022727272727272728, 0.52272727272727271],
[0.5, 0.030303030303030304, 0.53030303030303028],
[0.5, 0.03787878787878788, 0.53787878787878785],
[0.5, 0.045454545454545456, 0.54545454545454541],
[0.5, 0.053030303030303032, 0.55303030303030298],
[0.5, 0.060606060606060608, 0.56060606060606055],
[0.5, 0.068181818181818177, 0.56818181818181812],
[0.5, 0.07575757575757576, 0.5757575757575758],
[0.5, 0.083333333333333343, 0.58333333333333337],
[0.5, 0.090909090909090912, 0.59090909090909094],
[0.5, 0.098484848484848481, 0.59848484848484851],
[0.5, 0.10606060606060606, 0.60606060606060608],
[0.5, 0.11363636363636365, 0.61363636363636365],
[0.5, 0.12121212121212122, 0.62121212121212122],
[0.5, 0.12878787878787878, 0.62878787878787878],
[0.5, 0.13636363636363635, 0.63636363636363635],
[0.5, 0.14393939393939395, 0.64393939393939392],
[0.5, 0.15151515151515152, 0.65151515151515149],
[0.5, 0.15909090909090909, 0.65909090909090906],
[0.5, 0.16666666666666669, 0.66666666666666674],
[0.5, 0.17424242424242425, 0.67424242424242431],
[0.5, 0.18181818181818182, 0.68181818181818188],
[0.5, 0.18939393939393939, 0.68939393939393945],
[0.5, 0.19696969696969696, 0.69696969696969702],
[0.5, 0.20454545454545456, 0.70454545454545459],
[0.5, 0.21212121212121213, 0.71212121212121215],
[0.5, 0.2196969696969697, 0.71969696969696972],
[0.5, 0.22727272727272729, 0.72727272727272729],
[0.5, 0.23484848484848486, 0.73484848484848486],
[0.5, 0.24242424242424243, 0.74242424242424243],
[0.5, 0.25, 0.75],
[0.49305555555555558, 0.24652777777777779, 0.73958333333333337],
[0.4861111111111111, 0.24305555555555555, 0.72916666666666663],
[0.47916666666666669, 0.23958333333333334, 0.71875],
[0.47222222222222221, 0.2361111111111111, 0.70833333333333337],
[0.46527777777777779, 0.2326388888888889, 0.69791666666666663],
[0.45833333333333331, 0.22916666666666666, 0.6875],
[0.4513888888888889, 0.22569444444444445, 0.67708333333333337],
[0.44444444444444442, 0.22222222222222221, 0.66666666666666663],
[0.4375, 0.21875, 0.65625],
[0.43055555555555558, 0.21527777777777779, 0.64583333333333337],
[0.4236111111111111, 0.21180555555555555, 0.63541666666666674],
[0.41666666666666669, 0.20833333333333334, 0.625],
[0.40972222222222221, 0.2048611111111111, 0.61458333333333337],
[0.40277777777777779, 0.2013888888888889, 0.60416666666666674],
[0.39583333333333337, 0.19791666666666669, 0.59375],
[0.3888888888888889, 0.19444444444444445, 0.58333333333333337],
[0.38194444444444442, 0.19097222222222221, 0.57291666666666674],
[0.375, 0.1875, 0.5625],
[0.36805555555555558, 0.18402777777777779, 0.55208333333333326],
[0.3611111111111111, 0.18055555555555555, 0.54166666666666663],
[0.35416666666666669, 0.17708333333333334, 0.53125],
[0.34722222222222221, 0.1736111111111111, 0.52083333333333337],
[0.34027777777777779, 0.1701388888888889, 0.51041666666666674],
[0.33333333333333337, 0.16666666666666669, 0.5],
[0.3263888888888889, 0.16319444444444445, 0.48958333333333337],
[0.31944444444444442, 0.15972222222222221, 0.47916666666666669],
[0.3125, 0.15625, 0.46875],
[0.30555555555555558, 0.15277777777777779, 0.45833333333333337],
[0.29861111111111116, 0.14930555555555558, 0.44791666666666669],
[0.29166666666666669, 0.14583333333333334, 0.4375],
[0.28472222222222221, 0.1423611111111111, 0.42708333333333337],
[0.27777777777777779, 0.1388888888888889, 0.41666666666666669],
[0.27083333333333337, 0.13541666666666669, 0.40625],
[0.2638888888888889, 0.13194444444444445, 0.39583333333333337],
[0.25694444444444442, 0.12847222222222221, 0.38541666666666669],
[0.25, 0.125, 0.375],
[0.24305555555555558, 0.12152777777777779, 0.36458333333333337],
[0.2361111111111111, 0.11805555555555555, 0.35416666666666663],
[0.22916666666666669, 0.11458333333333334, 0.34375],
[0.22222222222222221, 0.1111111111111111, 0.33333333333333331],
[0.21527777777777779, 0.1076388888888889, 0.32291666666666669],
[0.20833333333333337, 0.10416666666666669, 0.31250000000000006],
[0.2013888888888889, 0.10069444444444445, 0.30208333333333337],
[0.19444444444444448, 0.097222222222222238, 0.29166666666666674],
[0.1875, 0.09375, 0.28125],
[0.18055555555555558, 0.09027777777777779, 0.27083333333333337],
[0.1736111111111111, 0.086805555555555552, 0.26041666666666663],
[0.16666666666666669, 0.083333333333333343, 0.25],
[0.15972222222222227, 0.079861111111111133, 0.23958333333333337],
[0.15277777777777779, 0.076388888888888895, 0.22916666666666674],
[0.14583333333333337, 0.072916666666666685, 0.21875],
[0.1388888888888889, 0.069444444444444448, 0.20833333333333337],
[0.13194444444444448, 0.065972222222222238, 0.19791666666666674],
[0.125, 0.0625, 0.1875],
[0.11805555555555558, 0.05902777777777779, 0.17708333333333337],
[0.11111111111111116, 0.05555555555555558, 0.16666666666666674],
[0.10416666666666669, 0.052083333333333343, 0.15625],
[0.097222222222222265, 0.048611111111111133, 0.14583333333333337],
[0.09027777777777779, 0.045138888888888895, 0.13541666666666674],
[0.08333333333333337, 0.041666666666666685, 0.125],
[0.076388888888888895, 0.038194444444444448, 0.11458333333333337],
[0.069444444444444475, 0.034722222222222238, 0.10416666666666674],
[0.0625, 0.03125, 0.09375],
[0.05555555555555558, 0.02777777777777779, 0.08333333333333337],
[0.04861111111111116, 0.02430555555555558, 0.072916666666666741],
[0.041666666666666685, 0.020833333333333343, 0.0625],
[0.034722222222222265, 0.017361111111111133, 0.05208333333333337],
[0.02777777777777779, 0.013888888888888895, 0.041666666666666741],
[0.02083333333333337, 0.010416666666666685, 0.03125],
[0.013888888888888895, 0.0069444444444444475, 0.02083333333333337],
[0.0069444444444444753, 0.0034722222222222376, 0.010416666666666741],
[0, 0, 0],
[0.0089285714285714281, 0.0089285714285714281, 0.0089285714285714281],
[0.017857142857142856, 0.017857142857142856, 0.017857142857142856],
[0.026785714285714284, 0.026785714285714284, 0.026785714285714284],
[0.035714285714285712, 0.035714285714285712, 0.035714285714285712],
[0.044642857142857137, 0.044642857142857137, 0.044642857142857137],
[0.053571428571428568, 0.053571428571428568, 0.053571428571428568],
[0.0625, 0.0625, 0.0625],
[0.071428571428571425, 0.071428571428571425, 0.071428571428571425],
[0.080357142857142849, 0.080357142857142849, 0.080357142857142849],
[0.089285714285714274, 0.089285714285714274, 0.089285714285714274],
[0.098214285714285712, 0.098214285714285712, 0.098214285714285712],
[0.10714285714285714, 0.10714285714285714, 0.10714285714285714],
[0.11607142857142856, 0.11607142857142856, 0.11607142857142856],
[0.125, 0.125, 0.125],
[0.13392857142857142, 0.13392857142857142, 0.13392857142857142],
[0.14285714285714285, 0.14285714285714285, 0.14285714285714285],
[0.15178571428571427, 0.15178571428571427, 0.15178571428571427],
[0.1607142857142857, 0.1607142857142857, 0.1607142857142857],
[0.16964285714285712, 0.16964285714285712, 0.16964285714285712],
[0.17857142857142855, 0.17857142857142855, 0.17857142857142855],
[0.1875, 0.1875, 0.1875],
[0.19642857142857142, 0.19642857142857142, 0.19642857142857142],
[0.20535714285714285, 0.20535714285714285, 0.20535714285714285],
[0.21428571428571427, 0.21428571428571427, 0.21428571428571427],
[0.2232142857142857, 0.2232142857142857, 0.2232142857142857],
[0.23214285714285712, 0.23214285714285712, 0.23214285714285712],
[0.24107142857142855, 0.24107142857142855, 0.24107142857142855],
[0.25, 0.25, 0.25],
[0.2589285714285714, 0.2589285714285714, 0.2589285714285714],
[0.26785714285714285, 0.26785714285714285, 0.26785714285714285],
[0.27678571428571425, 0.27678571428571425, 0.27678571428571425],
[0.2857142857142857, 0.2857142857142857, 0.2857142857142857],
[0.29464285714285715, 0.29464285714285715, 0.29464285714285715],
[0.30357142857142855, 0.30357142857142855, 0.30357142857142855],
[0.3125, 0.3125, 0.3125],
[0.3214285714285714, 0.3214285714285714, 0.3214285714285714],
[0.33035714285714285, 0.33035714285714285, 0.33035714285714285],
[0.33928571428571425, 0.33928571428571425, 0.33928571428571425],
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[0.3571428571428571, 0.3571428571428571, 0.3571428571428571],
[0.36607142857142855, 0.36607142857142855, 0.36607142857142855],
[0.375, 0.375, 0.375],
[0.3839285714285714, 0.3839285714285714, 0.3839285714285714],
[0.39285714285714285, 0.39285714285714285, 0.39285714285714285],
[0.40178571428571425, 0.40178571428571425, 0.40178571428571425],
[0.4107142857142857, 0.4107142857142857, 0.4107142857142857],
[0.4196428571428571, 0.4196428571428571, 0.4196428571428571],
[0.42857142857142855, 0.42857142857142855, 0.42857142857142855],
[0.4375, 0.4375, 0.4375],
[0.4464285714285714, 0.4464285714285714, 0.4464285714285714],
[0.45535714285714285, 0.45535714285714285, 0.45535714285714285],
[0.46428571428571425, 0.46428571428571425, 0.46428571428571425],
[0.4732142857142857, 0.4732142857142857, 0.4732142857142857],
[0.4821428571428571, 0.4821428571428571, 0.4821428571428571],
[0.49107142857142855, 0.49107142857142855, 0.49107142857142855],
[0.5, 0.5, 0.5],
[0.5, 0.49456521739130432, 0.50543478260869568],
[0.5, 0.4891304347826087, 0.51086956521739135],
[0.5, 0.48369565217391303, 0.51630434782608692],
[0.5, 0.47826086956521741, 0.52173913043478259],
[0.5, 0.47282608695652173, 0.52717391304347827],
[0.5, 0.46739130434782611, 0.53260869565217395],
[0.5, 0.46195652173913043, 0.53804347826086962],
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[0.5, 0.45108695652173914, 0.54891304347826086],
[0.5, 0.44565217391304346, 0.55434782608695654],
[0.5, 0.44021739130434784, 0.55978260869565222],
[0.5, 0.43478260869565216, 0.56521739130434778],
[0.5, 0.42934782608695654, 0.57065217391304346],
[0.5, 0.42391304347826086, 0.57608695652173914],
[0.5, 0.41847826086956519, 0.58152173913043481],
[0.5, 0.41304347826086957, 0.58695652173913038],
[0.5, 0.40760869565217395, 0.59239130434782605],
[0.5, 0.40217391304347827, 0.59782608695652173],
[0.5, 0.39673913043478259, 0.60326086956521741],
[0.5, 0.39130434782608697, 0.60869565217391308],
[0.5, 0.3858695652173913, 0.61413043478260865],
[0.5, 0.38043478260869568, 0.61956521739130432],
[0.5, 0.375, 0.625],
[0.5, 0.36956521739130432, 0.63043478260869568],
[0.5, 0.3641304347826087, 0.63586956521739135],
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[0.5, 0.35326086956521741, 0.64673913043478259],
[0.5, 0.34782608695652173, 0.65217391304347827],
[0.5, 0.34239130434782605, 0.65760869565217395],
[0.5, 0.33695652173913043, 0.66304347826086962],
[0.5, 0.33152173913043481, 0.66847826086956519],
[0.5, 0.32608695652173914, 0.67391304347826086],
[0.5, 0.32065217391304346, 0.67934782608695654],
[0.5, 0.31521739130434784, 0.68478260869565211],
[0.5, 0.30978260869565222, 0.69021739130434778],
[0.5, 0.30434782608695654, 0.69565217391304346],
[0.5, 0.29891304347826086, 0.70108695652173914],
[0.5, 0.29347826086956519, 0.70652173913043481],
[0.5, 0.28804347826086957, 0.71195652173913038],
[0.5, 0.28260869565217395, 0.71739130434782605],
[0.5, 0.27717391304347827, 0.72282608695652173],
[0.5, 0.27173913043478259, 0.72826086956521741],
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names = ["$\\Gamma$", "X", "W", "$\\Gamma$", "L", "W", "X"]
[options]
mode = "pw"
resolve_degenerate = 0.001
[output]
output = "gpaw_si_pw_cli.png"Download and unpack the GPAW plane-wave Si bundle. The 290 MB si8_pw.gpw restart is not included; generate it from this bundle with python generate_restart.py. This runs the pristine GPAW PW calculation on the exact 305-point path.
python generate_restart.py
python reproduce.py
unfolding --config unfold.toml
Structure and sampling
- Primitive cell: 2-atom fcc Si, lattice constant 5.43 Å.
- Supercell: 8-atom conventional cubic cell with
M = [[-1, 1, 1], [1, -1, 1], [1, 1, -1]]andA_sc = M @ A_prim. - Path: Γ–X–W–Γ–L–W–X, 305 fixture-generated points in primitive reciprocal fractional coordinates. The config lists the exact path so the mapped supercell momenta match the stored PW restart.
- Run: PBE, 340 eV plane-wave cutoff, 24 bands,
symmetry='off', andmode='all'so the restart contains wavefunctions.