Notebooks · lib/basis/pople631gs

The 6-31G* basis set, H through Ar, as a table

Generated by tools/basis_tables.py from the Basis Set Exchange (the basis_set_exchange package 0.12, data version 0 of the set, general contractions optimized). Do not edit; rerun the generator. The generator's docstring says why version 0, how shells are split and in what order they stand, and tools/basis_tables.py --check compares every element with PySCF 2.5.0's copy of the set.

basis_631gs() is the Basis record of lib/basis/basis: one row per segmented shell, (Z, l, nprim, p0) with p0 the row of its first primitive, and one row per primitive, (exponent, coefficient). Elements 1 to 18, 116 shells and 344 primitives, angular momentum up to d.

Used with import basis.pople631gs, and passed to molecule (lib/hf/molecule).

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[1]lines 20–258

from basis.basis import Basis, basis_check, basis_nao, basis_of, basis_rows, BS_NAO_LEN

BASIS_631GS_NSHELL = 116
BASIS_631GS_NPRIM = 344

#| (Z, l, nprim, p0), one segmented shell per row, by element.
def basis_631gs_shells_flat() -> Arr {
    return [1, 0, 3, 0, 1, 0, 1, 3, 2, 0, 3, 4, 2, 0, 1, 7,
        3, 0, 6, 8, 3, 0, 3, 14, 3, 0, 1, 17, 3, 1, 3, 18,
        3, 1, 1, 21, 3, 2, 1, 22, 4, 0, 6, 23, 4, 0, 3, 29,
        4, 0, 1, 32, 4, 1, 3, 33, 4, 1, 1, 36, 4, 2, 1, 37,
        5, 0, 6, 38, 5, 0, 3, 44, 5, 0, 1, 47, 5, 1, 3, 48,
        5, 1, 1, 51, 5, 2, 1, 52, 6, 0, 6, 53, 6, 0, 3, 59,
        6, 0, 1, 62, 6, 1, 3, 63, 6, 1, 1, 66, 6, 2, 1, 67,
        7, 0, 6, 68, 7, 0, 3, 74, 7, 0, 1, 77, 7, 1, 3, 78,
        7, 1, 1, 81, 7, 2, 1, 82, 8, 0, 6, 83, 8, 0, 3, 89,
        8, 0, 1, 92, 8, 1, 3, 93, 8, 1, 1, 96, 8, 2, 1, 97,
        9, 0, 6, 98, 9, 0, 3, 104, 9, 0, 1, 107, 9, 1, 3, 108,
        9, 1, 1, 111, 9, 2, 1, 112, 10, 0, 6, 113, 10, 0, 3, 119,
        10, 0, 1, 122, 10, 1, 3, 123, 10, 1, 1, 126, 10, 2, 1, 127,
        11, 0, 6, 128, 11, 0, 6, 134, 11, 0, 3, 140, 11, 0, 1, 143,
        11, 1, 6, 144, 11, 1, 3, 150, 11, 1, 1, 153, 11, 2, 1, 154,
        12, 0, 6, 155, 12, 0, 6, 161, 12, 0, 3, 167, 12, 0, 1, 170,
        12, 1, 6, 171, 12, 1, 3, 177, 12, 1, 1, 180, 12, 2, 1, 181,
        13, 0, 6, 182, 13, 0, 6, 188, 13, 0, 3, 194, 13, 0, 1, 197,
        13, 1, 6, 198, 13, 1, 3, 204, 13, 1, 1, 207, 13, 2, 1, 208,
        14, 0, 6, 209, 14, 0, 6, 215, 14, 0, 3, 221, 14, 0, 1, 224,
        14, 1, 6, 225, 14, 1, 3, 231, 14, 1, 1, 234, 14, 2, 1, 235,
        15, 0, 6, 236, 15, 0, 6, 242, 15, 0, 3, 248, 15, 0, 1, 251,
        15, 1, 6, 252, 15, 1, 3, 258, 15, 1, 1, 261, 15, 2, 1, 262,
        16, 0, 6, 263, 16, 0, 6, 269, 16, 0, 3, 275, 16, 0, 1, 278,
        16, 1, 6, 279, 16, 1, 3, 285, 16, 1, 1, 288, 16, 2, 1, 289,
        17, 0, 6, 290, 17, 0, 6, 296, 17, 0, 3, 302, 17, 0, 1, 305,
        17, 1, 6, 306, 17, 1, 3, 312, 17, 1, 1, 315, 17, 2, 1, 316,
        18, 0, 6, 317, 18, 0, 6, 323, 18, 0, 3, 329, 18, 0, 1, 332,
        18, 1, 6, 333, 18, 1, 3, 339, 18, 1, 1, 342, 18, 2, 1, 343]
}

#| (exponent, coefficient), one primitive per row.
def basis_631gs_prims_flat() -> Arr {
    return [18.731137, 0.0334946, 2.8253937, 0.23472695,
        0.6401217, 0.81375733, 0.1612778, 1.0,
        38.421634, 0.023766, 5.77803, 0.154679,
        1.241774, 0.46963, 0.297964, 1.0,
        642.41892, 0.0021426, 96.798515, 0.0162089,
        22.091121, 0.0773156, 6.2010703, 0.245786,
        1.9351177, 0.470189, 0.6367358, 0.3454708,
        2.3249184, -0.0350917, 0.6324306, -0.1912328,
        0.0790534, 1.0839878, 0.035962, 1.0,
        2.3249184, 0.0089415, 0.6324306, 0.1410095,
        0.0790534, 0.9453637, 0.035962, 1.0,
        0.2, 1.0, 1264.5857, 0.0019448,
        189.93681, 0.0148351, 43.159089, 0.0720906,
        12.098663, 0.2371542, 3.8063232, 0.4691987,
        1.2728903, 0.3565202, 3.1964631, -0.1126487,
        0.7478133, -0.2295064, 0.2199663, 1.1869167,
        0.0823099, 1.0, 3.1964631, 0.0559802,
        0.7478133, 0.2615506, 0.2199663, 0.7939723,
        0.0823099, 1.0, 0.4, 1.0,
        2068.8823, 0.0018663, 310.64957, 0.0142515,
        70.683033, 0.0695516, 19.86108, 0.2325729,
        6.2993048, 0.4670787, 2.127027, 0.3634314,
        4.727971, -0.1303938, 1.1903377, -0.1307889,
        0.3594117, 1.1309444, 0.1267512, 1.0,
        4.727971, 0.0745976, 1.1903377, 0.3078467,
        0.3594117, 0.7434568, 0.1267512, 1.0,
        0.6, 1.0, 3047.5249, 0.0018347,
        457.36951, 0.0140373, 103.94869, 0.0688426,
        29.210155, 0.2321844, 9.286663, 0.4679413,
        3.163927, 0.362312, 7.8682724, -0.1193324,
        1.8812885, -0.1608542, 0.5442493, 1.1434564,
        0.1687144, 1.0, 7.8682724, 0.0689991,
        1.8812885, 0.316424, 0.5442493, 0.7443083,
        0.1687144, 1.0, 0.8, 1.0,
        4173.511, 0.0018348, 627.4579, 0.013995,
        142.9021, 0.068587, 40.23433, 0.232241,
        12.82021, 0.46907, 4.390437, 0.360455,
        11.626358, -0.114961, 2.71628, -0.169118,
        0.772218, 1.145852, 0.2120313, 1.0,
        11.626358, 0.06758, 2.71628, 0.323907,
        0.772218, 0.740895, 0.2120313, 1.0,
        0.8, 1.0, 5484.6717, 0.0018311,
        825.23495, 0.0139501, 188.04696, 0.0684451,
        52.9645, 0.2327143, 16.89757, 0.470193,
        5.7996353, 0.3585209, 15.539616, -0.1107775,
        3.5999336, -0.1480263, 1.0137618, 1.130767,
        0.2700058, 1.0, 15.539616, 0.0708743,
        3.5999336, 0.3397528, 1.0137618, 0.7271586,
        0.2700058, 1.0, 0.8, 1.0,
        7001.71309, 0.0018196169, 1051.36609, 0.0139160796,
        239.28569, 0.0684053245, 67.3974453, 0.23318576,
        21.5199573, 0.471267439, 7.4031013, 0.356618546,
        20.8479528, -0.108506975, 4.80830834, -0.146451658,
        1.34406986, 1.12868858, 0.358151393, 1.0,
        20.8479528, 0.0716287243, 4.80830834, 0.345912103,
        1.34406986, 0.722469957, 0.358151393, 1.0,
        0.8, 1.0, 8425.85153, 0.0018843481,
        1268.5194, 0.0143368994, 289.621414, 0.0701096233,
        81.859004, 0.237373266, 26.2515079, 0.473007126,
        9.09472051, 0.348401241, 26.532131, -0.107118287,
        6.10175501, -0.146163821, 1.69627153, 1.1277735,
        0.4458187, 1.0, 26.532131, 0.0719095885,
        6.10175501, 0.349513372, 1.69627153, 0.719940512,
        0.4458187, 1.0, 0.8, 1.0,
        9993.2, 0.0019377, 1499.89, 0.014807,
        341.951, 0.072706, 94.6797, 0.252629,
        29.7345, 0.493242, 10.0063, 0.313169,
        150.963, -0.0035421, 35.5878, -0.043959,
        11.1683, -0.1097521, 3.90201, 0.187398,
        1.38177, 0.646699, 0.466382, 0.306058,
        0.497966, -0.248503, 0.084353, -0.131704,
        0.066635, 1.23352, 0.0259544, 1.0,
        150.963, 0.0050017, 35.5878, 0.035511,
        11.1683, 0.142825, 3.90201, 0.33862,
        1.38177, 0.451579, 0.466382, 0.273271,
        0.497966, -0.023023, 0.084353, 0.950359,
        0.066635, 0.059858, 0.0259544, 1.0,
        0.175, 1.0, 11722.8, 0.0019778,
        1759.93, 0.015114, 400.846, 0.073911,
        112.807, 0.249191, 35.9997, 0.487928,
        12.1828, 0.319662, 189.18, -0.0032372,
        45.2119, -0.041008, 14.3563, -0.1126,
        5.13886, 0.148633, 1.90652, 0.616497,
        0.705887, 0.364829, 0.92934, -0.21229,
        0.269035, -0.107985, 0.117379, 1.17584,
        0.0421061, 1.0, 189.18, 0.0049281,
        45.2119, 0.034989, 14.3563, 0.140725,
        5.13886, 0.333642, 1.90652, 0.44494,
        0.705887, 0.269254, 0.92934, -0.022419,
        0.269035, 0.19227, 0.117379, 0.846181,
        0.0421061, 1.0, 0.175, 1.0,
        13983.1, 0.00194267, 2098.75, 0.0148599,
        477.705, 0.0728494, 134.36, 0.24683,
        42.8709, 0.487258, 14.5189, 0.323496,
        239.668, -0.00292619, 57.4419, -0.037408,
        18.2859, -0.114487, 6.59914, 0.115635,
        2.49049, 0.612595, 0.94454, 0.393799,
        1.2779, -0.227606, 0.39759, 0.00144583,
        0.160095, 1.09279, 0.0556577, 1.0,
        239.668, 0.00460285, 57.4419, 0.033199,
        18.2859, 0.136282, 6.59914, 0.330476,
        2.49049, 0.449146, 0.94454, 0.265704,
        1.2779, -0.017513, 0.39759, 0.244533,
        0.160095, 0.804934, 0.0556577, 1.0,
        0.325, 1.0, 16115.9, 0.00195948,
        2425.58, 0.0149288, 553.867, 0.0728478,
        156.34, 0.24613, 50.0683, 0.485914,
        17.0178, 0.325002, 292.718, -0.00278094,
        69.8731, -0.0357146, 22.3363, -0.114985,
        8.15039, 0.0935634, 3.13458, 0.603017,
        1.22543, 0.418959, 1.72738, -0.24463,
        0.572922, 0.00431572, 0.222192, 1.09818,
        0.0778369, 1.0, 292.718, 0.00443826,
        69.8731, 0.0326679, 22.3363, 0.134721,
        8.15039, 0.328678, 3.13458, 0.44964,
        1.22543, 0.261372, 1.72738, -0.0177951,
        0.572922, 0.253539, 0.222192, 0.800669,
        0.0778369, 1.0, 0.45, 1.0,
        19413.3, 0.0018516, 2909.42, 0.0142062,
        661.364, 0.0699995, 185.759, 0.240079,
        59.1943, 0.484762, 20.031, 0.3352,
        339.478, -0.00278217, 81.0101, -0.0360499,
        25.878, -0.116631, 9.45221, 0.0968328,
        3.66566, 0.614418, 1.46746, 0.403798,
        2.15623, -0.252923, 0.748997, 0.0328517,
        0.283145, 1.08125, 0.0998317, 1.0,
        339.478, 0.00456462, 81.0101, 0.0336936,
        25.878, 0.139755, 9.45221, 0.339362,
        3.66566, 0.450921, 1.46746, 0.238586,
        2.15623, -0.0177653, 0.748997, 0.274058,
        0.283145, 0.785421, 0.0998317, 1.0,
        0.55, 1.0, 21917.1, 0.001869,
        3301.49, 0.01423, 754.146, 0.069696,
        212.711, 0.238487, 67.9896, 0.483307,
        23.0515, 0.338074, 423.735, -0.0023767,
        100.71, -0.031693, 32.1599, -0.113317,
        11.8079, 0.05609, 4.6311, 0.592255,
        1.87025, 0.455006, 2.61584, -0.250374,
        0.922167, 0.066957, 0.341287, 1.05451,
        0.117167, 1.0, 423.735, 0.004061,
        100.71, 0.030681, 32.1599, 0.130452,
        11.8079, 0.327205, 4.6311, 0.452851,
        1.87025, 0.256042, 2.61584, -0.014511,
        0.922167, 0.310263, 0.341287, 0.754483,
        0.117167, 1.0, 0.65, 1.0,
        25180.1, 0.001833, 3780.35, 0.014034,
        860.474, 0.069097, 242.145, 0.237452,
        77.3349, 0.483034, 26.247, 0.339856,
        491.765, -0.0022974, 116.984, -0.030714,
        37.4153, -0.112528, 13.7834, 0.045016,
        5.45215, 0.589353, 2.22588, 0.465206,
        3.18649, -0.25183, 1.14427, 0.061589,
        0.420377, 1.06018, 0.142657, 1.0,
        491.765, 0.0039894, 116.984, 0.030318,
        37.4153, 0.12988, 13.7834, 0.327951,
        5.45215, 0.453527, 2.22588, 0.252154,
        3.18649, -0.014299, 1.14427, 0.323572,
        0.420377, 0.743507, 0.142657, 1.0,
        0.75, 1.0, 28348.3, 0.00182526,
        4257.62, 0.0139686, 969.857, 0.0687073,
        273.263, 0.236204, 87.3695, 0.482214,
        29.6867, 0.342043, 575.891, -0.00215972,
        136.816, -0.0290775, 43.8098, -0.110827,
        16.2094, 0.0276999, 6.46084, 0.577613,
        2.65114, 0.488688, 3.86028, -0.255592,
        1.41373, 0.0378066, 0.516646, 1.08056,
        0.173888, 1.0, 575.891, 0.00380665,
        136.816, 0.0292305, 43.8098, 0.126467,
        16.2094, 0.32351, 6.46084, 0.454896,
        2.65114, 0.25663, 3.86028, -0.0159197,
        1.41373, 0.324646, 0.516646, 0.74399,
        0.173888, 1.0, 0.85, 1.0]
}

#| The 6-31G* basis set as a `Basis` record.
def basis_631gs() -> Basis {
    return basis_of(basis_631gs_shells_flat(), basis_631gs_prims_flat())
}

#| The Cartesian and spherical AO counts of one atom of each element, `1` to `18`,
#| as the generator counted them.
def basis_631gs_nao() -> Arr {
    return [2, 2, 2, 2, 15, 14, 15, 14, 15, 14, 15, 14,
        15, 14, 15, 14, 15, 14, 15, 14, 19, 18, 19, 18,
        19, 18, 19, 18, 19, 18, 19, 18, 19, 18, 19, 18]
}

test "the 6-31G* table covers H through Ar, each element's shells in one run" {
    bt631gs_b = basis_631gs()
    assert_near(len(bt631gs_b.shells), BASIS_631GS_NSHELL, 0.0)
    assert_near(len(bt631gs_b.prims), BASIS_631GS_NPRIM, 0.0)
    assert_near(basis_check(bt631gs_b), 0.0, 0.0)
    bt631gs_n = basis_rows(basis_631gs_nao(), BS_NAO_LEN)
    for bt631gs_z to len(bt631gs_n) {
        bt631gs_k = basis_nao(bt631gs_b, bt631gs_z + 1)
        assert_near(bt631gs_k[0], bt631gs_n[bt631gs_z, 0], 0.0)
        assert_near(bt631gs_k[1], bt631gs_n[bt631gs_z, 1], 0.0)
    }
}

from basis.basis import Basis, basis_check, basis_nao, basis_of, basis_rows, BS_NAO_LEN

BASIS_631GS_NSHELL = 116
BASIS_631GS_NPRIM = 344

#| (Z, l, nprim, p0), one segmented shell per row, by element.
def basis_631gs_shells_flat() -> Arr {
    return [1, 0, 3, 0, 1, 0, 1, 3, 2, 0, 3, 4, 2, 0, 1, 7,
        3, 0, 6, 8, 3, 0, 3, 14, 3, 0, 1, 17, 3, 1, 3, 18,
        3, 1, 1, 21, 3, 2, 1, 22, 4, 0, 6, 23, 4, 0, 3, 29,
        4, 0, 1, 32, 4, 1, 3, 33, 4, 1, 1, 36, 4, 2, 1, 37,
        5, 0, 6, 38, 5, 0, 3, 44, 5, 0, 1, 47, 5, 1, 3, 48,
        5, 1, 1, 51, 5, 2, 1, 52, 6, 0, 6, 53, 6, 0, 3, 59,
        6, 0, 1, 62, 6, 1, 3, 63, 6, 1, 1, 66, 6, 2, 1, 67,
        7, 0, 6, 68, 7, 0, 3, 74, 7, 0, 1, 77, 7, 1, 3, 78,
        7, 1, 1, 81, 7, 2, 1, 82, 8, 0, 6, 83, 8, 0, 3, 89,
        8, 0, 1, 92, 8, 1, 3, 93, 8, 1, 1, 96, 8, 2, 1, 97,
        9, 0, 6, 98, 9, 0, 3, 104, 9, 0, 1, 107, 9, 1, 3, 108,
        9, 1, 1, 111, 9, 2, 1, 112, 10, 0, 6, 113, 10, 0, 3, 119,
        10, 0, 1, 122, 10, 1, 3, 123, 10, 1, 1, 126, 10, 2, 1, 127,
        11, 0, 6, 128, 11, 0, 6, 134, 11, 0, 3, 140, 11, 0, 1, 143,
        11, 1, 6, 144, 11, 1, 3, 150, 11, 1, 1, 153, 11, 2, 1, 154,
        12, 0, 6, 155, 12, 0, 6, 161, 12, 0, 3, 167, 12, 0, 1, 170,
        12, 1, 6, 171, 12, 1, 3, 177, 12, 1, 1, 180, 12, 2, 1, 181,
        13, 0, 6, 182, 13, 0, 6, 188, 13, 0, 3, 194, 13, 0, 1, 197,
        13, 1, 6, 198, 13, 1, 3, 204, 13, 1, 1, 207, 13, 2, 1, 208,
        14, 0, 6, 209, 14, 0, 6, 215, 14, 0, 3, 221, 14, 0, 1, 224,
        14, 1, 6, 225, 14, 1, 3, 231, 14, 1, 1, 234, 14, 2, 1, 235,
        15, 0, 6, 236, 15, 0, 6, 242, 15, 0, 3, 248, 15, 0, 1, 251,
        15, 1, 6, 252, 15, 1, 3, 258, 15, 1, 1, 261, 15, 2, 1, 262,
        16, 0, 6, 263, 16, 0, 6, 269, 16, 0, 3, 275, 16, 0, 1, 278,
        16, 1, 6, 279, 16, 1, 3, 285, 16, 1, 1, 288, 16, 2, 1, 289,
        17, 0, 6, 290, 17, 0, 6, 296, 17, 0, 3, 302, 17, 0, 1, 305,
        17, 1, 6, 306, 17, 1, 3, 312, 17, 1, 1, 315, 17, 2, 1, 316,
        18, 0, 6, 317, 18, 0, 6, 323, 18, 0, 3, 329, 18, 0, 1, 332,
        18, 1, 6, 333, 18, 1, 3, 339, 18, 1, 1, 342, 18, 2, 1, 343]
}

#| (exponent, coefficient), one primitive per row.
def basis_631gs_prims_flat() -> Arr {
    return [18.731137, 0.0334946, 2.8253937, 0.23472695,
        0.6401217, 0.81375733, 0.1612778, 1.0,
        38.421634, 0.023766, 5.77803, 0.154679,
        1.241774, 0.46963, 0.297964, 1.0,
        642.41892, 0.0021426, 96.798515, 0.0162089,
        22.091121, 0.0773156, 6.2010703, 0.245786,
        1.9351177, 0.470189, 0.6367358, 0.3454708,
        2.3249184, -0.0350917, 0.6324306, -0.1912328,
        0.0790534, 1.0839878, 0.035962, 1.0,
        2.3249184, 0.0089415, 0.6324306, 0.1410095,
        0.0790534, 0.9453637, 0.035962, 1.0,
        0.2, 1.0, 1264.5857, 0.0019448,
        189.93681, 0.0148351, 43.159089, 0.0720906,
        12.098663, 0.2371542, 3.8063232, 0.4691987,
        1.2728903, 0.3565202, 3.1964631, -0.1126487,
        0.7478133, -0.2295064, 0.2199663, 1.1869167,
        0.0823099, 1.0, 3.1964631, 0.0559802,
        0.7478133, 0.2615506, 0.2199663, 0.7939723,
        0.0823099, 1.0, 0.4, 1.0,
        2068.8823, 0.0018663, 310.64957, 0.0142515,
        70.683033, 0.0695516, 19.86108, 0.2325729,
        6.2993048, 0.4670787, 2.127027, 0.3634314,
        4.727971, -0.1303938, 1.1903377, -0.1307889,
        0.3594117, 1.1309444, 0.1267512, 1.0,
        4.727971, 0.0745976, 1.1903377, 0.3078467,
        0.3594117, 0.7434568, 0.1267512, 1.0,
        0.6, 1.0, 3047.5249, 0.0018347,
        457.36951, 0.0140373, 103.94869, 0.0688426,
        29.210155, 0.2321844, 9.286663, 0.4679413,
        3.163927, 0.362312, 7.8682724, -0.1193324,
        1.8812885, -0.1608542, 0.5442493, 1.1434564,
        0.1687144, 1.0, 7.8682724, 0.0689991,
        1.8812885, 0.316424, 0.5442493, 0.7443083,
        0.1687144, 1.0, 0.8, 1.0,
        4173.511, 0.0018348, 627.4579, 0.013995,
        142.9021, 0.068587, 40.23433, 0.232241,
        12.82021, 0.46907, 4.390437, 0.360455,
        11.626358, -0.114961, 2.71628, -0.169118,
        0.772218, 1.145852, 0.2120313, 1.0,
        11.626358, 0.06758, 2.71628, 0.323907,
        0.772218, 0.740895, 0.2120313, 1.0,
        0.8, 1.0, 5484.6717, 0.0018311,
        825.23495, 0.0139501, 188.04696, 0.0684451,
        52.9645, 0.2327143, 16.89757, 0.470193,
        5.7996353, 0.3585209, 15.539616, -0.1107775,
        3.5999336, -0.1480263, 1.0137618, 1.130767,
        0.2700058, 1.0, 15.539616, 0.0708743,
        3.5999336, 0.3397528, 1.0137618, 0.7271586,
        0.2700058, 1.0, 0.8, 1.0,
        7001.71309, 0.0018196169, 1051.36609, 0.0139160796,
        239.28569, 0.0684053245, 67.3974453, 0.23318576,
        21.5199573, 0.471267439, 7.4031013, 0.356618546,
        20.8479528, -0.108506975, 4.80830834, -0.146451658,
        1.34406986, 1.12868858, 0.358151393, 1.0,
        20.8479528, 0.0716287243, 4.80830834, 0.345912103,
        1.34406986, 0.722469957, 0.358151393, 1.0,
        0.8, 1.0, 8425.85153, 0.0018843481,
        1268.5194, 0.0143368994, 289.621414, 0.0701096233,
        81.859004, 0.237373266, 26.2515079, 0.473007126,
        9.09472051, 0.348401241, 26.532131, -0.107118287,
        6.10175501, -0.146163821, 1.69627153, 1.1277735,
        0.4458187, 1.0, 26.532131, 0.0719095885,
        6.10175501, 0.349513372, 1.69627153, 0.719940512,
        0.4458187, 1.0, 0.8, 1.0,
        9993.2, 0.0019377, 1499.89, 0.014807,
        341.951, 0.072706, 94.6797, 0.252629,
        29.7345, 0.493242, 10.0063, 0.313169,
        150.963, -0.0035421, 35.5878, -0.043959,
        11.1683, -0.1097521, 3.90201, 0.187398,
        1.38177, 0.646699, 0.466382, 0.306058,
        0.497966, -0.248503, 0.084353, -0.131704,
        0.066635, 1.23352, 0.0259544, 1.0,
        150.963, 0.0050017, 35.5878, 0.035511,
        11.1683, 0.142825, 3.90201, 0.33862,
        1.38177, 0.451579, 0.466382, 0.273271,
        0.497966, -0.023023, 0.084353, 0.950359,
        0.066635, 0.059858, 0.0259544, 1.0,
        0.175, 1.0, 11722.8, 0.0019778,
        1759.93, 0.015114, 400.846, 0.073911,
        112.807, 0.249191, 35.9997, 0.487928,
        12.1828, 0.319662, 189.18, -0.0032372,
        45.2119, -0.041008, 14.3563, -0.1126,
        5.13886, 0.148633, 1.90652, 0.616497,
        0.705887, 0.364829, 0.92934, -0.21229,
        0.269035, -0.107985, 0.117379, 1.17584,
        0.0421061, 1.0, 189.18, 0.0049281,
        45.2119, 0.034989, 14.3563, 0.140725,
        5.13886, 0.333642, 1.90652, 0.44494,
        0.705887, 0.269254, 0.92934, -0.022419,
        0.269035, 0.19227, 0.117379, 0.846181,
        0.0421061, 1.0, 0.175, 1.0,
        13983.1, 0.00194267, 2098.75, 0.0148599,
        477.705, 0.0728494, 134.36, 0.24683,
        42.8709, 0.487258, 14.5189, 0.323496,
        239.668, -0.00292619, 57.4419, -0.037408,
        18.2859, -0.114487, 6.59914, 0.115635,
        2.49049, 0.612595, 0.94454, 0.393799,
        1.2779, -0.227606, 0.39759, 0.00144583,
        0.160095, 1.09279, 0.0556577, 1.0,
        239.668, 0.00460285, 57.4419, 0.033199,
        18.2859, 0.136282, 6.59914, 0.330476,
        2.49049, 0.449146, 0.94454, 0.265704,
        1.2779, -0.017513, 0.39759, 0.244533,
        0.160095, 0.804934, 0.0556577, 1.0,
        0.325, 1.0, 16115.9, 0.00195948,
        2425.58, 0.0149288, 553.867, 0.0728478,
        156.34, 0.24613, 50.0683, 0.485914,
        17.0178, 0.325002, 292.718, -0.00278094,
        69.8731, -0.0357146, 22.3363, -0.114985,
        8.15039, 0.0935634, 3.13458, 0.603017,
        1.22543, 0.418959, 1.72738, -0.24463,
        0.572922, 0.00431572, 0.222192, 1.09818,
        0.0778369, 1.0, 292.718, 0.00443826,
        69.8731, 0.0326679, 22.3363, 0.134721,
        8.15039, 0.328678, 3.13458, 0.44964,
        1.22543, 0.261372, 1.72738, -0.0177951,
        0.572922, 0.253539, 0.222192, 0.800669,
        0.0778369, 1.0, 0.45, 1.0,
        19413.3, 0.0018516, 2909.42, 0.0142062,
        661.364, 0.0699995, 185.759, 0.240079,
        59.1943, 0.484762, 20.031, 0.3352,
        339.478, -0.00278217, 81.0101, -0.0360499,
        25.878, -0.116631, 9.45221, 0.0968328,
        3.66566, 0.614418, 1.46746, 0.403798,
        2.15623, -0.252923, 0.748997, 0.0328517,
        0.283145, 1.08125, 0.0998317, 1.0,
        339.478, 0.00456462, 81.0101, 0.0336936,
        25.878, 0.139755, 9.45221, 0.339362,
        3.66566, 0.450921, 1.46746, 0.238586,
        2.15623, -0.0177653, 0.748997, 0.274058,
        0.283145, 0.785421, 0.0998317, 1.0,
        0.55, 1.0, 21917.1, 0.001869,
        3301.49, 0.01423, 754.146, 0.069696,
        212.711, 0.238487, 67.9896, 0.483307,
        23.0515, 0.338074, 423.735, -0.0023767,
        100.71, -0.031693, 32.1599, -0.113317,
        11.8079, 0.05609, 4.6311, 0.592255,
        1.87025, 0.455006, 2.61584, -0.250374,
        0.922167, 0.066957, 0.341287, 1.05451,
        0.117167, 1.0, 423.735, 0.004061,
        100.71, 0.030681, 32.1599, 0.130452,
        11.8079, 0.327205, 4.6311, 0.452851,
        1.87025, 0.256042, 2.61584, -0.014511,
        0.922167, 0.310263, 0.341287, 0.754483,
        0.117167, 1.0, 0.65, 1.0,
        25180.1, 0.001833, 3780.35, 0.014034,
        860.474, 0.069097, 242.145, 0.237452,
        77.3349, 0.483034, 26.247, 0.339856,
        491.765, -0.0022974, 116.984, -0.030714,
        37.4153, -0.112528, 13.7834, 0.045016,
        5.45215, 0.589353, 2.22588, 0.465206,
        3.18649, -0.25183, 1.14427, 0.061589,
        0.420377, 1.06018, 0.142657, 1.0,
        491.765, 0.0039894, 116.984, 0.030318,
        37.4153, 0.12988, 13.7834, 0.327951,
        5.45215, 0.453527, 2.22588, 0.252154,
        3.18649, -0.014299, 1.14427, 0.323572,
        0.420377, 0.743507, 0.142657, 1.0,
        0.75, 1.0, 28348.3, 0.00182526,
        4257.62, 0.0139686, 969.857, 0.0687073,
        273.263, 0.236204, 87.3695, 0.482214,
        29.6867, 0.342043, 575.891, -0.00215972,
        136.816, -0.0290775, 43.8098, -0.110827,
        16.2094, 0.0276999, 6.46084, 0.577613,
        2.65114, 0.488688, 3.86028, -0.255592,
        1.41373, 0.0378066, 0.516646, 1.08056,
        0.173888, 1.0, 575.891, 0.00380665,
        136.816, 0.0292305, 43.8098, 0.126467,
        16.2094, 0.32351, 6.46084, 0.454896,
        2.65114, 0.25663, 3.86028, -0.0159197,
        1.41373, 0.324646, 0.516646, 0.74399,
        0.173888, 1.0, 0.85, 1.0]
}

#| The 6-31G* basis set as a `Basis` record.
def basis_631gs() -> Basis {
    return basis_of(basis_631gs_shells_flat(), basis_631gs_prims_flat())
}

#| The Cartesian and spherical AO counts of one atom of each element, `1` to `18`,
#| as the generator counted them.
def basis_631gs_nao() -> Arr {
    return [2, 2, 2, 2, 15, 14, 15, 14, 15, 14, 15, 14,
        15, 14, 15, 14, 15, 14, 15, 14, 19, 18, 19, 18,
        19, 18, 19, 18, 19, 18, 19, 18, 19, 18, 19, 18]
}

test "the 6-31G* table covers H through Ar, each element's shells in one run" {
    bt631gs_b = basis_631gs()
    assert_near(len(bt631gs_b.shells), BASIS_631GS_NSHELL, 0.0)
    assert_near(len(bt631gs_b.prims), BASIS_631GS_NPRIM, 0.0)
    assert_near(basis_check(bt631gs_b), 0.0, 0.0)
    bt631gs_n = basis_rows(basis_631gs_nao(), BS_NAO_LEN)
    for bt631gs_z to len(bt631gs_n) {
        bt631gs_k = basis_nao(bt631gs_b, bt631gs_z + 1)
        assert_near(bt631gs_k[0], bt631gs_n[bt631gs_z, 0], 0.0)
        assert_near(bt631gs_k[1], bt631gs_n[bt631gs_z, 1], 0.0)
    }
}