Notebooks · lib/basis/sto3g

The STO-3G 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_sto3g() 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, 66 shells and 198 primitives, angular momentum up to p.

Used with import basis.sto3g, and passed to molecule (lib/hf/molecule).

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[1]lines 20–173

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

BASIS_STO3G_NSHELL = 66
BASIS_STO3G_NPRIM = 198

#| (Z, l, nprim, p0), one segmented shell per row, by element.
def basis_sto3g_shells_flat() -> Arr {
    return [1, 0, 3, 0, 2, 0, 3, 3, 3, 0, 3, 6, 3, 0, 3, 9,
        3, 1, 3, 12, 4, 0, 3, 15, 4, 0, 3, 18, 4, 1, 3, 21,
        5, 0, 3, 24, 5, 0, 3, 27, 5, 1, 3, 30, 6, 0, 3, 33,
        6, 0, 3, 36, 6, 1, 3, 39, 7, 0, 3, 42, 7, 0, 3, 45,
        7, 1, 3, 48, 8, 0, 3, 51, 8, 0, 3, 54, 8, 1, 3, 57,
        9, 0, 3, 60, 9, 0, 3, 63, 9, 1, 3, 66, 10, 0, 3, 69,
        10, 0, 3, 72, 10, 1, 3, 75, 11, 0, 3, 78, 11, 0, 3, 81,
        11, 0, 3, 84, 11, 1, 3, 87, 11, 1, 3, 90, 12, 0, 3, 93,
        12, 0, 3, 96, 12, 0, 3, 99, 12, 1, 3, 102, 12, 1, 3, 105,
        13, 0, 3, 108, 13, 0, 3, 111, 13, 0, 3, 114, 13, 1, 3, 117,
        13, 1, 3, 120, 14, 0, 3, 123, 14, 0, 3, 126, 14, 0, 3, 129,
        14, 1, 3, 132, 14, 1, 3, 135, 15, 0, 3, 138, 15, 0, 3, 141,
        15, 0, 3, 144, 15, 1, 3, 147, 15, 1, 3, 150, 16, 0, 3, 153,
        16, 0, 3, 156, 16, 0, 3, 159, 16, 1, 3, 162, 16, 1, 3, 165,
        17, 0, 3, 168, 17, 0, 3, 171, 17, 0, 3, 174, 17, 1, 3, 177,
        17, 1, 3, 180, 18, 0, 3, 183, 18, 0, 3, 186, 18, 0, 3, 189,
        18, 1, 3, 192, 18, 1, 3, 195]
}

#| (exponent, coefficient), one primitive per row.
def basis_sto3g_prims_flat() -> Arr {
    return [3.42525091, 0.15432897, 0.62391373, 0.53532814,
        0.1688554, 0.44463454, 6.36242139, 0.15432897,
        1.158923, 0.53532814, 0.31364979, 0.44463454,
        16.119575, 0.15432897, 2.9362007, 0.53532814,
        0.7946505, 0.44463454, 0.6362897, -0.09996723,
        0.1478601, 0.39951283, 0.0480887, 0.70011547,
        0.6362897, 0.15591627, 0.1478601, 0.60768372,
        0.0480887, 0.39195739, 30.167871, 0.15432897,
        5.4951153, 0.53532814, 1.4871927, 0.44463454,
        1.3148331, -0.09996723, 0.3055389, 0.39951283,
        0.0993707, 0.70011547, 1.3148331, 0.15591627,
        0.3055389, 0.60768372, 0.0993707, 0.39195739,
        48.791113, 0.15432897, 8.8873622, 0.53532814,
        2.405267, 0.44463454, 2.2369561, -0.09996723,
        0.5198205, 0.39951283, 0.1690618, 0.70011547,
        2.2369561, 0.15591627, 0.5198205, 0.60768372,
        0.1690618, 0.39195739, 71.616837, 0.15432897,
        13.045096, 0.53532814, 3.5305122, 0.44463454,
        2.9412494, -0.09996723, 0.6834831, 0.39951283,
        0.2222899, 0.70011547, 2.9412494, 0.15591627,
        0.6834831, 0.60768372, 0.2222899, 0.39195739,
        99.106169, 0.15432897, 18.052312, 0.53532814,
        4.8856602, 0.44463454, 3.7804559, -0.09996723,
        0.8784966, 0.39951283, 0.2857144, 0.70011547,
        3.7804559, 0.15591627, 0.8784966, 0.60768372,
        0.2857144, 0.39195739, 130.70932, 0.15432897,
        23.808861, 0.53532814, 6.4436083, 0.44463454,
        5.0331513, -0.09996723, 1.1695961, 0.39951283,
        0.380389, 0.70011547, 5.0331513, 0.15591627,
        1.1695961, 0.60768372, 0.380389, 0.39195739,
        166.67913, 0.15432897, 30.360812, 0.53532814,
        8.2168207, 0.44463454, 6.4648032, -0.09996723,
        1.5022812, 0.39951283, 0.4885885, 0.70011547,
        6.4648032, 0.15591627, 1.5022812, 0.60768372,
        0.4885885, 0.39195739, 207.01561, 0.15432897,
        37.708151, 0.53532814, 10.205297, 0.44463454,
        8.2463151, -0.09996723, 1.9162662, 0.39951283,
        0.6232293, 0.70011547, 8.2463151, 0.15591627,
        1.9162662, 0.60768372, 0.6232293, 0.39195739,
        250.77243, 0.1543289673, 45.678511, 0.5353281423,
        12.362388, 0.4446345422, 12.040193, -0.09996722919,
        2.7978819, 0.3995128261, 0.909958, 0.7001154689,
        1.4787406, -0.219620369, 0.4125649, 0.2255954336,
        0.1614751, 0.900398426, 12.040193, 0.155916275,
        2.7978819, 0.6076837186, 0.909958, 0.3919573931,
        1.4787406, 0.01058760429, 0.4125649, 0.5951670053,
        0.1614751, 0.462001012, 299.2374, 0.1543289673,
        54.50647, 0.5353281423, 14.75158, 0.4446345422,
        15.12182, -0.09996722919, 3.513987, 0.3995128261,
        1.142857, 0.7001154689, 1.395448, -0.219620369,
        0.389326, 0.2255954336, 0.15238, 0.900398426,
        15.12182, 0.155916275, 3.513987, 0.6076837186,
        1.142857, 0.3919573931, 1.395448, 0.01058760429,
        0.389326, 0.5951670053, 0.15238, 0.462001012,
        351.4214767, 0.1543289673, 64.01186067, 0.5353281423,
        17.32410761, 0.4446345422, 18.89939621, -0.09996722919,
        4.391813233, 0.3995128261, 1.42835397, 0.7001154689,
        1.395448293, -0.219620369, 0.3893265318, 0.2255954336,
        0.1523797659, 0.900398426, 18.89939621, 0.155916275,
        4.391813233, 0.6076837186, 1.42835397, 0.3919573931,
        1.395448293, 0.01058760429, 0.3893265318, 0.5951670053,
        0.1523797659, 0.462001012, 407.7975514, 0.1543289673,
        74.28083305, 0.5353281423, 20.10329229, 0.4446345422,
        23.19365606, -0.09996722919, 5.389706871, 0.3995128261,
        1.752899952, 0.7001154689, 1.478740622, -0.219620369,
        0.4125648801, 0.2255954336, 0.1614750979, 0.900398426,
        23.19365606, 0.155916275, 5.389706871, 0.6076837186,
        1.752899952, 0.3919573931, 1.478740622, 0.01058760429,
        0.4125648801, 0.5951670053, 0.1614750979, 0.462001012,
        468.3656378, 0.1543289673, 85.31338559, 0.5353281423,
        23.08913156, 0.4446345422, 28.03263958, -0.09996722919,
        6.514182577, 0.3995128261, 2.118614352, 0.7001154689,
        1.743103231, -0.219620369, 0.4863213771, 0.2255954336,
        0.1903428909, 0.900398426, 28.03263958, 0.155916275,
        6.514182577, 0.6076837186, 2.118614352, 0.3919573931,
        1.743103231, 0.01058760429, 0.4863213771, 0.5951670053,
        0.1903428909, 0.462001012, 533.1257359, 0.1543289673,
        97.1095183, 0.5353281423, 26.28162542, 0.4446345422,
        33.32975173, -0.09996722919, 7.745117521, 0.3995128261,
        2.518952599, 0.7001154689, 2.029194274, -0.219620369,
        0.5661400518, 0.2255954336, 0.2215833792, 0.900398426,
        33.32975173, 0.155916275, 7.745117521, 0.6076837186,
        2.518952599, 0.3919573931, 2.029194274, 0.01058760429,
        0.5661400518, 0.5951670053, 0.2215833792, 0.462001012,
        601.3456136, 0.1543289673, 109.5358542, 0.5353281423,
        29.64467686, 0.4446345422, 38.96041889, -0.09996722919,
        9.053563477, 0.3995128261, 2.944499834, 0.7001154689,
        2.129386495, -0.219620369, 0.5940934274, 0.2255954336,
        0.232524141, 0.900398426, 38.96041889, 0.155916275,
        9.053563477, 0.6076837186, 2.944499834, 0.3919573931,
        2.129386495, 0.01058760429, 0.5940934274, 0.5951670053,
        0.232524141, 0.462001012, 674.4465184, 0.1543289673,
        122.8512753, 0.5353281423, 33.24834945, 0.4446345422,
        45.16424392, -0.09996722919, 10.495199, 0.3995128261,
        3.413364448, 0.7001154689, 2.621366518, -0.219620369,
        0.731354605, 0.2255954336, 0.2862472356, 0.900398426,
        45.16424392, 0.155916275, 10.495199, 0.6076837186,
        3.413364448, 0.3919573931, 2.621366518, 0.01058760429,
        0.731354605, 0.5951670053, 0.2862472356, 0.462001012]
}

#| The STO-3G basis set as a `Basis` record.
def basis_sto3g() -> Basis {
    return basis_of(basis_sto3g_shells_flat(), basis_sto3g_prims_flat())
}

#| The Cartesian and spherical AO counts of one atom of each element, `1` to `18`,
#| as the generator counted them.
def basis_sto3g_nao() -> Arr {
    return [1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5,
        5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 9, 9,
        9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]
}

test "the STO-3G table covers H through Ar, each element's shells in one run" {
    btsto3g_b = basis_sto3g()
    assert_near(len(btsto3g_b.shells), BASIS_STO3G_NSHELL, 0.0)
    assert_near(len(btsto3g_b.prims), BASIS_STO3G_NPRIM, 0.0)
    assert_near(basis_check(btsto3g_b), 0.0, 0.0)
    btsto3g_n = basis_rows(basis_sto3g_nao(), BS_NAO_LEN)
    for btsto3g_z to len(btsto3g_n) {
        btsto3g_k = basis_nao(btsto3g_b, btsto3g_z + 1)
        assert_near(btsto3g_k[0], btsto3g_n[btsto3g_z, 0], 0.0)
        assert_near(btsto3g_k[1], btsto3g_n[btsto3g_z, 1], 0.0)
    }
}

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

BASIS_STO3G_NSHELL = 66
BASIS_STO3G_NPRIM = 198

#| (Z, l, nprim, p0), one segmented shell per row, by element.
def basis_sto3g_shells_flat() -> Arr {
    return [1, 0, 3, 0, 2, 0, 3, 3, 3, 0, 3, 6, 3, 0, 3, 9,
        3, 1, 3, 12, 4, 0, 3, 15, 4, 0, 3, 18, 4, 1, 3, 21,
        5, 0, 3, 24, 5, 0, 3, 27, 5, 1, 3, 30, 6, 0, 3, 33,
        6, 0, 3, 36, 6, 1, 3, 39, 7, 0, 3, 42, 7, 0, 3, 45,
        7, 1, 3, 48, 8, 0, 3, 51, 8, 0, 3, 54, 8, 1, 3, 57,
        9, 0, 3, 60, 9, 0, 3, 63, 9, 1, 3, 66, 10, 0, 3, 69,
        10, 0, 3, 72, 10, 1, 3, 75, 11, 0, 3, 78, 11, 0, 3, 81,
        11, 0, 3, 84, 11, 1, 3, 87, 11, 1, 3, 90, 12, 0, 3, 93,
        12, 0, 3, 96, 12, 0, 3, 99, 12, 1, 3, 102, 12, 1, 3, 105,
        13, 0, 3, 108, 13, 0, 3, 111, 13, 0, 3, 114, 13, 1, 3, 117,
        13, 1, 3, 120, 14, 0, 3, 123, 14, 0, 3, 126, 14, 0, 3, 129,
        14, 1, 3, 132, 14, 1, 3, 135, 15, 0, 3, 138, 15, 0, 3, 141,
        15, 0, 3, 144, 15, 1, 3, 147, 15, 1, 3, 150, 16, 0, 3, 153,
        16, 0, 3, 156, 16, 0, 3, 159, 16, 1, 3, 162, 16, 1, 3, 165,
        17, 0, 3, 168, 17, 0, 3, 171, 17, 0, 3, 174, 17, 1, 3, 177,
        17, 1, 3, 180, 18, 0, 3, 183, 18, 0, 3, 186, 18, 0, 3, 189,
        18, 1, 3, 192, 18, 1, 3, 195]
}

#| (exponent, coefficient), one primitive per row.
def basis_sto3g_prims_flat() -> Arr {
    return [3.42525091, 0.15432897, 0.62391373, 0.53532814,
        0.1688554, 0.44463454, 6.36242139, 0.15432897,
        1.158923, 0.53532814, 0.31364979, 0.44463454,
        16.119575, 0.15432897, 2.9362007, 0.53532814,
        0.7946505, 0.44463454, 0.6362897, -0.09996723,
        0.1478601, 0.39951283, 0.0480887, 0.70011547,
        0.6362897, 0.15591627, 0.1478601, 0.60768372,
        0.0480887, 0.39195739, 30.167871, 0.15432897,
        5.4951153, 0.53532814, 1.4871927, 0.44463454,
        1.3148331, -0.09996723, 0.3055389, 0.39951283,
        0.0993707, 0.70011547, 1.3148331, 0.15591627,
        0.3055389, 0.60768372, 0.0993707, 0.39195739,
        48.791113, 0.15432897, 8.8873622, 0.53532814,
        2.405267, 0.44463454, 2.2369561, -0.09996723,
        0.5198205, 0.39951283, 0.1690618, 0.70011547,
        2.2369561, 0.15591627, 0.5198205, 0.60768372,
        0.1690618, 0.39195739, 71.616837, 0.15432897,
        13.045096, 0.53532814, 3.5305122, 0.44463454,
        2.9412494, -0.09996723, 0.6834831, 0.39951283,
        0.2222899, 0.70011547, 2.9412494, 0.15591627,
        0.6834831, 0.60768372, 0.2222899, 0.39195739,
        99.106169, 0.15432897, 18.052312, 0.53532814,
        4.8856602, 0.44463454, 3.7804559, -0.09996723,
        0.8784966, 0.39951283, 0.2857144, 0.70011547,
        3.7804559, 0.15591627, 0.8784966, 0.60768372,
        0.2857144, 0.39195739, 130.70932, 0.15432897,
        23.808861, 0.53532814, 6.4436083, 0.44463454,
        5.0331513, -0.09996723, 1.1695961, 0.39951283,
        0.380389, 0.70011547, 5.0331513, 0.15591627,
        1.1695961, 0.60768372, 0.380389, 0.39195739,
        166.67913, 0.15432897, 30.360812, 0.53532814,
        8.2168207, 0.44463454, 6.4648032, -0.09996723,
        1.5022812, 0.39951283, 0.4885885, 0.70011547,
        6.4648032, 0.15591627, 1.5022812, 0.60768372,
        0.4885885, 0.39195739, 207.01561, 0.15432897,
        37.708151, 0.53532814, 10.205297, 0.44463454,
        8.2463151, -0.09996723, 1.9162662, 0.39951283,
        0.6232293, 0.70011547, 8.2463151, 0.15591627,
        1.9162662, 0.60768372, 0.6232293, 0.39195739,
        250.77243, 0.1543289673, 45.678511, 0.5353281423,
        12.362388, 0.4446345422, 12.040193, -0.09996722919,
        2.7978819, 0.3995128261, 0.909958, 0.7001154689,
        1.4787406, -0.219620369, 0.4125649, 0.2255954336,
        0.1614751, 0.900398426, 12.040193, 0.155916275,
        2.7978819, 0.6076837186, 0.909958, 0.3919573931,
        1.4787406, 0.01058760429, 0.4125649, 0.5951670053,
        0.1614751, 0.462001012, 299.2374, 0.1543289673,
        54.50647, 0.5353281423, 14.75158, 0.4446345422,
        15.12182, -0.09996722919, 3.513987, 0.3995128261,
        1.142857, 0.7001154689, 1.395448, -0.219620369,
        0.389326, 0.2255954336, 0.15238, 0.900398426,
        15.12182, 0.155916275, 3.513987, 0.6076837186,
        1.142857, 0.3919573931, 1.395448, 0.01058760429,
        0.389326, 0.5951670053, 0.15238, 0.462001012,
        351.4214767, 0.1543289673, 64.01186067, 0.5353281423,
        17.32410761, 0.4446345422, 18.89939621, -0.09996722919,
        4.391813233, 0.3995128261, 1.42835397, 0.7001154689,
        1.395448293, -0.219620369, 0.3893265318, 0.2255954336,
        0.1523797659, 0.900398426, 18.89939621, 0.155916275,
        4.391813233, 0.6076837186, 1.42835397, 0.3919573931,
        1.395448293, 0.01058760429, 0.3893265318, 0.5951670053,
        0.1523797659, 0.462001012, 407.7975514, 0.1543289673,
        74.28083305, 0.5353281423, 20.10329229, 0.4446345422,
        23.19365606, -0.09996722919, 5.389706871, 0.3995128261,
        1.752899952, 0.7001154689, 1.478740622, -0.219620369,
        0.4125648801, 0.2255954336, 0.1614750979, 0.900398426,
        23.19365606, 0.155916275, 5.389706871, 0.6076837186,
        1.752899952, 0.3919573931, 1.478740622, 0.01058760429,
        0.4125648801, 0.5951670053, 0.1614750979, 0.462001012,
        468.3656378, 0.1543289673, 85.31338559, 0.5353281423,
        23.08913156, 0.4446345422, 28.03263958, -0.09996722919,
        6.514182577, 0.3995128261, 2.118614352, 0.7001154689,
        1.743103231, -0.219620369, 0.4863213771, 0.2255954336,
        0.1903428909, 0.900398426, 28.03263958, 0.155916275,
        6.514182577, 0.6076837186, 2.118614352, 0.3919573931,
        1.743103231, 0.01058760429, 0.4863213771, 0.5951670053,
        0.1903428909, 0.462001012, 533.1257359, 0.1543289673,
        97.1095183, 0.5353281423, 26.28162542, 0.4446345422,
        33.32975173, -0.09996722919, 7.745117521, 0.3995128261,
        2.518952599, 0.7001154689, 2.029194274, -0.219620369,
        0.5661400518, 0.2255954336, 0.2215833792, 0.900398426,
        33.32975173, 0.155916275, 7.745117521, 0.6076837186,
        2.518952599, 0.3919573931, 2.029194274, 0.01058760429,
        0.5661400518, 0.5951670053, 0.2215833792, 0.462001012,
        601.3456136, 0.1543289673, 109.5358542, 0.5353281423,
        29.64467686, 0.4446345422, 38.96041889, -0.09996722919,
        9.053563477, 0.3995128261, 2.944499834, 0.7001154689,
        2.129386495, -0.219620369, 0.5940934274, 0.2255954336,
        0.232524141, 0.900398426, 38.96041889, 0.155916275,
        9.053563477, 0.6076837186, 2.944499834, 0.3919573931,
        2.129386495, 0.01058760429, 0.5940934274, 0.5951670053,
        0.232524141, 0.462001012, 674.4465184, 0.1543289673,
        122.8512753, 0.5353281423, 33.24834945, 0.4446345422,
        45.16424392, -0.09996722919, 10.495199, 0.3995128261,
        3.413364448, 0.7001154689, 2.621366518, -0.219620369,
        0.731354605, 0.2255954336, 0.2862472356, 0.900398426,
        45.16424392, 0.155916275, 10.495199, 0.6076837186,
        3.413364448, 0.3919573931, 2.621366518, 0.01058760429,
        0.731354605, 0.5951670053, 0.2862472356, 0.462001012]
}

#| The STO-3G basis set as a `Basis` record.
def basis_sto3g() -> Basis {
    return basis_of(basis_sto3g_shells_flat(), basis_sto3g_prims_flat())
}

#| The Cartesian and spherical AO counts of one atom of each element, `1` to `18`,
#| as the generator counted them.
def basis_sto3g_nao() -> Arr {
    return [1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5,
        5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 9, 9,
        9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]
}

test "the STO-3G table covers H through Ar, each element's shells in one run" {
    btsto3g_b = basis_sto3g()
    assert_near(len(btsto3g_b.shells), BASIS_STO3G_NSHELL, 0.0)
    assert_near(len(btsto3g_b.prims), BASIS_STO3G_NPRIM, 0.0)
    assert_near(basis_check(btsto3g_b), 0.0, 0.0)
    btsto3g_n = basis_rows(basis_sto3g_nao(), BS_NAO_LEN)
    for btsto3g_z to len(btsto3g_n) {
        btsto3g_k = basis_nao(btsto3g_b, btsto3g_z + 1)
        assert_near(btsto3g_k[0], btsto3g_n[btsto3g_z, 0], 0.0)
        assert_near(btsto3g_k[1], btsto3g_n[btsto3g_z, 1], 0.0)
    }
}