Notebooks · lib/basis/def2tzvp

The def2-TZVP 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_def2tzvp() 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, 193 shells and 374 primitives, angular momentum up to f.

Used with import basis.def2tzvp, and passed to molecule (lib/hf/molecule).

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[1]lines 20–293

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

BASIS_DEF2TZVP_NSHELL = 193
BASIS_DEF2TZVP_NPRIM = 374

#| (Z, l, nprim, p0), one segmented shell per row, by element.
def basis_def2tzvp_shells_flat() -> Arr {
    return [1, 0, 3, 0, 1, 0, 1, 3, 1, 0, 1, 4, 1, 1, 1, 5,
        2, 0, 3, 6, 2, 0, 1, 9, 2, 0, 1, 10, 2, 1, 1, 11,
        3, 0, 6, 12, 3, 0, 2, 18, 3, 0, 1, 20, 3, 0, 1, 21,
        3, 0, 1, 22, 3, 1, 1, 23, 3, 1, 1, 24, 3, 1, 1, 25,
        4, 0, 6, 26, 4, 0, 2, 32, 4, 0, 1, 34, 4, 0, 1, 35,
        4, 0, 1, 36, 4, 1, 2, 37, 4, 1, 1, 39, 4, 1, 1, 40,
        4, 2, 1, 41, 5, 0, 6, 42, 5, 0, 2, 48, 5, 0, 1, 50,
        5, 0, 1, 51, 5, 0, 1, 52, 5, 1, 4, 53, 5, 1, 1, 57,
        5, 1, 1, 58, 5, 2, 1, 59, 5, 2, 1, 60, 5, 3, 1, 61,
        6, 0, 6, 62, 6, 0, 2, 68, 6, 0, 1, 70, 6, 0, 1, 71,
        6, 0, 1, 72, 6, 1, 4, 73, 6, 1, 1, 77, 6, 1, 1, 78,
        6, 2, 1, 79, 6, 2, 1, 80, 6, 3, 1, 81, 7, 0, 6, 82,
        7, 0, 2, 88, 7, 0, 1, 90, 7, 0, 1, 91, 7, 0, 1, 92,
        7, 1, 4, 93, 7, 1, 1, 97, 7, 1, 1, 98, 7, 2, 1, 99,
        7, 2, 1, 100, 7, 3, 1, 101, 8, 0, 6, 102, 8, 0, 2, 108,
        8, 0, 1, 110, 8, 0, 1, 111, 8, 0, 1, 112, 8, 1, 4, 113,
        8, 1, 1, 117, 8, 1, 1, 118, 8, 2, 1, 119, 8, 2, 1, 120,
        8, 3, 1, 121, 9, 0, 6, 122, 9, 0, 2, 128, 9, 0, 1, 130,
        9, 0, 1, 131, 9, 0, 1, 132, 9, 1, 4, 133, 9, 1, 1, 137,
        9, 1, 1, 138, 9, 2, 1, 139, 9, 2, 1, 140, 9, 3, 1, 141,
        10, 0, 6, 142, 10, 0, 2, 148, 10, 0, 1, 150, 10, 0, 1, 151,
        10, 0, 1, 152, 10, 1, 4, 153, 10, 1, 1, 157, 10, 1, 1, 158,
        10, 2, 1, 159, 10, 2, 1, 160, 10, 3, 1, 161, 11, 0, 7, 162,
        11, 0, 3, 169, 11, 0, 2, 172, 11, 0, 1, 174, 11, 0, 1, 175,
        11, 1, 5, 176, 11, 1, 1, 181, 11, 1, 1, 182, 11, 1, 1, 183,
        11, 2, 1, 184, 11, 2, 1, 185, 11, 2, 1, 186, 12, 0, 7, 187,
        12, 0, 3, 194, 12, 0, 2, 197, 12, 0, 1, 199, 12, 0, 1, 200,
        12, 1, 5, 201, 12, 1, 1, 206, 12, 1, 1, 207, 12, 1, 1, 208,
        12, 2, 1, 209, 12, 2, 1, 210, 12, 2, 1, 211, 13, 0, 7, 212,
        13, 0, 3, 219, 13, 0, 2, 222, 13, 0, 1, 224, 13, 0, 1, 225,
        13, 1, 5, 226, 13, 1, 1, 231, 13, 1, 1, 232, 13, 1, 1, 233,
        13, 1, 1, 234, 13, 2, 2, 235, 13, 2, 1, 237, 13, 3, 1, 238,
        14, 0, 7, 239, 14, 0, 3, 246, 14, 0, 2, 249, 14, 0, 1, 251,
        14, 0, 1, 252, 14, 1, 5, 253, 14, 1, 1, 258, 14, 1, 1, 259,
        14, 1, 1, 260, 14, 1, 1, 261, 14, 2, 2, 262, 14, 2, 1, 264,
        14, 3, 1, 265, 15, 0, 7, 266, 15, 0, 3, 273, 15, 0, 2, 276,
        15, 0, 1, 278, 15, 0, 1, 279, 15, 1, 5, 280, 15, 1, 1, 285,
        15, 1, 1, 286, 15, 1, 1, 287, 15, 1, 1, 288, 15, 2, 2, 289,
        15, 2, 1, 291, 15, 3, 1, 292, 16, 0, 7, 293, 16, 0, 3, 300,
        16, 0, 2, 303, 16, 0, 1, 305, 16, 0, 1, 306, 16, 1, 5, 307,
        16, 1, 1, 312, 16, 1, 1, 313, 16, 1, 1, 314, 16, 1, 1, 315,
        16, 2, 2, 316, 16, 2, 1, 318, 16, 3, 1, 319, 17, 0, 7, 320,
        17, 0, 3, 327, 17, 0, 2, 330, 17, 0, 1, 332, 17, 0, 1, 333,
        17, 1, 5, 334, 17, 1, 1, 339, 17, 1, 1, 340, 17, 1, 1, 341,
        17, 1, 1, 342, 17, 2, 2, 343, 17, 2, 1, 345, 17, 3, 1, 346,
        18, 0, 7, 347, 18, 0, 3, 354, 18, 0, 2, 357, 18, 0, 1, 359,
        18, 0, 1, 360, 18, 1, 5, 361, 18, 1, 1, 366, 18, 1, 1, 367,
        18, 1, 1, 368, 18, 1, 1, 369, 18, 2, 2, 370, 18, 2, 1, 372,
        18, 3, 1, 373]
}

#| (exponent, coefficient), one primitive per row.
def basis_def2tzvp_prims_flat() -> Arr {
    return [34.061341, 0.0060251978, 5.1235746, 0.045021094,
        1.1646626, 0.20189726, 0.32723041, 1.0,
        0.10307241, 1.0, 0.8, 1.0,
        98.078321616, 0.0075803064967, 14.764404247, 0.054848620937,
        3.3185831473, 0.22074382186, 0.87413869551, 1.0,
        0.24459897208, 1.0, 1.0, 1.0,
        6269.262801, 0.00020540968826, 940.31612431, 0.0015916554089,
        214.22107528, 0.0082869829707, 60.759840184, 0.033856374249,
        19.915152032, 0.11103225876, 7.3171509797, 0.27449383329,
        2.9724674216, 0.23792456411, 1.2639852314, 0.30765411924,
        0.51427489953, 1.0, 0.077030885901, 1.0,
        0.028938896433, 1.0, 3.327, 1.0,
        0.4, 1.0, 0.06, 1.0,
        4700.2365626, 0.00023584389316, 704.82845622, 0.0018243791019,
        160.43110478, 0.0093966148224, 45.425347336, 0.036908924159,
        14.798334125, 0.10897561281, 5.3512452537, 0.21694284551,
        2.1542044819, 0.44695408857, 0.933637444, 0.20866985771,
        0.18791432989, 1.0, 0.074648267947, 1.0,
        0.032650484598, 1.0, 0.71695694366, -0.16877854032,
        0.1954193286, -0.51403419628, 3.6316917145, 1.0,
        0.06051546589, 1.0, 0.18, 1.0,
        8564.8660687, 0.00022837198155, 1284.1516263, 0.0017682576447,
        292.27871604, 0.0091407080516, 82.775469176, 0.036342638989,
        27.017939269, 0.11063458441, 9.814961966, 0.23367344321,
        3.9318559059, 0.41818777978, 1.6595599712, 0.22325473798,
        0.35762965239, 1.0, 0.14246277496, 1.0,
        0.060560594768, 1.0, 22.453875803, 0.0050265575179,
        5.104505833, 0.032801738965, 1.4986081344, 0.13151230768,
        0.50927831315, 0.33197167769, 0.18147077798, 1.0,
        0.064621893904, 1.0, 0.661, 1.0,
        0.199, 1.0, 0.49, 1.0,
        13575.349682, 0.00022245814352, 2035.233368, 0.0017232738252,
        463.22562359, 0.0089255715314, 131.20019598, 0.035727984502,
        42.853015891, 0.11076259931, 15.584185766, 0.24295627626,
        6.2067138508, 0.41440263448, 2.5764896527, 0.23744968655,
        0.57696339419, 1.0, 0.22972831358, 1.0,
        0.095164440028, 1.0, 34.697232244, 0.0053333657805,
        7.9582622826, 0.035864109092, 2.3780826883, 0.14215873329,
        0.81433208183, 0.34270471845, 0.28887547253, 1.0,
        0.10056823671, 1.0, 1.097, 1.0,
        0.318, 1.0, 0.761, 1.0,
        19730.800647, 0.00021887984991, 2957.8958745, 0.0016960708803,
        673.22133595, 0.0087954603538, 190.68249494, 0.035359382605,
        62.295441898, 0.11095789217, 22.654161182, 0.24982972552,
        8.9791477428, 0.40623896148, 3.686300237, 0.24338217176,
        0.84660076805, 1.0, 0.33647133771, 1.0,
        0.13647653675, 1.0, 49.20038051, 0.0055552416751,
        11.346790537, 0.038052379723, 3.4273972411, 0.14953671029,
        1.1785525134, 0.3494930523, 0.41642204972, 1.0,
        0.14260826011, 1.0, 1.654, 1.0,
        0.469, 1.0, 1.093, 1.0,
        27032.382631, 0.00021726302465, 4052.3871392, 0.0016838662199,
        922.3272271, 0.0087395616265, 261.24070989, 0.035239968808,
        85.354641351, 0.11153519115, 31.035035245, 0.25588953961,
        12.260860728, 0.39768730901, 4.9987076005, 0.2462784943,
        1.1703108158, 1.0, 0.46474740994, 1.0,
        0.18504536357, 1.0, 63.274954801, 0.0060685103418,
        14.627049379, 0.041912575824, 4.4501223456, 0.16153841088,
        1.5275799647, 0.35706951311, 0.52935117943, 1.0,
        0.1747842127, 1.0, 2.314, 1.0,
        0.645, 1.0, 1.428, 1.0,
        35479.100441, 0.00021545014888, 5318.4728983, 0.0016700686527,
        1210.4810975, 0.0086733211476, 342.8551814, 0.035049933175,
        112.01943181, 0.11165320133, 40.714740248, 0.25988506647,
        16.039678111, 0.3942296688, 6.503818674, 0.24998238551,
        1.5440477509, 1.0, 0.61223452862, 1.0,
        0.24027979698, 1.0, 80.233900483, 0.0063685999134,
        18.594010743, 0.04430314353, 5.6867902653, 0.16867248708,
        1.9511006294, 0.36166346255, 0.66970211298, 1.0,
        0.2165130041, 1.0, 3.107, 1.0,
        0.855, 1.0, 1.917, 1.0,
        45069.464022, 0.00021687155182, 6755.9768656, 0.0016812736757,
        1537.6502864, 0.0087356062782, 435.51697667, 0.035361266922,
        142.28655638, 0.11321521454, 51.692153804, 0.26654653104,
        20.31587049, 0.39631959951, 8.2021942646, 0.25582811251,
        1.9681276278, 1.0, 0.77904756001, 1.0,
        0.30229502043, 1.0, 99.782996032, 0.0065569234163,
        23.176124101, 0.045888009138, 7.1163945872, 0.17331287812,
        2.4418711435, 0.36475267512, 0.83389605766, 1.0,
        0.26607311301, 1.0, 4.014, 1.0,
        1.096, 1.0, 2.544, 1.0,
        26041.109927, 0.00061806342811, 3906.1268548, 0.0047748604414,
        888.97454993, 0.024471684829, 251.45497961, 0.094755394977,
        81.650143512, 0.2686749692, 28.904158401, 0.4792547544,
        10.625782932, 0.33248591469, 53.769410179, 0.019527731872,
        16.308243025, 0.092648010794, 2.3730384125, -0.39938670172,
        0.95730772603, 1.6428595391, 0.40806460959, 0.55692596966,
        0.049967582329, 1.0, 0.01926861625, 1.0,
        138.07979989, 0.0057951891929, 32.232700393, 0.041620846251,
        9.981607536, 0.16281916885, 3.4822033928, 0.36011784647,
        1.229913462, 0.44858979889, 0.41743959423, 1.0,
        0.091, 1.0, 0.03, 1.0,
        2.609, 1.0, 0.43, 1.0,
        0.1, 1.0, 31438.349555, 0.00060912311326,
        4715.5153354, 0.0047066196465, 1073.1629247, 0.024135820657,
        303.57238768, 0.093628959834, 98.626251042, 0.26646742093,
        34.943808417, 0.47890929917, 12.859785199, 0.33698490286,
        64.876913004, 0.019180889307, 19.725520777, 0.090913704392,
        2.8951804339, -0.39563756125, 1.196045471, 1.6827603373,
        0.54329451156, 0.52141091954, 0.10099104092, 1.0,
        0.036865728085, 1.0, 179.87189612, 0.0053799549018,
        42.120069376, 0.039318014098, 13.120503032, 0.15740129476,
        4.6257503609, 0.35919094128, 1.6695211016, 0.4553337931,
        0.58551012105, 1.0, 0.18914796195, 1.0,
        0.053768755187, 1.0, 3.444, 1.0,
        0.29, 1.0, 0.07, 1.0,
        37792.550772, 0.00057047888709, 5668.0682165, 0.0044093016538,
        1289.8582841, 0.022630967411, 364.86596028, 0.088025644295,
        118.57631515, 0.25223701612, 42.024867605, 0.45960547169,
        15.499501629, 0.33277886014, 75.208026598, 0.01925056019,
        23.031408972, 0.087906743952, 3.6348797649, -0.34246704535,
        1.6065049957, 1.5106266058, 0.76103394581, 0.5807101647,
        0.16556708849, 1.0, 0.060041577113, 1.0,
        452.52303192, 0.0023110812466, 107.08195049, 0.018568641823,
        34.131021255, 0.087216237035, 12.587037428, 0.26902101523,
        4.9811919704, 0.52128324272, 2.00703509, 1.0,
        0.80083714374, 1.0, 0.20178927472, 1.0,
        0.057895550392, 1.0, 1.57, 0.2,
        0.333, 1.0, 0.111, 1.0,
        0.244, 1.0, 44773.358078, 0.00055914765868,
        6717.1992104, 0.0043206040189, 1528.8960325, 0.02218709646,
        432.54746585, 0.086489249116, 140.61505226, 0.24939889716,
        49.857636724, 0.46017197366, 18.434974885, 0.34250236575,
        86.533886111, 0.021300063007, 26.624606846, 0.094676139318,
        4.4953057159, -0.32616264859, 2.103504571, 1.398080385,
        1.0106094922, 0.63865786699, 0.23701751489, 1.0,
        0.085703405362, 1.0, 394.47503628, 0.0026285693959,
        93.137683104, 0.020556257749, 29.519608742, 0.092070262801,
        10.781663791, 0.25565889739, 4.1626574778, 0.42111707185,
        1.6247972989, 1.0, 0.54306660493, 1.0,
        0.20582073956, 1.0, 0.070053487306, 1.0,
        2.303, 0.2, 0.476, 1.0,
        0.16, 1.0, 0.336, 1.0,
        52426.999233, 0.000552071641, 7863.2660552, 0.0042678595308,
        1789.5227333, 0.021931529186, 506.27300165, 0.085667168373,
        164.60698546, 0.24840686605, 58.391918722, 0.46336753971,
        21.643663201, 0.35350558156, 99.01383762, 0.021895679958,
        30.550439817, 0.095650470295, 5.4537087661, -0.29454270186,
        2.6503362563, 1.32943812, 1.2726688867, 0.66109396473,
        0.31645005203, 1.0, 0.11417466938, 1.0,
        472.27219248, 0.0025710623052, 111.58882756, 0.020250297999,
        35.445936418, 0.091580716787, 12.990776875, 0.25749454014,
        5.0486221658, 0.42862899758, 1.9934049566, 1.0,
        0.6652728443, 1.0, 0.25516832128, 1.0,
        0.090357762251, 1.0, 3.12, 0.2,
        0.648, 1.0, 0.218, 1.0,
        0.452, 1.0, 60700.928104, 0.00054695944225,
        9102.6106854, 0.0042297224557, 2071.4166009, 0.021747824159,
        586.02476821, 0.085100053589, 190.55395021, 0.24799128459,
        67.63038426, 0.46703640406, 25.127306905, 0.3643458755,
        112.5746301, 0.02167004024, 34.795554217, 0.09360230176,
        6.5115556215, -0.26068001422, 3.2399032261, 1.2842089435,
        1.5477160881, 0.66036416584, 0.40541030112, 1.0,
        0.14550651059, 1.0, 564.36716027, 0.0024796796317,
        133.42624379, 0.01967793025, 42.468271189, 0.089980008258,
        15.61652758, 0.25705880575, 6.1093988469, 0.43515167292,
        2.4404160198, 1.0, 0.83882201296, 1.0,
        0.312887469, 1.0, 0.10770109004, 1.0,
        3.756, 0.2, 0.812, 1.0,
        0.273, 1.0, 0.557, 1.0,
        69507.990945, 0.00054314897497, 10426.15688, 0.0041990463961,
        2373.2334061, 0.021592141679, 671.56420071, 0.084598850094,
        218.4199979, 0.24757249724, 77.572249714, 0.47016930228,
        28.888815277, 0.37436370716, 127.10527185, 0.025182166603,
        39.339582961, 0.10786112456, 7.6740679989, -0.27408821574,
        3.874562763, 1.3213875014, 1.8385832573, 0.68636955368,
        0.50229057542, 1.0, 0.1796272342, 1.0,
        666.50423284, 0.0023632663836, 157.6424169, 0.018879300374,
        50.262520978, 0.087206341273, 18.536078105, 0.2528561297,
        7.2940532777, 0.4350715482, 2.9433248995, 1.0,
        1.0404970818, 1.0, 0.3845641508, 1.0,
        0.13069642732, 1.0, 4.61, 0.2,
        1.011, 1.0, 0.339, 1.0,
        0.706, 1.0, 79111.422998, 0.00051029325002,
        11864.746009, 0.0039463036981, 2700.1642973, 0.02030707391,
        763.95943485, 0.079691825214, 248.45150561, 0.23420623836,
        88.283581, 0.44833849481, 32.948607069, 0.364081674,
        142.55358, 0.026387407001, 44.163688009, 0.11226433999,
        8.9524995, -0.26178922001, 4.5546920941, 1.3002484998,
        2.1444079001, 0.67197237009, 0.60708777004, 1.0,
        0.21651431999, 1.0, 776.77541998, 0.0022028005003,
        183.80107018, 0.017694180008, 58.694003175, 0.082431293717,
        21.701591695, 0.24207278863, 8.5821489635, 0.42263558251,
        3.4922679161, 1.0, 1.2637426998, 1.0,
        0.46607870005, 1.0, 0.15766003, 1.0,
        5.551, 0.2, 1.235, 1.0,
        0.412, 1.0, 0.89, 1.0]
}

#| The def2-TZVP basis set as a `Basis` record.
def basis_def2tzvp() -> Basis {
    return basis_of(basis_def2tzvp_shells_flat(), basis_def2tzvp_prims_flat())
}

#| The Cartesian and spherical AO counts of one atom of each element, `1` to `18`,
#| as the generator counted them.
def basis_def2tzvp_nao() -> Arr {
    return [6, 6, 6, 6, 14, 14, 20, 19, 36, 31, 36, 31,
        36, 31, 36, 31, 36, 31, 36, 31, 35, 32, 35, 32,
        42, 37, 42, 37, 42, 37, 42, 37, 42, 37, 42, 37]
}

test "the def2-TZVP table covers H through Ar, each element's shells in one run" {
    btdef2tzvp_b = basis_def2tzvp()
    assert_near(len(btdef2tzvp_b.shells), BASIS_DEF2TZVP_NSHELL, 0.0)
    assert_near(len(btdef2tzvp_b.prims), BASIS_DEF2TZVP_NPRIM, 0.0)
    assert_near(basis_check(btdef2tzvp_b), 0.0, 0.0)
    btdef2tzvp_n = basis_rows(basis_def2tzvp_nao(), BS_NAO_LEN)
    for btdef2tzvp_z to len(btdef2tzvp_n) {
        btdef2tzvp_k = basis_nao(btdef2tzvp_b, btdef2tzvp_z + 1)
        assert_near(btdef2tzvp_k[0], btdef2tzvp_n[btdef2tzvp_z, 0], 0.0)
        assert_near(btdef2tzvp_k[1], btdef2tzvp_n[btdef2tzvp_z, 1], 0.0)
    }
}

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

BASIS_DEF2TZVP_NSHELL = 193
BASIS_DEF2TZVP_NPRIM = 374

#| (Z, l, nprim, p0), one segmented shell per row, by element.
def basis_def2tzvp_shells_flat() -> Arr {
    return [1, 0, 3, 0, 1, 0, 1, 3, 1, 0, 1, 4, 1, 1, 1, 5,
        2, 0, 3, 6, 2, 0, 1, 9, 2, 0, 1, 10, 2, 1, 1, 11,
        3, 0, 6, 12, 3, 0, 2, 18, 3, 0, 1, 20, 3, 0, 1, 21,
        3, 0, 1, 22, 3, 1, 1, 23, 3, 1, 1, 24, 3, 1, 1, 25,
        4, 0, 6, 26, 4, 0, 2, 32, 4, 0, 1, 34, 4, 0, 1, 35,
        4, 0, 1, 36, 4, 1, 2, 37, 4, 1, 1, 39, 4, 1, 1, 40,
        4, 2, 1, 41, 5, 0, 6, 42, 5, 0, 2, 48, 5, 0, 1, 50,
        5, 0, 1, 51, 5, 0, 1, 52, 5, 1, 4, 53, 5, 1, 1, 57,
        5, 1, 1, 58, 5, 2, 1, 59, 5, 2, 1, 60, 5, 3, 1, 61,
        6, 0, 6, 62, 6, 0, 2, 68, 6, 0, 1, 70, 6, 0, 1, 71,
        6, 0, 1, 72, 6, 1, 4, 73, 6, 1, 1, 77, 6, 1, 1, 78,
        6, 2, 1, 79, 6, 2, 1, 80, 6, 3, 1, 81, 7, 0, 6, 82,
        7, 0, 2, 88, 7, 0, 1, 90, 7, 0, 1, 91, 7, 0, 1, 92,
        7, 1, 4, 93, 7, 1, 1, 97, 7, 1, 1, 98, 7, 2, 1, 99,
        7, 2, 1, 100, 7, 3, 1, 101, 8, 0, 6, 102, 8, 0, 2, 108,
        8, 0, 1, 110, 8, 0, 1, 111, 8, 0, 1, 112, 8, 1, 4, 113,
        8, 1, 1, 117, 8, 1, 1, 118, 8, 2, 1, 119, 8, 2, 1, 120,
        8, 3, 1, 121, 9, 0, 6, 122, 9, 0, 2, 128, 9, 0, 1, 130,
        9, 0, 1, 131, 9, 0, 1, 132, 9, 1, 4, 133, 9, 1, 1, 137,
        9, 1, 1, 138, 9, 2, 1, 139, 9, 2, 1, 140, 9, 3, 1, 141,
        10, 0, 6, 142, 10, 0, 2, 148, 10, 0, 1, 150, 10, 0, 1, 151,
        10, 0, 1, 152, 10, 1, 4, 153, 10, 1, 1, 157, 10, 1, 1, 158,
        10, 2, 1, 159, 10, 2, 1, 160, 10, 3, 1, 161, 11, 0, 7, 162,
        11, 0, 3, 169, 11, 0, 2, 172, 11, 0, 1, 174, 11, 0, 1, 175,
        11, 1, 5, 176, 11, 1, 1, 181, 11, 1, 1, 182, 11, 1, 1, 183,
        11, 2, 1, 184, 11, 2, 1, 185, 11, 2, 1, 186, 12, 0, 7, 187,
        12, 0, 3, 194, 12, 0, 2, 197, 12, 0, 1, 199, 12, 0, 1, 200,
        12, 1, 5, 201, 12, 1, 1, 206, 12, 1, 1, 207, 12, 1, 1, 208,
        12, 2, 1, 209, 12, 2, 1, 210, 12, 2, 1, 211, 13, 0, 7, 212,
        13, 0, 3, 219, 13, 0, 2, 222, 13, 0, 1, 224, 13, 0, 1, 225,
        13, 1, 5, 226, 13, 1, 1, 231, 13, 1, 1, 232, 13, 1, 1, 233,
        13, 1, 1, 234, 13, 2, 2, 235, 13, 2, 1, 237, 13, 3, 1, 238,
        14, 0, 7, 239, 14, 0, 3, 246, 14, 0, 2, 249, 14, 0, 1, 251,
        14, 0, 1, 252, 14, 1, 5, 253, 14, 1, 1, 258, 14, 1, 1, 259,
        14, 1, 1, 260, 14, 1, 1, 261, 14, 2, 2, 262, 14, 2, 1, 264,
        14, 3, 1, 265, 15, 0, 7, 266, 15, 0, 3, 273, 15, 0, 2, 276,
        15, 0, 1, 278, 15, 0, 1, 279, 15, 1, 5, 280, 15, 1, 1, 285,
        15, 1, 1, 286, 15, 1, 1, 287, 15, 1, 1, 288, 15, 2, 2, 289,
        15, 2, 1, 291, 15, 3, 1, 292, 16, 0, 7, 293, 16, 0, 3, 300,
        16, 0, 2, 303, 16, 0, 1, 305, 16, 0, 1, 306, 16, 1, 5, 307,
        16, 1, 1, 312, 16, 1, 1, 313, 16, 1, 1, 314, 16, 1, 1, 315,
        16, 2, 2, 316, 16, 2, 1, 318, 16, 3, 1, 319, 17, 0, 7, 320,
        17, 0, 3, 327, 17, 0, 2, 330, 17, 0, 1, 332, 17, 0, 1, 333,
        17, 1, 5, 334, 17, 1, 1, 339, 17, 1, 1, 340, 17, 1, 1, 341,
        17, 1, 1, 342, 17, 2, 2, 343, 17, 2, 1, 345, 17, 3, 1, 346,
        18, 0, 7, 347, 18, 0, 3, 354, 18, 0, 2, 357, 18, 0, 1, 359,
        18, 0, 1, 360, 18, 1, 5, 361, 18, 1, 1, 366, 18, 1, 1, 367,
        18, 1, 1, 368, 18, 1, 1, 369, 18, 2, 2, 370, 18, 2, 1, 372,
        18, 3, 1, 373]
}

#| (exponent, coefficient), one primitive per row.
def basis_def2tzvp_prims_flat() -> Arr {
    return [34.061341, 0.0060251978, 5.1235746, 0.045021094,
        1.1646626, 0.20189726, 0.32723041, 1.0,
        0.10307241, 1.0, 0.8, 1.0,
        98.078321616, 0.0075803064967, 14.764404247, 0.054848620937,
        3.3185831473, 0.22074382186, 0.87413869551, 1.0,
        0.24459897208, 1.0, 1.0, 1.0,
        6269.262801, 0.00020540968826, 940.31612431, 0.0015916554089,
        214.22107528, 0.0082869829707, 60.759840184, 0.033856374249,
        19.915152032, 0.11103225876, 7.3171509797, 0.27449383329,
        2.9724674216, 0.23792456411, 1.2639852314, 0.30765411924,
        0.51427489953, 1.0, 0.077030885901, 1.0,
        0.028938896433, 1.0, 3.327, 1.0,
        0.4, 1.0, 0.06, 1.0,
        4700.2365626, 0.00023584389316, 704.82845622, 0.0018243791019,
        160.43110478, 0.0093966148224, 45.425347336, 0.036908924159,
        14.798334125, 0.10897561281, 5.3512452537, 0.21694284551,
        2.1542044819, 0.44695408857, 0.933637444, 0.20866985771,
        0.18791432989, 1.0, 0.074648267947, 1.0,
        0.032650484598, 1.0, 0.71695694366, -0.16877854032,
        0.1954193286, -0.51403419628, 3.6316917145, 1.0,
        0.06051546589, 1.0, 0.18, 1.0,
        8564.8660687, 0.00022837198155, 1284.1516263, 0.0017682576447,
        292.27871604, 0.0091407080516, 82.775469176, 0.036342638989,
        27.017939269, 0.11063458441, 9.814961966, 0.23367344321,
        3.9318559059, 0.41818777978, 1.6595599712, 0.22325473798,
        0.35762965239, 1.0, 0.14246277496, 1.0,
        0.060560594768, 1.0, 22.453875803, 0.0050265575179,
        5.104505833, 0.032801738965, 1.4986081344, 0.13151230768,
        0.50927831315, 0.33197167769, 0.18147077798, 1.0,
        0.064621893904, 1.0, 0.661, 1.0,
        0.199, 1.0, 0.49, 1.0,
        13575.349682, 0.00022245814352, 2035.233368, 0.0017232738252,
        463.22562359, 0.0089255715314, 131.20019598, 0.035727984502,
        42.853015891, 0.11076259931, 15.584185766, 0.24295627626,
        6.2067138508, 0.41440263448, 2.5764896527, 0.23744968655,
        0.57696339419, 1.0, 0.22972831358, 1.0,
        0.095164440028, 1.0, 34.697232244, 0.0053333657805,
        7.9582622826, 0.035864109092, 2.3780826883, 0.14215873329,
        0.81433208183, 0.34270471845, 0.28887547253, 1.0,
        0.10056823671, 1.0, 1.097, 1.0,
        0.318, 1.0, 0.761, 1.0,
        19730.800647, 0.00021887984991, 2957.8958745, 0.0016960708803,
        673.22133595, 0.0087954603538, 190.68249494, 0.035359382605,
        62.295441898, 0.11095789217, 22.654161182, 0.24982972552,
        8.9791477428, 0.40623896148, 3.686300237, 0.24338217176,
        0.84660076805, 1.0, 0.33647133771, 1.0,
        0.13647653675, 1.0, 49.20038051, 0.0055552416751,
        11.346790537, 0.038052379723, 3.4273972411, 0.14953671029,
        1.1785525134, 0.3494930523, 0.41642204972, 1.0,
        0.14260826011, 1.0, 1.654, 1.0,
        0.469, 1.0, 1.093, 1.0,
        27032.382631, 0.00021726302465, 4052.3871392, 0.0016838662199,
        922.3272271, 0.0087395616265, 261.24070989, 0.035239968808,
        85.354641351, 0.11153519115, 31.035035245, 0.25588953961,
        12.260860728, 0.39768730901, 4.9987076005, 0.2462784943,
        1.1703108158, 1.0, 0.46474740994, 1.0,
        0.18504536357, 1.0, 63.274954801, 0.0060685103418,
        14.627049379, 0.041912575824, 4.4501223456, 0.16153841088,
        1.5275799647, 0.35706951311, 0.52935117943, 1.0,
        0.1747842127, 1.0, 2.314, 1.0,
        0.645, 1.0, 1.428, 1.0,
        35479.100441, 0.00021545014888, 5318.4728983, 0.0016700686527,
        1210.4810975, 0.0086733211476, 342.8551814, 0.035049933175,
        112.01943181, 0.11165320133, 40.714740248, 0.25988506647,
        16.039678111, 0.3942296688, 6.503818674, 0.24998238551,
        1.5440477509, 1.0, 0.61223452862, 1.0,
        0.24027979698, 1.0, 80.233900483, 0.0063685999134,
        18.594010743, 0.04430314353, 5.6867902653, 0.16867248708,
        1.9511006294, 0.36166346255, 0.66970211298, 1.0,
        0.2165130041, 1.0, 3.107, 1.0,
        0.855, 1.0, 1.917, 1.0,
        45069.464022, 0.00021687155182, 6755.9768656, 0.0016812736757,
        1537.6502864, 0.0087356062782, 435.51697667, 0.035361266922,
        142.28655638, 0.11321521454, 51.692153804, 0.26654653104,
        20.31587049, 0.39631959951, 8.2021942646, 0.25582811251,
        1.9681276278, 1.0, 0.77904756001, 1.0,
        0.30229502043, 1.0, 99.782996032, 0.0065569234163,
        23.176124101, 0.045888009138, 7.1163945872, 0.17331287812,
        2.4418711435, 0.36475267512, 0.83389605766, 1.0,
        0.26607311301, 1.0, 4.014, 1.0,
        1.096, 1.0, 2.544, 1.0,
        26041.109927, 0.00061806342811, 3906.1268548, 0.0047748604414,
        888.97454993, 0.024471684829, 251.45497961, 0.094755394977,
        81.650143512, 0.2686749692, 28.904158401, 0.4792547544,
        10.625782932, 0.33248591469, 53.769410179, 0.019527731872,
        16.308243025, 0.092648010794, 2.3730384125, -0.39938670172,
        0.95730772603, 1.6428595391, 0.40806460959, 0.55692596966,
        0.049967582329, 1.0, 0.01926861625, 1.0,
        138.07979989, 0.0057951891929, 32.232700393, 0.041620846251,
        9.981607536, 0.16281916885, 3.4822033928, 0.36011784647,
        1.229913462, 0.44858979889, 0.41743959423, 1.0,
        0.091, 1.0, 0.03, 1.0,
        2.609, 1.0, 0.43, 1.0,
        0.1, 1.0, 31438.349555, 0.00060912311326,
        4715.5153354, 0.0047066196465, 1073.1629247, 0.024135820657,
        303.57238768, 0.093628959834, 98.626251042, 0.26646742093,
        34.943808417, 0.47890929917, 12.859785199, 0.33698490286,
        64.876913004, 0.019180889307, 19.725520777, 0.090913704392,
        2.8951804339, -0.39563756125, 1.196045471, 1.6827603373,
        0.54329451156, 0.52141091954, 0.10099104092, 1.0,
        0.036865728085, 1.0, 179.87189612, 0.0053799549018,
        42.120069376, 0.039318014098, 13.120503032, 0.15740129476,
        4.6257503609, 0.35919094128, 1.6695211016, 0.4553337931,
        0.58551012105, 1.0, 0.18914796195, 1.0,
        0.053768755187, 1.0, 3.444, 1.0,
        0.29, 1.0, 0.07, 1.0,
        37792.550772, 0.00057047888709, 5668.0682165, 0.0044093016538,
        1289.8582841, 0.022630967411, 364.86596028, 0.088025644295,
        118.57631515, 0.25223701612, 42.024867605, 0.45960547169,
        15.499501629, 0.33277886014, 75.208026598, 0.01925056019,
        23.031408972, 0.087906743952, 3.6348797649, -0.34246704535,
        1.6065049957, 1.5106266058, 0.76103394581, 0.5807101647,
        0.16556708849, 1.0, 0.060041577113, 1.0,
        452.52303192, 0.0023110812466, 107.08195049, 0.018568641823,
        34.131021255, 0.087216237035, 12.587037428, 0.26902101523,
        4.9811919704, 0.52128324272, 2.00703509, 1.0,
        0.80083714374, 1.0, 0.20178927472, 1.0,
        0.057895550392, 1.0, 1.57, 0.2,
        0.333, 1.0, 0.111, 1.0,
        0.244, 1.0, 44773.358078, 0.00055914765868,
        6717.1992104, 0.0043206040189, 1528.8960325, 0.02218709646,
        432.54746585, 0.086489249116, 140.61505226, 0.24939889716,
        49.857636724, 0.46017197366, 18.434974885, 0.34250236575,
        86.533886111, 0.021300063007, 26.624606846, 0.094676139318,
        4.4953057159, -0.32616264859, 2.103504571, 1.398080385,
        1.0106094922, 0.63865786699, 0.23701751489, 1.0,
        0.085703405362, 1.0, 394.47503628, 0.0026285693959,
        93.137683104, 0.020556257749, 29.519608742, 0.092070262801,
        10.781663791, 0.25565889739, 4.1626574778, 0.42111707185,
        1.6247972989, 1.0, 0.54306660493, 1.0,
        0.20582073956, 1.0, 0.070053487306, 1.0,
        2.303, 0.2, 0.476, 1.0,
        0.16, 1.0, 0.336, 1.0,
        52426.999233, 0.000552071641, 7863.2660552, 0.0042678595308,
        1789.5227333, 0.021931529186, 506.27300165, 0.085667168373,
        164.60698546, 0.24840686605, 58.391918722, 0.46336753971,
        21.643663201, 0.35350558156, 99.01383762, 0.021895679958,
        30.550439817, 0.095650470295, 5.4537087661, -0.29454270186,
        2.6503362563, 1.32943812, 1.2726688867, 0.66109396473,
        0.31645005203, 1.0, 0.11417466938, 1.0,
        472.27219248, 0.0025710623052, 111.58882756, 0.020250297999,
        35.445936418, 0.091580716787, 12.990776875, 0.25749454014,
        5.0486221658, 0.42862899758, 1.9934049566, 1.0,
        0.6652728443, 1.0, 0.25516832128, 1.0,
        0.090357762251, 1.0, 3.12, 0.2,
        0.648, 1.0, 0.218, 1.0,
        0.452, 1.0, 60700.928104, 0.00054695944225,
        9102.6106854, 0.0042297224557, 2071.4166009, 0.021747824159,
        586.02476821, 0.085100053589, 190.55395021, 0.24799128459,
        67.63038426, 0.46703640406, 25.127306905, 0.3643458755,
        112.5746301, 0.02167004024, 34.795554217, 0.09360230176,
        6.5115556215, -0.26068001422, 3.2399032261, 1.2842089435,
        1.5477160881, 0.66036416584, 0.40541030112, 1.0,
        0.14550651059, 1.0, 564.36716027, 0.0024796796317,
        133.42624379, 0.01967793025, 42.468271189, 0.089980008258,
        15.61652758, 0.25705880575, 6.1093988469, 0.43515167292,
        2.4404160198, 1.0, 0.83882201296, 1.0,
        0.312887469, 1.0, 0.10770109004, 1.0,
        3.756, 0.2, 0.812, 1.0,
        0.273, 1.0, 0.557, 1.0,
        69507.990945, 0.00054314897497, 10426.15688, 0.0041990463961,
        2373.2334061, 0.021592141679, 671.56420071, 0.084598850094,
        218.4199979, 0.24757249724, 77.572249714, 0.47016930228,
        28.888815277, 0.37436370716, 127.10527185, 0.025182166603,
        39.339582961, 0.10786112456, 7.6740679989, -0.27408821574,
        3.874562763, 1.3213875014, 1.8385832573, 0.68636955368,
        0.50229057542, 1.0, 0.1796272342, 1.0,
        666.50423284, 0.0023632663836, 157.6424169, 0.018879300374,
        50.262520978, 0.087206341273, 18.536078105, 0.2528561297,
        7.2940532777, 0.4350715482, 2.9433248995, 1.0,
        1.0404970818, 1.0, 0.3845641508, 1.0,
        0.13069642732, 1.0, 4.61, 0.2,
        1.011, 1.0, 0.339, 1.0,
        0.706, 1.0, 79111.422998, 0.00051029325002,
        11864.746009, 0.0039463036981, 2700.1642973, 0.02030707391,
        763.95943485, 0.079691825214, 248.45150561, 0.23420623836,
        88.283581, 0.44833849481, 32.948607069, 0.364081674,
        142.55358, 0.026387407001, 44.163688009, 0.11226433999,
        8.9524995, -0.26178922001, 4.5546920941, 1.3002484998,
        2.1444079001, 0.67197237009, 0.60708777004, 1.0,
        0.21651431999, 1.0, 776.77541998, 0.0022028005003,
        183.80107018, 0.017694180008, 58.694003175, 0.082431293717,
        21.701591695, 0.24207278863, 8.5821489635, 0.42263558251,
        3.4922679161, 1.0, 1.2637426998, 1.0,
        0.46607870005, 1.0, 0.15766003, 1.0,
        5.551, 0.2, 1.235, 1.0,
        0.412, 1.0, 0.89, 1.0]
}

#| The def2-TZVP basis set as a `Basis` record.
def basis_def2tzvp() -> Basis {
    return basis_of(basis_def2tzvp_shells_flat(), basis_def2tzvp_prims_flat())
}

#| The Cartesian and spherical AO counts of one atom of each element, `1` to `18`,
#| as the generator counted them.
def basis_def2tzvp_nao() -> Arr {
    return [6, 6, 6, 6, 14, 14, 20, 19, 36, 31, 36, 31,
        36, 31, 36, 31, 36, 31, 36, 31, 35, 32, 35, 32,
        42, 37, 42, 37, 42, 37, 42, 37, 42, 37, 42, 37]
}

test "the def2-TZVP table covers H through Ar, each element's shells in one run" {
    btdef2tzvp_b = basis_def2tzvp()
    assert_near(len(btdef2tzvp_b.shells), BASIS_DEF2TZVP_NSHELL, 0.0)
    assert_near(len(btdef2tzvp_b.prims), BASIS_DEF2TZVP_NPRIM, 0.0)
    assert_near(basis_check(btdef2tzvp_b), 0.0, 0.0)
    btdef2tzvp_n = basis_rows(basis_def2tzvp_nao(), BS_NAO_LEN)
    for btdef2tzvp_z to len(btdef2tzvp_n) {
        btdef2tzvp_k = basis_nao(btdef2tzvp_b, btdef2tzvp_z + 1)
        assert_near(btdef2tzvp_k[0], btdef2tzvp_n[btdef2tzvp_z, 0], 0.0)
        assert_near(btdef2tzvp_k[1], btdef2tzvp_n[btdef2tzvp_z, 1], 0.0)
    }
}