2.5. Atomic integration grids

2.5.1. Built-in grids

The table below lists the number of grid points in each built-in atomic integration grid in HORTON. For the heavier elements (after Kr), the grids are calibrated based on reference computations with pseudo potentials. The last digit in the grid name refers to the number of significant digits obtained with these grids on diatomic benchmarks.

Element Z Zeff tv-13.7-3 tv-13.7-4 tv-13.7-5 tv-13.7-6 tv-13.7-7 tv-13.7-8
coarse medium fine veryfine ultrafine insane
H 1 1 604 928 1984 3154 4546 6622
He 2 2 680 1428 2104 3298 4998 7234
Li 3 3 1416 3558 8066 19718 28146 52228
Be 4 4 1140 2370 6378 9038 23522 34894
B 5 5 1136 2490 3558 8190 11722 29646
C 6 6 1536 2490 5214 8314 8314 31764
N 7 7 1372 2306 3354 8234 18082 39504
O 8 8 1612 3754 5414 7746 18938 40012
F 9 9 1212 2918 6302 9966 13602 40904
Ne 10 10 1840 3414 5606 8778 18998 38116
Na 11 11 2066 4470 10110 21890 33076 73164
Mg 12 12 2346 5122 8158 17546 42384 75514
Al 13 13 1982 6370 6370 23338 46954 46954
Si 14 14 1874 2642 7238 20430 40104 49096
P 15 15 3086 4614 10506 15258 46456 70876
S 16 16 2402 8498 12162 12162 49628 80972
Cl 17 17 2254 6770 6770 20630 44192 48538
Ar 18 18 2814 4802 11014 24038 58602 67344
K 19 19 2862 9710 14590 31796 58566 79976
Ca 20 20 3210 6874 16962 25126 67666 97256
Sc 21 21 3142 4814 16402 23342 44348 89152
Ti 22 22 2510 7786 10986 16542 35432 79040
V 23 23 3118 4798 10850 16850 53212 83928
Cr 24 24 3698 3698 11438 20018 55124 73896
Mn 25 25 3878 3878 13066 34474 65012 89916
Fe 26 26 3386 5194 12358 19386 54572 72600
Co 27 27 3818 4634 9854 25946 54356 102196
Ni 28 28 3942 5670 13142 20302 61932 87716
Cu 29 29 2778 10278 16286 36220 46310 46310
Zn 30 30 4050 10798 18882 50232 52794 52794
Ga 31 31 4262 10422 26582 56758 63532 63532
Ge 32 32 3798 8138 24992 43248 48600 –
As 33 33 3270 10230 28534 42460 44294 44294
Se 34 34 1586 3106 6070 12398 43600 43600
Br 35 35 3682 7506 7506 51386 62096 62096
Kr 36 36 6550 9978 37152 41514 41514 –
Rb 37 9 2768 7662 15870 29758 54196 68138
Sr 38 10 2360 5298 14598 27266 48612 78458
Y 39 11 2844 5970 12542 24838 46326 75068
Zr 40 12 1956 4720 11494 22034 42674 72940
Nb 41 13 1964 4676 12882 23678 35878 63660
Mo 42 14 1788 3708 10638 15662 30454 53504
Tc 43 15 1636 3792 7530 15170 33138 58100
Ru 44 16 1680 2980 7450 15582 40914 55316
Rh 45 17 2484 3972 7394 15638 38578 52740
Pd 46 18 2076 5158 11070 15662 39894 68412
Ag 47 19 1680 4190 8782 26122 49164 65284
Cd 48 20 2596 5462 11926 16582 40696 72186
In 49 21 2284 3738 7122 16114 31886 44696
Sn 50 22 1352 4146 8482 17126 25974 47272
Sb 51 23 2388 4834 9974 20454 42416 71886
Te 52 24 2040 3790 8438 19294 40376 50820
I 53 25 2116 4358 8174 18498 35636 50172
Xe 54 26 2008 4402 9630 21350 42868 75950
Cs 55 9 2728 8426 16798 31698 55320 86878
Ba 56 10 4032 7026 14698 28110 47764 61420
La 57 11 2372 4646 13250 26742 49180 63652
Hf 72 12 3908 6362 15054 28302 51658 64868
Ta 73 13 2928 4950 10806 15646 32130 58028
W 74 14 2000 5870 9234 18634 36038 63440
Re 75 15 3404 5882 9114 19114 34294 59132
Os 76 16 1964 7190 11466 21886 41698 71900
Ir 77 17 3244 5114 12334 22718 46926 78872
Pt 78 18 1996 6134 9998 15174 39990 65648
Au 79 19 2052 3836 9566 19354 37734 63976
Hg 80 20 1904 4626 6494 18530 29042 50036
Tl 81 21 2672 3954 10890 21154 41916 68886
Pb 82 22 2436 5514 7630 19862 43276 56760
Bi 83 23 2540 4802 11070 22566 41604 72014
Po 84 24 1308 2906 8318 17434 36680 47564
At 85 25 2188 4226 8358 18038 36636 50940
Rn 86 26 1964 5710 12130 18734 33336 58950

2.5.2. The --grid option

The scripts horton-atomdb.py and horton-wpart.py have a --grid option to specify the atomic integration grids. This option may be used to control the numerical accuracy of the output. This option takes one argument that may have any of the following four formats:

  1. A filename of with atomic grid specifications in the same format as those found in ${HORTONDATA}/grids.

  2. A filename of a file in ${HORTONDATA}/grids without the extension .txt. (These are discussed above.)

  3. Equivalently to the previous point, one of the following names: coarse, medium, fine, veryfine, ultrafine and insane.

  4. A string with the following format: rname:rmin:rmax:nrad:nll, with the following meaning for the keywords:

    • rname specifies the type of radial grid. It can be linear, exp or power.
    • rmin and rmax specify the first and the last radial grid point in angstroms.
    • nrad is the number of radial grid points.
    • nll is the number of points for the angular Lebedev-Laikov grid. It must be one of the following values: 6, 14, 26, 38, 50, 74, 86, 110, 146, 170, 194, 230, 266, 302, 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030, 2354, 2702, 3074, 3470, 3890, 4334, 4802, 5294, 5810