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CNEO: CNEO-DFT energy and force Energy and force for constrained nuclear-electronic orbital density functional theory (J. Chem. Theory Comput. 2025, 21, 16, 7865–7877). `POTENTIAL CNEO` triggers CNEO calculations for certain atom kinds (hydrogen is the most common, but no limit in principle) and nuclear basis functions are supplied by `BASIS_SET NUC basis_name`. PB series basis sets for proton are provided in `data/NUCLEAR_BASIS_SETS`. The `MASS` can be tuned to simulate isotopes such as deuterium, however, one should be careful that basis functions need to be changed accordingly. One simple modification to PB4-D with scaled exponents that is suitable for deuterium is also added to `data/NUCLEAR_BASIS_SETS` Note that GAPW is mandatory for atoms with quantum nuclei in CNEO-DFT calculations, and pseudopotentials or even `GPW_TYPE T` can be used for atom kinds with conventional classical nuclei. For the electronic part, k-points can be enabled. However, this k-points setting will not affect the quantum nuclear part. This is because even quantum nuclei are delocalized as compared to conventional classical point charges, they are still relatively localized. Therefore, a distinguishable-particle approximation is used for quantum nuclei. This is similar to the Gamma-point approximation for indistinguishable quantum nuclei, with the added benefit that each quantum nucleus only involves a small Kohn-Sham equation with localized basis functions, and multiple quantum nuclei create multiple coupled Kohn-Sham equations, instead of a giant one in the indistinguishable fermion case.
2025-08-31 12:49:45 -05:00
# PB series nuclear basis sets are from
# J. Chem. Phys. 152, 244123 (2020); doi: 10.1063/5.0009233
# Table 1. Table S2 for PB4-F2a.
H PB4-D
9
1 0 0 1 1
1.9570000000 1.0000000000
1 0 0 1 1
8.7340000000 1.0000000000
1 0 0 1 1
16.0100000000 1.0000000000
1 0 0 1 1
31.9970000000 1.0000000000
1 1 1 1 1
9.4380000000 1.0000000000
1 1 1 1 1
13.7950000000 1.0000000000
1 1 1 1 1
24.0280000000 1.0000000000
1 2 2 1 1
10.5240000000 1.0000000000
1 2 2 1 1
19.0160000000 1.0000000000
#
# scale PB4-D's exponents by sqrt(m_{deuteron}/m_{proton})
# use this for deuterium
H PB4-D_D
9
1 0 0 1 1
2.7669291965160787 1.0000000000
1 0 0 1 1
12.34867634255055 1.0000000000
1 0 0 1 1
22.635940948504047 1.0000000000
1 0 0 1 1
45.23936305617014 1.0000000000
1 1 1 1 1
13.344035644720874 1.0000000000
1 1 1 1 1
19.504235189544865 1.0000000000
1 1 1 1 1
33.97229163714273 1.0000000000
1 2 2 1 1
14.879490477330203 1.0000000000
1 2 2 1 1
26.886012059759704 1.0000000000
#
# scale PB4-D's exponents by sqrt(m_{antimuon}/m_{proton})
# use this for muonium (experimental)
H PB4-D_Mu
9
1 0 0 1 1
0.656717216271848 1.0000000000
1 0 0 1 1
2.9308983990384876 1.0000000000
1 0 0 1 1
5.372530726884153 1.0000000000
1 0 0 1 1
10.737343264716566 1.0000000000
1 1 1 1 1
3.1671420987090966 1.0000000000
1 1 1 1 1
4.6292355638580185 1.0000000000
1 1 1 1 1
8.063158545007646 1.0000000000
1 2 2 1 1
3.5315748513259724 1.0000000000
1 2 2 1 1
6.381264478602688 1.0000000000
#
H PB4-F1
10
1 0 0 1 1
5.9730000000 1.0000000000
1 0 0 1 1
10.6450000000 1.0000000000
1 0 0 1 1
17.9430000000 1.0000000000
1 0 0 1 1
28.9500000000 1.0000000000
1 1 1 1 1
7.6040000000 1.0000000000
1 1 1 1 1
14.7010000000 1.0000000000
1 1 1 1 1
23.3080000000 1.0000000000
1 2 2 1 1
9.0110000000 1.0000000000
1 2 2 1 1
19.7870000000 1.0000000000
1 3 3 1 1
10.9140000000 1.0000000000
#
H PB4-F2
11
1 0 0 1 1
5.9730000000 1.0000000000
1 0 0 1 1
10.6450000000 1.0000000000
1 0 0 1 1
17.9430000000 1.0000000000
1 0 0 1 1
28.9500000000 1.0000000000
1 1 1 1 1
7.6040000000 1.0000000000
1 1 1 1 1
14.7010000000 1.0000000000
1 1 1 1 1
23.3080000000 1.0000000000
1 2 2 1 1
9.0110000000 1.0000000000
1 2 2 1 1
19.7870000000 1.0000000000
1 3 3 1 1
10.9140000000 1.0000000000
1 3 3 1 1
20.9850000000 1.0000000000
#
H PB4-F2a
11
1 0 0 1 1
5.2290000000 1.0000000000
1 0 0 1 1
9.3370000000 1.0000000000
1 0 0 1 1
17.0180000000 1.0000000000
1 0 0 1 1
30.5080000000 1.0000000000
1 1 1 1 1
8.4840000000 1.0000000000
1 1 1 1 1
13.9930000000 1.0000000000
1 1 1 1 1
23.8090000000 1.0000000000
1 2 2 1 1
9.3170000000 1.0000000000
1 2 2 1 1
19.2670000000 1.0000000000
1 3 3 1 1
10.5360000000 1.0000000000
1 3 3 1 1
19.5740000000 1.0000000000
#
H PB5-D
12
1 0 0 1 1
1.9080000000 1.0000000000
1 0 0 1 1
9.0510000000 1.0000000000
1 0 0 1 1
15.0510000000 1.0000000000
1 0 0 1 1
29.7660000000 1.0000000000
1 0 0 1 1
40.1350000000 1.0000000000
1 1 1 1 1
4.9070000000 1.0000000000
1 1 1 1 1
10.0880000000 1.0000000000
1 1 1 1 1
15.8930000000 1.0000000000
1 1 1 1 1
25.7740000000 1.0000000000
1 2 2 1 1
10.3520000000 1.0000000000
1 2 2 1 1
18.3580000000 1.0000000000
1 2 2 1 1
36.3660000000 1.0000000000
#
H PB5-F
14
1 0 0 1 1
4.1890000000 1.0000000000
1 0 0 1 1
6.2310000000 1.0000000000
1 0 0 1 1
14.6240000000 1.0000000000
1 0 0 1 1
20.4810000000 1.0000000000
1 0 0 1 1
48.5090000000 1.0000000000
1 1 1 1 1
2.3490000000 1.0000000000
1 1 1 1 1
7.5970000000 1.0000000000
1 1 1 1 1
18.5210000000 1.0000000000
1 1 1 1 1
30.5960000000 1.0000000000
1 2 2 1 1
8.9710000000 1.0000000000
1 2 2 1 1
17.9560000000 1.0000000000
1 2 2 1 1
21.2990000000 1.0000000000
1 3 3 1 1
10.3210000000 1.0000000000
1 3 3 1 1
26.9100000000 1.0000000000
#
H PB5-G
15
1 0 0 1 1
3.2830000000 1.0000000000
1 0 0 1 1
7.6130000000 1.0000000000
1 0 0 1 1
16.0770000000 1.0000000000
1 0 0 1 1
20.4570000000 1.0000000000
1 0 0 1 1
47.0110000000 1.0000000000
1 1 1 1 1
3.1670000000 1.0000000000
1 1 1 1 1
7.7850000000 1.0000000000
1 1 1 1 1
18.9850000000 1.0000000000
1 1 1 1 1
29.4250000000 1.0000000000
1 2 2 1 1
10.2390000000 1.0000000000
1 2 2 1 1
17.2980000000 1.0000000000
1 2 2 1 1
20.6820000000 1.0000000000
1 3 3 1 1
10.9300000000 1.0000000000
1 3 3 1 1
25.9720000000 1.0000000000
1 4 4 1 1
10.5130000000 1.0000000000
#
H PB6-D
15
1 0 0 1 1
2.5130000000 1.0000000000
1 0 0 1 1
4.8400000000 1.0000000000
1 0 0 1 1
9.0880000000 1.0000000000
1 0 0 1 1
16.2310000000 1.0000000000
1 0 0 1 1
31.1100000000 1.0000000000
1 0 0 1 1
38.7540000000 1.0000000000
1 1 1 1 1
2.1740000000 1.0000000000
1 1 1 1 1
5.8970000000 1.0000000000
1 1 1 1 1
9.9960000000 1.0000000000
1 1 1 1 1
16.3470000000 1.0000000000
1 1 1 1 1
25.7160000000 1.0000000000
1 2 2 1 1
2.9300000000 1.0000000000
1 2 2 1 1
11.0150000000 1.0000000000
1 2 2 1 1
17.2560000000 1.0000000000
1 2 2 1 1
25.5410000000 1.0000000000
#
H PB6-F
18
1 0 0 1 1
2.8120000000 1.0000000000
1 0 0 1 1
5.7030000000 1.0000000000
1 0 0 1 1
10.2020000000 1.0000000000
1 0 0 1 1
15.4500000000 1.0000000000
1 0 0 1 1
29.1350000000 1.0000000000
1 0 0 1 1
39.7530000000 1.0000000000
1 1 1 1 1
1.4170000000 1.0000000000
1 1 1 1 1
6.8840000000 1.0000000000
1 1 1 1 1
10.4500000000 1.0000000000
1 1 1 1 1
16.1870000000 1.0000000000
1 1 1 1 1
26.4470000000 1.0000000000
1 2 2 1 1
4.4830000000 1.0000000000
1 2 2 1 1
9.8700000000 1.0000000000
1 2 2 1 1
18.3130000000 1.0000000000
1 2 2 1 1
25.3470000000 1.0000000000
1 3 3 1 1
6.0010000000 1.0000000000
1 3 3 1 1
10.3220000000 1.0000000000
1 3 3 1 1
24.4090000000 1.0000000000
#
H PB6-G
20
1 0 0 1 1
2.0160000000 1.0000000000
1 0 0 1 1
3.0490000000 1.0000000000
1 0 0 1 1
6.3500000000 1.0000000000
1 0 0 1 1
8.9100000000 1.0000000000
1 0 0 1 1
19.5000000000 1.0000000000
1 0 0 1 1
29.2960000000 1.0000000000
1 1 1 1 1
2.6380000000 1.0000000000
1 1 1 1 1
3.7160000000 1.0000000000
1 1 1 1 1
5.9780000000 1.0000000000
1 1 1 1 1
16.2520000000 1.0000000000
1 1 1 1 1
25.1140000000 1.0000000000
1 2 2 1 1
2.2050000000 1.0000000000
1 2 2 1 1
3.6540000000 1.0000000000
1 2 2 1 1
9.1040000000 1.0000000000
1 2 2 1 1
24.0390000000 1.0000000000
1 3 3 1 1
3.8450000000 1.0000000000
1 3 3 1 1
9.9210000000 1.0000000000
1 3 3 1 1
22.5700000000 1.0000000000
1 4 4 1 1
10.0620000000 1.0000000000
1 4 4 1 1
24.2670000000 1.0000000000
#
H PB6-H
21
1 0 0 1 1
1.3860000000 1.0000000000
1 0 0 1 1
3.2490000000 1.0000000000
1 0 0 1 1
9.5620000000 1.0000000000
1 0 0 1 1
12.4850000000 1.0000000000
1 0 0 1 1
21.4290000000 1.0000000000
1 0 0 1 1
36.9310000000 1.0000000000
1 1 1 1 1
1.3990000000 1.0000000000
1 1 1 1 1
4.2400000000 1.0000000000
1 1 1 1 1
9.9300000000 1.0000000000
1 1 1 1 1
18.3760000000 1.0000000000
1 1 1 1 1
24.1190000000 1.0000000000
1 2 2 1 1
2.6070000000 1.0000000000
1 2 2 1 1
5.1410000000 1.0000000000
1 2 2 1 1
7.7500000000 1.0000000000
1 2 2 1 1
20.7680000000 1.0000000000
1 3 3 1 1
0.5090000000 1.0000000000
1 3 3 1 1
9.1290000000 1.0000000000
1 3 3 1 1
26.4080000000 1.0000000000
1 4 4 1 1
9.4450000000 1.0000000000
1 4 4 1 1
28.4070000000 1.0000000000
1 5 5 1 1
10.1930000000 1.0000000000
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