How to run CIS from single-reference ground state?
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Stefanos Carlström
Apr 22, 2021, 4:00:34 AM4/22/21
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Dear DIRAC experts,
In our research group, we’re developing a few different programs for solving the time-dependent Schrödinger and Dirac equations, starting from a configuration-interaction singles Ansatz. Since we are working with atoms, we employ the full spherical symmetry and resolve the wavefunction on a radial grid.
To make sure that we are describing the correct physics, a sanity check that we can make is to diagonalize our CIS Hamiltonian and see that the first few states are where we expect them to be. We then of course need to compare with results from another code, computed at the same level of correlation. For the non-relativistic code, we usually compare with CIS results from GAMESS-US, and now we’re trying to do the same for the relativistic code, using DIRAC, but we have hit a few stumbling blocks. To simplify matters, we will start with helium, and come back to the heavier noble gases when we understand what we’re doing.
Basis set considerations
What is a good basis set to use for these calculations? In the non-relativistic case, we would typically use the appropriate aug-cc-pVTZ basis set from basissetexchange.org, augmenting it by Kaufmann’s basis set for Rydberg states,
- Kaufmann, K., Baumeister, W., & Jungen, M. (1989). Universal gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions. Journal of Physics B: Atomic, Molecular and Optical Physics, 22(14), 2223–2240. http://dx.doi.org/10.1088/0953-4075/22/14/007
centred at the geometric centre of the molecule, usually including SPD functions, n=1–10. In our tries with Dirac, we have added this by placing a dummy atom of charge 0 at the origin:
DIRAC
C 2
2. 1
He 0.0 0.0 0.0
LARGE BASIS cc-pVTZ
0. 1
XX 0.0 0.0 0.0
LARGE EXPLICIT 3 10 10 10
# Kaufmann S
f 1 1
0.2456452307 1.000
f 1 1
0.0984957303 1.000
f 1 1
0.0527254253 1.000
f 1 1
0.0327747599 1.000
f 1 1
0.0223273940 1.000
f 1 1
0.0161821668 1.000
f 1 1
0.0122644524 1.000
f 1 1
0.0096146323 1.000
f 1 1
0.0077392515 1.000
f 1 1
0.0063634916 1.000
# Kaufmann P
f 1 1
0.4300821797 1.000
f 1 1
0.1693411217 1.000
f 1 1
0.0898938939 1.000
f 1 1
0.0556108739 1.000
f 1 1
0.0377659963 1.000
f 1 1
0.0273115991 1.000
f 1 1
0.0206658552 1.000
f 1 1
0.0161806024 1.000
f 1 1
0.0130115697 1.000
f 1 1
0.0106899459 1.000
# Kaufmann D
f 1 1
0.6225574689 1.000
f 1 1
0.2421608120 1.000
f 1 1
0.1278395922 1.000
f 1 1
0.0788349837 1.000
f 1 1
0.0534280775 1.000
f 1 1
0.0385826541 1.000
f 1 1
0.0291633439 1.000
f 1 1
0.0228151816 1.000
f 1 1
0.0183348599 1.000
f 1 1
0.0150554867 1.000
FINISH
Is this the way to go about it? Note that these extra basis functions typically lead to severe linear dependencies, but an SVD followed by dropping the vectors corresponding to the smallest singular values usually works. Is there a parameter to set this tolerance?
We noticed that if we use the .X2C Hamiltonian, DIRAC errored out saying that the basis set had to be decontracted (why?), so for now we use .DOSSSS.
Configuration-interaction
We have already received some help by Trond via mail (thank you!), but we are still not completely successful.
Our relativistic code is at the moment limited to Δmⱼ=0 (corresponding to linear polarization in the dipole approximation); is then the correct subduction to linear+time reversal symmetry (what is the name of that group by the way, D∞h ⊗ ?) to only consider excited states in the symmetries 0g and 0u? The non-relativistic code has no such limitation, and thus we include all symmetries in the reference GAMESS run.
Results
Non-relativistic, all symmetries
As computed by GAMESS-US.
---------------------------------------------------------------------
CI-SINGLES EXCITATION ENERGIES
STATE HARTREE EV KCAL/MOL CM-1 NM
---------------------------------------------------------------------
3A1 0.7280721825 19.8119 456.8723 159793.37 62.58
1A1 0.7763551104 21.1257 487.1703 170390.25 58.69
3B2 0.7802581271 21.2319 489.6194 171246.86 58.40
3E 0.7802585790 21.2319 489.6197 171246.96 58.40
3E 0.7802585790 21.2319 489.6197 171246.96 58.40
1B2 0.7971095599 21.6905 500.1939 174945.33 57.16
1E 0.7971096265 21.6905 500.1939 174945.34 57.16
1E 0.7971096265 21.6905 500.1939 174945.34 57.16
3A1 0.8466969214 23.0398 531.3104 185828.49 53.81
1A1 0.8576491795 23.3378 538.1831 188232.24 53.13
3B2 0.8586597290 23.3653 538.8172 188454.03 53.06
3E 0.8587365996 23.3674 538.8654 188470.90 53.06
3E 0.8587365996 23.3674 538.8654 188470.90 53.06
3A1 0.8624981463 23.4698 541.2258 189296.46 52.83
3A1 0.8624981464 23.4698 541.2258 189296.46 52.83
3B2 0.8624981464 23.4698 541.2258 189296.46 52.83
3E 0.8624981464 23.4698 541.2258 189296.46 52.83
3E 0.8624981464 23.4698 541.2258 189296.46 52.83
1A1 0.8625873768 23.4722 541.2818 189316.05 52.82
1A1 0.8625873768 23.4722 541.2818 189316.05 52.82
1B2 0.8625873768 23.4722 541.2818 189316.05 52.82
1E 0.8625873768 23.4722 541.2818 189316.05 52.82
1E 0.8625873768 23.4722 541.2818 189316.05 52.82
1B2 0.8637633378 23.5042 542.0198 189574.14 52.75
1E 0.8639344196 23.5089 542.1271 189611.69 52.74
1E 0.8639344196 23.5089 542.1271 189611.69 52.74
3A1 0.8815186316 23.9873 553.1614 193470.98 51.69
1A1 0.8871177731 24.1397 556.6749 194699.85 51.36
3B2 0.8912167664 24.2512 559.2470 195599.47 51.12
3E 0.8941858612 24.3320 561.1102 196251.11 50.96
3E 0.8941858612 24.3320 561.1102 196251.11 50.96
1B2 0.8956626129 24.3722 562.0369 196575.22 50.87
3A1 0.8971961772 24.4140 562.9992 196911.80 50.78
3B1 0.8971961772 24.4140 562.9992 196911.80 50.78
3E 0.8971961772 24.4140 562.9992 196911.80 50.78
3E 0.8971961772 24.4140 562.9992 196911.80 50.78
3B2 0.8971961772 24.4140 562.9992 196911.80 50.78
1A1 0.8973317667 24.4176 563.0843 196941.56 50.78
1B1 0.8973317667 24.4176 563.0843 196941.56 50.78
1E 0.8973317667 24.4176 563.0843 196941.56 50.78
1B2 0.8973317667 24.4176 563.0843 196941.56 50.78
1E 0.8973317667 24.4176 563.0843 196941.56 50.78
1E 0.8994390921 24.4750 564.4066 197404.06 50.66
1E 0.8994390921 24.4750 564.4066 197404.06 50.66
3A1 0.9111122165 24.7926 571.7316 199966.02 50.01
1A1 0.9201467139 25.0385 577.4009 201948.86 49.52
3B2 0.9339127950 25.4131 586.0392 204970.17 48.79
1B2 0.9412019536 25.6114 590.6132 206569.95 48.41
3E 0.9461349992 25.7456 593.7088 207652.63 48.16
3E 0.9461349992 25.7456 593.7088 207652.63 48.16
3A1 0.9487668642 25.8173 595.3603 208230.26 48.02
3B1 0.9487668642 25.8173 595.3603 208230.26 48.02
3B2 0.9487668642 25.8173 595.3603 208230.26 48.02
3E 0.9487668642 25.8173 595.3603 208230.26 48.02
3E 0.9487668642 25.8173 595.3603 208230.26 48.02
1A1 0.9490936586 25.8262 595.5653 208301.98 48.01
1B1 0.9490936586 25.8262 595.5653 208301.98 48.01
1E 0.9490936586 25.8262 595.5653 208301.98 48.01
1E 0.9490936586 25.8262 595.5653 208301.98 48.01
1B2 0.9490936586 25.8262 595.5653 208301.98 48.01
1E 0.9553617401 25.9967 599.4986 209677.67 47.69
1E 0.9553617401 25.9967 599.4986 209677.67 47.69
3A1 0.9648560147 26.2551 605.4564 211761.42 47.22
1A1 0.9813100869 26.7028 615.7815 215372.67 46.43
3B2 1.0021194914 27.2691 628.8396 219939.81 45.47
1B2 1.0134993574 27.5787 635.9805 222437.40 44.96
3A1 1.0301525948 28.0319 646.4306 226092.36 44.23
3B1 1.0301525949 28.0319 646.4306 226092.36 44.23
3E 1.0301525949 28.0319 646.4306 226092.36 44.23
3E 1.0301525949 28.0319 646.4306 226092.36 44.23
3B2 1.0301525949 28.0319 646.4306 226092.36 44.23
1A1 1.0308928291 28.0520 646.8951 226254.82 44.20
1B1 1.0308928291 28.0520 646.8951 226254.82 44.20
1B2 1.0308928292 28.0520 646.8951 226254.82 44.20
1E 1.0308928292 28.0520 646.8951 226254.82 44.20
1E 1.0308928292 28.0520 646.8951 226254.82 44.20
3E 1.0355787410 28.1795 649.8356 227283.26 44.00
3E 1.0355787410 28.1795 649.8356 227283.26 44.00
1E 1.0509067551 28.5966 659.4540 230647.37 43.36
1E 1.0509067551 28.5966 659.4540 230647.37 43.36
3A1 1.0681099640 29.0648 670.2492 234423.04 42.66
1A1 1.0974835052 29.8640 688.6814 240869.79 41.52
3B2 1.1088776536 30.1741 695.8313 243370.51 41.09
1B2 1.1261954385 30.6453 706.6984 247171.33 40.46
3A1 1.1541083497 31.4049 724.2140 253297.50 39.48
3B1 1.1541083497 31.4049 724.2140 253297.50 39.48
3B2 1.1541083498 31.4049 724.2140 253297.50 39.48
3E 1.1541083498 31.4049 724.2140 253297.50 39.48
3E 1.1541083498 31.4049 724.2140 253297.50 39.48
1A1 1.1556982942 31.4482 725.2117 253646.46 39.42
1B1 1.1556982942 31.4482 725.2117 253646.46 39.42
1E 1.1556982943 31.4482 725.2117 253646.46 39.42
1E 1.1556982943 31.4482 725.2117 253646.46 39.42
1B2 1.1556982943 31.4482 725.2117 253646.46 39.42
3E 1.1879709081 32.3263 745.4631 260729.48 38.35
3E 1.1879709081 32.3263 745.4631 260729.48 38.35
1E 1.2139340867 33.0328 761.7552 266427.74 37.53
1E 1.2139340867 33.0328 761.7552 266427.74 37.53
3A1 1.2762826475 34.7294 800.8796 280111.66 35.70
3B2 1.2783816306 34.7865 802.1967 280572.34 35.64
Relativistic, 0g and 0u only, via KR-CI
(Actually with 1g and 1u too, but they turned out to be empty)
If we are reading the output correctly, we have the following excited states:
| Symmetry | Total energy [Ha] | Excitation energy [Ha] | Excitation energy [eV] |
|----------+-------------------+------------------------+------------------------|
| 0g | -2.86135495 | 0.00000000 | 0.000000 |
| 0g | -2.05930807 | 0.80204688 | 21.824498 |
| 0g | -2.05530605 | 0.80604890 | 21.933397 |
| 0u | -2.03359937 | 0.82775558 | 22.524057 |
| 0u | -2.03359935 | 0.82775560 | 22.524058 |
| 0u | -2.03359907 | 0.82775588 | 22.524065 |
| 0u | -2.03304511 | 0.82830984 | 22.539139 |
| 0g | -1.99231534 | 0.86903961 | 23.647437 |
| 0g | -1.99231529 | 0.86903966 | 23.647438 |
| 0u | -1.98355301 | 0.87780194 | 23.885869 |
The first excited state, which we expect would be the 1s 2s ³S₁ mⱼ=0 at around 19.81 eV, seems to end up at 21.82 eV instead.
Relativistic, all symmetries, via linear response
These results are possibly “too good”, i.e. not at the CIS level, but they seem reasonably close to the non-relativistic results.
Level eigenvalue (eV) Eigenvalue (cm-1) 0g+| 0g-| 1g | 2g | 3g | 0u+| 0u-| 1u | 2u| 3u|
0 0.000000000 0.000000 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
1 19.694344025 158845.613383 0| 1| 2| 0| 0| 0| 0| 0| 0| 0|
2 21.101135473 170192.152788 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
3 21.214382087 171105.548421 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
4 21.214408990 171105.765410 0| 0| 0| 0| 0| 1| 0| 2| 0| 0|
5 21.214462809 171106.199490 0| 0| 0| 0| 0| 0| 1| 2| 2| 0|
6 21.684963039 174901.040158 0| 0| 0| 0| 0| 1| 0| 2| 0| 0|
7 23.021176003 185678.325630 0| 1| 2| 0| 0| 0| 0| 0| 0| 0|
8 23.331545173 188181.622068 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
9 23.361170044 188420.562791 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
10 23.361177689 188420.624450 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
11 23.361177733 188420.624810 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
12 23.361193040 188420.748265 0| 0| 0| 0| 0| 0| 0| 0| 2| 0|
13 23.361193088 188420.748657 0| 0| 0| 0| 0| 0| 1| 2| 0| 0|
14 23.470811852 189304.883699 0| 1| 2| 0| 0| 0| 0| 0| 0| 0|
15 23.470813514 189304.897105 1| 0| 0| 1| 0| 0| 0| 0| 0| 0|
16 23.470813993 189304.900972 0| 0| 2| 1| 0| 0| 0| 0| 0| 0|
17 23.470816444 189304.920737 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
18 23.470816765 189304.923325 0| 0| 2| 1| 0| 0| 0| 0| 0| 0|
19 23.470816957 189304.924877 0| 1| 0| 0| 2| 0| 0| 0| 0| 0|
20 23.473245940 189324.515951 0| 0| 2| 1| 0| 0| 0| 0| 0| 0|
21 23.473246752 189324.522500 1| 0| 0| 1| 0| 0| 0| 0| 0| 0|
22 23.503200943 189566.119369 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
23 23.503201111 189566.120724 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
24 23.979882012 193410.811870 0| 1| 2| 0| 0| 0| 0| 0| 0| 0|
25 24.136300854 194672.415036 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
26 24.255818220 195636.387707 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
27 24.255823629 195636.431333 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
28 24.255824738 195636.440273 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
29 24.255835951 195636.530713 0| 0| 0| 0| 0| 0| 0| 0| 2| 0|
30 24.255837301 195636.541605 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
31 24.255837659 195636.544495 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
32 24.379937205 196637.474932 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
33 24.379940350 196637.500304 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
34 24.418568780 196949.059635 0| 1| 0| 0| 0| 0| 0| 0| 0| 0|
35 24.418568921 196949.060771 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
36 24.418569832 196949.068122 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
37 24.418570052 196949.069892 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
38 24.418573195 196949.095246 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
39 24.418573375 196949.096694 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
40 24.418575685 196949.115326 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
41 24.418589798 196949.229156 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
42 24.418589840 196949.229497 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
43 24.418590400 196949.234008 0| 1| 0| 0| 0| 0| 0| 0| 0| 0|
44 24.418590449 196949.234404 0| 0| 0| 0| 2| 0| 0| 0| 0| 0|
45 24.422288851 196979.064035 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
46 24.422289181 196979.066695 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
47 24.422306564 196979.206894 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
48 24.422306600 196979.207188 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
49 24.781515752 199876.424686 0| 1| 2| 0| 0| 0| 0| 0| 0| 0|
50 25.032171835 201898.102539 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
51 25.432987322 205130.897796 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
52 25.432995207 205130.961394 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
53 25.432998468 205130.987698 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
54 25.433015504 205131.125101 0| 0| 0| 0| 0| 0| 0| 0| 2| 0|
55 25.433020316 205131.163910 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
56 25.433021320 205131.172010 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
57 25.639970905 206800.333154 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
58 25.639979595 206800.403240 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
59 25.831916926 208348.482373 0| 1| 0| 0| 0| 0| 0| 0| 0| 0|
60 25.831917376 208348.486004 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
61 25.831918934 208348.498569 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
62 25.831919606 208348.503989 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
63 25.831927544 208348.568015 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
64 25.831928110 208348.572583 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
65 25.831933466 208348.615776 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
66 25.831983119 208349.016260 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
67 25.831983325 208349.017920 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
68 25.831984296 208349.025749 0| 1| 0| 0| 0| 0| 0| 0| 0| 0|
69 25.831984515 208349.027518 0| 0| 0| 0| 2| 0| 0| 0| 0| 0|
70 25.840923647 208421.126485 0| 0| 2| 0| 0| 0| 0| 0| 0| 0|
71 25.840924683 208421.134844 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
72 25.840982640 208421.602299 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
73 25.840982865 208421.604114 0| 0| 0| 1| 0| 0| 0| 0| 0| 0|
74 26.235555385 211604.046440 0| 1| 2| 0| 0| 0| 0| 0| 0| 0|
75 26.690840785 215276.171211 1| 0| 0| 0| 0| 0| 0| 0| 0| 0|
76 27.341965867 220527.849712 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
77 27.341978634 220527.952683 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
78 27.341984116 220527.996895 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
79 27.342011777 220528.219999 0| 0| 0| 0| 0| 0| 0| 0| 2| 0|
80 27.342019955 220528.285959 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
81 27.342021634 220528.299503 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
82 27.661164409 223102.359840 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
83 27.661179396 223102.480715 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
84 30.336533517 244680.669146 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
85 30.336552784 244680.824545 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
86 30.336563719 244680.912741 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
87 30.336606782 244681.260067 0| 0| 0| 0| 0| 0| 0| 0| 2| 0|
88 30.336625191 244681.408551 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
89 30.336628413 244681.434532 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
90 30.842121060 248758.508109 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
91 30.842152799 248758.764100 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
92 35.309523818 284790.545043 0| 0| 0| 0| 0| 0| 1| 0| 0| 0|
93 35.309561787 284790.851283 0| 0| 0| 0| 0| 1| 0| 0| 0| 0|
94 35.309579665 284790.995479 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
95 35.309662672 284791.664977 0| 0| 0| 0| 0| 0| 0| 0| 2| 0|
96 35.309690333 284791.888082 0| 0| 0| 0| 0| 0| 0| 2| 0| 0|
Conclusion
What mistakes are we making, when trying to use KRCI?
Kind regards,
Stefanos Carlström and Felipe Zapata
Knecht Stefan
Apr 23, 2021, 10:10:55 AM4/23/21
to <dirac-users@googlegroups.com>
Dear Stefanos and Felipe,
as far as the basis set choice is concerned, hopefully Ken Dyall might shed further light on this issue for relativistic calculations.
I will take a look at the KRCI run and come back to you with comments/suggestions. Your approach described below looks reasonable at a first glance and there should be no reason
why KRCI should not yield similar results as GAMESS-US for an atom such as He.
As to the X2C failure: by default, DIRAC uses the standard basis sets (such as aug-cc-pVTZ) in contracted form for elements up to Z=35 (if I remember correctly).
For technical reasons mainly, X2C requires any basis set to be in uncontracted form. You can request this in Dirac with
**INTEGRALS
*READIN
.UNCONTR
For the additional basis functions (Kaufmann’s basis), it might be a better idea to define one’s own basis set file starting from the uncontracted aug-cc-PVTZ basis and add the Kaufmann basis functions to it.
This avoids the somewhat awkward situation of having a ghost center put on top of an atom center.
with best regards
Stefan
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<helium.zip>
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PD Dr. Stefan Knecht
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Abteilung SHE Chemie
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Trond SAUE
Apr 23, 2021, 11:21:41 AM4/23/21
to dirac...@googlegroups.com
Dear Stefanos and Felipe,
I agree with Stefan that your first goal would be to reproduce your GAMESS-US results with DIRAC. For that you should probably have a look here
http://www.diracprogram.org/doc/release-19/tutorials/reproducing_nr_results.html
Then there is another important thing to note: The present version of DIRAC has linear supersymmetry (in the next release we also have atomic supersymmetry at the SCF level). Please note, though, that what is reported in the output is 2 * MJ, to avoid printing half-integer. Since helium has an even number of electrons, there can be no contributions from 2 M_J = 1. I chose to work with 2 M_J = 0 since this will contribute to any value of J, and so you should get all states.
All the best,
Trond
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Trond Saue
Laboratoire de Chimie et Physique Quantiques
UMR 5626 CNRS --- Université Toulouse III-Paul Sabatier
118 route de Narbonne, F-31062 Toulouse, France
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DIRAC : http://www.diracprogram.org/
ESQC : http://www.esqc.org/
Book: Principles and Practices of Molecular Properties: Theory, Modeling, and Simulations
Trond Saue
Laboratoire de Chimie et Physique Quantiques
UMR 5626 CNRS --- Université Toulouse III-Paul Sabatier
118 route de Narbonne, F-31062 Toulouse, France
Phone : +33/561556361 Fax: +33/561556065
Mail : trond...@irsamc.ups-tlse.fr
Web : http://dirac.ups-tlse.fr/saue
DIRAC : http://www.diracprogram.org/
ESQC : http://www.esqc.org/
Book: Principles and Practices of Molecular Properties: Theory, Modeling, and Simulations
Kenneth Dyall
Apr 23, 2021, 1:08:02 PM4/23/21
to Dirac Users
Dear Stefanos and Felipe,
As far as basis sets are concerned, the basis sets I developed (dyall-*) are designed in the same way as cc-pVNZ, but have a larger SCF set, which might be an advantage. However, you would have to supplement them for the excited states, by adding a lot of diffuse functions. Looking at the Kaufman sets, I can see why there is severe linear dependence. The smallest 3 or 4 basis functions are too close to each other: the ratio between adjacent exponents is much less than the rule-of-thumb 1.4 needed for avoiding linear dependence. For production (rather than testing), you might consider using an even-tempered set that covers the same range of exponents. A ratio of 1.6 gives an approximate 5z basis quality; 1.5 would give about 6z quality.
All the best,
Ken.
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FELIPE ZAPATA ABELLAN
Apr 30, 2021, 9:43:51 AM4/30/21
to dirac-users
Dear all
Thanks a lot for your answers.
We have tried now to run a "less relativistic" calculation on He by increasing the speed of light (changing the Hamiltonian from .DOSSS to .NONREL or .LEVY-LEBLOND doesn't work with KRCI).
As you can see in the attached file ".4zp" the energy of the first excited state doesn't improve. Since we are using a simple basis set and a less relativistic Hamiltonian and we have still the same problem, maybe the issue is related to the atomic symmetry?
Kind regards
Stefanos and Felipe
FELIPE ZAPATA ABELLAN
Apr 30, 2021, 9:45:21 AM4/30/21
to dirac-users
Attached the zip file with the outputs with different Hamiltonians.
Knecht Stefan
Apr 30, 2021, 11:23:30 AM4/30/21
to <dirac-users@googlegroups.com>
Dear Stefanos, dear Felipe,
thanks for the simplified input/output. I just ran it myself and with a different CI program in DIRAC as well and they all seem to agree.
It’s odd that the first excited state is that much off.
I will try to dig a bit deeper and return to you ASAP.
with best regards
Stefan
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<he.zip>
Trond SAUE
Apr 30, 2021, 11:46:41 AM4/30/21
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Hi,
did you run GAMESS and DIRAC non-relativistically with exactly the same basis ?
You should be able to reproduce the CIS results using TD-HF, but only in the Tamm-Dancoff approximation, which unfortunately is available on a branch for the moment....
Knecht Stefan
Apr 30, 2021, 4:41:11 PM4/30/21
to <dirac-users@googlegroups.com>
Hi,
could you please also post the GAMESS-US input? So far, I can’t see what goes wrong. Even with FCI the first excited state is off essentially the same as for CIS… with three different CI programs in Dirac.
with best regards
Stefan
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Stefanos Carlström
May 1, 2021, 5:17:42 AM5/1/21
to dirac-users
Dear Dirac experts,
After experimenting some more, we found that it is necessary to use the aug-cc-pVTZ basis set to get the first excited state correct; without the augmentation both GAMESS-US and DIRAC fail. However, it is not as simple as that, since including the Kaufmann basis set improves the energies a lot in GAMESS-US, but not in DIRAC, which is very puzzling.
Please find attached GAMESS-US inputs/outputs, as well as DIRAC outputs for the various calculations presented below.
Results
Legend:
- G = GAMESS-US
- D = DIRAC
- cc3 = cc-pVTZ
- a3 = aug-cc-pVTZ
- K = Kaufmann
cc-pVTZ
| G cc3 | Energy [Ha] | D cc3 | Energy [Ha] | G cc3+K | Energy [Ha] | D cc3+K | Energy [Ha] |
|-------+---------------+-------+-------------+---------+---------------+---------+-------------|
| 0 | -2.8611533448 | 0g | -2.86128509 | 0 | -2.8612230831 | 0g | -2.86135495 |
| 3A1 | -1.9026121159 | 0g | -1.90277195 | 3A1 | -2.1331510157 | 0g | -2.05930807 |
| 1A1 | -1.6550771749 | 0g | -1.65522465 | 1A1 | -2.0848680510 | 0g | -2.05530605 |
| 3E | -1.2361363415 | 0u | -1.23635387 | 3B2 | -2.0809585356 | 0u | -2.03359937 |
| 3E | -1.2361363415 | 0u | -1.23633415 | 3E | -2.0809575430 | 0u | -2.03359935 |
| 3B2 | -1.2361363415 | 0u | -1.23629470 | 3E | -2.0809575430 | 0u | -2.03359907 |
| 1E | -0.9710213014 | 0u | -0.97122834 | 1B2 | -2.0641130813 | 0u | -2.03304511 |
| 1E | -0.9710213014 | | | 1E | -2.0641130436 | 0g | -1.99231534 |
| 1B2 | -0.9710213014 | | | 1E | -2.0641130436 | 0g | -1.99231529 |
| 3A1 | 1.5882636791 | 0g | 1.58641641 | 3A1 | -2.0145262383 | 0u | -1.98355301 |
| 1A1 | 2.0129696834 | | | 1A1 | -2.0035739711 | | |
| 3A1 | 3.4411015101 | | | 3B2 | -2.0025618687 | | |
| 3E | 3.4411015101 | | | 3E | -2.0024516788 | | |
| 3A1 | 3.4411015101 | | | 3E | -2.0024516788 | | |
| 3A1 | 3.4411015101 | | | 3B2 | -1.9987185923 | | |
| 3A1 | 3.4411015101 | | | 3A1 | -1.9987185923 | | |
aug-cc-pVTZ
| G a3 | Energy [Ha] | D a3 | Energy [Ha] | G a3+K | Energy [Ha] | D a3+K | Energy [Ha] |
|------+---------------+------+-------------+--------+---------------+--------+-------------|
| gst | -2.8611834261 | 0g | -2.86131503 | gst | -2.8612230241 | 0g | -2.86135495 |
| 3A1 | -2.1309232768 | 0g | -2.13103685 | 3A1 | -2.1331508416 | 0g | -2.05930807 |
| 1A1 | -2.0689992401 | 0g | -2.06910570 | 1A1 | -2.0848679137 | 0g | -2.05530605 |
| 3A1 | -1.9755771846 | 0u | -1.97568789 | 3B2 | -2.0809648970 | 0u | -2.03359937 |
| 3A1 | -1.9755771846 | 0u | -1.97568437 | 3E | -2.0809644452 | 0u | -2.03359935 |
| 3A1 | -1.9755771846 | 0u | -1.97567732 | 3E | -2.0809644452 | 0u | -2.03359907 |
| 1E | -1.9006822341 | | | 1B2 | -2.0641134642 | 0u | -2.03304511 |
| 1B2 | -1.9006822341 | 0u | -1.90079325 | 1E | -2.0641133976 | 0g | -1.99231534 |
| 1E | -1.9006822341 | | | 1E | -2.0641133976 | 0g | -1.99231529 |
| 3A1 | -1.6592704144 | 0g | -1.65943722 | 3A1 | -2.0145261028 | 0u | -1.98355301 |
| 1A1 | -1.4507229333 | 0g | -1.45088269 | 1A1 | -2.0035738446 | | |
| 3A1 | -0.9672893269 | 0g | -0.96746177 | 3B2 | -2.0025632951 | | |
| 3A1 | -0.9672893269 | 0g | -0.96745567 | 3E | -2.0024864245 | | |
| 3A1 | -0.9672893269 | 0g | -0.96744650 | 3E | -2.0024864245 | | |
| 3A1 | -0.9672893269 | | | 3A1 | -1.9987248778 | | |
| 3A1 | -0.9672893269 | | | 3A1 | -1.9987248778 | | |
Some observations
- GAMESS-US and DIRAC give similar energies when using cc-pVTZ only or aug-cc-pVTZ only, which is reassuring.
- DIRAC gives reasonable energies when using cc-pVTZ+Kaufmann when running linear response instead of CIS (see first post).
- GAMESS-US is able to compensate for the lack of the augmented basis functions, when combining with the Kaufmann basis, DIRAC only partly, perhaps related to the next point;
- DIRAC does not give good energies with aug-cc-pVTZ+Kaufmann, surprisingly. Perhaps this is related to the fact that we had to limit the virtuals GAS shell (
2 2 / 10 8), since we ran into out-of-memory problems? In fact the energies are worse than when only using aug-cc-pVTZ. - Perhaps it would be useful to learn how to replace/model the Kaufmann basis set for the Rydberg states using the well-tempered or even-tempered series of basis functions instead.
Feature request
It would be very nice if the excited states of all symmetries were gathered into a table, sorted by energy, after the KR-CI calculation (similar to the way it is presented by the linear response calculation).
Kind regards
Felipe and Stefanos
Kenneth Dyall
May 1, 2021, 2:05:23 PM5/1/21
to Dirac Users
One thought about the degradation of the results with aug-cc-pvtz+Kaufmann is linear dependence. Even with the elimination of the linearly dependent canonical basis functions, it's still possible to get large cancellations due to large coefficients with opposite signs in the eigenfunctions of the overlap matrix (i.e. the canonical basis functions). A good rule of thumb is to ensure that the ratio between any two Gaussian exponents is not smaller than about 1.4 (obviously the ratio is defined as the larger over the smaller).
Restricting the virtual space could also be a problem, as you might be throwing out useful functions and keeping garbage (in the worst case). Usually not the case but a possibility.
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Kenneth Dyall
May 1, 2021, 2:07:31 PM5/1/21
to Dirac Users
Another suggestion: if they are available for the atom you are looking at, you might consider the d-aug-cc-pvtz and t-aug-cc-pvtz basis sets. I would expect you would see improvement as you go from single to double to triple augmentation.
Kenneth Dyall
May 1, 2021, 2:14:27 PM5/1/21
to Dirac Users
And yet another basis set suggestion, on your last point: you could indeed use an even-tempered series. As a rule of thumb, to develop an even-tempered series for a given zeta level (2z, 3z, 4z) you can use the ratio 10**(1/n). So for a tz basis the ratio is about 2.2. I suggest taking the smallest exponent in the cc-pvtz set and dividing it by this number to generate the next in the series, and so on.
Kenneth Dyall
May 1, 2021, 2:16:03 PM5/1/21
to Dirac Users
Sorry, I missed something in the last message: the procedure of developing the even-tempered series should be done for each angular momentum in the basis.
Peterson, Kirk
May 1, 2021, 2:39:19 PM5/1/21
to dirac...@googlegroups.com
Of course an even-tempered extension in each angular momentum is exactly how the d-aug, t-aug, etc. sets are derived from the normal aug-cc-pVDZ sets. So what Ken recommends would give you a series of basis sets that are well defined in the literature and would systematically converge to the Kaufmann basis set limit but without linear dependency issues.
best, -Kirk
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Peterson, Kirk
May 1, 2021, 3:11:59 PM5/1/21
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maybe it was obvious, but I meant to type aug-cc-pVnZ and not aug-cc-pVDZ below.
best, -Kirk
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Paul Bagus
May 1, 2021, 4:22:55 PM5/1/21
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I may be missing something but doesn’t the Lowdin orthogonalization with removal of vectors with small eigenvalues of S avoid the problem of near liner dependence? Granted one has to choose threshold so that the number of basis functions deleted is the same on the region of the potential curve (surface) of interest but this is fairly straightforward to insure.
Regards, Paul Bagus
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Kenneth Dyall
May 1, 2021, 4:44:17 PM5/1/21
to Dirac Users
Yes, indeed, that's the point of it. But if there's severe linear dependence, the condition number can be very large, which means that you might have a large amount of garbage in the diagonalization of S. The condition number gives an indication of how many figures of accuracy you have lost. However, it would matter how the garbage is distributed. My current observations on an overlap matrix for an even-tempered basis with a condition number of 10^6 is that the eigenvectors are all orthogonal to 14 or more figures, but the small eigenvalues are inaccurate. So throwing them out is the right thing to do, but if they are kept, the symmetric orthonormalization will only be good to, say 10 figures. If you try to reconstruct S from the eigenvalues and eigenvectors, the result may be accurate to 10^-14, but if the off-diagonal elements of S are 10^-7, you now only have 7 figures in these elements.
I picked up some of this at NASA when Charlie Baschlicher was doing calculations; the high virtuals had large coefficients (> 100.0) of opposite signs, and the cancellations produced some garbage (numerical noise) in the results.
So one has to be careful with linear dependence, and keep it out in the first place, if at all possible.
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Kenneth Dyall
May 1, 2021, 4:58:43 PM5/1/21
to Dirac Users
I just did an (energy) optimization of some Gaussian basis functions for the 2s orbital in the He 1s^1 2s^1 state (average configuration). Here's the resulting orbitals:
1s+ 2s+
1 2.4007259E+03 1.8256071E-04 -2.8707433E-05
2 3.5909034E+02 1.3311854E-03 -2.0951667E-04
3 8.1629274E+01 6.9006546E-03 -1.0895994E-03
4 2.3093205E+01 2.8270519E-02 -4.5121875E-03
5 7.5121596E+00 9.5062952E-02 -1.5617534E-02
6 2.6760196E+00 2.5384867E-01 -4.4496294E-02
7 1.0012602E+00 4.4959024E-01 -9.5450467E-02
8 3.8473637E-01 2.9452448E-01 -1.3174222E-01
9 1.4913937E-01 1.1964599E-02 -2.0616166E-02
10 6.3630732E-02 6.1117133E-03 3.1319259E-01
11 2.5946075E-02 -3.3222686E-03 5.6340839E-01
12 1.0767066E-02 1.0158470E-03 2.4894631E-01
Knecht Stefan
May 3, 2021, 6:45:52 AM5/3/21
to <dirac-users@googlegroups.com>
Dear all,
thanks for the suggestions and the lively discussion so far.
@Felipe and Stefanos: I have noted your feature request for the next release version. In the meantime, there is already something close to what you requested if you ask for any property calculation
(in the attached output: .OMEGAQ which calculates the expectation values for <S_z> and <L_z> to analyse the contributions to the Omega value) in KRCI in addition to the energy optimisation.
The attached output shows the CIS data for the
t-aug-cc-pVQZ
basis set, that is a triply-augmented one. Dirac does generate the basis set on the fly. :)
There was no problem to include ALL orbitals in the KRCI run, i.e. I specified
.GAS SHELLS
2
1 2 / 1 0
2 2 / 31 46
As you can see below, the position of the first excited state fits nicely with what one would expect.
with best regards
Stefan
KRCI_CIS / t-aug-cc-pVQZ
List of eigenstates in property calculation (sorted)
____________________________________________________________________________________________________________________
Level | abs. eigenvalue | rel. eigenvalue (a.u.) | rel. eigenvalue (eV) | rel. eigenvalue (cm-1) | irrep
0 -2.8615230710 0.000000000000 0.000000000000 0.000000000000 (0g )
1 -2.1333985678 0.728124503201 19.813277067552 159804.856829129072 (0g )
2 -2.1333985678 0.728124503201 19.813277067552 159804.856829129189 (2g )
3 -2.0845162378 0.777006833152 21.143433026835 170533.288168823550 (0g )
4 -2.0810872474 0.780435823605 21.236740610388 171285.864584120020 (0u )
5 -2.0810872426 0.780435828406 21.236740741005 171285.865637619892 (2u )
6 -2.0810872426 0.780435828406 21.236740741005 171285.865637620387 (0u )
7 -2.0810872330 0.780435838006 21.236741002240 171285.867744621559 (0u )
8 -2.0810872330 0.780435838006 21.236741002240 171285.867744622519 (2u )
9 -2.0810872330 0.780435838006 21.236741002240 171285.867744622810 (4u )
10 -2.0641471644 0.797375906612 21.697703751543 175003.783054882340 (0u )
11 -2.0641471644 0.797375906612 21.697703751543 175003.783054884581 (2u )
12 -2.0139681864 0.847554884602 23.063143301395 186016.795744762610 (0g )
13 -2.0139681864 0.847554884602 23.063143301396 186016.795744764851 (2g )
14 -2.0015184572 0.860004613828 23.401917691604 188749.195475510875 (0g )
15 -1.9991616873 0.862361383742 23.466048667946 189266.446683264512 (0u )
16 -1.9991616852 0.862361385822 23.466048724549 189266.447139792872 (0u )
17 -1.9991616852 0.862361385822 23.466048724549 189266.447139793367 (2u )
18 -1.9991616810 0.862361389982 23.466048837753 189266.448052849533 (0u )
19 -1.9991616810 0.862361389982 23.466048837754 189266.448052850639 (2u )
20 -1.9991616810 0.862361389982 23.466048837754 189266.448052850639 (4u )
21 -1.9903103868 0.871212684157 23.706904822042 191209.082577896741 (0u )
22 -1.9903103868 0.871212684157 23.706904822043 191209.082577897847 (2u )
23 -1.9878879589 0.873635112148 23.772822445667 191740.744067809137 (0g )
24 -1.9878879589 0.873635112148 23.772822445667 191740.744067810156 (2g )
25 -1.9878879582 0.873635112775 23.772822462725 191740.744205395575 (0g )
26 -1.9878879582 0.873635112775 23.772822462725 191740.744205396099 (2g )
27 -1.9878879573 0.873635113715 23.772822488313 191740.744411776104 (0g )
28 -1.9878879573 0.873635113715 23.772822488313 191740.744411776628 (2g )
29 -1.9876705934 0.873852477636 23.778737261908 191788.450278111384 (0g )
30 -1.9876705934 0.873852477636 23.778737261908 191788.450278112141 (2g )
31 -1.9792114652 0.882311605817 24.008921865884 193645.014316323155 (2g )
32 -1.9792114652 0.882311605817 24.008921865884 193645.014316323824 (0g )
33 -1.9645749869 0.896948084129 24.407200730022 196857.349996313453 (0g )
34 -1.8939342500 0.967588820987 26.329433103008 212361.199667924404 (2u )
35 -1.8939342500 0.967588820987 26.329433103008 212361.199667925190 (0u )
36 -1.8939342492 0.967588821829 26.329433125911 212361.199852652731 (2u )
37 -1.8939342492 0.967588821829 26.329433125911 212361.199852653226 (0u )
38 -1.8939342481 0.967588822951 26.329433156451 212361.200098974397 (0u )
39 -1.8939030182 0.967620052811 26.330282964241 212368.054261045443 (0u )
40 -1.8037980756 1.057724995391 28.782163356454 232143.803305677196 (2g )
41 -1.8037980756 1.057724995391 28.782163356454 232143.803305678157 (0g )
42 -1.8037980725 1.057724998511 28.782163441366 232143.803990546236 (2g )
43 -1.8037980725 1.057724998511 28.782163441366 232143.803990546614 (0g )
44 -1.8037980678 1.057725003192 28.782163568736 232143.805017853039 (2g )
45 -1.8037980678 1.057725003192 28.782163568736 232143.805017853185 (0g )
46 -1.8008476837 1.060675387270 28.862447609351 232791.339475293615 (0g )
47 -1.6726064185 1.188916652472 32.352070205188 260937.043864027364 (0g )
48 -1.5185359626 1.342987108359 36.544540884299 294751.600353170303 (0g )
49 -1.0237984244 1.837724646601 50.007035111331 403333.939114134118 (0g )
50 -1.0237984045 1.837724666509 50.007035653052 403333.943483412266 (0g )
51 -1.0237983746 1.837724696371 50.007036465636 403333.950037342845 (0g )
52 -0.9948151898 1.866707881227 50.795709102430 409695.023845484830 (0g )
________________________________________________________________________________________________________
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Stefanos Carlström
May 3, 2021, 7:19:12 AM5/3/21
to dirac-users
Dear all,
Very nice! In fact, I don’t know if the feature request is necessary anymore, since adding .OMEGAQ prints what we need.
However, I noticed that if I request more roots than are generated (e.g. 4u only generates two roots, even if I request 5), then the property calculation fails with an end-of-file error, simply because there are not enough roots in the output file for that symmetry. Because of that, one needs to know how many roots to ask for beforehand. Is it possible to change the behaviour to “compute no more than n roots”?
In the meantime, I’ve been playing around with combining Dyall’s triple-ζ basis with Kaufmann, but only up to n = 5, which allows me to converge a few more higher-lying states (I also tweaked .SCREEN and .LINDEP, unsure if they have a large effect; tweaking .THRFAC seems to worsen things):
____________________________________________________________________________________________________________________
Level | abs. eigenvalue | rel. eigenvalue (a.u.) | rel. eigenvalue (eV) | rel. eigenvalue (cm-1) | irrep
0 -2.8617963946 0.000000000000 0.000000000000 0.000000000000 (0g )
1 -2.1337697083 0.728026686357 19.810613315416 159783.388550650066 (0g )
2 -2.1337697083 0.728026686358 19.810613315438 159783.388550826581 (2g )
3 -2.0852844947 0.776511899968 21.129963054038 170424.662930403050 (0g )
4 -2.0810193099 0.780777084720 21.246024631779 171360.762781363213 (0u )
5 -2.0810182839 0.780778110710 21.246052550388 171360.987960151775 (0u )
6 -2.0810182839 0.780778110710 21.246052550389 171360.987960159284 (2u )
7 -2.0810162316 0.780780162994 21.246108395856 171361.438384273642 (4u )
8 -2.0810162316 0.780780162994 21.246108395857 171361.438384280453 (2u )
9 -2.0810162316 0.780780162994 21.246108395857 171361.438384283392 (0u )
10 -2.0636476346 0.798148760035 21.718731949716 175173.404815713817 (0u )
11 -2.0636476346 0.798148760035 21.718731949718 175173.404815731745 (2u )
12 -2.0092935631 0.852502831502 23.197781429832 187102.744609706104 (0g )
13 -2.0092935631 0.852502831503 23.197781429849 187102.744609841291 (2g )
14 -1.9914198626 0.870376532085 23.684149549847 191025.568454768189 (0g )
15 -1.9717829713 0.890013423356 24.218496527735 195335.367925857630 (0u )
16 -1.9717821513 0.890014243333 24.218518840451 195335.547890064889 (0u )
17 -1.9717821513 0.890014243333 24.218518840451 195335.547890066868 (2u )
18 -1.9717805111 0.890015883586 24.218563474004 195335.907883986103 (4u )
19 -1.9717805111 0.890015883586 24.218563474004 195335.907883987966 (2u )
20 -1.9717805111 0.890015883586 24.218563474004 195335.907883988781 (0u )
21 -1.9706159904 0.891180404286 24.250251693299 195591.490635285649 (0g )
22 -1.9706159904 0.891180404287 24.250251693320 195591.490635457303 (2g )
23 -1.9706158047 0.891180589972 24.250256746073 195591.531388661126 (0g )
24 -1.9706158047 0.891180589972 24.250256746073 195591.531388661184 (4g )
25 -1.9706158047 0.891180589973 24.250256746084 195591.531388748757 (2g )
26 -1.9706155258 0.891180868870 24.250264335259 195591.592599582043 (4g )
27 -1.9706155258 0.891180868870 24.250264335259 195591.592599582480 (0g )
28 -1.9706155258 0.891180868870 24.250264335260 195591.592599586409 (2g )
29 -1.9702454989 0.891550895765 24.260333278974 195672.804115869891 (4g )
30 -1.9702454989 0.891550895765 24.260333278974 195672.804115870706 (0g )
31 -1.9702454989 0.891550895765 24.260333278975 195672.804115875479 (2g )
32 -1.9553352127 0.906461181965 24.666062793935 198945.233681943209 (0u )
33 -1.9553352127 0.906461181965 24.666062793936 198945.233681951504 (2u )
34 -1.9088570083 0.952939386366 25.930799035383 209146.020455372694 (0g )
35 -1.9088570083 0.952939386366 25.930799035397 209146.020455483551 (2g )
36 -1.8774875152 0.984308879408 26.784406338805 216030.828374273551 (0g )
37 -1.8005533101 1.061243084567 28.877892494878 232915.934684483364 (0u )
38 -1.8005516064 1.061244788212 28.877938853407 232916.308591278648 (0u )
39 -1.8005516064 1.061244788212 28.877938853408 232916.308591280074 (2u )
40 -1.8005481984 1.061248196235 28.878031590439 232917.056565957842 (0u )
41 -1.8005481984 1.061248196235 28.878031590439 232917.056565957901 (2u )
42 -1.7998912260 1.061905168662 28.895908719047 233061.245347045682 (2g )
43 -1.7998912260 1.061905168662 28.895908719049 233061.245347059477 (0g )
44 -1.7998907629 1.061905631718 28.895921319443 233061.346976104891 (4g )
45 -1.7998907629 1.061905631718 28.895921319445 233061.346976119850 (0g )
46 -1.7998907629 1.061905631718 28.895921319455 233061.346976197732 (2g )
47 -1.7998900679 1.061906326769 28.895940232756 233061.499522278580 (0g )
48 -1.7998900679 1.061906326769 28.895940232757 233061.499522285623 (2g )
49 -1.7979356584 1.063860736237 28.949122418170 233490.442819521384 (0g )
50 -1.7698626576 1.091933737022 29.713027606788 239651.754315810744 (0u )
51 -1.7112662351 1.150530159527 31.307517327655 252512.182539455214 (0g )
52 -1.6584771225 1.203319272113 32.743982111560 264098.053559784719 (0g )
53 -1.4761518845 1.385644510100 37.705304072825 304113.817940229026 (0g )
54 -1.4761508231 1.385645571509 37.705332955243 304114.050892663072 (0g )
55 -1.4761492302 1.385647164443 37.705376301166 304114.400501144875 (0g )
56 -1.4697234165 1.392072978145 37.880231581716 305524.703594109043 (0g )
________________________________________________________________________________________________________
Now I will see if I can translate these findings to 4-component krypton and 2-component xenon with an RECP.
Kind regards,
Stefanos
Knecht Stefan
May 3, 2021, 7:49:17 AM5/3/21
to dirac...@googlegroups.com
Dear Stefanos,
that looks promising. :)
As to the “compute no more than n roots” issue, you can easily fix this (thanks for noticing this bug) by introducing the following line in
src/krmc/krci_ctl.F
after line 1478 (as shown in the “git diff” output below) and recompile Dirac:
NKRCI_CIROOTS(IOPT_SYMMETRY) = NCIROOT
I am adding this fix to the release branch of Dirac as well, hopefully it will make it in time.
diff --git a/src/krmc/krci_ctl.F b/src/krmc/krci_ctl.F
index 995aa660a..c3764d1d5 100644
--- a/src/krmc/krci_ctl.F
+++ b/src/krmc/krci_ctl.F
@@ -1495,6 +1495,7 @@ C
& 'INFO: Only ',NZCONF,' determinants in this symmetry',
% 'INFO: Number of CI roots therefore reduced to ',NZCONF
NCIROOT = NZCONF
+ NKRCI_CIROOTS(IOPT_SYMMETRY) = NCIROOT
END IF
C
C ***************************************************
with best regards
Stefan
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<he-krci-accurate_He-dyall-3Z+Kaufmann5.zip>
Trond SAUE
May 3, 2021, 8:00:27 AM5/3/21
to dirac...@googlegroups.com
Hi Stefanos,
why do you ask for 4u ?
All the best,
Trond
On 5/3/21 1:19 PM, Stefanos Carlström
wrote:
(e.g.
4u
only generates two roots,
--
Stefanos Carlström
May 3, 2021, 8:25:14 AM5/3/21
to dirac-users
Dear Stefan, dear Trond,
@Stefan Fantastic, that seems to do the trick!
@Trond, simply because I saw that Stefan added that in his calculation :) If you look closely in the table in my previous post, you’ll find these states:
7 -2.0810162316 0.780780162994 21.246108395856 171361.438384273642 (4u )
18 -1.9717805111 0.890015883586 24.218563474004 195335.907883986103 (4u )
so it does contribute to the spectrum. When Felipe does CI from the relativistic code, it is limited to m_j=0, but for my 2-component non-relativistic code, which supports RECPs, there is no limitation on m_j, so typically I would want to generate all excited states in all symmetries below say a certain energy.
Kind regards,
Stefanos
Trond SAUE
May 3, 2021, 9:12:20 AM5/3/21
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Dear Stefanos,
I am glad that things work. I did not include other states than 0g and 0u since this will cover all terms (it suffices to have on mj-component of each).
All the best,
Trond
Knecht Stefan
May 3, 2021, 9:42:02 AM5/3/21
to <dirac-users@googlegroups.com>
Hi,
Trond is of course right. It should suffice to run 0g and 0u with KRCI (yielding the mj=0 component) since all mj-components of each J state are degenerate.
If you don’t know the atomic spectrum, though, it might of course help to identify the actual J state if you ask for solutions of mj-components > 0 within a certain energy range…
with best regards
Stefan
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Stefanos Carlström
May 3, 2021, 9:49:01 AM5/3/21
to dirac-users
Dear all,
Yes, that makes sense. I usually use the multiplicity of the eigenvalues to (tentatively) identify which `J` a multiplet has. Do the `m_j` of linear symmetry coincide with those of spherical symmetry, or only for `m_j=0`?
Kind regards,
Stefanos
Trond SAUE
May 3, 2021, 9:49:40 AM5/3/21
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THey coincide with those of spherical symmetry.
On 5/3/21 3:49 PM, Stefanos Carlström
wrote:
Do the `m_j` of linear symmetry coincide with those of spherical symmetry, or only for `m_j=0`?
--
Kenneth Dyall
May 3, 2021, 7:19:17 PM5/3/21
to Dirac Users
I've started optimizing Rydberg functions for the dyall.3z basis sets; so far I have the 3s,3p,3d for Ne, 4s,4p,3d,4f for Ar, 5s,5p,4d,4f for Kr; in other words the lowest n for each symmetry. I'm planning to add them to a branch of the Dirac repository. The initial goal is to cover the rare gases at the 3z and 4z levels. (I'm not sure about doing 2z, it's likely too small to be useful, but if anyone thinks otherwise, let me know.) I'm thinking about how to do the higher n values; I'll have to do a little coding for that, I think, but it might not be too difficult. If there are other series of interest, I could prioritize those when I'm done with these ones.
Extending with even-tempered sets is also likely to be productive, as you can go a long way without running into too much linear dependence. For extension to higher n values, you can do that without too much difficulty, given the automatic extension in Dirac.
All the best,
Ken.
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