How to run CIS from single-reference ground state?

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Stefanos Carlström

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Apr 22, 2021, 4:00:34 AMApr 22
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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

helium.zip

Knecht Stefan

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Apr 23, 2021, 10:10:55 AMApr 23
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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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Trond SAUE

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Apr 23, 2021, 11:21:41 AMApr 23
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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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Kenneth Dyall

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Apr 23, 2021, 1:08:02 PMApr 23
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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

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Apr 30, 2021, 9:43:51 AMApr 30
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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

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Apr 30, 2021, 9:45:21 AMApr 30
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Attached the zip file with the outputs with different Hamiltonians. 

FELIPE ZAPATA ABELLAN

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Apr 30, 2021, 9:45:39 AMApr 30
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he.zip

Knecht Stefan

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Apr 30, 2021, 11:23:30 AMApr 30
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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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Trond SAUE

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Apr 30, 2021, 11:46:41 AMApr 30
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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

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Apr 30, 2021, 4:41:11 PMApr 30
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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

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May 1, 2021, 5:17:42 AMMay 1
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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

helium-2021-05-01.zip

Stefanos Carlström

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May 1, 2021, 9:26:50 AMMay 1
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Apologies for the empty zip file, thanks to Jos Suijker for pointing this out!
helium-2021-05-01.zip

Kenneth Dyall

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May 1, 2021, 2:05:23 PMMay 1
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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.

Kenneth Dyall

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May 1, 2021, 2:07:31 PMMay 1
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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

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May 1, 2021, 2:14:27 PMMay 1
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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

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May 1, 2021, 2:16:03 PMMay 1
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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

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May 1, 2021, 2:39:19 PMMay 1
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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

Peterson, Kirk

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May 1, 2021, 3:11:59 PMMay 1
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maybe it was obvious, but I meant to type aug-cc-pVnZ and not aug-cc-pVDZ below.

 

best,  -Kirk

Paul Bagus

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May 1, 2021, 4:22:55 PMMay 1
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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

Kenneth Dyall

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May 1, 2021, 4:44:17 PMMay 1
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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.

Kenneth Dyall

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May 1, 2021, 4:58:43 PMMay 1
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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


The first 9 exponents are from the dyall.v3z basis; the remaining 3 were optimized. The three added exponents essentially sample the range covered by the Kaufmann basis without the linear dependence issues, and of course the quality matches that of the ground state basis set, namely triple zeta.

Knecht Stefan

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May 3, 2021, 6:45:52 AMMay 3
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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  )
  ________________________________________________________________________________________________________




krci_cis_he.out

Stefanos Carlström

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May 3, 2021, 7:19:12 AMMay 3
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

he-krci-accurate_He-dyall-3Z+Kaufmann5.zip

Knecht Stefan

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May 3, 2021, 7:49:17 AMMay 3
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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

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May 3, 2021, 8:00:27 AMMay 3
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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

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May 3, 2021, 8:25:14 AMMay 3
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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

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May 3, 2021, 9:12:20 AMMay 3
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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

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May 3, 2021, 9:42:02 AMMay 3
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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

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May 3, 2021, 9:49:01 AMMay 3
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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

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May 3, 2021, 9:49:40 AMMay 3
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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

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May 3, 2021, 7:19:17 PMMay 3
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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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