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I was running a simple CASSCF calculation in PySCF on the TMM biradical. It was a CASSCF (4,4) state averaged calculation where the energies of the first 3 roots were calculated. The simulation output contained the following table.

** Largest CI components **
  [alpha occ-orbitals] [beta occ-orbitals]  state 0   CI coefficient
  [0 1]                [0 2]                           0.680999601372
  [0 2]                [0 1]                          -0.680999601372
  [1 2]                [0 3]                           0.162876965573
  [0 3]                [1 2]                          -0.162876965573
  [alpha occ-orbitals] [beta occ-orbitals]  state 1   CI coefficient
  [0 1]                [0 1]                           0.521598297554
  [0 1]                [0 2]                          -0.296126060144
  [0 1]                [1 2]                          -0.235407708465
  [0 1]                [0 3]                          -0.106906206218
  [0 2]                [0 1]                          -0.296126060144
  [0 2]                [0 2]                          -0.521414937085
  [0 2]                [1 2]                          -0.133788127011
  [0 2]                [0 3]                           0.190214831302
  [1 2]                [0 1]                          -0.235407708465
  [1 2]                [0 2]                          -0.133788127011
  [0 3]                [0 1]                          -0.106906206218
  [0 3]                [0 2]                           0.190214831302
  [alpha occ-orbitals] [beta occ-orbitals]  state 2   CI coefficient
  [0 1]                [0 1]                           0.275144934363
  [0 1]                [0 2]                           0.518472331429
  [0 1]                [1 2]                          -0.131745811887
  [0 1]                [0 3]                           0.201009810870
  [0 2]                [0 1]                           0.518472331429
  [0 2]                [0 2]                          -0.313130614232
  [0 2]                [1 2]                           0.232139108556
  [0 2]                [0 3]                           0.115309844670
  [1 2]                [0 1]                          -0.131745811887
  [1 2]                [0 2]                           0.232139108556
  [0 3]                [0 1]                           0.201009810870
  [0 3]                [0 2]                           0.115309844670

I am having trouble making sense of this table. I don't understand how to interpret the alpha and beta occupied orbitals. How can I find the active space configuration from this table?.

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  • 1
    $\begingroup$ +1 Welcome to our forum. $\endgroup$
    – Camps
    Oct 30, 2023 at 13:52
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    $\begingroup$ Can you post your image as a code block? This will make it easier for future visitors to read your question. $\endgroup$
    – Tyberius
    Nov 1, 2023 at 0:52
  • $\begingroup$ I have updated the question $\endgroup$ Nov 1, 2023 at 12:09
  • $\begingroup$ Please ask your second question in a new post. I already removed it for you. $\endgroup$ Nov 1, 2023 at 12:13

1 Answer 1

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You have 4 electrons in 4 spatial orbitals. Number the orbitals 0, 1, 2, and 3.

Look at the lowest root. It is an open shell singlet. The spatial orbital 0 is doubly occupied, and then you have (12-21)/sqrt(2) as the most important configuration state, followed by (03-12)/sqrt(2).

In the first excited state, orbitals 0 and 1 are doubly occupied in the leading determinant, which is the Hartree-Fock state. However, its amplitude is just 0.592, which means that only 0.592^2 ~ 35% of the electron density comes from this determinant.

Does this help?

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  • $\begingroup$ Thank you for the reply. Could you explain what you mean by the (03-31)/sqrt(2) state?. $\endgroup$ Oct 31, 2023 at 6:08
  • $\begingroup$ Sorry, I was referring to the [ 1 2 ] alpha [ 0 3 ] beta - [ 0 3 ] alpha [ 1 2 ] beta in the CI listing. This is the difference between talking about determinants or configuration state functions, which are eigenfunctions of the spin. $\endgroup$ Oct 31, 2023 at 16:17
  • $\begingroup$ Got it. Thanks! $\endgroup$ Oct 31, 2023 at 18:45

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