Confusion on the sign of CI coefficient in singlet state CI wavefunction #3181
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Hello all, with corresponding Looking at the alpha and beta occupations, state 2 appears to be an open-shell singlet state which is an approximate linear combination of |
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There is an extra sign to keep track of, corresponding to PySCF's convention: |αβ00⟩ = -1 * S0- * S1+ |βα00⟩ because |αβ00⟩ = α0† β1† |vac⟩ That is to say, the absolute normal order defined in the FCI module of PySCF is spin-major, spatial-minor. All of the β electron creation operators are to the right of the α electron creation operators, regardless of the spatial orbital they operate on. This corresponds to the data structure of FCI vectors in PySCF, in which the rows are different α determinants and the columns are different β determinants. |
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Thanks I got it!. But isn't this relation also true if convention is switched, ie |
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Yeah, the intuitive relation |αβ00⟩ = S0- * S1+ |βα00⟩ requires the convention |αβ00⟩ = α0† β1† |vac⟩ that is, spatial-major instead of spin-major order. In this case, it doesn't matter whether α is before or after β, but it does matter whether the subscript 0,1 or the spin α,β is what determines the position of the operator. |
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I understand now. Thanks a lot! |
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There is an extra sign to keep track of, corresponding to PySCF's convention:
|αβ00⟩ = -1 * S0- * S1+ |βα00⟩
because
|αβ00⟩ = α0† β1† |vac⟩
|βα00⟩ = α1† β0† |vac⟩
That is to say, the absolute normal order defined in the FCI module of PySCF is spin-major, spatial-minor. All of the β electron creation operators are to the right of the α electron creation operators, regardless of the spatial orbital they operate on. This corresponds to the data structure of FCI vectors in PySCF, in which the rows are different α determinants and the columns are different β determinants.