In a calculation of for example a Li-Atom in a DZ basis we have 4 MO.
For the alpha string (containing two electrons), that means we have for a FCI calculation the determinants: |12>, |13>, |14>, |23>, |24>, |34> (electrons in MO 1 and 2, 1 and 3 and so on).
If I wanted to do a truncated CI calculation (CIS for example) only singly excited wavefunctions would contribute.
My (maybe extremely dumb) question now is: Are the determinants |23> and |24> singly excited or doubly excited? Is it the excitation $$a^\dagger_3a_1|12> = |32> = -|23>$$ or is it $$a^\dagger_2a_1 a^\dagger_3a_2|12> = |23>$$ Or is it both? And the coupling (1,-1) so to say determines whether this in used as a single or doubly excited determinant?
EDIT: From the "Molecular Electronic Structure Theory" book by Helgaker, Jorgensen and Olsen, from the chapter 11.8.5 (Direct CI algorithms for RAS Calculations) I read "In CISD theory, there are three such classes (string classes): class 0, with no electrons in virtual space; class 1, with one electron in virtual space; and class 2, with two electrons in virtual space".
This for me reads as if |23> would count as a class 1 string and not a class 2.