S2_expval Function

public pure function S2_expval(nI, nJ) result(res)

Evaluates $< D_i | S^2 | D_j >$

Only the singly occupied (open-shell) orbitals are relevant for the evaluation. Is nonzero only, if the spin projection of bra and ket are the same. Uses the second quantisation expression for the spin operator with $S^2 = S_z ( S_z - 1) + S_{+} S_{-}$.

Since $S_z$ is basically a particle counting operator, the first summand only appears in the diagonal, i.e. all(nI == nJ).

The second summand is nonzero only, if $D_i$ and $D_j$ differ not at all, or if they differ by exactly one spin exchange. In the former case it evaluates to the number of open shell $\alpha$ electrons, in the latter case it is always one.

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	nI(:)	The bra Slater determinant in nI format.
integer,	intent(in)			::	nJ(:)	The ket Slater determinant in nI format.

Return Value real(kind=dp)

The matrix element. It is real even for complex NECI.

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