The (independent) orbital rotation parameter κ pq does not span all MOs. The SA-CASSCF energy is invariant to rotations among inactive (doubly occupied), active, and secondary (virtual) orbitals; thus, rotations in the diagonal subspaces do not change the SA-CASSCF energy. Furthermore, the orthonormalization condition of the MO guarantees that the rotation of pq and qp is redundant. The pq for κ pq therefore spans only the lower (or upper) part of the off-diagonal blocks: (p, q) ∈ (active, inactive), (secondary, inactive), (secondary, active).