To implement a constrained CASSCF theory, we must establish the necessary nomenclature conventions. Henceforward, we let i, j represent inactive (i.e. fully occupied) orbitals; t, u, v, w, x, y represent active orbitals; a represent an (empty) virtual orbital; and m, n, p, q, r, s represent arbitrary orbitals. Clearly, the identity can be resolved as Î = Pinactive + Pactive + Pvirtual (1) where Pinactive , Pactive and Pvirtual are projection operators onto the inactive, active, and virtual orbitals. Subscripts α, β index electronic spin. p α refers to a spin orbital while p refers to a spatial orbital. We index atomic orbitals with greek letters µ and ν.