So far, we have not distinguished between spin orbitals and spatial orbitals. But clearly there are more decisions to make when dealing with spin orbitals: we can number all the alpha spin orbitals first, then the beta, or we can number according to irrep (Pitzer ordering) and then put all alpha spin orbitals first within each irrep, etc. While the use of spin orbitals complicates matters, the possible extensions of the spatial orbital numbering schemes are transparent and thus we will restrict our attention to spatial orbitals.