GHF is size-consistent, size-extensive, invariant to occupied-occupied and virtual-virtual orbital rotations, and active-space-free. The cost of the self-consistent-field calculation to obtain a GHF wavefunction scales as O(N 4 ), where N is proportional to system size. As will be discussed in detail below, the GHF wavefunction can be mapped to a multi-determinant form, and breaking S 2 and S z symmetries often improves the physical description of strongly correlated electronic states.