The exact wavefunction of molecules reflects the full set of physical symmetries inherent to its Hamiltonian, such as the anti-symmetry with respect to exchange of electrons. Molecular systems are known to possess many physical symmetries beyond the fermionic constraint, such as total spin, Ŝ2 , spin along a designated axis, Ŝz , time reversal, T , and complex conjugation, K. Enforcing all these requirements in HF theory yields the Restricted HF (RHF)