instead of real (non-complex) one-component orbitals needed for non-relativistic or scalar-relativistic treatments. The Hartree-Fock and Kohn-Sham equations are now spinor equations with a complex Fock operator

The wavefunction is no longer eigenfunction of the spin operator, the spin vector is no longer an observable.

In case of DFT for open-shell systems rotational invariance of the exchange-correlation energy was ensured by the non-collinear approach. In this approach the exchange-correlation energy is a functional of the particle density and the absolute value of the spin-vector density ( are the Pauli matrices)

This quantity replaces the spin-density (difference between density of alpha and beta electrons) of non- or scalar-relativistic treatments.

For closed-shell species the Kramers-restricted scheme, a generalization of the RHF-scheme of one component treatments, is applicable.