The foundations of the ROHF method were first formulated by Clemens C. J. Roothaan in a celebrated paper[1] and then extended by various authors, see e.g. [2][3][4] for in-depth discussions.
As with restricted Hartree–Fock theory for closed shell molecules, it leads to Roothaan equations written in the form of a generalized eigenvalue problem where
Unlike restricted Hartree–Fock theory for closed shell molecules, the form of the Fock matrix is not unique.
In contrast to unrestricted Hartree–Fock (UHF), the ROHF wave function is a satisfactory eigenfunction of the total spin operator,
[5] However, different choices of reference orbitals have shown to provide similar results,[6] and thus many different post-HFk methods have been implemented in a variety of electronic structure packages.