Restricted open-shell Hartree-Fock procedure

Hurley, A. C., Introduction to the Electron Theory of Small Molecules Academic Press, New York, 1976. The restricted open-shell Hartree-Fock procedure, which we have not expanded upon is described. 

In FIF calculations on open-shell molecules, a complication arises because in addition to doubly occupied and virtual MOs, there are now also singly occupied MOs (one in the case of radicals and two in the case of triplet diradicals). In a first attempt to construct a ground state wavefunction Pq for such a molecule, a Slater determinant may be set up that contains the appropriate number of singly occupied MOs and leaves all the others occupied by two electrons of opposite spin. This type of wavefunction is called restricted open-shell Hartree-Fock (ROHF) restricted because the electrons of opposite spin in the closed shells are constrained to occupy MOs / that are spatially identical for electrons of a ( up ) and p ( down ) spin. A procedure to variationally optimize such a wavefunction for open-shell systems has been devised. ... 

In the cases other than [case A] and [case B), so called "open-shell SCF methods are employed. The orbital concept becomes not quite certain. The methods are divided into classes which are "restricted 18> and "unrestricted 19> Hartree-Fock procedures. In the latter case the wave function obtained is no longer a spin eigenfunction. 

With radicals there is no convenient method like the Hartree-Fock-Roothaan procedure commonly used for closed-shell systems. In contrast, the open-shell theory is typical of a number of methods suggested which differ in accuracy from the viewpoint of true SCF theory, in range of applicability, complexity, and computing feasibility. A critical survey of open-shell SCF methods reported by Berthier D covers the literature up to 1962. We shall not duplicate that review here we propose rather to note some features of open-shell methods relevant to their computation feasibility and to mention procedures published after 1962. The unrestricted treatments that assume different space orbitals for different spins will be disregarded here because the restricted wave functions... 

In this subsection, we describe restricted closed-shell calculations on the ground state of H2. As we will see, there is a very basic deficiency in such calculations at long bond lengths. Later in this chapter, when we describe unrestricted open-shell calculations, we will return to minimal basis H2 and partially correct this deficiency. Some of the results obtained here will also be used in later chapters when we use the minimal basis H2 model to illustrate procedures that go beyond the Hartree-Fock approximation. 

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