Bond breaking Hartree-Fock theory

We start with paper [1]. This work had put forward a first possible definition of the EUE density for an arbitrary wave function with any permitted spin value s > 0. As mentioned in the introduction, our main interest is the case of singlet states, and for them the EUE effects are really important and interesting. Indeed, for nonzero spin states (doublet-state radicals, triplet-state diradicals etc.), the manifestations of unpaired electrons can be described even within the restricted open-shell Hartree-Fock (ROHF) theory. The latter characterizes the unpaired spins by standard spin density matrices. In the singlet state, the spin density matrix disappears [2], and yet, electron correlation enforces electrons to be unpaired if physical and chemical circumstances require it (e.g., in bond breaking processes). 

The use of a Hartree-Fock reference function is ubiquitous in molecular electronic structure theory because of the beneficial computational consequences of the orthogonality of the Hartree-Fock molecular orbitals. However, many quantum chemical studies require the use of a multi-reference formalism. For example, studies of systems involving bond breaking processes almost invariably require the use of a reference function constructed as a linear combination of a number of reference functions. For cases where electron correlation effects are large and, in particular, when the Hartree-Fock model gives qualitatively incorrect results, the system is said to be strongly correlated. 

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