Historical precedent. PCILO method

An early example implementing the general approach to take into account first the intrabond correlation, is presented by the PCILO - perturbational configuration interaction of localized orbitals method [121,122], As one of its authors, J.-P. Malrieu mentions in [122], the PCILO method opposes the majority of the QC methods in all the fundamental concepts. In contrast to the majority of the methods based on the variational principle, the PCILO method is based on estimating the energy by perturbation theory. Also, the majority of the QC methods use one-electron HFR approximation, at least as an intermediate construct, whereas the PCILO is claimed to addresses directly the V-electron wave function and takes into account all surviving matrix elements of the electron-electron interactions. In contrast with other QC 

All these statements, although correct in principle, are not precise from the technical point of view. For example, the zero approximate wave function in the PCILO method is a one-electron approximate function constructed from the bond wave functions determined by an a posteriori localization procedure from an HFR function. Thus the bond orbitals appear after a unitary transformation of the canonical MOs, which correspond to some more or less arbitrary localization criteria [123-125]. 

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