Generalized Valence Bond Perfect-Pairing Made Versatile Through Electron-Pairs Embedding

We present an electron-pairs-based method employing a generalized valence bond perfect-pairing (GVB-PP) ansatz that provides a uniformly accurate description of systems where various types of electron correlation play a role and the GVB-PP wave function is a suitable reference. In the proposed EERPA-GVB approach, a GVB-PP energy is amended by adding correlation among electron pairs. The latter is achieved by embedding single pairs or couples of pairs in the environment of the other electron fragments and separately accounting for intra- and interfragment correlation effects. For this purpose, we employ truncated extended random phase approximation equations. Application of EERPA-GVB to systems governed by both short-range (energy barriers) and long-range (molecular interactions) correlation effects proves the good accuracy of the method. Moreover, EERPA-GVB is shown to cure a notorious problem of uncorrelated electron-pair models, namely, spatial symmetry breaking in aromatic molecules, using the example of benzene. We have also successfully applied EERPA-GVB to a challenging problem of a phase transition of the boron chain system, where the correlation changes its character along the reaction path. The accuracy and versatility of EERPA-GVB are accompanied by its attractively low computational cost. By truncation of the extended RPA equations and consideration of only at most two-fragment correlation contributions, the cost of computing the EERPA correlation energy is reduced to scale only quadratically with the number of pairs of electrons.