SR-MBPT

Cluster expansion representation of a wave-function built from a single determinant reference function [1] has been eminently successful in treating electron correlation effects with high accuracy for closed shell atoms and molecules. The cluster expansion approach provides size-extensive energies and is thus the method of choice for large systems. The two principal modes of cluster expansion developments in Quantum Chemistry have been the use of single reference many-body perturbation theory (SR-MBPT) [2] and the non-perturbative single reference Coupled Cluster (SRCC) theory [3,4]. While the former is computationally economical for the first few orders of the perturbation expansion... 

The MC-QDPT(2) theory starts with fixed coeflicients for the model space functions, unlike in our SS-MRPT theories. It is also not fully extensive. We also present the second order SR-MBPT and the effective hamiltoni in based MR-MBPT results, since we want to investigate to what extent the SR-MBPT results behave poorly at the quasi-degenerate regions, and the MR-MBPT results sense the presence of intruders. Hq in both SR-MBPT and MR-MBPT is taken as in the standard EN partitioning, which is structurally closer to our choice for Hq the two SS-MRPT methods. 

Consequently, within the spin free JV-electron Hilbert space, the MBPT for OSS states can be formulated as a SR theory with the spin free reference o), Eq-4, and the UGA representation of the perturbed and unperturbed Hamiltonians. The resulting theory has formally the same appearance as the spin orbital based MBPT theories for CS or HS OS cases. 

The need for the inclusion of higher-order effects increases with the degree of quasidegeneracy of the state considered. For this reason, much effort has been devoted to the formulation of the so-called MR MBPT [28-30]. Here, however, a number of ambiguities arises, which often limits the development of practical algorithms (c/, e.g. attempts to extend the so-called CAS-PT2 method, which is based on the complete active space self-consistent field (CAS SCF) reference, to higher than the second order). In fact, we shall see that the same problem manifests itself, even when extending the standard SR CC theory to the MR case. 

BWPT = Brillouin-Wigner perturbation theory EN = Epstein-Nesbet FCI = full Cl MBPT = many-body perturbation theory MRS PT = multireference state perturbation theory PT = perturbation theory RSPT = Rayleigh-SchrSdinger perturbation theory SRS PT = single-reference state perturbation theory. 

In contrast to Cl, the CC approaches, even at the SR level, very efficiently account for the dynamic correlation thanks to the exponential CC Ansatz for the wave operator. The general form of the CC wave function also automatically guarantees the size-extensivity of the computed energies [as do, in fact, the individual linked diagrams of the many-body perturbation theory (MBPT)]. Unfortunately, this size-extensive property is of a little use when the nondynamic correlation is not properly accounted for. Indeed, the CCSD PECs often display an artificial "hump in the region of intermediate internuclear separations, as well as grossly erroneous asymptotic behavior in the completely dissociated limit [cf., e.g. the CCSD PECs for N2 in Refs. (5,9)]. 

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