Approximate account of connected quadruply excited clusters in single-reference coupled-cluster theory via cluster analysis of the projected unrestricted Hartree-Fock wave function

Abstract

Extension of the applicability of the closed-shell coupled-cluster ͑CC͒ theory with doubly ͑CCD͒ or singly and doubly ͑CCSD͒ excited clusters to quasidegenerate situations requires the inclusion of the connected triply and quadruply excited cluster components T 3 and T 4 . Since an explicit consideration of these clusters for larger systems is computationally very demanding, we explore the possibility of estimating the T 4 contribution using the projected unrestricted Hartree-Fock ͑PUHF͒ wave function. The resulting CCDQЈ and CCSDQЈ approaches are shown to correctly approximate the effect of the quadruply (QЈ) excited T 4 clusters, even when the PUHF wave function itself cannot serve as a good source of the lower-order pair-cluster components. It is important that the results of the cluster analysis of the PUHF solution are used directly and no further approximations are made. Only when both pair-cluster and T 4 cluster components are reasonably well approximated by the PUHF wave function, the T 4 cluster contributions cancel out certain CCSD diagrams, and good CC results can be obtained with the approximate coupled-pair approaches. It is also demonstrated that it may be more difficult to balance T 3 and T 4 clusters relying on simple perturbative approaches, such as CCSDQЈϩT͑CCSDQЈ͒. The results of formal considerations, including a thorough investigation of the cluster structure of the PUHF wave function, are illustrated on several examples. These include a few model systems composed of four and eight hydrogen atoms in various geometrical arrangements, as described using minimum and double zeta plus polarization basis sets, for which the exact full configuration interaction data are available. The orthogonally spin-adapted formulation of CC theory is used throughout. ͓S1050-2947͑96͒07407-0͔ PACS number͑s͒: 31.10.ϩz, 31.15.Dv, 31.15.Ar, 31.25.Ϫv

Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations

“…This fact was already noted in Ref. 19; these authors also introduced the operator K 2 and we have borrowed their notation. However, they did not point out that the PHF wave function could be expressed as a polynomial of the double-excitation operator K 2 , a key result needed for solving the u a i amplitudes as we do here.…”

Can Single-Reference Coupled Cluster Theory Describe Static Correlation?

“…Numerous authors have proposed methods that yield reasonable predictions in the presence of near degeneracies by modifying coupled cluster theory or variants thereof. [8][9][10][11][12][13][14][15][16][17][18][19][20] We would like a simple conceptual framework which allows us to identify the offending terms in traditional coupled cluster theory so that by excluding them we can avoid the downfall of the method. Of course, this is easier said than done, but we here show one particular case which substantially removes the typical failures in repulsive Hamiltonians.…”

Density-based errors in mixed-basis mean-field electronic structure, with implications for embedding and QM/MM methods

“…Many studies demonstrate that the approximate coupled-pair approach with approximate quadruples (ACPQ) is superior to the full CCSD method for strongly correlated systems [12][13][14]16]. At the same time the accuracy of ACPQ in the weakly correlated regime is similar to that of CCSD [9,14].…”