Following the ideas laid down by Nooijen and Nakatsuji, several authors have considered an intriguing possibility of representing the exact many-electron wave functions by the exponential cluster expansions involving two-body correlation operators. In particular, inspired by the symmetric form of the Horn–Weinstein exact energy formula, and exploiting the variational principle and numerical analysis, we have demonstrated that one can obtain nearly exact ground-state wave functions for a few many-electron systems using the exponential cluster expansion involving a finite two-body operator acting on the Hartree–Fock determinant [P. Piecuch et al., Phys. Rev. Lett. 90 (2003) 113001]. After summarizing these earlier findings and making some additional comments on the nature of the exponential cluster expansions involving two-body correlation operators, we examine the following issues: (i) the improvements in the accuracy and convergence toward the full configuration interaction (CI) limit offered by cluster operators containing two-body as well as one-body components, (ii) the improvements in the accuracy resulting from the use of multi-determinantal reference states, and (iii) the potential accuracy of the exponential wave function expansions involving finite one- and two-body cluster operators in excited-state calculations. All calculations are performed for an eight electron model system, which is simple enough to allow for the exact, full CI, and other electronic structure calculations, which has fewer independent parameters in the Hamiltonian than the dimension of the corresponding full CI problem, and which enables one to examine ground and excited states with a varying degree of configurational quasi-degeneracy by simple changes in the corresponding nuclear geometry.

10axact many-electron wave functions; Generalized coupled-cluster methods; Two-body correlation operators; Nooijen's conjecture; Variational calculations; Multi-determinantal reference states; Excited states1 aFan, P.-D.1 aPiecuch, P. uhttps://icer.msu.edu/intriguing-accuracies-exponential-wave-function-expansions-exploiting-finite-two-body-correlation01260nas a2200205 4500008004100000245004300041210004200084260001200126300001100138490000700149520068900156100001500845700001700860700001600877700002600893700001700919700001900936700001600955856008300971 2005 eng d00aAb Initio Coupled-Cluster Study of 16O0 aAb Initio CoupledCluster Study of 16O c06/2005 a2125010 v943 aWe report converged results for the ground and excited states and matter density of 16O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and algorithms developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a one-particle, one-hole nature, but it cannot describe the first-excited 0+ state. Incorporation of triples has no effect on the latter finding.

1 aWłoch, M.1 aDean, D., J.1 aGour, J., R1 aHjorth-Jensen}, M., {1 aKowalski, K.1 aPapenbrock, T.1 aPiecuch, P. uhttps://icer.msu.edu/research/publications/ab-initio-coupled-cluster-study-16o