On the use of Brillouin-Wigner perturbation theory for many-body systems

Abstract

The use of Brillouin-Wigner perturbation theory in describing many-body systems is critically re-examined.

RADIATIVE L-SHELL TRANSITIONS IN Fe XIX AND Fe XX IONS

“…Here, we further analyze these transitions and expand our calculations to other transitions in Fe xix and Fe xx. For these calculations, we use the ab initio configuration interaction (CI) Dirac-Fock-Sturm (MDFS) method combined with second-order Brillouin-Wigner perturbation theory (BWPT; Lennard-Jones 1930;Brillouin 1932;Wigner 1935;Hubac & Wilson 2000) with a full implementation of relativistic, correlation, and quantum electrodynamic effects. For each electronic state, spatially localized single-electron orbitals are optimized using the Dirac-Fock method.…”

On the Estimation of the Remainder Term in Møller-Plesset MP2 Theory from Limited Configuration Interaction

“…In this paper, we consider the use of limited configuration interaction in obtaining an estimate for R. We restrict our attention to a non-degenerate ground state and employ the Brillouin-Wigner perturbation expansion [20][21][22][23] in our analysis. The energy of such a system is given by…”

Four-Reference State-Specific Brillouin-Wigner Coupled-Cluster Method: Study of the IBr Molecule

“…Since the derivation of the state-specific Brillouin-Wigner coupled-cluster theory has been presented for the general multireference case previously [3,5], and details of the implementation for closed-shell molecules have also been published [4], we give here only a brief review of the method and the relevant working equations.…”

“…This paper is a continuation of our previous studies [1][2][3][4][5][6][7][8][9] on the development of a multi-reference coupled-cluster (MRCC) method that would be free of the problem of intruder states and that would be amenable to treatment of systems requiring more than two reference configurations. Avoidance of intruder states was achieved by using the Brillouin-Wigner (BW) resolvent, and simplicity of the method and feasibility of calculations were achieved by subjecting the BWCCSD method to a state-specific form [2][3][4].…”

“…For merits of the statespecific BW theory we paid the price that the method was not size extensive any longer. We developed therefore an a posteriori correction [5,6] for eliminating the size-inconsistent terms in the amplitudes. Again, the correction in its original implementation [6] was confined to two-reference cases.…”