Brillouin–Wigner Expansions for Molecular Electronic Structure

Abstract

The use of Brillouin–Wigner expansions in describing electron correlation effects in systems requiring the use of a multireference formalism is described. Brillouin–Wigner‐based methods avoid the intruder state problem which plagues Rayleigh–Schrödinger‐based methods. Such methods can be applied to many‐body systems either (i) by applying the Brillouin–Wigner expansion to solve the equations of an explicitly many‐body method; or (ii) by developing a posteriori corrections. The Brillouin–Wigner coupled cluster theory is presented in both its single reference and multireference forms. Single and multireference configuration interaction expansions are described together with the accompanying a posteriori correction procedures.

Many-body Brillouin–Wigner second-order perturbation theory: an application to the autoaromatisation of hex-3-ene-1,5-diyne (the Bergman reaction)

“…In the many-body Brillouin-Wigner theory advocated in the present work, calculations are carried out in the BrillouinWigner formalism and then a posteriori modification is made to recover a fully many-body theory. A more detailed description of the many-body BrillouinWigner formalism can be found elsewhere [12][13][14].…”

“…One of the most promising of these approaches is based on the use of Brillouin-Wigner expansions [12][13][14]. Historically, Brillouin-Wigner methods [15][16][17] have been regarded [18][19][20][21] as unsuitable for many-body systems containing the exact energy in denominator factors which destroys their extensivity.…”

“…(For reviews, see, for example, Lindgren and Morrison [19], Mukherjee and Pal [28], Hirao [29], Paldus and Li [3,30], Kaldor [31], Piecuch and coworkers [32,33], Hubac˘and Wilson [12,13]. ) Most published formulations employ RayleighSchro¨dinger perturbation theory in a 'perturb then diagonalise' approach, i.e.…”