Many‐body Brillouin–Wigner second‐order perturbation theory: A robust and efficient approach to the multireference correlation problem

Abstract

ABSTRACT:The multireference, state-specific, second-order, Brillouin-Wigner perturbation theory is presented as a robust approach to the electron correlation problem for systems demanding the use of a multireference function. A posteriori modifications are made which, in the case of a single reference function, recover the well known formula of second-order many-body perturbation theory (MBPT2), i.e. Møller-Plesset (MP2) theory, and in the multireference case can be shown to be equivalent to state-specific multireference Rayleigh-Schrödinger-like perturbation theory. It is shown that multireference many-body Brillouin-Wigner perturbation theory when restricted to second-order is a true many-body theory, that is, it is a theory, which has the property of extensivity.

Second‐order state‐specific multireference Møller Plesset perturbation theory: Application to energy surfaces of diimide, ethylene, butadiene, and cyclobutadiene

“…In view of these issues, much attention has been given to the so‐called state‐selective or state‐specific (SS) MR approaches. In the past two decades, the interest in the development of SS methods for an accurate treatment of correlation effects within the MR framework has grown noticeably 6–12. The MRPT‐based SS approach permits performing calculations for one state at a time and provides a very efficient way of computing state energy per se and mapping PES of the target state.…”

“…The various CASPT2,7 MRMPPT,6 and its multistate variant that is referred to as MCQDPT18 methods by and large avoid the size‐consistency error, but not rigorously. For avoiding the intruder state problem in Brillouin–Wigner (BW) multireference perturbation theory (BWPT), Hubač‐Wilson and coworkers8, 9 paid the price of losing size extensivity. However, using a posteriori adjustment for lack of extensivity [based on a transition from a BW expansion to an expansion based on Rayleigh–Schrödinger (RS) perturbation theory] in second‐order BW multireference perturbation theory, we arrive at a theory that can be seen to be size extensive.…”

“…Multiple iterations or the converged RS type of results will, however, unfortunately bring back the problem of potential intruders. We refer the interested reader to the original publications for further details 9. The size extensivity is not manifested explicitly in GVVPT213 because of the explicit use of Hilbert space projectors.…”

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

“…Given the success of 'MP2' theory for problems for which a single reference function is appropriate, it is important to determine the extent to which the corresponding Brillouin-Wigner method is applicable in a state specific formulation with a posteriori modification to problems which demand to use of a multireference approach [26]. In a previous paper, [27] a comparison of (single reference) MP2 and (multireference) second-order modified Brillouin-Wigner calculations has been reported for the dissociation of the first-row diatomic hydride molecules BH and FH using basis sets for which the corresponding full configuration interaction calculations can be carried out.…”

State-specific complete active space multireference Møller–Plesset perturbation approach for multireference situations: illustrating the bond breaking in hydrogen halides

“…Although formally simple in conjunction with an explicit intruderfree nature, the BWPT2 method due to Hubač et al[23][24][25] is not rigorously size-extensive. In the first applications of BWPT2, no correction to the size-inextensivity was attempted.…”