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

Abstract

The multireference, state specific, second-order, Brillouin–Wigner perturbation theory is applied to the autoaromatisation of hex-3-ene-1,5-diyne, the Bergman reaction. Calculations are reported for the reactant (hex-3-ene-1,5-diyne), the transition state and the product (1,4-didehydrobenzene). 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, i.e. Møller–Plesset (MP2) theory, and in the multireference case can be shown to be equivalent to state-specfic multireference Rayleigh–Schrödinger-like perturbation theory. Calculations are performed for a sequence of correlation consistent basis sets and, by extrapolation, complete basis set limits of the energetics of the Bergman reaction are estimated.

Keywords:

• electron correlation
• multireference
• Brillouin–Wigner
• perturbation theory
• Bergman reaction

Acknowledgement

PP and PM acknowledge support from the VEGA Grant agency, Slovakia, under project number V-521-06-00. JP and IH acknowledge support by the Grant Agency of the Czech Republic under project number 203/04/0425. This work was supported by the Slovak Research and Development Agency under the contract No. APVV-20-018405.

Notes

Notes

1. The intruder state problem has been discussed by many authors. We mention two recent studies: one by Paldus and Li 9 on the intruder state problem in state-universal coupled cluster theory and the other by Perrine et al. 10 on quadratic Padé approximants and the intruder state problem in multireference perturbation methods. The intruder state problem has also been studied in the nuclear physics literature (e.g. 11).

2. In a recent paper, Chaundhuri et al. 35 provide an appraisal of multireference perturbation theories basd on benchmark calculations for a number of small molecules.

3. A pedagogical presentation of multireference many-body perturbation theory is given by Kucharski and Bartlett 80.

4. Direct Inversion of the Iterative Subspace extrapolation which was introduced by Pulay 85.