Accounting for the exact degeneracy and quasidegeneracy in the automerization of cyclobutadiene via multireference coupled-cluster methods

The automerization of cyclobutadiene (CBD) is employed to test the performance of the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (RMR CCSD) that employs a modest-size MR CISD wave function as an external source for the most important (primary) triples and quadruples in order to account for the nondynamic correlation effects in the presence of quasidegeneracy, as well as of its perturbatively corrected version accounting for the remaining (secondary) triples [RMR CCSD(T)]. The experimental results are compared with those obtained by the standard CCSD and CCSD(T) methods, by the state universal (SU) MR CCSD and its state selective or state specific (SS) version as formulated by Mukherjee (SS MRCC or MkMRCC) and, wherever available, by the Brillouin-Wigner MRCC [MR BWCCSD(T)] method. Both restricted Hartree-Fock (RHF) and multiconfigurational self-consistent field (MCSCF) molecular orbitals are employed. For a smaller STO-3G basis set we also make a comparison with the exact full configuration interaction (FCI) results. Both fundamental vibrational energies-as obtained via the integral averaging method (IAM) that can handle anomalous potentials and automatically accounts for anharmonicity- and the CBD automerization barrier for the interconversion of the two rectangular structures are considered. It is shown that the RMR CCSD(T) potential has the smallest nonparallelism error relative to the FCI potential and the corresponding fundamental vibrational frequencies compare reasonably well with the experimental ones and are very close to those recently obtained by other authors. The effect of anharmonicity is assessed using the second-order perturbation theory (MP2). Finally, the invariance of the RMR CC methods with respect to orbital rotations is also examined.