Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2

Abstract

Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409–418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.

Reference Energies for Double Excitations: Improvement and Extension

“…Our TBE is very close to the reference value of 4.66 eV chosen by Thiel and co-workers, obtained from multireference Møller–Plesset perturbation theory and basis set extrapolation . It also matches the internally contracted multireference CCSD (icMRCCSD) result in the TZVP basis set reported in ref (4.68 eV). It is worth mentioning the equally remarkable agreement for hexatriene (5.44 eV from icMRCCSD/TZVP compared with our TBE of 5.435 eV) and butadiene (6.52 eV from icMRCCSD/TZVP compared with our TBE of 6.515 eV).…”

“…It also matches the internally contracted multireference CCSD (icMRCCSD) result in the TZVP basis set reported in ref (4.68 eV). It is worth mentioning the equally remarkable agreement for hexatriene (5.44 eV from icMRCCSD/TZVP compared with our TBE of 5.435 eV) and butadiene (6.52 eV from icMRCCSD/TZVP compared with our TBE of 6.515 eV). We notice, however, that the geometries employed in ref are not the same as ours.…”