Application of the CC(<i>P</i>;<i>Q</i>) Hierarchy of Coupled-Cluster Methods to the Beryllium Dimer

The performance of coupled-cluster approaches with higher-than-doubly excited clusters, including the CCSD­(T), CCSD(2)_T, CR-CC­(2,3), CCSD­(TQ), and CR-CC­(2,4) corrections to CCSD, the active-space CCSDt, CCSDtq, and CCSDTq methods, and the CC­(t;3), CC­(t,q;3), CC­(t,q;3,4), and CC­(q;4) corrections to CCSDt, CCSDtq, and CCSDTq resulting from the CC­(<i>P</i>;<i>Q</i>) formalism, in reproducing the CCSDT and CCSDTQ potential energy curves and vibrational term values characterizing Be₂ in its electronic ground state is assessed. The correlation-consistent aug-cc-pV<i>n</i>Z and aug-cc-pCV<i>n</i>Z (<i>n</i> = T and Q) basis sets are employed. Among the CCSD-based corrections, the completely renormalized CR-CC­(2,3) and CR-CC­(2,4) approaches perform the best. The CC­(t;3), CC­(t,q;3), CC­(t,q;3,4), and CC­(q;4) methods, especially CC­(t;3) and CC­(q;4), outperform other employed approaches in reproducing the CCSDT and CCSDTQ data. Composite schemes combining the all-electron CCSDT calculations extrapolated to the complete basis set limit with the frozen-core CC­(q;4) and CCSDTQ computations using the aug-cc-pVTZ basis to account for connected quadruple excitations reproduce the latest experimental vibrational spectrum of Be₂ to within 4–5 cm^–1, when the vibrational spacings are examined, with typical errors being below 1–2 cm^–1. The resulting binding energies and equilibrium bond lengths agree with their experimentally derived counterparts to within ∼10 cm^–1 and 0.01 Å

The Cobalt–Methyl Bond Dissociation in Methylcobalamin: New Benchmark Analysis Based on Density Functional Theory and Completely Renormalized Coupled-Cluster Calculations

The Co–C_Me bond dissociation in methylcobalamin (MeCbl), modeled by the Im–[Co^IIIcorrin]–Me⁺ system consisting of 58 atoms, is examined using the coupled-cluster (CC), density-functional theory (DFT), complete-active-space self-consistent-field (CASSCF), and CASSCF-based second-order perturbation theory (CASPT2) approaches. The multilevel variant of the local cluster-in-molecule framework, employing the completely renormalized (CR) CC method with singles, doubles, and noniterative triples, termed CR-CC(2,3), to describe higher-order electron correlation effects in the region where the Co–C_Me bond breaking takes place, and the canonical CC approach with singles and doubles (CCSD) to capture the remaining correlation effects, abbreviated as CR-CC(2,3)/CCSD, is used to obtain the benchmark potential energy curve characterizing the Co–C_Me dissociation in the MeCbl cofactor. The Co–C_Me bond dissociation energy (BDE) resulting from the CR-CC(2,3)/CCSD calculations for the Im–[Co^IIIcorrin]–Me⁺ system using the 6-31G* basis set, corrected for the zero-point energies (ZPEs) and the effect of replacing the 6-31G* basis by 6-311++G**, is about 38 kcal/mol, in excellent agreement with the experimental values characterizing MeCbl of 37 ± 3 and 36 ± 4 kcal/mol. Of all DFT functionals examined, the best dissociation energies and the most accurate description of the Co–C_Me bond breaking in the Im–[Co^IIIcorrin]–Me⁺ system are provided by B97-D and BP86 corrected for dispersion using the D3 correction of Grimme et al., which give 35 and 40 kcal/mol, respectively, when the 6-311++G** basis set is employed and when the results are corrected for ZPEs and basis set superposition error. None of the other DFT approaches examined provide results that fall into the experimental range of the Co–C_Me dissociation energies in MeCbl of 32–40 kcal/mol. The hybrid DFT functionals with a substantial amount of the Hartree–Fock (HF) exchange, such as B3LYP, considerably underestimate the calculated dissociation energies, with the magnitude of the error being proportional to the percentage of the HF exchange in the functional. It is argued that the overstabilization of diradical structures that emerge as the Co–C_Me bond is broken and, to some extent, the neglect of dispersion interactions at shorter Co–C_Me distances, postulated in previous studies, are the main factors that explain the substantial underestimation of the Co–C_Me BDE by B3LYP and other hybrid functionals. Our calculations suggest that CASSCF and CASPT2 may have difficulties with providing a reliable description of the Co–C_Me bond breaking in MeCbl, since using adequate active spaces is prohibitively expensive