Generalized Energy-Based Fragmentation CCSD(T)-F12a Method and Application to the Relative Energies of Water Clusters (H₂O)₂₀

The generalized energy-based fragmentation (GEBF) approach has been implemented for the explicitly correlated F12a of coupled-cluster with the noniterative triples corrections [CCSD­(T)-F12a] method for medium- and large-sized systems. By combining the canonical Hartree–Fock (HF) total energies and the GEBF-X correlation energies, the GEBF-X/HF method is illustrated to be more accurate than the origin GEBF-X method, where X could be any electron correlation method, such as second-order Møller–Plesset perturbation theory (MP2), MP2-F12, CCSD­(T), and CCSD­(T)-F12a. By combining the GEBF-X/HF results at the MP2-F12 and CCSD­(T)-F12a levels, we can approximately achieve the CCSD­(T) complete basis set (CBS) limit. Our test calculations for 10 low-energy isomers of water 20-mers show that for the relative energies of large water clusters, both the basis set and high-level electron correlation effects should be taken into account, in which the former is even more important. In addition, the GEBF-CCSD­(T)/HF method at the CBS limit is used to evaluate 32 levels of density functional theory (DFT) methods. The results show that the DFT methods are difficult to predict the relative energies between the isomers of water 20-mers. The GEBF-CCSD­(T)/HF method at the CBS limit is expected to be a benchmark for DFT and other electron correlation methods for medium- and large-sized systems with complex structures, in which both the basis set and electron correlation effects are important