Benchmark Relative Energies for Large Water Clusters with the Generalized Energy-Based Fragmentation Method

The generalized energy-based fragmentation (GEBF) method has been applied to investigate relative energies of large water clusters (H₂O)_<i>n</i> (<i>n</i> = 32, 64) with the coupled-cluster singles and doubles with noniterative triple excitations (CCSD­(T)) and second-order Møller–Plesset perturbation theory (MP2) at the complete basis set (CBS) limit. Here large water clusters are chosen to be representative structures sampled from molecular dynamics (MD) simulations of liquid water. Our calculations show that the GEBF method is capable of providing highly accurate relative energies for these water clusters in a cost-effective way. We demonstrate that the relative energies from GEBF-MP2/CBS are in excellent agreement with those from GEBF-CCSD­(T)/CBS for these water clusters. With the GEBF-CCSD­(T)/CBS relative energies as the benchmark results, we have assessed the performance of several theoretical methods widely used for <i>ab initio</i> MD simulations of liquids and aqueous solutions. These methods include density functional theory (DFT) with a number of different functionals, MP2, and density functional tight-binding (the third generation, DFTB3 in short). We find that MP2/aug-cc-pVDZ and several DFT methods (such as LC-ωPBE-D3 and ωB97XD) with the aug-cc-pVTZ basis set can provide satisfactory descriptions for these water clusters. Some widely used functionals (such as B3LYP, PBE0) and DFTB3 are not accurate enough for describing the relative energies of large water clusters. Although the basis set dependence of DFT is less than that of <i>ab initio</i> electron correlation methods, we recommend the combination of a few best functionals and large basis sets (at least aug-cc-pVTZ) in theoretical studies on water clusters or aqueous solutions