The Quality of Embedding Charges Is Critical for Convergence of Many-Body Expansions When BSSE Is Absent

There is conflicting evidence in the literature concerning the benefits of charge embedding on the convergence of many-body expansions (MBEs). Using a systematic series of water and ion-water clusters of varying size, this study indicates that the effects of charge embedding can be masked by basis set superposition error (BSSE). When BSSE is removed, this study demonstrates that charge embedding can significantly accelerate MBE convergence, where the electrostatically embedded two-body method, EE-MBE(2), can often yield accuracy close to the four-body method, MBE(4). Contrary to previous studies on smaller systems, this work shows that the performance of EE-MBE is highly sensitive to the charge model, with the best performance obtained when the natural population analysis (NPA) charge model is used and generated at the same level of theory used in the subsystem and supersystem calculations. It was demonstrated that the "3c" composite method, PBEh-3c, yields NPA atomic charges that are in excellent agreement with those obtained from supersystem density functional theory calculations. The linear-scaling X-Polarization method provides a more general approach to estimating these supersystem QM atomic charges, but its performance depends on how the fragments are defined.