Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H₂O)₃₇, four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H₂O)₂₀ isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500–1800 basis functions.

中文翻译：

---

了解大型系统的多主体扩展。三，四体术语，平衡修正和临界值的关键作用

该系列的论文I和II [RM理查德等。，J. Chem。物理 141，014108（2014）; KU Lao等。，同上。[ 144，164105（2016）]试图阐明影响多体膨胀（MBE）的精度和准确性问题，这些问题仅在较大的系统中才会体现出来，因此在文献中很少受到关注。已显示多体平衡法（CP）校正可加快MBE的收敛速度，否则会遭受基集叠加误差如何影响子系统与超级系统计算之间的不匹配的困扰。在大小不超过（H ₂ O）_37的水簇中，四体项被证明对于获得总相互作用能和相对异构体能的精确结果都是必要的，但是四聚体的绝对数量使得必须使用截止方案。预测（H ₂ O）_20的相对能量异构体，引入了两个基于较低理论水平的近似值，并且发现ONIOM类型的程序相对于适当的MBE基准已经很好地收敛，即，在相同理论水平上进行了CP校正的超级系统计算。使用基于能量的截止方案的结果表明，如果可以获得子系统能量的合理近似值（例如，基于经典的多极子），则与采用基于距离的阈值相比，所需子系统计算的数量可以大大减少。最终结果是不需要电荷嵌入的几种准确的四体方法，并且在诸如aug-cc-pVTZ之类的大型基集中稳定，而这些方法有时被证明对基于片段的量子化学方法来说是有问题的。即使采用积极的门槛，