Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering , Georgia Institute of Technology , Atlanta , Georgia 30332-0400 , United States.
J Chem Theory Comput. 2018 May 8;14(5):2386-2400. doi: 10.1021/acs.jctc.7b01232. Epub 2018 Apr 18.
Fragment-based methods promise accurate energetics at a cost that scales linearly with the number of fragments. This promise is founded on the premise that the many-body expansion (or another similar energy decomposition) needs to only consider spatially local many-body interactions. Experience and chemical intuition suggest that typically at most four-body interactions are required for high accuracy. Bettens and co-workers [ J. Chem. Theory Comput. 2014 9, 3699-3707] published a detailed study showing that for moderately sized water clusters, basis set superposition error (BSSE) undermines this premise. Ultimately, they were able to overcome BSSE by performing all computations in the supersystem basis set, but such a solution destroys the reduced computational scaling of fragment-based methods. Their findings led them to suggest that there is "trouble with the many-body expansion". Since then, a subsequent follow-up study from Bettens and co-workers [ J. Chem.
Comput. 2015, 11, 5132-5143] as well as a related study by Mayer and Bakó [ J. Chem. Theory Comput. 2017, 13, 1883-1886] have proposed new frameworks for understanding BSSE in the many-body expansion. Although the two frameworks ultimately propose the same working set of equations to the BSSE problem, their interpretations are quite different, even disagreeing on whether or not the solution is an approximation. In this work we propose a more general BSSE framework. We then show that, somewhat paradoxically, the two interpretations are compatible and amount to two different "normalization" conditions. Finally, we consider applications of these BSSE frameworks to small water clusters, where we focus on replicating high-accuracy coupled cluster benchmarks. Ultimately, we show for water clusters, using the present framework, that one can obtain results that are within ±0.5 kcal mol of the coupled cluster complete basis set limit without considering anymore than a correlated three-body computation in a quadruple-ζ basis set and a four-body triple-ζ Hartree-Fock computation.
片段方法承诺以与片段数量线性比例的成本提供准确的能量。这一承诺基于这样一个前提，即多体展开（或其他类似的能量分解）只需要考虑空间局部多体相互作用。经验和化学直觉表明，通常最多需要四体相互作用才能达到高精度。Bettens 及其同事 [J. Chem. Theory Comput. 2014, 9, 3699-3707] 发表了一项详细的研究，表明对于中等大小的水分子簇，基组叠加误差 (BSSE) 破坏了这一前提。最终，他们通过在超体系基组中进行所有计算来克服 BSSE，但这种解决方案破坏了片段方法的降低计算规模。他们的发现导致他们认为“多体展开存在问题”。从那以后，Bettens 及其同事的后续跟进研究 [J. Chem. Theory Comput. 2015, 11, 5132-5143] 以及 Mayer 和 Bakó 的相关研究 [J. Chem. Theory Comput. 2017, 13, 1883-1886] 提出了理解多体展开中 BSSE 的新框架。尽管这两个框架最终为 BSSE 问题提出了相同的工作方程组，但它们的解释却大不相同，甚至在解决方案是否是近似值的问题上也存在分歧。在这项工作中，我们提出了一个更通用的 BSSE 框架。然后我们表明，有些矛盾的是，这两种解释是兼容的，相当于两种不同的“归一化”条件。最后，我们考虑将这些 BSSE 框架应用于小水分子簇，我们专注于复制高精度耦合簇基准。最终，我们表明，对于水分子簇，使用本框架，在四重 ζ 基组中进行相关的三体计算和四体三 ζ Hartree-Fock 计算后，就可以获得与耦合簇完全基组极限相差在 ±0.5 kcal/mol 以内的结果。
