Modrzejewski Marcin, Yourdkhani Sirous, Śmiga Szymon, Klimeš Jiří
Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Pasteura 1, Poland.
Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic.
J Chem Theory Comput. 2021 Feb 9;17(2):804-817. doi: 10.1021/acs.jctc.0c00966. Epub 2021 Jan 14.
The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH···(HO), is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.
分子团簇或固体能量的多体展开（MBE）提供了一种方法，可用于检测和分析理论方法中的误差。如果仅考虑系统的总能量，这些误差可能会被忽略。在这方面，甲烷分子与其包围的十二面体水笼CH···(HO)之间的相互作用，是对包括密度泛函理论（DFT）近似在内的近似方法的严格测试。杂化和半局域DFT近似在该系统中表现不稳定，三体和四体非加和项的符号和大小均不正确。在此，我们分析了不同MBE贡献中的这些定性误差在多大程度上传递给了后Kohn-Sham随机相位近似（RPA），RPA使用近似的Kohn-Sham轨道作为输入。结果揭示了DFT输入态的质量与RPA结果之间的相关性。此外，重整化单粒子能量（RSE）修正在多体展开的所有阶次中都起着关键作用。对于二聚体，RSE校正了每个测试的Kohn-Sham模型（广义梯度近似（GGA）、元GGA、（元）GGA杂化以及相关水平的优化有效势）下RPA的结合不足。值得注意的是，在RPA中包含单粒子也可以校正三体和四体非加和能量的错误符号，并减轻对多体展开的过高高阶贡献。RPA误差主要由紧密团簇的贡献主导。作为一种适用于大系统的可行方法，我们建议用CCSD(T)能量替换那些紧密贡献，并使用超分子或周期性RPA将其余的多体贡献求和至无穷大。作为这种方法的一个示例，我们表明，对于RPA(PBE0)+RSE，只需将CCSD(T)应用于二聚体和30个紧密的氢键三聚体，即可将甲烷-水笼相互作用能计算到参考值的1.6%以内。
