多体非共价体系中的无规相近似：十二面体水笼中的甲烷
Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage
摘要：
分子团簇或固体能量的多体展开（MBE）提供了一种方法来检测和分析理论方法的错误，如果只考虑系统的总能量，这些错误可能会被忽视。在这方面，甲烷分子和其封闭的十二面体水笼CH $_4$（H $_2$ O）$_{20}$之间的相互作用是对近似方法的严格测试，包括密度泛函理论（DFT）近似。混合和半局部DFT近似的行为不稳定的这个系统，与三体和四体非加性条款既没有正确的符号和幅度。在这里，我们分析在何种程度上这些定性错误在不同的分子束外延的贡献传达后Kohn-Sham随机相位近似（RPA）。结果揭示了DFT输入态的质量和RPA结果之间的相关性。此外，重整化单能（RSE）修正在分子束外延的所有阶次中都起着至关重要的作用。对于二聚体，RSE校正了每个测试的Kohn-Sham模型的RPA结合不足：广义梯度近似（GGA），元GGA，（Meta）GGA混合，以及在相关水平上的优化有效势。值得注意的是，在RPA中包含单体也可以纠正三体和四体非加性能量的错误符号，以及减轻对MBE的过度高阶贡献。RPA误差主要由紧凑的集群的贡献。作为一个可行的方法，大系统，我们建议取代这些紧凑的贡献与CCSD（T）的能量和总结剩余的多体贡献到无穷大的超分子或周期RPA。作为这种方法的演示，我们表明，对于RPA（PBE 0）+RSE，将CCSD（T）应用于二聚体和30个紧凑的氢键三聚体足以使甲烷-水笼相互作用能在参考值的1.6%以内。
英文摘要：
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$_4$(H$_2$O)$_{20}$, 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). 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 MBE. 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 MBE. 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.
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