School of Physics and Physical Engineering, Qufu Normal University, 273165 Qufu, China.
Phys Chem Chem Phys. 2018 Aug 29;20(34):22084-22098. doi: 10.1039/c8cp02932f.
The complete basis set (CBS) limit is secluded in calculations of electronic structure, and hence CBS extrapolation draws immediate attention. Of the highest importance is the extremely slow-convergent correlation energy as obtained both from Møller-Plesset perturbation theory (MP2) and the gold standard coupled cluster singles, doubles, and perturbative triples method [CCSD(T)], both picked as the focal point. Because today's massive electronic structure calculations demand schemes for CBS extrapolation from the lowest rungs of the hierarchical staircase, the focus is also on how minimal and subminimal basis sets can help in the endeavour. The above has prompted, for the first time, the development of a reliable analytic variant of the unified singlet- and triplet-pair extrapolation (USTE) scheme, which is next utilized to hierarchize any arbitrary basis set. With all available basis set families for molecular orbital calculations systematized as subminimal, minimal and extended from the fraction of correlation energy that they can recover, the full approach is simple and general, yet reliable, and hereby illustrated for basis sets as small as Huzinaga MINI and as extended as the sophisticated ansatzes that are utilized in modern explicitly correlated MP2-F12 and CCSD(T)-F12 calculations. Extensively tested with up to 26 basis sets from various families, the reported results show that CBS extrapolation from a (subminimal, extended) basis-set pair yields correlation energies that outperform by far those obtained from Kohn-Sham density functional theory (KS DFT). When employing two subminimal basis sets, the results may still outperform KS-DFT but at a drastically smaller computational cost. To further gauge its performance, the new method is utilized to calculate the energies of all 45 isomers of C8H8 recently reported at a high ab initio level, with the present results showing excellent agreement with the available data. The present cost-effective approach may therefore be expected to have a broad impact on chemistry and even materials science.
完全基组（CBS）极限是电子结构计算中的一个重要概念，因此 CBS 外推法引起了人们的关注。最重要的是，无论是从 Møller-Plesset 微扰理论（MP2）还是从黄金标准耦合簇单双激发和微扰三激发方法（CCSD(T)）中得到的，关联能的收敛速度都非常慢，这两种方法都被选为重点。由于当今大规模的电子结构计算需要从层次结构的最低梯级进行 CBS 外推的方案，因此重点也放在了最小和亚最小基组如何帮助这一努力。上述情况促使首次开发了可靠的统一单重态和三重态对外推（USTE）方案的解析变体，该方案随后用于对任意基组进行分层。通过将分子轨道计算的所有可用基组族系统化为亚最小、最小和扩展，以它们能够恢复的关联能分数为依据，整个方法简单通用，但又可靠，并且在此为最小的 Huzinaga MINI 基组和扩展的现代显式相关 MP2-F12 和 CCSD(T)-F12 计算中使用的复杂基组进行了说明。通过多达 26 种来自不同族的基组进行了广泛测试，报告的结果表明，从（亚最小、扩展）基组对进行 CBS 外推可以得到远远超过 Kohn-Sham 密度泛函理论（KS DFT）的关联能。当使用两个亚最小基组时，结果可能仍然优于 KS-DFT，但计算成本要低得多。为了进一步评估其性能，该新方法用于计算最近在高从头算水平报道的 C8H8 的所有 45 种异构体的能量，本研究结果与现有数据具有极好的一致性。因此，这种具有成本效益的方法有望对化学甚至材料科学产生广泛的影响。
