According to the classification of Jacob's Ladder proposed by Perdew, density functional approximations (DFAs) on the top (fifth) rung add the information of the unoccupied Kohn–Sham orbitals, which hold the promise to enter the heaven of chemical accuracy. In other words, we expect that a much higher accuracy with a broader applicability than the existing DFAs would eventually be achieved on the fifth rung. Nonetheless, Jacob's Ladder itself does not offer a recipe for how to manipulate the unoccupied Kohn–Sham orbitals on the construction of a successful fifth rung DFA. In this article, we briefly review two successful types of the fifth rung DFAs, that is, random‐phase approximation (RPA) and doubly hybrid approximation (DHA). The limitations of RPA and DHA will be introduced in the context of the so‐called self‐interaction error (SIE)/nondynamic correlation error (NCE) dilemma in the world of density functional theory. We propose the development strategy for DHAs to address the general concern about the future of advanced DFAs on the fifth rung. We share our experience here, based on the relevant efforts recently made by the authors and their co‐workers, aiming to resolve the SIE/NCE dilemma and to extend the applicability of DHAs from the chemistry of the main group elements to that of the transition metals.

中文翻译：

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在雅各布的密度泛函理论的阶梯上：解决SIE和NCE的困境

根据Perdew提出的Jacob's Ladder的分类，在顶部（第五个）横档上的密度泛函近似（DFA）添加了未占用的Kohn-Sham轨道的信息，这有望进入化学准确性的天堂。换句话说，我们期望在第五梯级上最终将获得比现有DFA更高的准确性和更广泛的适用性。然而，雅各布的阶梯本身并未提供如何在成功的第五级DFA建造中操纵空置的科恩-深井轨道的方法。在本文中，我们简要回顾了第五种梯级DFA的两种成功类型，即随机相位近似（RPA）和双重混合近似（DHA）。RPA和DHA的局限性将在密度泛函理论世界中所谓的自交互误差（SIE）/非动态相关误差（NCE）困境的背景下引入。我们提出DHA的开发策略，以解决人们对第五梯级高级DFA的未来的普遍关注。在作者和他们的同事最近做出的相关努力的基础上，我们在这里分享我们的经验，旨在解决SIE / NCE难题，并将DHA的适用性从主要组元素的化学延伸到过渡的化学金属。