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WIREs Comput Mol Sci
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On the top rung of Jacob's ladder of density functional theory: Toward resolving the dilemma of SIE and NCE

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Abstract 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. This article is categorized under: Electronic Structure Theory > Density Functional Theory Software > Quantum Chemistry
Illustration of Jacob's Ladder of DFT
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Histogram of percentage errors for various methods for 13 reaction energies in transition‐metal chemistry. Each vertical bar represents errors in 8% range. The cases with error larger (or lower) than 20% (or −20%) are grouped together to be outliers
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Histogram of percentage errors for various methods for 23 reaction energies in main‐group chemistry. Each vertical bar represents errors in 8% range. The cases with error larger (or lower) than 20% (or −20%) are grouped together to be outliers
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Fractional‐charge errors for C atom (a) and fractional‐spin errors for N atom (b) of SCAN, PBE0, and several fifth rung DFAs. Nelec denotes the electron number in the system while Nβ − Nα denotes the difference between the electron numbers in different spin channels
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Fractional‐charge (a) and fractional‐spin errors (b) of SCAN, PBE0, and several fifth rung DFAs for H atom. Nelec denotes the electron number in the system while Nβ − Nα denotes the difference between the electron numbers in different spin channels
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Decomposition of the dRPA correlation model in the context of the spin‐distinctive ACFD framework
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(a) N2 and (b) C2 dissociation curves without breaking spin and charge symmetry. NAO‐VCC‐4Z108 basis sets have been used for all calculations
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(a) and (b) H2 dissociation curves without breaking spin and charge symmetry. NAO‐VCC‐4Z108 basis sets have been used for all calculations
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Illustration of adiabatic‐connection approach in DFT
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(a) N2 and (b) C2 dissociation curves without breaking spin and charge symmetry. NAO‐VCC‐4Z108 basis sets have been used for all calculations. The exact curves were produced with the FHI‐aims110 and the quantum Monte Carlo framework of Booth et al.118 using the same basis set of NAO‐VCC‐4Z108
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(a) and (b) H2 dissociation curves without breaking spin and charge symmetry. NAO‐VCC‐4Z108 basis sets have been used for all calculations. The exact curve of dissociation was produced by using CCSD method109 implemented in FHI‐aims110 with the same basis set of NAO‐VCC‐4Z108
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Fractional charge (a) and fractional‐spin (b) errors for the H atom. Nelec denotes the number of electrons in the system, while Nβ − Nα denotes the difference between the electron numbers in different spin channels
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Software > Quantum Chemistry
Electronic Structure Theory > Density Functional Theory

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