Describing strong correlation with fractional-spin correction in density functional theory

Su, Neil Qiang; Li, Chen; Yang, Weitao

doi:10.1073/pnas.1807095115

Cited by 70 publications

(62 citation statements)

References 88 publications

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“…The ability to evaluate the exact xc potentials from ground-state electron densities, enabled by this method, will provide a powerful tool in the future testing and development of approximate xc functionals. Further, it paves the way for using machine learning to construct the functional dependence of on , i.e., , providing another avenue to develop density functionals 24,42,43 that can systematically improve both ground-state densities and energies 44 as well as satisfy the known conditions on the exact functional 45–47 .…”

Section: Discussionmentioning

confidence: 99%

Exact exchange-correlation potentials from ground-state electron densities

2019

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The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity—the electron density—without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis—a systematically convergent and complete basis—to discretize the problem. We demonstrate the accuracy and efficacy of our approach for both weakly and strongly correlated molecular systems, including up to 58 electrons, showing relevance to realistic polyatomic molecules.

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Section: Discussionmentioning

confidence: 99%

Exact exchange-correlation potentials from ground-state electron densities

2019

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“…The SIE/NCE dilemma can be observed from the fractional-spin and fractional-charge errors of current DFAs. 123 These understandings have been used as tools to construct certain corrections to remove the fractional-spin and fractional-charge errors as in the localized orbital scaling correction (LOSC) 124,125 methods, which can be applied to semilocal DFAs of rungs 1-3. Here, we focus on the development of fifth rung DFAs.…”

Section: Sie/nce Dilemma In Dftmentioning

confidence: 99%

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

Zhang

2020

WIREs Comput Mol Sci

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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.

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“…Especially in the case of complex, heterogeneous materials, the great majority of first-principles simulations are conducted using density functional theory (DFT), which is in principle exact but in practice requires approximations to enable calculations. Within its various approximations, DFT has been extremely successful in predicting numerous properties of solids, liquids, and molecules, and in providing key interpretations to a variety of experimental results; however it is often inadequate to describe so-called strongly-correlated electronic states 1,2 . We will use here the intuitive notion of strong correlation as pertaining to electronic states that cannot be described by static mean-field theories.…”

Section: Introductionmentioning

confidence: 99%

Quantum simulations of materials on near-term quantum computers

2020

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Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environment. Here, we present a quantum embedding theory for the calculation of strongly-correlated electronic states of active regions, with the rest of the system described within density functional theory. We demonstrate the accuracy and effectiveness of the approach by investigating several defect quantum bits in semiconductors that are of great interest for quantum information technologies. We perform calculations on quantum computers and show that they yield results in agreement with those obtained with exact diagonalization on classical architectures, paving the way to simulations of realistic materials on near-term quantum computers.

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Describing strong correlation with fractional-spin correction in density functional theory

Cited by 70 publications

References 88 publications

Exact exchange-correlation potentials from ground-state electron densities

Exact exchange-correlation potentials from ground-state electron densities

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

Quantum simulations of materials on near-term quantum computers

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