Adiabatic-connection approach to Kohn-Sham theory

Harris, J.

doi:10.1103/physreva.29.1648

Cited by 340 publications

(163 citation statements)

References 24 publications

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“…(6) is rigorously established. It is useful to be reminded here that the functional V SCE ee [ρ] corresponds to the λ → ∞ limit [6,7] of the traditional adiabatic connection of DFT [22][23][24][25] in which a functional F λ [ρ], depending on a real parameter λ, is defined as…”

Section: Results: An Overviewmentioning

confidence: 99%

Optimal-transport formulation of electronic density-functional theory

2012

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The most challenging scenario for Kohn-Sham density-functional theory, that is, when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated here as an optimal transport (or mass transportation theory) problem, a well-established field of mathematics and economics. In practice, we show that to solve the problem of finding the minimum possible internal repulsion energy for N electrons in a given density ρ(r) is equivalent to find the optimal way of transporting N − 1 times the density ρ into itself, with the cost function given by the Coulomb repulsion. We use this link to set the strong-interaction limit of density-functional theory on firm ground and to discuss the potential practical aspects of this reformulation.

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Section: Results: An Overviewmentioning

confidence: 99%

Optimal-transport formulation of electronic density-functional theory

2012

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“…This approach paved the way to the development of more complex approximations such as TPSS, 33 a non-empirical meta-GGA, or the global-hybrid (GH) PBE0 2,3 rooted in the AC model. 25 Starting by the definition of the exchange-correlation contribution, E xc , to the total KS energy defined as:…”

Section: Theorymentioning

confidence: 99%

“…Toulouse et al, making use of the Adiabatic Connection (AC) formalism 25 , derived a series of one-parameter DHs, and pointed out the existence of a quadratic (a c =a 2…”

Section: Introductionmentioning

confidence: 99%

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

et al. 2016

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ConspectusDensity Functional Theory (DFT) emerged in the last two decades as the most reliable tool the description and prediction of properties of molecular systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing Density Functional Approximations (DFAs).Indeed, the Achilles' heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the '90s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on model. In such a way, a whole family of non-empirical functionals, spanning on the highest rungs of the Perdew's quality scale, is now available and competitive with other -more empirical-DFAs. This is a previous version of the article published in Accounts of Chemical Research. 2016Research. , 49(8): 1503Research. -1513Research. . doi:10.1021 2 Discussion of selected cases, ranging from thermochemistry and reactions to weak interactions and excitations energies, not only show the large range of applicability of non-empirical DFAs, but also underline how increasing the number of theoretical constrains parallel with an improvement of the DFA's numerical performances. This fact further consolidates the strong theoretical framework of non-empirical DFAs.Finally, even if non-empirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all technical enhancements developed for speeding-up post-HartreeFock methods, there is a substantial hope for their near future routine application to the description and prediction of complex chemical systems and reactions.

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“…In particular, the Adiabatic Connection Model (ACM) [17] allows for defining the exchange-correlation contribution, E xc , to the total Kohn-Sham (KS) energy as:…”

Section: Theoretical Framework 21 Generalities: Acm and Associated Fmentioning

confidence: 99%

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

Sancho‐García

Adamo

2013

Phys. Chem. Chem. Phys.

109

108

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We review in this Perspective why and how double-hybrid density functionals have become new leading actors in the field of computational chemistry, thanks to the combination of an unprecedented accuracy together with large robustness and reliability. Similarly to their predecessors, the widely employed hybrid density functionals, they are rooted on the Adiabatic Connection Method from which they emerge in a natural way. We present recent achievements concerning applications to chemical systems of the most interest, and current extensions to deal with challenging issues such as non-covalent interactions and excitation energies. These promising methods, despite a slightly higher computational cost than other typical density-based models, are called to play a key role in the near future and can thus pave the way towards new discoveries or advances.2

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Adiabatic-connection approach to Kohn-Sham theory

Cited by 340 publications

References 24 publications

Optimal-transport formulation of electronic density-functional theory

Optimal-transport formulation of electronic density-functional theory

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

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