Leading Correction to the Local Density Approximation for Exchange in Large-
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Argaman, Nathan; Redd, Jeremy; Cancio, Antonio C.; Burke, Kieron

doi:10.1103/physrevlett.129.153001

Cited by 9 publications

(20 citation statements)

References 37 publications

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“…We thank Kieron Burke and Nathan Argaman for confirming our numerical findings of Figures and , for sharing a preliminary version of their independent work on the logarithmic contribution of the second-order gradient term for exchange, and for insightful discussions. This work was funded by The Netherlands Organisation for Scientific Research, under Vici grant 724.017.001.…”

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confidence: 56%

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Gradient Expansions for the Large-Coupling Strength Limit of the Møller–Plesset Adiabatic Connection

Daas

Kooi

Grooteman

et al. 2022

J. Chem. Theory Comput.

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mentioning

confidence: 56%

“…A detailed derivation of the behavior of I GEA2 [ρ], as a function of N for neutral atoms and for Bohr atoms, confirming the numerical evidence reported here, is also being performed independently by Argaman et al…”

Section: Second-order Gradient Expansion For E El[ρ]mentioning

confidence: 99%

Gradient Expansions for the Large-Coupling Strength Limit of the Møller–Plesset Adiabatic Connection

Daas

Kooi

Grooteman

et al. 2022

J. Chem. Theory Comput.

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“…The accuracy of the ground-state properties of electronic systems depends on the XC functional approximation (density functional approximationDFA). The nonempirical XC functionals are developed by satisfying many quantum mechanical exact constraints − such as density scaling rules of XC functionals due to coordinate transformations, ,− second (and fourth) order gradient expansion of exchange and correlation energies, − low density, and high density limit of the correlation energy functional, − asymptotic behavior of the XC energy density or potential, − quasi-two-dimensional (quasi-2D) behavior of the XC energy, − and exact properties of the XC hole. ,− …”

Section: Introductionmentioning

confidence: 99%

Semilocal Meta-GGA Exchange–Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations

Jana,

Śmiga,

Constantin

et al. 2023

J. Phys. Chem. A

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The incorporation of a strong-interaction regime within the approximate semilocal exchange−correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high-and low-density limits of the Tao−Perdew− Staroverov−Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.

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“…Physical many-electron systems do not arise by filling more and more particles in a fixed density profile, but by adding particles in an external potential. In order to study the gradient expansion for physically relevant systems, several authors considered neutral atoms, [25][26][27]276 in which N = Z electrons are bound by a point charge Z, and so-called Bohr atoms, 27,274,277 in which the external potential is −1/r and the electron-electron interaction is set to zero. These systems define a sequence of N -electron densities ρ Sqc N (r),…”

Section: Densities With Asymptotic Particle-number Scalingmentioning

confidence: 99%

“…In Chapter 6, Gradient expansions for closed shell systems are introduced for the leading order and first subleading order term of the strong coupling limit. The techniques used are based on the particle number scaling technique [25][26][27] that was previously used to investigate the large Z limit of atoms and has played a major role in functional development of new (Meta) Generalized Gradient Expansions (m)GGA, such as SCAN 28 and PBEsol 29 . Chapter 7 contains a excursion from the MP AC, where instead the same techniques explained in Chapter 6 are used to find more accurate gradient expansions in the strong interaction limit of DFT.…”

Section: Introductionmentioning

confidence: 99%

The Strong Interaction Limit of the Møller-Plesset Adiabatic Connection

Daas

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All the information needed to describe chemical reactions can be obtained by solving the time dependent Schrödinger equation. However, this is only viable for the smallest of systems and for any chemically relevant system approximations are needed. The most used method for quantum chemical simulations is Density Functional Theory (DFT), which is formally exact and uses instead of the multidimensional wavefunction the three-dimensional electron density. However, for DFT calculations to be feasible and computationally inexpensive, approximations need to be made to the exchange correlation energy, which is the only part that cannot be calculated exactly. A systematic way to make approximations to the exchange correlation energy is the adiabatic connection, which links the non-interacting Kohn-Sham system, which can be solved exactly, to the physical system. Most DFT functionals can now be understood as linear extrapolations from the Kohn-Sham system to the physical system. However, getting accurate results from extrapolating information is generally a hard problem, which even the most sophisticated machine learning algorithms struggle with, compared to interpolating them. Therefore, the mathematical structure of the strong interaction limit of DFT was derived, which is an exactly solvable system that can be used as the endpoint for future interpolations, which in turn lead to the creation of a new class of DFT functionals. Interestingly, we can also link a different non-interacting system, the Hartree-Fock system, to the physical system, which lead to the creation of the Møller-Plesset Adiabatic Connection (MPAC), which has as small coupling limit the Møller-Plesset Perturbation Theory (MPPT) series. This adiabatic connection allows us to obtain the correlation energy via interpolations functionals, although the strong coupling limit needs to be derived first. In this work, the strong coupling limit of the MPAC was studied for the hydrogen atom and the results of the first three leading order terms were generalized to many-electron systems with different spins. After that accurate gradient expansion approximations were derived for the first two leading order terms to make these functionals more computationally viable. For this a compact representation, based on the large Z limit, is introduced to find the best coefficient for the gradient expansion. This inspired a subsequent investigation into the DFT adiabatic connection, which showed a surprising symmetry between the magnitude of the gradient expansion coefficient of the weak interaction limit (exchange energy) and strong interaction limit. Lastly a new class of interpolation functions was introduced for the MPAC to tackle non-covalent interactions (NCIs). These were shown to be competitive with dispersion corrected hybrid and double hybrid functionals at the computational cost of double hybrids. However, cost saving techniques as well as regularization were used to not only make the calculations computationally cheaper but also to further improve the accuracy of the method. This resulted in new functionals that can tackle a variety of NCIs and outperform dispersion corrected (double) hybrid functionals.

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Leading Correction to the Local Density Approximation for Exchange in Large- Z Atoms

Cited by 9 publications

References 37 publications

Gradient Expansions for the Large-Coupling Strength Limit of the Møller–Plesset Adiabatic Connection

Gradient Expansions for the Large-Coupling Strength Limit of the Møller–Plesset Adiabatic Connection

Semilocal Meta-GGA Exchange–Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations

The Strong Interaction Limit of the Møller-Plesset Adiabatic Connection

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