Coulomb holes and correlation potentials in the helium atom

Slamet, Marlina; Sahni, Viraht

doi:10.1103/physreva.51.2815

Cited by 33 publications

(28 citation statements)

References 53 publications

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“…The physical meaning of the Coulomb hole radius is to define a sphere of radius R c around an electron where the probability of finding another electron is reduced by the correlation (because the correlation hole is negative inside this region). Analogously, outside the region enclosed by the Coulomb hole radius (u ≥ R c ) the probability to find a second electron is enhanced by the correlation effects 58 . The Coulomb hole radius is thus a meaningful quantity to be investigated.…”

Section: Coulomb Hole Radiusmentioning

confidence: 98%

Construction of a general semilocal exchange-correlation hole model: Application to nonempirical meta-GGA functionals

2013

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Using a reverse-engineering method we construct a meta-generalized gradient approximation (meta-GGA) angle-averaged exchange-correlation hole model which has a general applicability. It satisfies known exact hole constraints and can exactly recover the exchange-correlation energy density of any reasonable meta-GGA exchange-correlation energy functional satisfying a minimal set of exact properties. The hole model is applied to several non-empirical meta-GGA functionals: the Tao-Perdew-Staroverov-Scuseria (TPSS), the revised TPSS (revTPSS) and the recently Balanced LOCalization (BLOC) meta-GGA of L.A. Constantin, E. Fabiano, and F. Della Sala, (J. Chem. Theory Comput. 9, 2256 (2013)). The empirical M06-L meta-GGA functional is also considered. Real-space analyses of atoms and ions as well as wave-vector analyses of jellium surface energies, show that the meta-GGA hole models, in particular the BLOC one, are very realistic and can reproduce many features of benchmark XC holes. In addition, the BLOC hole model can be used to estimate with good accuracy the Coulomb hole radius of small atoms and ions. Thus, the proposed meta-GGA hole models provide a valuable tool to validate in detail existing meta-GGA functionals, and can be further used in the development of DFT methods beyond the semilocal level of theory.

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Section: Coulomb Hole Radiusmentioning

confidence: 98%

Construction of a general semilocal exchange-correlation hole model: Application to nonempirical meta-GGA functionals

2013

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“…We recall that the Coulomb hole radius is the smallest distance (u = 0) where the correlation hole equals zero. This is an important quantity to define the effect of correlation on the distribution of the electrons in the vicinity of each other 91,96 . The data in the table confirm that the GAPloc functional is the most accurate for the description of the Coulomb hole, with a MAE of 0.04 Bohr and a MARE of 5%.…”

Section: Real-space Analysis Of Gaplocmentioning

confidence: 99%

Generalized Gradient Approximation Correlation Energy Functionals Based on the Uniform Electron Gas with Gap Model

Fabiano

Trevisanutto

Terentjevs

et al. 2014

J. Chem. Theory Comput.

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We studied uniform electron gas with a gap model in the context of density functional theory. On the basis of this analysis, we constructed two local gap models that are used in generalized gradient approximation (GGA) correlation functionals that satisfy numerous exact constraints for correlation energy. The first one, named GAPc, fulfills the full second-order correlation gradient expansion at any density regime and is very accurate for jellium surfaces, comparable to state-of-the-art GGAs for atomic systems and molecular systems, and is well compatible with known semilocal exchanges. The second functional, named GAPloc, satisfies the same exact conditions, except that the second-order gradient expansion is sacrificed for a better behavior under the Thomas-Fermi scaling and a more realistic correlation energy density of the helium atom. The GAPloc functional displays a high accuracy for atomic correlation energies, still preserving a reasonable behavior for jellium surfaces. Moreover, it shows a higher compatibility with the Hartree-Fock exchange than other semilocal correlation functionals. This feature is explained in terms of the real-space analysis of the GAPloc correlation energy.

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“…When both Pauli and Coulomb correlations are considered, the corresponding potential Wyc(r) of the work formalism is the work done to move an electron in the forcefield of the Fermi-Coulomb hole charge distribution pxc(r, r'). As such, it represents [14,15,18] the exchange and Coulomb repulsion components of the Kohn-Sham theory exchange-correlation potential vx,(r) = 6E,J p]/6p(r). [The potential vx,(r) in addition contains the correlation contribution to the kinetic energy].…”

Section: (5)mentioning

confidence: 99%

Exchange potentials at a metal surface

Solomatin

Sahni

1995

Int. J. Quantum Chem.

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rnIn this article we have determined the structure of the exchange potential uJo)(r) at a jellium metal surface previously derived by restricted functional differentiation of the exchange energy functional. The potential, which depends on the Slater potential due to the Fermi hole, the density, and their gradients, is obtained analytically for the orbitals of the infinite barrier model. We have also determined the exchange potential W,(r> of the work formalism, which is the work done to move an electron in the forcefield of the Fermi hole, for the same model effective potential, the field being derived analytically. A comparison of these potentials shows them to be close approximations. The functional derivative v;O)(r) is further provided a physical interpretation by rewriting it in Slaterpotential form. The corresponding effective Fermi hole charge distribution, also determined analytically, has a dynamic structure as a function of electron position similar to that of the Fermi hole but smaller in magnitude. Finally, proofs are provided of the satisfaction by vJo)(r> of the virial theorem sum rule, the second functional derivative condition, and the sum rule relating the exchange potential to its functional derivative.

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Coulomb holes and correlation potentials in the helium atom

Cited by 33 publications

References 53 publications

Construction of a general semilocal exchange-correlation hole model: Application to nonempirical meta-GGA functionals

Construction of a general semilocal exchange-correlation hole model: Application to nonempirical meta-GGA functionals

Generalized Gradient Approximation Correlation Energy Functionals Based on the Uniform Electron Gas with Gap Model

Exchange potentials at a metal surface

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