Molecular exchange-correlation Kohn–Sham potential and energy density from <i>ab</i> <i>initio</i> first- and second-order density matrices: Examples for XH (X=Li, B, F)

Gritsenko, O. V.; Leeuwen, Robert van; Baerends, Evert Jan

doi:10.1063/1.471602

Cited by 92 publications

(73 citation statements)

References 45 publications

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“…can be recognized only by the change of the slope of m xc at that point. This is a characteristic feature of a covalent bond X±H, which has been established previously also for the BH molecule [24]. For larger z the potential m xc approaches smoothly its Coulombic asymptotics m xc z 3 À1az.…”

Section: Results For Chmentioning

confidence: 76%

“…Considering ®rst the ensemble solutions we note that the kinetic energies s of the KS ensemble solution are consistently higher than their HF counterparts HF , with the corresponding dierence being increased with increasing (C±C). As was established previously for other molecules [24,25], this is due to the contraction of the correlated q around the nuclei as compared with the HF density q HF , and the increasing non-dynamical correlation at larger bond distances, which is neglected in the HF approximation. On the other hand, the ensemble exchange energies i x are close to the HF ones i HF x for the ensembles with a weak accidental degeneracy, and i x are somewhat larger (in absolute magnitude) than i HF x for medium and strong ensembles.…”

Section: Results For Chmentioning

confidence: 77%

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One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH 2 and C 2

Schipper

Gritsenko

Baerends

1998

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

134

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The possibility that the Kohn-Sham (KS) solution for a noninteracting auxiliary electron system is not the conventional one-determinantal pure state but a few-determinantal ensemble has been investigated. The KS solutions (the exchange-correlation potential v xc and the orbitals) have not been approximated by localdensity or density-gradient approximations but have been constructed from an accurate ab initio electron density. The lowest singlet states of the CH 2 and C 2 molecules have been selected for this investigation since for these cases the ground-state wave function W is nondegenerate but has an essentially multideterminantal character (electron correlation is strong). For C 2 the dependence of the type of KS solution on the bond distance R(C±C) has been studied at the QZ level. For the shortest distance considered, R(C±C) 1X8 a.u., a pure-state KS solution has been obtained. For the equilibrium distance e C±C 2X348 a.u. and at larger distances ensemble solutions have been obtained with widely varying weights of the individual determinants, depending on the bond distance. For CH 2 the dependence of the type of KS solution on the basis has been studied: calculation in the triple zeta (TZ) basis for the KS orbitals yields an ensemble solution, while the purestate KS solution has been obtained in the quadruple zeta (QZ) basis. The form of the KS orbitals has been compared with that of the natural orbitals (NOs). It has been shown for the model example of the stretched H 2 molecule as well as for CH 2 and C 2 Y that the KS orbitals of the pure state may be rather dierent from the corresponding NOsY while the occupied KS orbitals of the ensemble solution can be considered as plausible approximations to the corresponding NOs.

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Section: Results For Chmentioning

confidence: 76%

Section: Results For Chmentioning

confidence: 77%

One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH 2 and C 2

Schipper

Gritsenko

Baerends

1998

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

134

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“…We close this section with a comment concerning a feature of the LB scheme for constructing x , which has allowed us to apply this scheme with reasonable accuracy to the construction of atomic and molecular x [3,16,17] from Gaussian CI densities. It can be observed in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…A more direct test is of course a comparison between approximate and exact exchange-correlation energy densities. It has been demonstrated, however, that in order to calculate the exact (a very accurate) exchange-correlation energy density e x r from an accurate wavefunction, a necessary step is the determination of the KS orbitals, and hence, the KS potential, from the diagonal density qr corresponding to the given wavefunction [2,3].…”

Section: Introductionmentioning

confidence: 99%

Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

Schipper

Gritsenko

Baerends

1997

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

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A new method based on linear response theory is proposed for the determination of the KohnSham potential corresponding to a given electron density. The method is very precise and aords a comparison between Kohn-Sham potentials calculated from correlated reference densities expressed in Slater-(STO) and Gaussian-type orbitals (GTO). In the latter case the KS potential exhibits large oscillations that are not present in the exact potential. These oscillations are related to similar oscillations in the local error function d i r h À e i u i r when SCF orbitals (either KohnSham or Hartree-Fock) are expressed in terms of Gaussian basis functions. Even when using very large Gaussian basis sets, the oscillations are such that extreme care has to be exercised in order to distinguish genuine characteristics of the KS potential, such as intershell peaks in atoms, from the spurious oscillations. For a density expressed in GTOs, the Laplacian of the density will exhibit similar spurious oscillations. A previously proposed iterative local updating method for generating the Kohn-Sham potential is evaluated by comparison with the present accurate scheme. For a density expressed in GTOs, it is found to yield a smooth`a verage'' potential after a limited number of cycles. The oscillations that are peculiar to the GTO density are constructed in a slow process requiring very many cycles.

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“…For this reason, several authors [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] have used accurate many-body solutions of prototypical strongly correlated systems to obtain (by inversion) and characterize the exact noninteracting KS system. The exact properties needed to describe strong correlation in KS DFT have also been set in a transparent framework [5,26].…”

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confidence: 99%

Strong Correlation in Kohn-Sham Density Functional Theory

2012

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We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe. DOI: 10.1103/PhysRevLett.109.246402 PACS numbers: 71.15.Mb, 31.15.ec, 73.21.Hb In principle, Kohn-Sham (KS) density functional theory (DFT) [1,2] should yield the exact ground-state density and energy of any many-electron system, including physical situations in which electronic correlation is very strong, representing them in terms of noninteracting electrons. Currently available approximations for KS DFT, however, fail at properly describing systems approaching the Mott insulating regime [3], the breaking of the chemical bond [4,5], and localization in low-density nanodevices [6][7][8], to name a few examples (for a recent review, see Ref.[9]). Artificially breaking the spin (or other) symmetry can mimic some (but not all) strong-correlation effects, at the price of a wrong characterization of several properties and of a partial loosening of the rigorous KS DFT framework.Indeed, it is very counterintuitive that strongly correlated systems, in which the electron-electron repulsion plays a prominent role, can be exactly represented in terms of noninteracting electrons. For this reason, several authors [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] have used accurate many-body solutions of prototypical strongly correlated systems to obtain (by inversion) and characterize the exact noninteracting KS system. The exact properties needed to describe strong correlation in KS DFT have also been set in a transparent framework [5,26]. These works made it all the more evident how difficult it is to find adequate approximations of the exact KS system, so that, albeit theoretically possible, it may seem unrealistic to describe strongly correlated systems with KS DFT [9].Here, we address this skepticism by showing that the strong-interaction limit of the Hohenberg-Kohn (HK) energy density functional yields approximations capturing strong-correlation effects within the noninteracting restricted self-consistent KS scheme.The Letter is organized as follows. First, we introduce the formalism, using the strong-interaction limit of the HK functional to transform exactly an important part of the manybody interaction into an effective local one-body potential, in a physically transparent way. We then present pilot self-consistent Kohn-Sham calculations, showing that this potential is indeed able to capture strong-correlation effects way beyond t...

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Molecular exchange-correlation Kohn–Sham potential and energy density from ab initio first- and second-order density matrices: Examples for XH (X=Li, B, F)

Cited by 92 publications

References 45 publications

One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH 2 and C 2

One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH 2 and C 2

Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

Strong Correlation in Kohn-Sham Density Functional Theory

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