Electron correlation in a hard spherical external potential: Wigner molecule formation and hybridization

Thompson, David C.; Alavi, Ali

doi:10.1103/physrevb.69.201302

Cited by 17 publications

(20 citation statements)

References 8 publications

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“…The opposite behavior is observed with respect to m. Futhermore, as R (or, equivalently, n) increases, the electrons tend to localize on opposite sides of the sphere due to the dominance of the Coulomb interaction as the density decreases [34,35]. Such Wigner crystallization [45] has also been observed in other systems [5,10,46].…”

Section: E)mentioning

confidence: 77%

“…In quantum chemistry, a famous example of this is the Hooke's law atom [2][3][4][5], which consists of a pair of electrons, repelling Coulombically but trapped in a harmonic external potential. This model and others [6][7][8][9][10][11][12] have been used extensively to test various approximations [13][14][15][16][17][18][19][20] within density functional theory (DFT) [21][22][23] and explicitly correlated methods [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Excited states of spherium

Loos

Gill

2010

Molecular Physics

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We report analytic solutions of a recently discovered quasi-exactly solvable model consisting of two electrons, interacting {\em via} a Coulomb potential, but restricted to remain on the surface of a $\mathcal{D}$-dimensional sphere. Polynomial solutions are found for the ground state, and for some higher ($L\le3$) states. Kato cusp conditions and interdimensional degeneracies are discussed.Comment: 6 pages, 2 figures, to appear in Mol. Phy

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Section: E)mentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Excited states of spherium

Loos

Gill

2010

Molecular Physics

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“…The UHF result reflects the Coulomb interaction between two electrons localized on opposite sides of the sphere [17], a phenomenon known as Wigner crystallization [10,11]. The difference between the UHF and exact energies (i.e.…”

Section: B Unrestricted Hartree-fockmentioning

confidence: 99%

“…A related system, studied by Alavi and co-workers [7][8][9], consists of two electrons, interacting through a Coulomb potential, but confined within a ball of radius R. This possesses a number of interesting features, including the formation of a "Wigner molecule" for large R [10]. The spontaneous formation of such molecules can also occur in quantum dots and is analogous to the Wigner crystallization [11] of the uniform electron gas.…”

Section: Introductionmentioning

confidence: 99%

Ground state of two electrons on a sphere

Loos

Gill²

2009

Phys. Rev. A

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We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius R. We have used electronic structure models ranging from restricted and unrestricted Hartree-Fock theory to explicitly correlated treatments, the last of which lead to near-exact wavefunctions and energies for any value of R. Møller-Plesset energy corrections (up to fifth-order) are also considered, as well as the asymptotic solution in the large-R regime.

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“…In this regime, one may anticipate the onset of Wigner crystallization and multireference charac- ter. [50][51][52][53] While this physics could be approximately addressed via spin-symmetry breaking, we do not pursue this approach here.…”

Section: A Spectral Properties and Peak Positionmentioning

confidence: 99%

Quantum plasmons and intraband excitons in doped nanoparticles: Failure of the Tamm-Dancoff approximation and importance of electron-hole attraction

Lau¹,

Berkelbach²

2019

Preprint

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We use excited-state quantum chemistry techniques to investigate the intraband absorption of doped semiconductor nanoparticles as a function of doping density, nanoparticle radius, and material properties. The excess electrons are modeled as interacting particles confined in a sphere. We compare the predictions of various single-excitation theories, including time-dependent Hartree-Fock, the random-phase approximation, and configuration interaction with single excitations. We find that time-dependent Hartree-Fock most accurately describes the character of the excitation, as compared to equation-of-motion coupled-cluster theory with single and double excitations. The excitation evolves from confinement-dominated, to excitonic, to plasmonic with increasing number of electrons at fixed density, and the threshold number of electrons to produce a plasmon increases with density due to quantum confinement. Exchange integrals (attractive electron-hole interactions) are essential to properly describe excitons, and de-excitations (i.e. avoidance of the Tamm-Dancoff approximation) are essential to properly describe plasmons. We propose a schematic model whose analytic solutions closely reproduce our numerical calculations. Our results are in good agreement with experimental spectra of doped ZnO nanoparticles at a doping density of 1.4 × 10 20 cm −3 .

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Electron correlation in a hard spherical external potential: Wigner molecule formation and hybridization

Cited by 17 publications

References 8 publications

Excited states of spherium

Excited states of spherium

Ground state of two electrons on a sphere

Quantum plasmons and intraband excitons in doped nanoparticles: Failure of the Tamm-Dancoff approximation and importance of electron-hole attraction

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