Ground-state correlation energies for two- to ten-electron atomic ions

Davidson, Ernest R.; Hagstrom, Stanley A.; Chakravorty, Subhas J.; Umar, V.M.; Fischer, Charlotte Froese

doi:10.1103/physreva.44.7071

Cited by 389 publications

(246 citation statements)

References 46 publications

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“…Below we present electron correlation energies for some atoms and ions [50,51] and a test set of reaction energies [18]. The correlation energy from the different RPA approximations E RPA c has been calculated starting from a self-consistent DFT calculation based on the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

Mussard¹,

Rocca²,

Jansen

et al. 2016

J. Chem. Theory Comput.

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Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental to improve over direct RPA results.

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Section: Numerical Resultsmentioning

confidence: 99%

“…To verify the accuracy of the RPA-based approximations we compared the obtained results with the full configuration interaction (FCI) quality correlation energy estimates by Davidson and collaborators [50,51]. in the calculations.…”

Section: B Atomic Correlation Energiesmentioning

confidence: 99%

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

Mussard¹,

Rocca²,

Jansen

et al. 2016

J. Chem. Theory Comput.

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“…The exact nonrelativistic energy of the ground state of the carbon atom has been estimated to be -37.8450 a.u. [27] We can use this value and the Hartree-Fock energy of -37.689 a.u. to compute the percentages of the correlation energy recovered.…”

Section: Resultsmentioning

confidence: 99%

Interpretation of Hund’s multiplicity rule for the carbon atom

Hongo

Maezono

Kawazoe

et al. 2004

The Journal of Chemical Physics

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Hund's multiplicity rule is investigated for the carbon atom using quantum Monte Carlo methods.Our calculations give an accurate account of electronic correlation and obey the virial theorem to high accuracy. This allows us to obtain accurate values for each of the energy terms and therefore to give a convincing explanation of the mechanism by which Hund's rule operates in carbon. We find that the energy gain in the triplet with respect to the singlet state is due to the greater electron-nucleus attraction in the higher spin state, in accordance with Hartree-Fock calculations and studies including correlation. The method used here can easily be extended to heavier atoms.

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“…[13][14][15][16] Because of the lack of accurate KS solutions, traditional Hartree-Fock based exchange and correlation energies have been used in DFT to obtain reference E x and E c values. In particular, E x is approximated with the corresponding HF exchange energy E x HF , between the empirical total nonrelativistic electronic energy of a system E obtained from the spectroscopic data [17][18][19] and the HF electronic energy E HF , E c ϷE c HF ϭEϪE HF .…”

Section: ͑12͒mentioning

confidence: 99%

Exchange and correlation energy in density functional theory: Comparison of accurate density functional theory quantities with traditional Hartree–Fock based ones and generalized gradient approximations for the molecules Li2, N2, F2

Gritsenko

Schipper

Baerends

1997

The Journal of Chemical Physics

206

115

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The density functional definition of exchange and correlation differs from the traditional one. In order to calculate the density functional theory ͑DFT͒, quantities accurately, molecular Kohn-Sham ͑KS͒ solutions have been obtained from ab initio wave functions for the homonuclear diatomic molecules Li 2 , N 2 , F 2 . These afford the construction of the KS determinant ⌿ s and the calculation of its total electronic energy E KS and the kinetic, nuclear-attraction and Coulomb repulsion components T s , V, W H as well as the ͑DFT͒ exchange energy E x and correlation energy E c . Comparison of these DFT quantities has been made on one hand with the corresponding HartreeFock ͑HF͒ quantities and on the other hand with local density approximation ͑LDA͒ and generalized gradient approximation ͑GGA͒. Comparison with HF shows that the correlation errors in the components T, V, and W H of the total energy are much larger for HF than KS determinantal wave functions. However, the total energies E KS and E HF appear to be close to each other, as well as the exchange energies E x and E x HF and correlation energies E c and E c HF . The KS determinantal wave function and the KS orbitals therefore correspond to much improved kinetic and Coulombic energies, while having only a slightly larger total correlation energy. It is stressed that these properties of the Kohn-Sham orbitals make them very suitable for use in the molecular orbital theories of chemistry. Comparison of the accurate Kohn-Sham exchange and correlation energies with LDA and GGA shows that the GGA exchange energies are consistently too negative, while the GGA correlation energies are not negative enough. It is argued that the GGA exchange functionals represent effectively not only exchange, but also the molecular non-dynamical correlation, while the GGA correlation functionals represent dynamical correlation only. © 1997 American Institute of Physics. ͓S0021-9606͑97͒00337-1͔

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Ground-state correlation energies for two- to ten-electron atomic ions

Cited by 389 publications

References 46 publications

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

Interpretation of Hund’s multiplicity rule for the carbon atom

Exchange and correlation energy in density functional theory: Comparison of accurate density functional theory quantities with traditional Hartree–Fock based ones and generalized gradient approximations for the molecules Li2, N2, F2

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