On the evaluation of the correlation energy and the total non-relativistic born-oppenheimer energy for the water molecule

Gritsenko, O. V.; Данилова, Светлана Валерьевна; Zhanpeisov, Nurbosyn U.; Malkin, Vladimir G.; Zhidomirov, G. M.

doi:10.1016/0009-2614(87)87166-x

Cited by 5 publications

(9 citation statements)

References 21 publications

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“…The boundary conditions fulfilled at zero interelectronic separation are -+ -0.0104 ln p, for p -+ oo. - (20) This model is an extension of a previous approach [23,29,30] that was only applied to the integrals (r» p-(»)): g, (r,2; p (ri); A) v*12 --0 (r» p-(»)) = dA[g, (r"; p {ri);A) -1]. o)g, (r,2, p (ri);A) Ag, (r"; p (ri); A) …”

Section: Energy Functionalmentioning

confidence: 96%

Weighted-density exchange and local-density Coulomb correlation energy functionals for finite systems: Application to atoms

Cordero

Rubio

et al. 1993

Phys. Rev. A

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A nonlocal exchange energy functional developed within the weighted spin-density approximation (WSDA) and a local Coulomb correlation energy functional are combined within the densityfunctional scheme for the calculation of the electronic structure of many-electron systems. Both functionals include alternative forms of the pair-correlation functions governing the size and shape of the Fermi and Coulomb holes. Self-consistent calculations have been performed for all atoms from He to Rn within the exchange-only USDA scheme. These have been compared to the results of similar calculations using Becke s exchange functional. Besides, the results of calculations for all atoms from He to Ar, including both exchange and correlation, are compared with those of the self-interaction-corrected method. In addition to obtaining accurate total, exchange, and correlation energies, we perform a successful calculation of the s -+ d interconfigurational energies (ICE's) for transition-metal atoms. The average error of the calculated ICE values for 3d atoms is only 0.2 eV. PACS number(s): 31.20.Sy, 31.20.Tz, 31.10.+z

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Section: Energy Functionalmentioning

confidence: 96%

Weighted-density exchange and local-density Coulomb correlation energy functionals for finite systems: Application to atoms

Cordero

Rubio

et al. 1993

Phys. Rev. A

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“…Nevertheless, the accurate estimation of the Coulomb correlation energy remains one of the main problems of the theory. Several years ago a local-density scheme for the calculation of the correlation energy E, based on the use of effective pair-correlation functions was proposed by Gritsenko and co-workers [2,3] and non-self-consistent calculations of E, were performed for closed-shell atoms [2], firstand second-row monohydrides [4], and the water molecule [5] using Hartree-Fock densities.…”

Section: Introductionmentioning

confidence: 99%

“…(n(r1)) k~[ n(rl)]~+D(n(r1)) (2' ) (18) Here the first, leading term describes the Coulomb correlation of electrons with opposite spins, while the second one corresponds to the subsidiary (at typical atomic densities) Coulomb correlation of electrons with the same has been applied previously [4,5] to perform non-selfconsistent calculations of the Coulomb correlation energy (2o) of atoms and molecules using for this purpose Hartree-Fock densities n(ri) [15 -18). In (18) and (19) r, (n(ri)) is the effective correlation radius that, according to [19,20], is set proportional to the Debye screening radius Bf or the Coulomb interaction.…”

Section: Introductionmentioning

confidence: 99%

“…(19). k was fitted in [5] to reproduce the correlation energies of atoms within a non-self-consistent scheme with G;(rig, n(ri)). In the next section this work is extended by presenting a self-consistent calculational LDA scheme.…”

Section: Introductionmentioning

confidence: 99%

“…0078 -i~/~. '(~( ))) where r, (n(ri)) and r (n(ri)) are determined from (19), (21), respectively, and a(n(ri)) is determined from the sum rule (5). By construction, the function (22) also satisfies the asymptotic condition (14).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Self-consistent local-density approximation with model Coulomb pair-correlation functions for electronic systems

Gritsenko

Rubio²,

Balbás³

et al. 1993

Phys. Rev. A

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The model Coulomb pair-correlation functions proposed several years ago by Gritsenko, Bagaturyants, Kazansky, and Zhidomirov are incorporated into the self-consistent local-density approximation (LDA) scheme for electronic systems. Different correlation functions satisfying well-established local boundary conditions and integral conditions have been tested by performing LDA calculations for closed-shell atoms. Those correlation functions contain a single parameter which can be optimized by fitting the atomic correlation energies to empirical data. In this way, a single (universal) value of the parameter is found to give a very good fit for all the atoms studied. The results provide a substantial improvement of calculated correlation energies as compared to the usual LDA functionals and the scheme should be useful for molecular and cluster calculations.PACS number(s): 31.20. Sy, 31.20.Tz, 31.10.+z

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Exchange and correlation in density functional theory

Alonso

Cordero

1995

Int. J. Quantum Chem.

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mThe accurate description of exchange and correlation effects is a key issue in density functional theory (DFT). In spite of its widespread use, the local density approximation ( I DA) has well-known deficiencies. In atoms, the empirical correlation energies are of the same magnitude as the errors of the LDA for exchange. This means that an accurate description of exchange in atoms or molecules is a prerequisite for the introduction of Coulomb correlation. One of the methods that today achieve such an accuracy is the weighted density approximation (WDA

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On the evaluation of the correlation energy and the total non-relativistic born-oppenheimer energy for the water molecule

Cited by 5 publications

References 21 publications

Weighted-density exchange and local-density Coulomb correlation energy functionals for finite systems: Application to atoms

Weighted-density exchange and local-density Coulomb correlation energy functionals for finite systems: Application to atoms

Self-consistent local-density approximation with model Coulomb pair-correlation functions for electronic systems

Exchange and correlation in density functional theory

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