On the exchange repulsion between beryllium atoms

Bulski, Marek

doi:10.1080/00268977500100991

Cited by 31 publications

(8 citation statements)

References 20 publications

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“…It has been calculated using valence-bond theory by Rosen results are much smaller than ours because they did not consider the terms of the third order in overlap integrals. At present, it is known [15,40,411 that these terms dominate the three-body short-range energy at larger internuclear distances.…”

mentioning

confidence: 99%

First‐Order perturbation treatment of the short‐range repulsion in a system of many closed‐shell atoms or molecules

Jeziorski¹,

Bulski²,

Piela³

1976

Int J of Quantum Chemistry

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167

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AbstractsAssuming a determinantal form for the wave-functions of free molecules, explicit formula for the first-order interaction energy of many closed-shell molecules has been derived. Provided that the determinants describing the free molecules are constructed from the Hartree-Fock orbitals, the two-, three-, and four-body effects predicted by the firstorder perturbation theory are closely related to those which one obtains in the framework of the Lowdin LCAO Mo-type approach. The results are illustrated by numerical calculations for the system of three ground-state helium atoms.Nous avons obtenu une formule explicite pour 1'Cnergie d'interaction du premier ordre de plusieurs molecules a couches completes en admettant que les fonctions d'onde des molhdes libres sont des determinants simples. Dans le cas ob ces determinants sont construits a partir des orbitales Hartree-Fock les effets assmiis a deux, trois ou quatre corps pridits par la thCorie des perturbations du premier ordre correspondent de pris a ceux que l'on obtient dans le cadre du procedk MO-LCAO de Lowdin. Les rlsultats sont illustrks par des calculs numbriques du systime de trois atomes de He dans leurs &tats fondamentaux.Explizite Formel fur die Wechselwirkungsenergie erster Ordnung zwischen vielen Molekiilen mit abgeschlossenen Schalen ist hergeleitet worden, wobei die Wellenfunktionen der freien Molekiile mit einfachen Determinanten angenahert werden. Wenn diese Determinanten von Hartree-Fock-Orbitalen konstruiert werden, schliessen sich die von der Storungstheorie erster Ordnung vorhergesagten Zwei-, Drei-und Vierkorpereffekte eng denen an, die im Rahmen des Lowdin'schen Mo-LcAo-Verfahrens erhalten werden. Diese Ergebnisse werden mit numerischen Berechnungen fur das System von drei Heliumatomen im Grundzustande illustriert.

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mentioning

confidence: 99%

First‐Order perturbation treatment of the short‐range repulsion in a system of many closed‐shell atoms or molecules

Jeziorski¹,

Bulski²,

Piela³

1976

Int J of Quantum Chemistry

Self Cite

167

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“…17 Bulski and collaborators have also computed E exch (1;0) ͓3,3͔in the S 3 approximation. 15,16 The results for He 3 , 14 Be 3 , 15 and Ne 3 16 in equilateral triangle configurations show that the S 3 approximation produces typical errors of a few percent at the van der Waals minimum region. For interatomic distances R about two times smaller than the dimer minimum, the terms beyond S 3 contribute 10% or more.…”

Section: First-order Nonadditivitymentioning

confidence: 94%

“…14 and applied to atomic trimers. [15][16][17] No molecular applications have been made so far; instead, recent work has utilized the Heitler-London expression, which is closely related 14 to E exch (1;0) ͓3,3͔ ͑differing by the ''zeroth-order'' exchange energy which is proportional to S 4 , where S denotes an overlap integral between orbitals of different monomers͒. The polarization component in the first-order with respect to V does not contribute to the nonadditivity, neither does the dispersion component in the second-order.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-adapted perturbation theory of three-body nonadditivity of intermolecular interaction energy

Lotrich

Szalewicz

1997

The Journal of Chemical Physics

120

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Articles you may be interested inTuned range-separated hybrid functionals in the symmetry-adapted perturbation theory An improved treatment of empirical dispersion and a many-body energy decomposition scheme for the explicit polarization plus symmetry-adapted perturbation theory (XSAPT) method J. Chem. Phys. 139, 034107 (2013); 10.1063/1.4813523Perturbation theory of three-body exchange nonadditivity and application to helium trimer The many-body symmetry-adapted perturbation theory of intermolecular interactions has been extended to the interactions of three closed-shell atoms or molecules. Orbital formulas for the nonadditivity of the second-and third-order induction energies, third-order induction-dispersion energy, and third-and fourth-order dispersion energies with neglect of intramonomer correlation effects have been derived from the polarization expansion. The first-order intramonomer correlation correction to the third-order dispersion energy has also been obtained. The symmetrized Rayleigh-Schrödinger energy expansion has been used to derive orbital formulas for the first-and second-order exchange energies with neglect of intramonomer correlation effects. The first-order exchange energy was approximated by the terms proportional up to the fourth power in the intermolecular overlap integrals. The second-order exchange energy was developed through the third power of the intermolecular overlap integrals.

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“…The calculation of first-order exchange components has been performed for atom trimers [23][24][25][26]. Moreover, the second-order exchange dispersion components were calculated for two-electron systems [27,28].…”

Section: Eto T = E~] + ~R + -(2) + F(e)mentioning

confidence: 99%

Intermolecular interaction energy of CH4 trimer by symmetry-adapted perturbation theory

1995

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The interaction energy for the cyclic CH 4 trimer is studied in terms of symmetry-adapted perturbation theory. The interaction energy around the van der Waals minimum is dominated by attractive dispersion energy, and the repulsive contribution at the smaller angle region is due to the first-order exchange energy. The total interaction energy is approximated by additive two-body components, because of a mutual cancellation between nonadditive three-body ones.KEY WORDS: CH 4 trimer; symmetry-adapted perturbation theory; nonadditive three-body effect.

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On the exchange repulsion between beryllium atoms

Cited by 31 publications

References 20 publications

First‐Order perturbation treatment of the short‐range repulsion in a system of many closed‐shell atoms or molecules

First‐Order perturbation treatment of the short‐range repulsion in a system of many closed‐shell atoms or molecules

Symmetry-adapted perturbation theory of three-body nonadditivity of intermolecular interaction energy

Intermolecular interaction energy of CH4 trimer by symmetry-adapted perturbation theory

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