The theory of intermolecular forces in the region of small orbital overlap

Murrell, J. N.; Randić, Milan; Williams, Denis R.

doi:10.1098/rspa.1965.0081

Cited by 272 publications

(25 citation statements)

References 3 publications

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“…It has been calculated using valence-bond theory by Rosen It should also be noted that there exist perturbational calculations by Williams, Schaad, and Murrell [12]. These authors examined the nonadditivity of the exchange energy defined by Murrell, Randik, and Williams [20]. However, their results are much smaller than ours because they did not consider the terms of the third order in overlap integrals.…”

Section: Numerical Example: Interaction Of Three Ground-state Helium mentioning

confidence: 84%

“…The method proposed is quite general and can also be employed for the evaluation of the nondiagonal matrix elements needed in the calculations of the exchange polarization energy [20] or the intramolecular correlation effect [8]. We present the exact closed-form formula for E/&) rather than a power series expansion in intermolecular overlap integrals.…”

Section: Introductionmentioning

confidence: 99%

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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

166

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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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Section: Numerical Example: Interaction Of Three Ground-state Helium mentioning

confidence: 84%

Section: Introductionmentioning

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

166

View full text Add to dashboard Cite

show abstract

“…This is analogous to the charge-transfer interaction first described by Murrel, 146 which was later modeled empirically with force fields, 147 and which is now also one of the contributions in the SIBFA model. 148 When the dissociated fragments are not neutral, a trivial Coulomb term is also present.…”

Section: Dissociation In Acks2mentioning

confidence: 99%

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

Verstraelen

Ayers

Speybroeck

et al. 2013

The Journal of Chemical Physics

101

135

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“…Bader et al (6) (the definition of nonadditive contributions to the energy will be discussed in the following section). They reached the following conclusion: nonadditive contributions to the energy of He, calculated at the LCAO-MO-SCF level of approximation, were 10 times larger than estimated before by perturbation treatments (7). Still, their relative role in He, binding was at most a few percent of the pairwise additive contributions (6).…”

Section: Introductionmentioning

confidence: 77%

Non-additivity of intermolecular forces in helium and beryllium clusters

Novaro¹

1996

Can. J. Chem.

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New results on nonadditive effects on small beryllium clusters are presented using the LCAO-MO-SCF method including variational and perturbational (MP-4) configuration effects. Three-and four-body contributions to the interaction energy of these clusters are dominant, and are used to explain the very different behaviour of bulk beryllium as compared to liquid helium. This is relevant because the atomic ground states of Be and He are strikingly similar (ls'2s2: IS, and 1s' : IS,) and also HeZ and Be2 share the honour of being the two hardest-to-detect dimers in the whole periodic system. The similitude is lost for larger He,, and Be,, systems because the former, as was shown by R.F.W. Bader 25 years ago, have very small three-body energies ( 5 1%). Be,, clusters will be shown here to have three-body energies that actually outweigh the painvise additive ones. The consequences of this are discussed.Key words: intermolecular forces, non-additivity, He and Be clusters. Mots clCs : forces intermolCculaires, non-additivitk, agrCgats de He et Be.[Traduit par la redaction]

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The theory of intermolecular forces in the region of small orbital overlap

Cited by 272 publications

References 3 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

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

Non-additivity of intermolecular forces in helium and beryllium clusters

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