Long- and intermediate-range interaction between two ground state hydrogen atoms

AbstractsAccurate variational energies have been calculated for three lowest sigma states of the HeH+ ion. This includes the ground state (5 < R < 9 a.u.) which dissociates into He + H + , as well as the A 'Z+ state (4 < R < 10) and the a 3Z+ state (3 < R < 10) which both dissociate into He+ + H. The variational results are compared with those obtained using a perturbation theory expansion.Des energies variationelles de haute prkcision ont ete calculkes pour les ktats sigma les plus bas de l'ion HeH+. Ceci inclue I'ktat fondamental (5 < R < 9 a.u.) qui dissocie en He + H + , ainsi que l'etat A '8+(4 < R < 10) et l'etat a '8+ (3 < R < 10) que dissocient tous les deux en He+ + H. Les resultats variationnels sont comparb a ce qu'on obtient par un developpement perturbationnel.Genaue Variationsenergien sind fur die drei tiefsten Sigma-zustande des Ions HeH + berechnet worden. Dies bedeutet dass Berechnungen fur die folgende Zustande gemacht worden sind: den Grundzustand (5 < R < 9 at.E.), der in He + H + dissoziiert, die Zustande A IZ+ (4 < R < 10) und a 3Cc (3 < R < 10) die beide in He+ + H dissoziieren. Die variationalen Ergebnisse werden mit entsprechenden Resultaten von Storungsentwicklungen verglichen.

Long‐ and intermediate‐range interaction in three lowest sigma states of the HeH⁺ ion

Kołos

1976

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

Jeziorski¹,

Bulski²,

Piela³

1976

166

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.

Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions

Deal

Young

1976

AbstractsThe evaluation of interatomic interactions at large separations ( R ) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third-and higher-order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R -I . This last approximation, using an approximate perturbing Hamiltonian to evaluate a second-order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the H-H+ interaction are given: the error incurred by truncating the spherical-harmonic expansion is bounded, the R expansion is corrected for the overlap of the "atomic" charge distributions, and the R expansion is analyzed to see why it works as well as it does.Dans I'evaluation des interactions interatomiques a grandes separations ( R ), on nkglige