Multipole structure of exchange polarization energy for H<sub>2</sub><sup>+</sup> Ion

Chałasiński, Grzegorz; Jeziorski, Bogumił

doi:10.1002/qua.560070412

Cited by 13 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additional calculations of the componnets E00exch_disp , E01exch_disp, and E02each_disp showed, however, that these quantities were negligible, representing less than 1 per cent of Eexoh_disp. A very similar observation concerning the importance of Edisp ~176 Edisp ~ and Edisp ~ has been made by Kreek and Meath [15].…”

Section: Numerical Results and Discussion Klsupporting

confidence: 58%

“…We found that at the van der Waals minimum, R--8-0 bohr, Eexch_disp 11= 0"0924 K what represents only 18-6 per cent of the exchange polarization energy for this system [23]. It is worthwhile to stress that the observed behaviour of the exchange dispersion energy is in sharp contrast to behaviour of the exchange induction energy for which the multipole expansion was shown to converge quite satisfactorily [15].…”

Section: Numerical Results and Discussion Klmentioning

confidence: 84%

“…and B.J.) [15], who also analysed its rate of convergence and possible utility. Independently, Brumer and Karplus [16] introduced a somewhat different version of this expansion and applied it, on the semi-empirical level, to the interaction of ions within the alkali halide molecules [17].…”

mentioning

confidence: 99%

See 2 more Smart Citations

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

et al. 1977

Self Cite

View full text Add to dashboard Cite

The exchange dispersion energy for the interaction of two helium atoms is expressed as a sum of multipole components. In contrast to the analogous expansion for the dispersion energy the derived series converges very slowly and the rate of convergence does not improve with an increasing interatomic distance. Numerical calculations show that at the van der Waals minimum the first term of the series, referred to as dipole-dipole exchange energy, represents merely 17 per cent of the exchange dispersion energy. Moreover, even the inclusion of dipole-quadrupole and quadrupole-quadrupole terms can account for only half of the total exchange dispersion interaction. The above difficulty can be avoided by expanding the dispersion pair function in terms of ionic type or explicitly correlated functions. INTRODUCTIONA common practice in the theory of long-range intermolecular forces is to represent various contributions to the interaction energy by means of the so-called multipole expansions [1]. The interaction energies of the first and second order then acquire a simple physical interpretation as the result of the interaction of various permanent, induced or instantaneous multipoles [2]. A similar, though less transparent interpretation, can also be given to the third [3] and higher-order energies [4]. At large intermolecular distances the multipole expansions converge very fast and their application is very effective in practice. At smaller distances where the overlap between interacting systems cannot be neglected, e.g. at the van der Waals minimum region, the multipole expansions can still be made to converge, provided that the charge-overlap effects are properly taken into account [5,6]. In this region, however, the application of the usual RayleighSchr6dinger perturbation theory is no longer legitimate and a suitable symmetryadapted perturbation theory must be employed to allow for the exchange effects [7]. Among the theories proposed the Murrell-Shaw [8] and Musher-Amos [9] approach is distinguished for the simplicity and clear physical sense of the loworder contributions to the energy. When applied through the second order, this theory provides two new contributions: the first-order exchange energy, implicit in the Heitler-London treatment of short-range intermolecular forces [10] and the exchange polarization energy first derived by Murrell et al. [11]. The latter energy can be interpreted as arising from the antisymmetrization of the corrections to the wave function which are due to the induction and dispersion

show abstract

Section: Numerical Results and Discussion Klsupporting

confidence: 58%

Section: Numerical Results and Discussion Klmentioning

confidence: 84%

See 1 more Smart Citation

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

et al. 1977

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the H2+ ion the exchange induction term efficiently approximated second-and higher-order exchange effects. 98 Later, however, it was found that the sum of the induction and exchange induction contributions failed to reproduce the mutual deformation effect arising at the SCF level between closed-shell atoms. 56,96,99,100 This fact was attributed to the weak symmetry forcing applied in the exchange polarization term.101,102 It turned out that exchange effects are crucial in the mutual deformation of closed-shell atoms and ions.102,103 These effects can be accounted for only by an exchange perturbation formalism with strong symmetry forcing.101 (Strong symmetry forcing, as opposed to weak symmetry forcing, considers symmetry constraints and electrostatic effects simultaneously.12) It is still not clear whether the exchange dispersion term suffers from the same problem.…”

Section: Problems With the Exchange Induction Termmentioning

confidence: 99%

Weak interactions between small systems. Models for studying the nature of intermolecular forces and challenging problems for ab initio calculations

Chałasiński¹,

Gutowski²

1988

Chem. Rev.

284

110

View full text Add to dashboard Cite

Symmetry forcing and convergence properties of perturbation expansions for molecular interaction energies

Jeziorski

Szalewicz

Chałasiński

1978

Int J of Quantum Chemistry

136

View full text Add to dashboard Cite

AbstractsThe convergence properties of perturbation theories for molecular interaction energies are tested by performing high-accuracy high-order numerical calculations for a ground-state hydrogen atom interacting with a proton. It is shown that a strong symmetry forcing used in the EisenschitzLondon-Hirschfelder-van der Avoird (EL-HAV) theory leads to rapidly convergent perturbation expansion whereas a weak symmetry forcing, peculiar to the Murrell-Shaw-Musher-Amos (MSMA) theory, is not able to guarantee the convergence of the resulting perturbation series. The perturbation expansion introduced recently by Jeziorski and Koios and corresponding to an intermediate symmetry forcing is shown to converge rapidly ensuring the correct asymptotic behavior of the interaction energy calculated through second order. Despite the divergence of the resulting perturbation series the MSMA theory is shown to give very useful results at the distances corresponding to the van der Waals minimum. In this region, however, virtually the same results can be obtained by using a simpler theory employing a properly symmetrized wave function of the usual RayleighSchrodinger (RS) polarization theory.Ler proprietts de convergence des methodes de perturbation utilisCes pour les energies d'interaction rnolkculaire, ont ete testtes par des calculs numtriques de haute prtcision pour des ordres Clevts pour un atome d'hydroghe dans I'Ctat fondamental qui interagit avec un proton. I1 est dtmontrt qu'avec une forte contrainte de symttrie, d'un type utilisC dans la thtorie de EisenschitzLondon-Hirschfelder-van der Avoird (EL-HAV) on obtient un dtveloppment qui converge rapidement. tandis qu'unc contrainte de syrnttrie faible. utiliste dans la thkorie de Murrell-ShawMusher-Amos (MSMA), ne peut pas garantir la convergence du dkveloppment de perturbation correspondant. Le dbveloppment introduit rkemment par Jeziorski et Kotos, qui correspond a une contrainte de symitrie intermidiaire, converge rapidement et assure un comportement asymptotique correct d e I'knergie d'interaction calculte jusqu'au second ordre. MalgrC la divergence d e sa serie d e perturbation la thiorie MSMA donne des rksultats trks utiles i des distances qui correspondent au minimum de van der Waals. Dans cette rkgion-ci on peut cependant obtenir pratiquement les m&mes rtsultats par une thkorie simple, qui n'utilise qu'une fonction d'onde symttriste du type employe dans la thCorie ol-dinaire de polarisation Rayleigh-Schrodinger (RS).Die Konvergenzeigenschaften der fur molekulare Wechselwirkungsenergien gebrauchlichen Storungsmethoden sind durch numerische Berechnungen fur ein mit einem Proton wechselwirkenden Wasserstoffatom getestet worden. Diese Rechnungen wurden zu hoher Ordnung und rnit hoher Genauigkeit ausgefiirht. Es wird gezeigt, dass der in der Eisenschitz-London-Hirschfeldervan der Avoird'schen Theorie (EL-HAV) verwendete starke Symmetriezwang zu einer schnellkonvergenten Storungsentwicklung fiihrt, wahrend der fur die Murrell-Shaw-Musher-Amos'sche Theorie (

show abstract

Multipole structure of exchange polarization energy for H₂⁺ Ion

Cited by 13 publications

References 28 publications

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

Weak interactions between small systems. Models for studying the nature of intermolecular forces and challenging problems for ab initio calculations

Symmetry forcing and convergence properties of perturbation expansions for molecular interaction energies

Contact Info

Product

Resources

About

Multipole structure of exchange polarization energy for H2+ Ion

Cited by 13 publications

References 28 publications

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

Weak interactions between small systems. Models for studying the nature of intermolecular forces and challenging problems for ab initio calculations

Symmetry forcing and convergence properties of perturbation expansions for molecular interaction energies

Contact Info

Product

Resources

About

Multipole structure of exchange polarization energy for H₂⁺ Ion