Convergence of Intermolecular Force Series

Tang

The Journal of Chemical Physics

et al. 2012

The multipole expansion of the polarization interaction between a charged particle and an electrically neutral object has long been known to be asymptotic in nature, i.e., the multiple expansion diverges at any finite distance from the atom. However, the multipole expansion of the polarization potential of a confined hydrogen atom is shown to be absolutely convergent at a distance outside the confinement radius, R(0), of the atom. The multipole expansion of the dispersion potential between two confined hydrogen atoms is also shown to be absolutely convergent provided the two atoms satisfy R > 2R(0), where R is the inter-nuclear separation. These results were established analytically using oscillator strength sum rules and verified numerically using a B-spline description of the hydrogen ground state and its excitation spectrum.

Section: Polarization Interaction For a Confined Hydrogen Atommentioning

confidence: 99%

mentioning

confidence: 99%

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Convergence of the multipole expansions of the polarization and dispersion interactions for atoms under confinement

Tang

The Journal of Chemical Physics

et al. 2012

“…[13] where N is the number of electrons and r 2ℓ−2 is a radial expectation value of the ground state wave function. This expression reduces to the well known Thomas-Reiche-Kuhn sum rule S (1) (0) = N for ℓ = 1. For the hydrogen atom ground state, the sum rule is…”

Section: Polarization Interaction For a Confined Hydrogen Atommentioning

confidence: 99%

“…The polarization potential given by Eq. ( 1) eventually diverges as ℓ increases at any finite value of R [1,2]. Formal issues of a similar nature also lead to a problem in the multipole expansion of the atom-atom dispersion interaction.…”

mentioning

confidence: 99%

Convergence of the multipole expansion of the polarization interaction

Zhang,

Tang,

Zhang

et al. 2011

Preprint

The multipole expansion of the polarization interaction between a charged particle and an electrically charged particle has long been known to be asymptotic in nature, i.e. the multiple expansion diverges at any finite distance from the atom. However, it is shown that the multipole expansion of the polarization potential of a confined hydrogen atom is absolutely convergent at a distance outside the atoms confinement radius. It is likely that the multipole expansion of the dispersion interaction of two confined atoms will also be absolutely convergent provided the internuclear separation of the two atoms is sufficiency large to exclude any overlap between the electron charge clouds of the two atoms.

Int J of Quantum Chemistry

A note on the theory of interatomic long‐range forces

Fukui

Yamabe

1968

AbstractsA comment is made on the multipolar expansion formula of the long-range force between hydrogen atoms previously obtained. The second-order perturbation energy neglecting exchange in the framework of the Unsold approximation is evaluated exactly. An extension is made to helium atoms, and to other s-electron interactions. An approximate method is suggested to estimate the interatomic force between two atoms in general.On fait un commentaire sur un dtveloppement multipolaire de la force A longue portee entre deux atomes d'hydroghe, obtenu anterieurement. L'energie de perturbation du second ordre sans Cchange, est calculte exactement dans le cadre de I'approximation de Unsold. On traite aussi deux atomes de hClium ainsi que d'autres interactions d'tlectrons de type s. On propose une methode approximative pour estimer la force interatomique entre deux atomes en gtnkral.Es wurde eine Bemerkung uber eine vorher erhaltene Multipolentwicklung der zwischenatomaren Kraft zwei entfernter Wasserstoffatomen gemacht. Die Storungsenergie zweiter Ordnung ohne Austausch wurde im Rahmen der Unsoldapproximation genau ausgewertet. Eine Erweiterung wurde an Heliumatome und andere s-Elektronwechselwirkungen gemacht. Eine annahernde Methode fur die Abschatzung der interatomaren Kraft zwischen zwei Atomen wird vorgeschlagen.