The Equivalence of Variational and Perturbation Calculations of Small Disturbances

Dalgarno, A.; Lewis, J. T.

doi:10.1088/0370-1298/69/8/408

Cited by 59 publications

(63 citation statements)

References 6 publications

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“…5 to 8 because of the apparent geometry dependence. Our calculations do not provide numerical evidence for the asymptotically divergent (semiconvergent) character of the multipole expansion which has been proven theoretically [14,[83][84][85].…”

Section: )mentioning

confidence: 61%

Ab initio Studies of long range interactions between ethylene molecules in the multipole expansion

Mulder

Hemert

Wormer

et al. 1977

Theoret. Chim. Acta

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The multipole moments and multipole polarizabilities of ethylene and the long range coefficients for the interactions between two ethylene molecules have been calculated using LCAO-SCF wave functions. Subjecting different AO basis sets to a completeness test, we have shown that the inclusion of polarization functions slightly more diffuse than the valence orbitals is required for an appropriate description of the second order quantities. The (theoretical) Unsold procedure which is introduced to approximate the second order interaction energy, appears to be rather accurate and is prefer able for small basis sets.

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Section: )mentioning

confidence: 61%

Ab initio Studies of long range interactions between ethylene molecules in the multipole expansion

Mulder

Hemert

Wormer

et al. 1977

Theoret. Chim. Acta

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“…Nevertheless it is a very convenient one, since the error involved is of the order of the magnitude of the last term retained [7].…”

Section: Methodsmentioning

confidence: 99%

Long‐range interactions in the ground and two excited states of the HeH⁺ molecule

Piela

1969

Int J of Quantum Chemistry

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AbstractsThe long-range interaction energies for different dissociation products of the HeH+ molecule have been calculated using the Rayleigh-Schrijdinger perturbation theory up to the third order in the energy. The calculations were carried out for the ground state (He(ls2) + H+), the first excited state (H(1s) + He+(ls)) and the second excited state II(H(2pr) + He+( Is)). The unperturbed states correspond to the dissociation products denoted in parentheses. Assuming the overlap to be zero, expanding the interaction potential in the inverse powers of the internuclear distance R and using the familiarly known perturbation-variational technique, the coefficients of various powers of R-' in the energy expansion were evaluated. They correspond to different multipole-multipole interactions. The potential energy curves of all three states under consideration were calculated for large values of R. Also calculated were the multipole polarizabilities of the hydrogen atom in the 1s and 2pn states and of the helium atom in the ground state.L'tnergie d'interaction de longue portte entre des produits de dissociation difftrents de la moltcule HeH+ a t t t calculte par la mtthode de perturbation de RayleighSchrodinger jusqu'au troisitme ordre. Les calculs ont ett faits pour l'ttat fondamental (He(ls2) + Hf), pour le premier ttat excitt (H(1s) + He+(ls)) et pour le deuxitme ttat excitt lI(H(2pn) + He+(ls)). Les ttats non perturbts correspondent aux produits de dissociation indiquts en parenthtses. Supposant le recouvrement des orbitales atomiques ntgligeable, dtveloppant le potentiel d'interaction en puissances inverses de la distance internucltaire, R, et faisant usage de la mtthode variationelle bien connue des perturbations, l'auteur a calcult les coefficients des puissances de R-l dans le dtveloppement de l'tnergie. Ces coefficients correspondent B des interactions difftrentes multip6le-multip6le. Les courbes d'tnergie potentielle de tous les trois ttats ont t t t calcultes pour des grandes valeurs de R. Les polarisabilitts multipolaires de l'atome d'hydrogtne dans les ttats 1s et P p r et de l'atome d'htlium dans l'ttat fondamental ont aussi t t t calcultes.

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“…На практике прн суммировании асимптотического ряда его обрывают на чле-не, после которого начинается возрастание, далее берется сумма всех членов до наименьшего плюс половина наименьшего члена 165 . Для каче-ственных оценок при больших R достаточно вычислить первый член раз-ложения.…”

Section: E Int = E-(e a + E B )unclassified

Intermolecular interactions

Kaplan¹,

Rodimova²

1978

Usp. Fiz. Nauk

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The Equivalence of Variational and Perturbation Calculations of Small Disturbances

Cited by 59 publications

References 6 publications

Ab initio Studies of long range interactions between ethylene molecules in the multipole expansion

Ab initio Studies of long range interactions between ethylene molecules in the multipole expansion

Long‐range interactions in the ground and two excited states of the HeH⁺ molecule

Intermolecular interactions

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The Equivalence of Variational and Perturbation Calculations of Small Disturbances

Cited by 59 publications

References 6 publications

Ab initio Studies of long range interactions between ethylene molecules in the multipole expansion

Ab initio Studies of long range interactions between ethylene molecules in the multipole expansion

Long‐range interactions in the ground and two excited states of the HeH+ molecule

Intermolecular interactions

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Product

Resources

About

Long‐range interactions in the ground and two excited states of the HeH⁺ molecule