New Methods for Calculating Long‐Range Intermolecular Forces

Dalgarno, A.

doi:10.1002/9780470143582.ch3

Cited by 232 publications

(18 citation statements)

References 70 publications

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“…We investigate the 2S-1S interaction in the van der Waals regime (9). There is no exponential or oscillatory suppression of any atomic transition in this regime, but we can approximate…”

Section: A Formalismmentioning

confidence: 99%

“…Let us recall here that the general subject of long-range interactions of simple atoms is very well known to the physics community, and a few investigations on simple atomic systems can be found in Refs. [4,5,[8][9][10][11][12][13][14][15][16][17]. Various aspects of the problem have been studied in depth: e.g., the importance of multipole mixing effects, and of perturbations by hyperfine effects, has been stressed in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Long-range interactions of hydrogen atoms in excited states. I.2S−1Sinteractions and Dirac-δperturbations

et al. 2017

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The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6(2S; 1S) describing the interaction of metastable atomic hydrogen (2S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0/α, where a0 = /(αmc) is the Bohr radius and α is the fine structure constant, one finds the symmetry-dependent result E2S;1S(R) ≈ (−176.75 ± 27.98) E h (a0/R) 6 (E h denotes the Hartree energy). In the Casimir-Polder range a0/α ≪ R ≪ c/L, where L ≡ E 2S 1/2 − E 2P 1/2 is the Lamb shift energy, one finds E2S;1S(R) ≈ (−121.50 ± 46.61) E h (a0/R) 6 . In the the Lamb shift range R ≫ c/L, we find an oscillatory tail with a negligible interaction energy below 10 −36 Hz. Dirac-δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction, or, expressed differently, the shift of the hydrogen 2S hyperfine frequency due to interactions with neighboring 1S atoms. The 2S hyperfine frequency has recently been measured very accurately in atomic beam experiments.

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“…We investigate the 2S-1S interaction in the van der Waals regime (9). There is no exponential or oscillatory suppression of any atomic transition in this regime, but we can approximate…”

Section: A Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Long-range interactions of hydrogen atoms in excited states. I.2S−1Sinteractions and Dirac-δperturbations

et al. 2017

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“…respectively. Table I11 also contains semiempirical estimates (Dalgarno [25]) and lower bounds reported by Langhoff and Karplus [ 111. Four-dimensional 6.49 126.9 1 1 3 5…”

Section: Numerical Resultsmentioning

confidence: 99%

Dispersion coefficients and frequency-dependent polarizabilities

Ahlberg

2009

Int. J. Quantum Chem.

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Extensions of previous methods for obtaining two-and three-body dispersion coefficients are presented. Many-dimensional arrays in inner projections are utilized. The required matrix elements are expressed in terms of atomic frequency (Cauchy) moments. Approximate dynamic polarizabilities are derived using generalized inner projections, and a number of theorems for definite operators are extended to more general cases.Numerical results for both two-and three-body dispersion coefficients are reported.

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“…For two spherically symmetric atoms, this interaction can be written, 52,53 The dynamic polarization potential, Eq.…”

Section: Long-range Polarization and Dispersion Interactionsmentioning

confidence: 99%

“…52,53 This reduces the calculation of the C n parameters for two spherically symmetric atoms to summations over the products of the absorption oscillator strengths divided by an energy denominator. 52,53 This reduces the calculation of the C n parameters for two spherically symmetric atoms to summations over the products of the absorption oscillator strengths divided by an energy denominator.…”

Section: Long-range Polarization and Dispersion Interactionsmentioning

confidence: 99%

Long-range dispersion coefficients for Li, Li+, and Be+ interacting with the rare gases

Tang

Zhang

Zhou

et al. 2010

The Journal of Chemical Physics

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The long-range dispersion coefficients for the ground and excited states of Li, Li(+), and Be(+) interacting with the He, Ne, Ar, Kr, and Xe atoms in their ground states are determined. The variational Hylleraas method is used to determine the necessary lists of multipole matrix elements for He, Li, Li(+), and Be(+), while pseudo-oscillator strength distributions are used for the heavier rare gases. Some single electron calculations using a semiempirical Hamiltonian are also performed for Li and Be(+) and found to give dispersion coefficients in good agreement with the Hylleraas calculations. Polarizabilities are given for some of the Li and Li(+) states and the recommended (7)Li(+) polarizability including both finite-mass and relativistic effects was 0.192 486 a.u. The impact of finite-mass effects upon the dispersion coefficients has been given for some selected interatomic interactions.

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New Methods for Calculating Long‐Range Intermolecular Forces

Cited by 232 publications

References 70 publications

Long-range interactions of hydrogen atoms in excited states. I.2S−1Sinteractions and Dirac-δperturbations

Long-range interactions of hydrogen atoms in excited states. I.2S−1Sinteractions and Dirac-δperturbations

Dispersion coefficients and frequency-dependent polarizabilities

Long-range dispersion coefficients for Li, Li+, and Be+ interacting with the rare gases

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