Accurate variational calculation of upper and lower bounds of dispersion interaction constant of two hydrogen atoms

Abstract

The most accurate calculation of the dispersion interaction of two hydrogen atoms 'in the ground state was performed by Hirschfelder and Lowdin [l]. Using a modified variational procedure the numerical value 6.499026 (in atomic units) for the coefficient C, in the dispersion interaction formulaI n recent years several definite variational principles were proposed, which allow both the upper and lower bounds to be obtained for the second-order energy correction [2, 31 and for the static and dynamic polarizibilities [4].As far as we know, accurate variational calculations of the upper bound for the dispersion interaction constant C, of two hydrogen atoms have not been performed. In a recent work of Goodisman [5] only a rough estimate was obtained for the upper bound (C, < 7.326 a.u.).In our calculations the variational functional was taken in the form [4] (A is a real parameter, which does not equal zero. If function u is the exact solution of the Euler equationThe coefficient C, is the second-order correction for the system of two hydrogen atoms in the ground state under the perturbation of form xloxob +YI,&b -2 Z l a Z 2 b (or, equivalenty under the perturbation 1/6zl,,~2J. 13 -

Rayleigh scattering fromn=2 states of atomic hydrogen

“…In this work interest was focused on scattering from the complete n = 2 shell of a model atom (Coulomb field approximation), which implies a coherent summation over the contribution of the n = 2, l = 1 substates, rather than averaging over their incoherent contributions as needed for the case of a H atom. Scattering from the n=2 states was also considered by other authors, using somewhat different techniques (case 2s: Zernik [10], Klarsfeld [11,12], Granovski [13], Zon et al [-14], Adamov et al [15], Gontier and Trahin [16]; case 2p: Zonet al [14], see also Adamov et al [15]). The analytic results derived for the 2s case [9,[12][13][14] agree; however only limited computations have been performed (see [12]).…”

“…For the 2p case the existing formulas are either not directly applicable to 0340-2193/79/0293/0269/$02. 20 the case of hydrogen [9,15], or have been presented in an unwieldy form; no numerical evaluations have been published. In view of the experimental interest in this problem, we shall present in the following complete analytic results and a numerical evaluation for the cross sections of Rayleigh scattering from atomic H in the 2s and 2p states.…”

Variational bounds for imaginary frequency polarizability and dispersion interaction constant

“…The resulting bounds for C, are given in Table I11 where comparison is made with the variational calculations of Adamov, Balmakov and Rebane [16]. In the latter work bounds for C, were calculated in a straightforward way, as bounds for the second-order correction to energy of the system consisting of two hydrogen atoms.…”