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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 -

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