*
Chemical Physics Letters 195, 67-76 (1992)
*

Tatiana Cwiok^{a}, Bogumil Jeziorski^{a}, Wlodzimierz Kolos^{a},
Robert Moszynski^{a}, J. Rychlewski^{b}, and Krzysztof Szalewicz^{c}

^{a} Department of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland

^{b} Department of Chemistry, A. Mickiewicz University, ul. Grunwaldzka 6, 60-780 Poznan, Poland

^{c} Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA

*
Convergence properties and large-order behavior of the polarization expansion
for the interaction energy of hydrogen atoms
*

** Abstract **

High-order corrections in the polarization expansion for the interaction energy of two ground-state hydrogen atoms are
computed for a wide range of interatomic distances *R*. At large *R*, the convergence radius
of the expansion is
found to be only slightly greater than unity, e.g.
=1.0000000031 at the van der Waals minimum for the triplet state.
The branch points determining
are calculated and used in a convergence acceleration procedure, which shows that the
polarization expansion is a sum of two series - one converging quickly to the Coulomb energy and the other
*also converging*, although extremely slowly for large *R*, to the negative of the exchange energy. The total
series converges to the energy of the ground state of the hydrogen molecule. A simple formula describing the large-order
behavior of the polarization series at large *R* is derived and used to show
that the exchange energy can be accurately calculated from the knowledge of three consecutive large-order polarization energies.

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