Convergence radii of five intermolecular perturbation theories applied to the interaction between two hydrogen atoms

摘要

For H-2 at infinite separation R we show that the convergence radii can be calculated exactly for two perturbation theories and to high precision for three others. The key in each case is to calculate the lowest energy wave functions belonging to the two possible localizations of the electrons. By focusing on the localization of the electrons the two-electron eigenproblems are reduced to the solution of 2 one-electron problems. The wave functions and energies calculated at R = infinity are used to calculate approximately radii at finite separations. For two theories the dependence of the approximate radii on R is consistent with accurate published results. For two of the perturbation theories a very simple extrapolation procedure is shown to give radii with useful accuracy at R as small as 8 bohr. For the fifth case there are no accurate values known to which our approximate ones may be compared. Why the extrapolation procedure work is explained by a formal analysis based on the assumption of sufficiently large R. Understanding why our method works suggests how radii may be calculated for symmetry-adapted perturbation theories applied to systems more complex than H-2 (c) 2005 Wiley Periodicals, Inc.