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We calculate the singlet-triplet splitting for a couple of two-dimensionalelectrons in the potential of two positively charged impurities which arelocated out of plane. We consider different relations between verticaldistances of impurities $h_1$ and $h_2$ and their lateral distance $R$. Such asystem has never been studied in atomic physics but the methods, worked out forregular two-atomic molecules and helium atom, have been found to be useful.Analytical expressions for several different limiting configurations ofimpurities are obtained an interpolated formula for intermediate range ofparameters is proposed. The $R$-dependence of the splitting is shown to becomeweaker with increasing $h_1,h_2$.Comment: 14 pages, RevTeX, 5 figures. Submitted to Phys Rev.

Calculations of exchange interaction in the impurity band of two-dimensional semiconductors with out-of-plane impurities