I have read that exchange energy exists between non-degenerate levels $1s$ and $2s$ or between $1s$ and $2p_x$ in the Helium atom in the first excited level: $$K_s = \left< 1s(1)2s(2)|H'|1s(2)2s(1) \right> $$ $$K_p = \left< 1s(1)2p_x(2)|H'|1s(2)2p_x(1) \right> $$ What about the exchange between $2p_x$ and $2p_y$ in the next excited level? Is $$ \left< 2p_x(1)2p_y(2)|H'|2p_x(2)2p_y(1) \right> =0$$? Here, $$H'= \frac {e^2}{r_{12}} $$ is perturbation term. Thanks.

  • 2
    $\begingroup$ Short answer is yes, there are exchange energies among degenerate orbitals. Most often discussed with respect to d orbitals, probably because of stable transition metals with multiple unpaired electrons in d orbitals $\endgroup$
    – Andrew
    Nov 10, 2021 at 23:07


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