Is the reason why Hund's rule exists, that when electrons are in different orbitals (such as 2px, 2py, or 2pz), they are most stable (lowest energy)?

If the purpose is stability/lowest energy, wouldn't it make sense for a pair of electrons to occupy the same orbital first, before filling other ones? Because, for example, one lobe from 2px is closer to a lobe from 2py (or 2pz), than to the other lobe from 2px.

So, I'd assume that a pair electrons would likely be more further apart when both exist in the same 2px orbital (in opposite lobes), rather than when one exists in a lobe in 2px and one in 2py or 2pz, thus having the least energy and being the most stable.

Or does Hund's rule exist for a different reason, and I just have a fundamental misunderstanding?

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    $\begingroup$ Electrons do interact with each other and we need to consider the interaction energy as well. (1) Coulomb Interaction (EM nature) and (2) Exchange Interaction (QM nature). $\endgroup$ – K_inverse Aug 28 '18 at 1:25
  • $\begingroup$ @K_inverse Apologies for the late reply - I was in jail. If I understand you right, that's what I meant to ask about. For example, two electrons that exist on the same orbital 2px could mean that the electron density is spread the farthest apart since the two lobes that make up the orbital are 180 degrees. However, one lobe from 2px and one from another orbital like 2py are 90 degrees, and the electron density on the 2py lobe is, on average, closer to the electron density on the 2px, when compared with each lobe from 2px, where the lobes are opposite to eachother, therefore farther apart. $\endgroup$ – F22Raptor Mar 12 at 1:14

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