This was written in a lecture slide:

Two electrons present in the same d-orbital repel each other more strongly than do two electrons in the same s-orbital.

Why is there a difference in the amount of inter electronic repulsion in each orbital? Does it have to do with the shape of the orbital?

  • $\begingroup$ I thought 3-body interactions are not solvable. The interplay among 4s and 3d orbitals suggest nuclear attraction plays an important role. What is the basis for the assertion? Which s and which d? $\endgroup$
    – jimchmst
    Apr 14 at 19:16

2 Answers 2


It is related to the shape of these orbitals, but importantly, also with spin-orbit coupling. Two electrons in one orbital must have spin directions opposite to one another. There is no spin-orbit coupling in s-orbital, so these electrons repel only because of their charge. The electrons in d-orbital share a common direction of magnetic field to align relative to. Given that their preferred positions relative to the non-spherical shape of d-orbital and each other are near opposite ends along the direction of the magnetic field, their spin magnetic moments being opposite contributes to repulsion.


There are multiple reasons for the above mentioned phenomenon but mainly due to their shape and size. In detail:

enter image description here


1.Shielding: D-orbitals with double-dumbbell shape occupies larger volume of space then the small spherical s-orbitals. This leads to less shielding in d-orbitals.

2.Exchange energy: According to Pauli's exclusion principle,electrons occupying same orbital must have opposite spin states.This leads to a repulsive interplay called Exchange energy which is high in d-orbital due to its complex orientation.Hence,stronger repulsion between electrons.

3.Electron-electron repulsion: Due to the presence of nodal plane and multiple lobes,electrons are more spreaded which leads to more interaction and so, repulsion.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.