Do all five orbitals of the d-sub shell have equal energies?

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Discussion Overview

The discussion centers on the energy levels of the five orbitals within the d-sub shell, exploring whether they are degenerate in various contexts, including spherical environments and the effects of interactions and relativistic corrections.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants propose that in a spherical environment and neglecting interactions, all five d orbitals have equal energies.
  • Others argue that when including relativistic corrections, the d orbitals can split into groups with different energies due to spin-orbit coupling, although the differences may be slight.
  • A later reply asserts that once interactions are considered, the orbitals are no longer degenerate, as Hund's rules dictate a specific order for filling the orbitals based on energy levels.
  • Another participant simply states that all orbitals of any d-subshell are degenerate, suggesting a more straightforward view.

Areas of Agreement / Disagreement

Participants express differing views on the energy levels of d orbitals, with some asserting they are degenerate under certain conditions while others highlight the influence of interactions and relativistic effects leading to energy splitting.

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In a spherical environment and neglecting interactions, yes. Actually, even neglecting interactions if you include relativistic corrections (spin-orbit coupling) the 10 d orbitals will split into groups of j = 3/2 and j = 5/2, with different energies, although maybe only slightly different.

Once you include interactions, even in a spherical environment, no. Hund's rules give a specific order for filling the orbitals, and this is because other fillings will be higher in energy.
 
The simplest answer is Yes.
All the orbitals of any d-subshell are degenerate.
 

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