Final answer:
Electrons in d orbitals follow the aufbau principle, filling orbitals to minimize energy and according to Hund's rule, occupying degenerate orbitals singly before pairing. This is influenced by the pairing energy and octahedral field splitting.
Step-by-step explanation:
The occupation of degenerate orbitals by electrons, like those in the d orbitals, follows specific rules in quantum chemistry. According to the aufbau principle, these orbitals fill to give the lowest total energy, with electrons spreading out to occupy each orbital singly before any pairing occurs. This is due to the pairing energy (P), which is the energy required to pair two electrons within the same orbital due to their like charges repelling each other. Hund's rule also supports this distribution, asserting that electrons will singly occupy each orbital in a degenerate set before pairing. In an octahedral arrangement of transition-metal ions, the d orbitals split into different energy levels (eg and t2g orbitals), where the relative magnitudes of the pairing energy and the octahedral crystal field splitting (Aoct) determine which orbitals electrons will occupy.