# Why is up spin in the px orbital and down spin in the py orbital considered an excited state? [duplicate]

Why is this form of p orbital occupation an excited state? I understand that there should be one up spin and one down spin in one orbital box by Pauli's exclusion rule. But in the p orbitals, it doesn't matter, whether we put up spins first or down spins first according to Hund's rule. I thought unless up and down spin are in same box, they don't affect each other. But as what I thought is wrong, I would like to know the exact reason for this. Why is it considered to be an excited state?

• Hund's first rule states that the lowest energy atomic state is the one that maximizes the sum of the S values for all of the electrons in the open subshell. So, a state with unaligned spins in the p orbitals will be higher in energy than the one with aligned spins and thus it will not be the ground but an excited state. – Philipp Jul 31 '14 at 14:56
• – ron Aug 15 '14 at 21:32

Hund's rule of maximum multiplicity states that for a given electron configuration, the term with the lowest energy has a maximum multiplicity $2S+1$. $S$ is the total spin angular momentum of all electrons in the partially-filled subshell.

For the application of the rule, we consider the 2 electrons in the $p$ subshell and add up their spin quantum numbers to obtain $S$ and the multiplicity. For the ground state configuration, with both electrons "spin-up", we get

$$S=+\frac{1}{2}+(+\frac{1}{2})=1$$ $$2S+1=3$$

For your proposed configuration with one $p$ electron "spin-up" and the other one "spin down":

$$S=+\frac{1}{2}+(-\frac{1}{2})=0$$ $$2S+1=1$$

Since the multiplicity value is smaller, this configuration is not the one which is lowest in energy, and therefore cannot be regarded as the ground state.

This is a weird effect resulted from Pauli principle.

Naive oversimplificated version: since no two electrons with same spin may occupy the same place, if two electrons have opposite spin, a part of their time they spend very close to each other, and this results in increased electrostatic repulsion term in energy of the state, while in case two electrons have the same spin, they are always away of each other, so the global energy is lower.

For this effect to manifest, a a significant overlapping of orbitals occupied by electrons in consideration must occur. This usually is observed on atomic or molecular level, and sometimes on larger scale