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