What is Hund's Rule of Maximum Multiplicity?

Hund's Rule of Maximum Multiplicity just says that the most stable configuration of an atom or molecule TENDS TO BE the one with all unpaired electrons having parallel spins (if it is favorable).

So, say you have a set of #2p# orbitals (as usual, in context of surrounding atomic orbitals!) that contain #2# electrons.

#underbrace(ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "ul(color(white)(uarr darr)))_(2p)#

This configuration will be more unstable because the electrons have antiparallel spins:

#underbrace(ul(uarr color(white)(darr))" "ul(darr color(white)(darr))" "ul(color(white)(uarr darr)))_(2p)#

This configuration will be even more unstable because it adds electron repulsion:

#underbrace(ul(uarr darr)" "ul(color(white)(uarr darr))" "ul(color(white)(uarr darr)))_(2p)#

Depending on the orbital size, the atom may not care... For light atoms, this rule is especially important. There are exceptions, such as #W# being #5d^4# vs. #Cr# being #3d^5#.

[Heavier atoms may be fine with pairing electrons anyway, since orbital size and electron repulsion are inversely proportional.]