In Physics, Hund's rules determine which is the term symbol that corresponds to the ground state of a multi-electron atom.
Hund's rules are:
- Full shell and subshell do not contribute to total momenta S and L.
- The term with maximum multiplicity has lower energy level.
- For a given multiplicity, the term with the largest value of L has lowest energy.
- For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy. Otherwise, if shells are more than half-filled the term with highest value of J is the one with lowest energy.
Hund's rule #1
In full shells and subshells, all angular momenta cancel out, so they do not contribute to total momenta. The symbol term for full (sub)shells is 
.
Hund's rule #2
This rule deals with spin-spin interactions.
Maximum multiplicity is achieved with maximum total spin quantum number S.
Since electrons are fermions, their combined wave function must be antisymmetric due to Pauli exclusion principle. This wave function can be decomposed in a spatial part and a spin part. For a S = 1 (parallel spins) the spin part becomes symmetric (both electrons are equivalent), so the space part is forced to be antisymmetric. An antisymetric function changes its sign at some point, so the probability of finding two electrons together (given by the square of the wave function) drops to zero at that same point. This translates in the electrons being on average further apart, and so less shielded from each other. The nuclear attraction is greater, which pulls them closer to the nucleus and so they have less potential energy.
Hund's rule #3
This rule deals with orbit-orbit interactions. If all electrons are orbiting in the same direction (higher orbital angular momentum) they meet less often than is some of them orbit in opposite directions. In that last case the repulsive force increases, which separates electrons. This adds potential energy to them, so their energy level is higher.
Hund's rule #4
This rule is due to spin-orbit coupling.
External links
Hund's rules on HyperPhysics