Hund's Rule, developed by German spectroscopist Friedrich Hund, is a set of three empirical rules used to determine the term symbol of the ground electronic state. The term symbol is often used in physical chemistry to describe the electron configuration of a given atom with more detail than a typical shell notation would give (i.e., the 1s, 2s, 2p, and so on and so forth descriptions that are familiar to those who have taken high school chemistry).
The term symbol itself summarizes a great deal of information about the angular momentum of a molecule spinning in space, in terms of both the orbital angular momentum and the spin angular momentum. The symbol itself is composed of three pieces: the total orbital angular momentum (L), the total spin angular momentum (S), and the total angular momentum (J), which is the sum of L and S. Obtaining this information is often a target of research or of investigation into texts.
Hund's Rule breaks down to these three rules, which taken in order once one has derived the term symbol for a molecule, can determine the most stable state of a molecule:
- The state with the largest falue of S is the most stable (has the lowest energy), and stability decreases with decreasing S.
- For states with the same value of S, the state with the largest value of L is the most stable.
- If the states have the same value of L and S, then, for a subshell which is less than half filled, the state with the smallest value of J is the most stable; for a subshell that is more than half filled, the one with the largest value of J is the most stable.
Take, for example, carbon in its ground state. In its ground state, carbon has an electron configuration of p2. By referencing a table, we can quickly find that there are five possible term symbols for an atom with that ground state electron configuration: two with an S value of 1 and three with an S value of 3. We can eliminate the first two, because the latter three have an equal and a greater S value. We can also see from the table that they have equal L value. Since carbon in its ground state has a subshell that is less than half filled (p2), we rank the values by order of J values and discover we have one with J value of zero. This is the proper term symbol to describe carbon, given to us by Hund's Rule.