Term Symbol - Ground State Term Symbol

Ground State Term Symbol

It is relatively easy to calculate the term symbol for the ground state of an atom using Hund's rules. It corresponds with a state with maximal S and L.

1. Start with the most stable electron configuration. Full shells and subshells do not contribute to the overall angular momentum, so they are discarded.
   • If all shells and subshells are full then the term symbol is 1S₀.
2. Distribute the electrons in the available orbitals, following the Pauli exclusion principle. First, fill the orbitals with highest m_l value with one electron each, and assign a maximal m_s to them (i.e. +½). Once all orbitals in a subshell have one electron, add a second one (following the same order), assigning m_s = −½ to them.
3. The overall S is calculated by adding the m_s values for each electron. That is the same as multiplying ½ times the number of unpaired electrons. The overall L is calculated by adding the m_l values for each electron (so if there are two electrons in the same orbital, add twice that orbital's m_l).
4. Calculate J as
   • if less than half of the subshell is occupied, take the minimum value J = |L - S|;
   • if more than half-filled, take the maximum value J = L + S;
   • if the subshell is half-filled, then L will be 0, so J = S.

As an example, in the case of fluorine, the electronic configuration is 1s22s22p5.

1. Discard the full subshells and keep the 2p5 part. So there are five electrons to place in subshell p (l = 1).

2. There are three orbitals (m_l = 1, 0, −1) that can hold up to 2(2l + 1) = 6 electrons. The first three electrons can take m_s = ½ (↑) but the Pauli exclusion principle forces the next two to have m_s = −½ (↓) because they go to already occupied orbitals.

3. S = ½ + ½ + ½ − ½ − ½ = ½; and L = 1 + 0 − 1 + 1 + 0 = 1, which is "P" in spectroscopic notation.

4. As fluorine 2p subshell is more than half filled, J = L + S = . Its ground state term symbol is then 2S+1L_J = 2P_3⁄2.