The interaction between the spin angular momentum quantum numbers of two electrons gives rise to states of so called different spin multiplicity, such as singlet and doublet states.

The spin angular momentum of an electron may also interact with the orbital angular momentum of the electron to split the energies of the different levels, causing different transition energies to be observed. This effect is known as spin-orbit coupling.

The interaction of the spin angular momentum and the orbital angular momentum gives rise to the total angular momentum: when the spin and orbital angular momentum are parallel, the total angular momentum is high.

For a given electron the total angular momentum, j, is either l+s or l-s (with s = 1/2 for the electron), and the energy level corresponding l is therefore split into two terms for the different values of j.

The energy of the state characterized by the quantum numbers, l, s and j, is given by the expression:

Here, A is the spin-orbit coupling constant, and the degree of coupling increases as Z⁴ (where Z is the atomic number).

The total angular momentum of a single electron can also couple with the total angular momentum of other electrons, such that the total angular momentum of an atom as a whole can have a range of values, depending upon the exact occupation of the orbitals. The spin, orbital, and total angular momentum for an atom or ion in a given electronic configuration is expressed as a term symbol.

In light atoms, the spin-orbit coupling in individual electrons is weak, and instead the coupling of the spin angular momenta of different electrons, or the coupling of the orbital angular momenta of different atoms, is stronger. This type of spin-orbit coupling is known as the Russell-Saunders scheme, and gives rise to term symbols as shown, for a species with two electrons in d orbitals, in the table below.

An important consequence of term symbols is their use to express the ranges of S, L, and J which may be involves in allowed transitions between the levels the term symbols represent. These allowed transitions may be summarized as a set of selection rules:

These selection rules only apply in the Russell-Saunders coupling scheme. In heavier atoms, the coupling between the spin and orbital angular momentum of individual electrons is much stronger, and only the total angular momentum, J, is important. The selection rules based on the values of S and L therefore do not hold. A better coupling scheme for the heavy atoms is jj-coupling, where the total angular momentum of each electron is calculated first, and then these are coupled to give the overall total angular momentum of the atom.