For a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to , where is the total spin angular momentum for all electrons. The multiplicity is also equal to the number of unpaired electrons plus one.[4] Therefore, the term with lowest energy is also the term with maximum and maximum number of unpaired electrons with equal spin angular momentum (either +1/2 or -1/2).
For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number (for the operator ) lies lowest in energy. If the outermost shell is more than half-filled, the level with the highest value of is lowest in energy.
These rules specify in a simple way how usual energy interactions determine which term includes the ground state. The rules assume that the repulsion between the outer electrons is much greater than the spin–orbit interaction, which is in turn stronger than any other remaining interactions. This is referred to as the LS coupling regime.
Full shells and subshells do not contribute to the quantum numbers for total S, the total spin angular momentum and for L, the total orbital angular momentum. It can be shown that for full orbitals and suborbitals both the residual electrostatic energy (repulsion between electrons) and the spin–orbit interaction can only shift all the energy levels together. Thus when determining the ordering of energy levels in general only the outer valence electrons must be considered.
^G.L. Miessler and D.A. Tarr, Inorganic Chemistry (Prentice-Hall, 2nd edn 1999) ISBN0138418918, pp. 358–360
^T. Engel and P. Reid, Physical Chemistry (Pearson Benjamin-Cummings, 2006) ISBN080533842X, pp. 477–479
^G. Herzberg, Atomic Spectra and Atomic Structure (Dover Publications, 1944) ISBN0486601153, p. 135 (Although, Herzberg states these as being two rules rather than three.)