Term Symbols

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Page ID: 75030

Alexander Scheeline & Thomas M. Spudich
Analytical Sciences Digital Library

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At the left side of the periodic table (alkalis, alkaline earths) and for some transition metals (neutral copper is a classic), spectra are very similar to the hydrogen spectrum except that different L and mL values give distinguishable transitions. We thus write term symbols (energy level classifications) in the form

^2S+¹L_J^odd^/even.

S is the spin of the electron configuration, 0 if all electrons are paired, 1/2 if a single electron is unpaired, and either 0 or 1 of 2 electrons are unpaired. For every additional unpaired electron, one can have an additional factor of 1/2 spin, and 2S+1 can range from 1 (even numbers of unpaired electrons) or 2 (odd numbers of unpaired electrons) upward to 2S+1. The selection rules say that S can never change during a transition in the absence of an external magnetic field. However, for complex atoms, the actual energy states are mixtures of pure quantum number states, so the "rules' sometimes appear to be violated (nature never violates its own rules, but it may violate human-derived approximations to those rules). Instead of showing a number for L, we use a letter. For L=0, we use S, for L=1, P. Other pairings are (2,D), (3,F), (4,G), and so on through the English alphabet. J can range from L-S to L+S in integer increments. It is given as a number. Thus 3P states have J values of 1 (from L) - 1 (from S) = 0 to 1+1=2. That's ³P₀, ³P₁, and ³P₂. Finally is designation of odd and even states. If the highest total L for an electron configuration is an odd number (an odd number of electrons in an odd L state), the state is odd. Otherwise, the state is even. Thus, if all electrons are paired in closed shells except for 3 electrons in a p orbital, the terms that are possible are ⁴F₉_/2^o, ⁴F₇_/2^o, ⁴F₅_/2^o, ⁴F₃_/2^o, ²F₇_/2^o, and ²F₅_/2^o. If the state is even, one simply omits the trailing superscipt. Why even bother with this notation?

With the large number of energy levels in transition metals and actinides, there needs to be some way to make order out of chaos.
Selection rules based on these "Russell-Saunders" term symbols are a reasonably good approximation in figuring out what levels connect to what other levels. Such selection rules are: DL=0,±1, DS=0, DJ=0,±1 but not 0 to 0. These rules apply to "electric dipole transitions."
For some types of laser spectroscopy where multiple photons are involved in absorption transitions, the selection rules may differ, but the term symbols provide a convenient means to derive what allowed transitions to expect. For a 2 photon absorption, for example, DL=0, ±1, ±2, DS=0, DJ=0,±1, ±2, with DJ=0 allowed.

On the right side of the periodic table, the electron spin and orbital angular momentum interact so strongly that the spin/orbit coupling of individual electrons is more important that the total spin angular momentum or the total orbital momentum. "j-j" coupling is descriptive, and term symbols look like ¹[1/2,1/2]₀ and the like.