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The electron energy transfer diagrams I've been coming across all have energy levels labeled as e.g. $^{2}F_{5/2}$ or $^{4}S_{3/2}$. I've tried to Google "quantum energy level abbreviations" but haven't come across anything too useful, just explanations of electron configurations. Can anyone explain or point to a website or textbook that goes through what these numbers/letters/fractions mean for someone who's taken general chemistry but not quantum mechanics?

Thanks!

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    $\begingroup$ It's a bit tough to understand where these numbers come from without QM, and I don't really want to write any technical inaccuracies (because this topic is confusing enough for QM students and having another sloppy account online won't help). However, as a general chemistry student, perhaps you are aware of the quantum numbers of an electron: $(n, l, m_l, m_s)$. $m_s$ has to do with the spin of the electron, which is an "intrinsic angular momentum" of the electron. $m_l$ has to do with the orbital the electron is in, which confers a certain amount of angular momentum on the electron as well. $\endgroup$ – orthocresol♦ May 18 '17 at 14:27
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    $\begingroup$ ... If you add up the angular momenta of all the electrons in an atom, you can get the angular momentum of the atom. In short, then, the top-left number represents the spin angular momentum of an atom, the middle letter represents the orbital angular momentum of an atom, and the bottom-right number represents the total angular momentum of an atom, which is simply a sum of the previous two angular momenta. $\endgroup$ – orthocresol♦ May 18 '17 at 14:27
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Those are Russel Saunders atomic term symbols and represent the quantum numbers of the many-electron wave function.

The notation scheme is $^{2S+1}L_J$ where $2S+1$ is the spin multiplicity, $L$ is the angular momentum quantum number and $J$ is the total angular momentum due to the coupling between the former two.

There are also molecular term symbols using greek instead of latin letters for the angular momentum. Those are commonly used for diatomic molecules.

You should find the Russel Saunders Coupling scheme in standard physical and quantum chemistry books. Molecular term symbols are for example explained in detail in Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules by Herzberg and Huber (1950). This link may give you a preliminary idea : http://wwwchem.uwimona.edu.jm/courses/RScoupling.html

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