In 3d$^7$ ions, e.g. Co$^{2+}$, the ground state is $^4$F, and it contains different levels due to the crystal field, such as $^4T_{1g}$, $^4T_{2g}$ and $^4A_{2g}$. Can anyone tell me what exactly these symbols mean? I need to know the exact configuration, not just "the even/odd symmetry of wavefunction". Thanks in advance!

  • $\begingroup$ Chris, you need to check some material on the applications of molecular symmetry in Chemistry and crystal field theory. You can find an introduction in many Physical or Inorganic Chemistry textbooks. The notation relates to the symmetry of the central ion wavefunction and the electronic states of the same multiplicity you could build considering the valence electrons and the electronic configurations. Maybe someone can give you further directions. $\endgroup$
    – PAEP
    Commented Nov 21, 2023 at 21:40
  • $\begingroup$ These appear to be a mixture of Term Symbols and symmetry species in Oh point group. The superscript 4 could be spin multiplicity $2S+1=4$ with 3 electrons where $S=1/2$. The orbitals $T_{1g}$ etc have the symmetry properties given by their row in the point group. $\endgroup$
    – porphyrin
    Commented Nov 22, 2023 at 16:48

1 Answer 1


These are labels for irreducible representation in the Oh point group: http://symmetry.jacobs-university.de/cgi-bin/group.cgi?group=904&option=4 T and A are standard labels for triply and singly degenerate representations, the g denotes gerade (=even under inversion) and 1 and 2 are just labels. Functions in a specific irreducible representation transform in specific ways under the 48 symmetry operations in the Oh point group.

  • $\begingroup$ Thanks but as I said in the question, I need the exact configuration. For example, $^4$A$_{2g}$ for 3d7 means 4 electrons on t$_{2g}$ orbitals and 3 on e$_g$ orbital. Same for the $^4$T$_{2g}$, but what exactly is the difference? $\endgroup$
    – Chris Bohr
    Commented Nov 21, 2023 at 21:36

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