Symmetrized squares, electronic states and the Jahn-Teller effect

1 Symmetrized Squares, Electronic States and the Jahn-Teller Effect 

The symmetric and antisymmetric squares have special prominence in molecular spectroscopy as they give information about some of the simplest open-shell electronic states. A closed-shell configuration has a totally symmetric space function, arising from multiplication of all occupied orbital symmetries, one per electron. The required antisymmetry of the space/spin wavefunction as a whole is satisfied by the exchange-antisymmetric spin function, which returns Fq as the term symbol. In open-shell molecules belonging to a group without 

If an electronic state corresponds to occupation of a doubly degenerate orbital, say of symmetry r(e), the full square V (e) x T(e) gives the full set of possible symmetries of the space parts of the electronic wavefunction. The square divides into symmetric and antisymmetric components the symmetric component [T(e) ] is associated with singlet states (permutation-ally symmetric space part, permutationally antisymmetric spin part), and the antisymmetric component T(e) with triplet states (antisymmetric space part, symmetric spin part). When the two electrons are in orbitals belonging to different degenerate e pairs, the full set of symmetries in T e) x T e) is accessible as both singlets and triplets. 

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