Electronic States vs Molecular Levels

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The literature can be confusing in using the terminology of electronic states vs electrical levels. There is always an identity symmetry (E). The hexatriene molecule is symmetrical around the C2 axis. The C2 axis is perpendicular from the plane of the molecule. A rotation of 180 degrees brings the same structure. The sigma h denotes symmetry above and below the plane, there must be the same electronic density above the plane as below. There is also an inversion symmetry (i) where the C2 axis meets the plane . These together have a point group called C2h.

Molecular level is a one electron wavefunction which is by definition a molecular orbital. Molecular levels corresponds to molecular orbitals (HOMO, LUMO etc).

Molecular states which is what you can observe is a wavefunction that results from all the electrons in the molecule.