In the following picture you can see our excited state analysis methods (as described here) when applied to PPV. The model to understand this structure is to think of a hydrogen atom (or a "quasi-particle") in a one-dimensional box. First there are different translation states for the ground state of the hydrogen atom. These should be differentiated by a different number of nodal planes (shown in the first three cases). Then a different state of the "hydrogen atom" comes into play and there is a somewhat different shape. Unfortunately this method does not show any phases or signs but I still think one can recognize the nodal structure.

If there is a torsion in the center of the molecule, the situation changes. Now there are two equivalent, effectively decoupled, units. Therefore the excited states come in pairs, corresponding to the "+" and "-" linear combinations of the fragment states.

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