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Solutions for Conjugated Systems, Orbital Symmetry, and Ultraviolet Spectroscopy 35 Nodes are represented by dashed lines. (a) π1 π2 π3 π4∗ π5∗ π6∗ O O O π6∗ π5∗ π4∗ π3 π2 π1 (c) (b) two bonding interactions ⇒ allowed one antibonding interaction ⇒ forbidden HOMO* π4* HOMO π3 LUMOLUMO PhotochemicalThermal (d) Whether the triene is the HOMO and the alkene is the LUMO, or vice versa, the answer will be the same. 354