The Fukui approach, on the other hand, analyzes the interactions between the HOMO and LUMO of each of the reactants, or within a reactant. A process in which the HOMO-LUMO interaction is constructive (results in a net bonding interaction) is favorable and considered symmetry-allowed, while a process in which the HOMO-LUMO interaction is non-constructive (results in bonding and antibonding interactions that cancel) is disfavorable and considered symmetry-forbidden. The correlation diagram approach ("the conservation of orbital symmetry, vide supra"), as proposed by Woodward and Hoffmann and clarified by Longuet-Higgins and others, led to the general statement that a pericyclic reaction is allowed if the sum of the number of suprafacial 4"q" + 2 components and number of antarafacial 4"r" components is odd. Importantly, though conceptually distinct, aromatic transition state theory (Zimmerman and Dewar), frontier molecular orbital theory (Fukui), and the principle of orbital symmetry conservation (Woodward and Hoffmann) make identical predictions. Although orbital "symmetry" is used as a tool for sketching orbital and state correlation diagrams, the absolute presence or absence of a symmetry element is not critical for the determination of whether a reaction is allowed or forbidden. That is, the introduction of a simple substituent that formally disrupts a symmetry plane or axis (e.g., a methyl group) does not generally affect the assessment of whether a reaction is allowed or forbidden. Instead, the symmetry present in an unsubstituted analog is used to simplify the construction of orbital correlation diagrams and avoid the need to perform calculations. Only the phase relationships between orbitals are important when judging whether a reaction is "symmetry"-allowed or forbidden. Moreover, orbital correlations can still be made, even if there are no conserved symmetry elements (e.g., 1,5-sigmatropic shifts and ene reactions). For this reason, the Woodward–Hoffmann, Fukui, and Dewar–Zimmerman analyses are equally broad in their applicability, though a certain approach may be easier or more intuitive to apply than another, depending on the reaction one wishes to analyze. The Woodward–Hoffmann rules were first invoked to explain the observed stereospecificity of electrocyclic ring-opening and ring-closing reactions at the ends of open chain conjugated polyenes either by application of heat (thermal reactions) or application of light (photochemical reactions).