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If I understand correctly Frontier MO-theory is based on the perturbation theory of reactivity and the Woodward-Hoffmann rules consider conservation of orbital symmetry.

Does FMO use symmetry considerations?

Do the Woodward-Hoffman rules consider differences in HOMO/LUMO energies?

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    $\begingroup$ There are no orbital phases in the W-H approach. $\endgroup$
    – EJC
    Jul 26, 2016 at 21:44

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The FMO approach, based on perturbation theory, focuses on analyzing the relative energies and populations of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). It predicts that reactions are most favorable when the attacking species interacts with the region of highest electron density, which corresponds to the HOMO of the reacting molecule. Symmetry considerations are not a central aspect of FMO theory.

The Woodward-Hoffmann rules are rooted in the conversation of orbital symmetry. They provide guidelines for understanding the stereospecificity and regioselectivity of pericyclic reactions. For example electrocyclizations and [2+2] cycloadditions. These rules consider the symmetries of the orbitals involved in the reaction, specifically the frontier orbitals (HOMO & LUMO), and predict whether a given reaction is allowed or forbidden based on the conservation of these symmetries.

Regarding your second question, the Woodward-Hoffman rules do not directly consider differences in HOMO/LUMO energies. Instead, they focus of the symmetry of the frontier orbitals and their overlap in the reacting system to determine the feasibility of a particular pericyclic reaction. Please note that while both FMO theory and the Woodward-Hoffmann rules provide insights into chemical reactivity, they approach the topic from different perspectives and use different applications.

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