Orbital energy variations provide a physical basis for the Woodward-Hoffmann rules

Reactive orbital energy theory (ROET), an orbital-energy-based electronic-structure framework, elucidates the electron motions that drive pericyclic reactions and helps clarify the orbital-energy basis of WH-type stereoselectivity. For WH-allowed electrocyclic reactions, symmetry-conserving pathways are favored because the occupied reactive orbital (ORO) is strongly stabilized in the vicinity of the transition state, thereby lowering the barrier. This stabilization is correlated with symmetry-allowed occupied-occupied crossings between nearby occupied orbitals of different symmetry, which preserve the character of the ORO and facilitate the dominant occupied-virtual response. By contrast, in WH-forbidden pathways, a HOMO-LUMO crossing near the transition state is associated with an electrostatic force opposite to the reaction direction, thereby increasing the barrier. For the non-electrocyclic reactions examined here, ROET reveals that cycloadditions are driven by electron transfer from diene π orbitals. On the other hand, for the propylene-ethylene ene reaction, ROET shows that hydrogen migration is accompanied by redistribution of the ethylene-derived π component of the ORO into the developing σ-bonding framework. For many of the reactions examined here, the pericyclic step can be rationalized in terms of constructive orbital overlap within the ORO, whereas the sigmatropic rearrangements, including the Claisen rearrangement and hydrogen shifts, require consideration of additional occupied orbitals that exert large reaction-driving electrostatic forces near the TS. ROET thus provides an energetically grounded perspective that clarifies the origin of WH-type stereoselectivity in the electrocyclic reactions examined here and offers a common interpretive framework for the other pericyclic classes analyzed in this study.