Abstract
Both Fukui's frontier orbital (FO) theory and Woodward–Hoffmann's orbital symmetry conservation (W–H) theory are based on the molecular orbital theory. However, there are some obvious inconsistencies between the two theories in explaining the electron movement. The process of chemical reactions has been explained by the potential surface analysis based on the time-independent Schrödinger equation. However, this approach is not always appropriate for describing unsteady states, because the variable of reaction coordinate should be time t by its very nature. When considering the time-scale of chemical reactions for molecules, there is inherent uncertainty in the energy levels for the midway state of chemical reactions owing to the Heisenberg uncertainty principle. The states which can be accurately described by quantum mechanics exist discontinuously in chemical reactions. Such quantization of chemical reactions solves all noncrossing problems. We also show that such an essential fact leads to new concepts and theories in chemical reactions such as stable molecule, elementary reaction and minimum deformation of orbital phases. Finally, taking the regularity in organic reactions as an example, we demonstrate that FO theory and W–H theory can be unified consistently by the universally applicable "dynamic correlation diagram method."
Highlights
Since we are no longer restrained by the noncrossing rule, we propose the new concept of dynamic correlation diagrams that are drawn according to the idea of minimum deformation of molecular orbitals, which assume that the change of molecular orbital in elementary reactions proceeds with the least deformation
It has been more than 40 years since frontier orbital (FO) theory and WÀH theory was first held in high esteem
There is the criticism that FO theory cannot explain how molecular orbitals transform from the reactants to products except for the frontier orbitals.[50]
Summary
Fukui and Hoffman were awarded a Nobel Prize in 1981 for their pioneering theories which explain the regularity in organic reactions.1À6 there are obvious inconsistencies between frontier orbital (FO) theory and WoodwardÀHoffmann’s (WÀH) correlation diagram method, e.g., a contradiction of the electron movement in explaining the DielsÀAlder reaction of butadiene with ethylene.2,5À7 it has been pointed out that orbital correlation diagrams, regarded as an advanced application of the diatomic correlation diagram by Hund[8] and Mulliken[9] to organic reactions, are the foundation of WÀH rules, proper orbital correlation diagrams cannot be drawn for many reactions by WÀH’s method.[10]. Our concept remains unaccepted to this day, probably owing to traditional beliefs in both the BO approximation and the noncrossing rule. Nonadiabatic transition[19] has attracted much attention in the field of quantum chemistry and the limitation of the BO approximation has been pointed out.[20,21] Such non-BO quantum chemistry has indicated that the noncrossing problem is explained by the concept of \natural correlation or natural crossing,"22À25 \conical intersection"26À30 and/or \nonadiabatic transition."[20] when considering the time-scale of chemical reactions for molecules, there is inherent uncertainty in the energy levels for the midway state of chemical reactions owing to the Heisenberg uncertainty principle. We demonstrate the universal applicability of \the dynamic correlation diagram method."
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