Orbital Mixing Rules

p-Xylene Formation by Dehydrative Aromatization of a Diels–Alder Product in Lewis and Brønsted Acidic Zeolites

“…This lack of correlation does not imply that FMO fails in this instance, but rather that additional second-order–and possibly higher-order terms–in Fukui’s perturbative expansion of the energy and wave function must be considered. − Indeed, we have found that the calculated activation energies are better captured by the expression italicE normala = italica 0 + italica 1 / italicx + italica 2 / italicy where x = HOMO D –LUMO A and y = LUMO D –HOMO A ; the subscript D (A) stands for electron donor (acceptor). In FMO language, the terms x and y correspond to single-excitation configuration interaction contributions to the total wave function.…”

“…In the transition state, the π bond will be delocalized between the two moieties, and the orbital that describes this delocalization is mostly the superposition of the π in the dienophile (its HOMO) and the π 1 * + π 2 * in the diene (its LUMO); the y -term in eq captures this very contribution. A rigorous, theoretical justification for the inclusion of this term can be found in Fukui’s mathematical formulation of the FMO theory; , a more intuitive but equally illuminating discussion can be found in Woodward and Hoffmann’s seminal paper on the conservation of orbital symmetry . In the zeolite, the y -term is comparable in magnitude to the x -term and thus cannot be neglected.…”

Electrocatalytic Methane Functionalization with d0 Early Transition Metals Under Ambient Conditions

“…We propose that the electrochemically generated d 0 ‐M‐L ⋅+ intermediate is partly stabilized by the orbital delocalization between the metal's d orbitals and the radical‐bound O 2p orbital [7] . A corollary of this hypothesis is that a smaller energy difference between the metals’ d orbital and O 2p one in d 0 ‐M‐L ⋅+ warrants a more effective orbital delocalization, [20] a more stable d 0 ‐M‐L ⋅+ once electrochemically generated, and a larger probability of CH 4 activation despite CH 4 ′s limited solubility before the deactivation of d 0 ‐M‐L ⋅+ due to detrimental side reactions. As the energy differences between metals’ 3d (−9.2 to −10.7 eV) and O 2p (−15.8 eV) orbitals are appreciably smaller than that for 4d metals (−8.3 to −9.1 eV) and even smaller than 5d metals (−6.1 to −8.7 eV) (Table S3), the proposed mechanism predicts decreasing CH 4 ‐activating activities when the metal in d 0 ‐M‐L ⋅+ intermediate changes from Period 4 to Period 6, consistent with our experimental observation (Figure 4).…”