Orbital mixing rules

Keywords Chemical orbital theory. Electron delocalization. Frontier orbital. Orbital amplitude, Orbital energy, Orbital interaction. Orbital mixing rule, Orbital phase, Orbital phase continuity, Orbital phase environment. Orbital synunetry, Reactivity, Selectivity... 

The orbital mixing rules are described in detail and shown to be powerful for understanding and designing selective reactions in Chapter Orbital Mixing Rules and applied in chapter ji-Facial Selectivities of Diels-Alder reactions . 

Orthogonal orbitals and ( ) are mixed with each other by nearby electric charges [3]. Electrostatic orbital mixing rules state ... 

According to the frontier orbital theory, a bond preferentially forms between the atoms with the largest frontier orbital amplitudes (Sect. 3.4 in the Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). This is applicable for the regioselectivities of Diels-Alder reactions [15]. The orbital mixing rules are shown here to be useful to understand and design the regioselectivities. 

The orbital mixing rules are applied to the polarization of 7t of ethene by a C=0 group on the assumption that is lowered below The 7t orbital has mix in phase and the low lying tc orbital mix out of phase with (Scheme 16). As a result, the phase relation between t( and n is fixed. The amplitude is larger on C than on C and the carbonyl carbon. 

Ohwada and Shudo [26] showed that the regioselectivity of the nitrations was reversed by a remote carbonyl group (Scheme 27). The 4-position is more reactive than the 2-position. The reversed selectivity is explaned by the orbital mixing rules. The orbitals closest in energy to the HOMO are the next HOMO (NHOMO), i.e.. 

The orbital mixing theory was developed by Inagaki and Fukui [1] to predict the direction of nonequivalent orbital extension of plane-asymmetric olefins and to understand the n facial selectivity. The orbital mixing rules were successfully apphed to understand diverse chemical phenomena [2] and to design n facial selective Diels-Alder reactions [28-34], The applications to the n facial selectivities of Diels-Alder reactions are reviewed by Ishida and Inagaki elesewhere in this volume. Ohwada [26, 27, 35, 36] proposed that the orbital phase relation between the reaction sites and the groups in their environment could control the n facial selectivities and review the orbital phase environments and the selectivities elsewhere in this volume. Here, we review applications of the orbital mixing rules to the n facial selectivities of reactions other than the Diels-Alder reactions. 

Okada and Mukai [48] showed a preference for a contrasteric approach of singlet oxygen to anti face of 7-isopropylidene double bond in photooxidation of 7-isopropylidenenorbomene followed by reduction with dimethyl sulfide (Scheme 32). They explained the stereoselectivity by applying the orbital mixing rules (Scheme 33). The r orbital of the exocyclic double bond enlarges its extention in the anti face. 

The HOMO is an out-of-phase combination of the n orbitals of the exo- and endocyclic double bonds. According to the orbital mixing rules, the n orbital of the exocyclic double bond has the low-lying exocyclic a orbital out of phase with the... 

Fukui [51] predicted the deformation of the LUMO of cyclohexanone by the orbital mixing rule [1,2] and explained the origin of the % facial selectivity of the reduction of cyclohexanone. Tomoda and Senju [52] calculated the LUMO densities on the... 

The orbital mixing rules and their chemical consequences have been ongoing for more than 30 years and have provided impact on the studies of molecular properties and chemical reactions [53-56],... 

Steric repulsions come from two orbital-four electron interactions between two occupied orbitals. Facially selective reactions do occur in sterically unbiased systems, and these facial selectivities can be interpreted in terms of unsymmetrical K faces. Particular emphasis has been placed on the dissymmetrization of the orbital extension, i.e., orbital distortions [1, 2]. The orbital distortions are described in (Chapter Orbital Mixing Rules by Inagaki in this volume). Here, we review the effects of unsymmetrization of the orbitals due to phase environment in the vicinity of the reaction centers [3]. 

Keywords it-Facial selectivity, a/ir Interaction, CH/ir Interaction, Ciplak effect, Diels-AIder reaction, Electrostatic interaction, Orbital mixing rule. Orbital phase environment, Secondary orbital interaction, Steric repulsion, Torsional control... 

Deformation of Frontier Molecular Orbital (Orbital Mixing Rule)... 

Inagaki, Fujimoto and Fukui demonstrated that ir-facial selectivity in the Diels-Alder reaction of 5-acetoxy- and 5-chloro-l,3-cyclopentadienes, 1 and 2, can be explained in terms of deformation of a frontier molecular orbital FMO [2], The orbital mixing rule was proposed to predict the nonequivalent orbital deformation due to asymmetric perturbation of the substituent orbital (Chapter Orbital Mixing Rules by Inagaki in this volume). 

The orbital mixing rule demonstrates that the direction of the FMO extension is controlled by the relative energies of the Jt-HOMO (ej and the n-orbital of X (8 ). In the case of 5-acetoxy- and 5-chloro-l,3-cyclopentadienes, the jt-HOMO lies higher than n (e > ej. In this case, the ji-HOMO mainly contributes to the HOMO of the whole molecule by an out-of-phase combination with the low-lying n. The mixing of a-orbital takes place so as to be out-of-phase with the mediated orbital n. The HOMO at Cl and C4 extends more and rotates inwardly at the syn face with... 

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