Phase, orbital

The same conclusion may again be reached by considering only the HOMO orbital. Figure 15.24. For the conrotatory path the orbital interaction leads directly to a bonding orbital, while the orbital phases for the disrotatory motion lead to an anti-bonding orbital. 

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... 

We have learned the interactions of the same orbitals and chemical bonds between the same atoms. The orbital phase plays a crucial role in the energies and the spacial extensions of the bond orbitals. Here we learn interactions of different orbitals and amplitude of orbitals, using an example of polar bonds between different atoms. 

Scheme 26 Endo-selectivity of the Diels-Alder reactions and orbital phase environments...

Another theory as an important element of the chemical orbital theory is an orbital phase theory for cyclic interactions of more than two orbitals. The cyclic orbital interactions are controlled by the continuity-discontmuity of orbital phase [21-23]. 

The orbital phase theory includes the importance of orbital symmetry in chanical reactions pointed out by Fukui [11] in 1964 and estabhshed by Woodward and Holiimann [12,13] in 1965 as the stereoselection rule of the pericyclic reactions via cyclic transition states, and the 4n + 2n electron rule for the aromaticity by Hueckel. The pericyclic reactions and the cyclic conjugated molecules have a conunon feature or cychc geometries at the transition states and at the equihbrium structures, respectively. 

In 1982 the present author discovered cyclic orbital interactions in acyclic conjugation, and showed that the orbital phase continuity controls acyclic systems as well as the cyclic systems [23]. The orbital phase theory has thus far expanded and is still expanding the scope of its applications. Among some typical examples are included relative stabilities of cross vs linear polyenes and conjugated diradicals in the singlet and triplet states, spin preference of diradicals, regioselectivities, conformational stabilities, acute coordination angle in metal complexes, and so on. 

The orbital phase theory and its applications are reviewed in Chapter An Orbital Phase Theory . 

Keywords Cycloadditions, Chemical orbital theory. Donor-acceptor interaction. Electron delocalization band. Electron transfer band, Erontier orbital. Mechanistic spectrum, NAD(P)H reactions. Orbital amplitude. Orbital interaction. Orbital phase. Pseudoexcitation band. Quasi-intermediate, Reactivity, Selectivity, Singlet oxygen. Surface reactions... 

Scheme 12 Orbital phase environment in the EHels-Alder reactions of acetylenic aldehydes exo-selectivity...

Keywords Orbital mixing. Orbital amplitude. Orbital phase. Orbital polarization. Orbital deformation, Regioselectivity, Stereoselectivity, n Facial selectivity... 

Scheme 3c, d illustrates the orbital phase relation when (j) has (j) mix. An orbital energy level according to the theory of two-orbital interaction. The orbital lies below (j>. 

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. 

Bonds interact with one another in molecules. The bond interactions are accompanied by the delocahzation of electrons from bond to bond and the polarization of bonds. In this section, bond orbitals (bonding and antibonding orbitals of bonds) including non-bonding orbitals for lone pairs are shown to interact in a cychc manner even in non-cychc conjugation. Conditions are derived for effective cychc orbital interactions or for a continuous orbital phase. 

The electron delocalizations in the linear and cross-conjugated hexatrienes serve as good models to show cyclic orbital interaction in non-cyclic conjugation (Schemes 2 and 3), to derive the orbital phase continuity conditions (Scheme 4), and to understand the relative stabilities (Scheme 5) [15]. 

Scheme 4 Conditions tor the continuity of orbital phase ( ) electron accepting orbitals are in phase.

Here we derive the conditions of orbital phase for the cyclic orbital interactions. The A B delocalization is expressed by the interaction between the ground configuration C Q and the electron-transferred configuration tBp(A B) (Scheme 3). A pair of electrons occupies each bonding orbital in which is expressed by a single Slater determinant 0 ... 

The plus and minus signs imply that electrons accumulate in the overlap region when the orbitals are combined in phase and out of phase, respectively. The cyclic orbital interaction gives rise to stabilization when the orbitals between a and b, between b and c, and between b and c are combined in phase and when a and b are combined out of phase. These are the orbital phase conditions for the A—>C delocalization in the trienes. When all the phase conditions are simultaneously satisfied, the orbital phase is continuous. 

The orbital phase continuity conditions are summarized in Scheme 4. Cyclic orbital interactions give rise to stabilization when the orbitals simultaneously satisfy the following conditions ... 

The orbital phase continuity conditions stem from the intrinsic property of electrons. Electrons are fermions, and are described by wavefnnctions antisymmetric (change plus and minus signs) with respect to an interchange of the coordinates of an pair of particles. The antisymmetry principle is a more fnndamental principle than Pauli s exclusion principle. Slater determinants are antisymmetric, which is why the overlap integral between t(a c) given above has a negative... 

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