Orbital phase theory

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 . 

The orbital phase theory has been developed for the triplet states [19]. The orbital phase continuity conditions (Scheme 4) were shown to be applicable. We describe here, for example, the triplet states of the TMM and BD diradicals, with three a spin electrons and one 3 spin electron. The a and 3 spins are considered separately (Scheme 8). 

The orbital phase theory is applicable to the singlet diradicals [20]. The electron configuration of the singlet states of the cross- (TMM) and linear (BD) conjugate diradicals is shown in Scheme 9, where the mechanism of the delocalization of a and P spins between the radical centers through the double bond are separately illustrated by the arrows. The cyclic [-a-Tr-b-T -] interaction is readily seen to occur for the spin delocalizations. The p orbital a) in one radical center and the n orbital are occupied by a spins, and therefore, electron-donating orbitals. The p orbital (b) in the other radical center and the ii orbital are not occupied by a spins. 

A part of the chemical consequences of the cyclic orbital interactions in the cyclic conjngation is well known as the Hueckel rule for aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions [14]. In this section, we describe the basis for the rnles very briefly and other rules derived from or related to the orbital phase theory. The rules include kinetic stability (electron-donating and accepting abilities) of cyclic conjugate molecules (Sect. 2.2.2) and discontinnity of cyclic conjngation or inapplicability of the Hueckel rule to a certain class of conjngate molecnles (Sect. 2.2.3). Further applications are described in Sect. 4. 

The orbital phase theory can be applied to cyclically interacting systems which may be molecules at the equilibrium geometries or transition structures of reactions. The orbital phase continuity underlies the Hueckel rule for the aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions. 

The finding of the cyclic orbital interactions in non-cyclic conjugation opens a way to systematic understanding and designing of molecules and reactions in a unified manner. Here, we apply the orbital phase theory to non-cychc interactions of bonds, groups, molecules, cationic, anionic, and radical centers, lone pairs, etc. 

Here, the orbital phase theory sheds new light on the regioselectivities of reactions [29]. This suggests how widely or deeply important the role of the wave property of electrons in molecules is in chemistry. 

The orbital phase theory can be applied to the thermodynamic stability of the disubstituted benzene isomers. The cyclic orbital interaction in the benzene substituted with two EDGs is shown in Scheme 21. The orbital phase is continuous in the meta isomer and discontinuous in the ortho and para isomers (Scheme 22, cf. Scheme 4). 

The orbital phase theory was applied to the conformations of alkenes (a- and P-substituted enamines and vinyl ethers) [31] and alkynes [32], The conformational stabilities of acetylenic molecules are described here. 

From the orbital phase theory an outstanding electron-donating (accepting) bond toward both the C-H and C-C bonds is predicted to prefer as long sequential conjugation of mutually antiperiplanar bonds as possible. The electron delocalization... 

Stability of diradicals is important for photochemical reactions. Spin multiplicity of the ground states is critical for the molecular magnetic materials. The relative stability of singlet (triplet) isomers and the spin multiplicity of the ground states (spin preference) [48] has been described to introduce the orbital phase theory in Sects. 2.1.5 and 2.1.6. Applications for the design of diradicals are reviewed by Ma and Inagaki elsewhere in this volume. Here, we briefly summarize the applications. 

Bicyclic localized singlet 1,3-a-diradicals were theoretically designed by the orbital phase theory (Scheme 28c) [54]. 

Matrix isolation spectroscopy showed that the major product of the condensation of A1 and CO was not AlCO but AlfCOj [61, 62], Theoretical studies suggested that the C-Al-C angle in AlfCOj [63] and the C-Si-C angle in SifCOj [64] should be unusually acute (Scheme 29a). The orbital phase theory accounts for the acute coordination angles and the stabihty of AlfCOj relative to AlCO [65],... 

Orbitals interact in cyclic manners in cyclic molecules and at cyclic transition structures of chemical reactions. The orbital phase theory is readily seen to contain the Hueckel 4n h- 2 ti electron rule for aromaticity and the Woodward-Hof nann mle for the pericyclic reactions. Both rules have been well documented. Here we review the advances in the cyclic conjugation, which cannot be made either by the Hueckel rule or by the Woodward-Hoffmann rule but only by the orbital phase theory. 

Interactions of vicinal bonds have been extensively studied and are well known as hyperconjugation, resonance, and others [89-91], The a bonds vicinal to a reacting 71 bond have been proposed to participate in organic reactions and to control the selectivity [92, 93], Recently, we noticed the importance of the participation of the a bonds geminal to a reacting % bond (Scheme 35) [94] and have made extensive applications [95-102], Here, we present an orbital phase theory for the geminal bond participation and make a brief review. 

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