Frontier orbital scheme

Both the reactivity data in Tables 11.3 and 11.4 and the regiochemical relationships in Scheme 11.3 ean be understood on the basis of frontier orbital theory. In reactions of types A and B illustrated in Seheme 11.3, the frontier orbitals will be the diene HOMO and the dienophile LUMO. This is illustrated in Fig. 11.12. This will be the strongest interaction because the donor substituent on the diene will raise the diene orbitals in energy whereas the acceptor substituent will lower the dienophile orbitals. The strongest interaction will be between j/2 and jc. In reactions of types C and D, the pairing of diene LUMO and dienophile HOMO will be expected to be the strongest interaction because of the substituent effects, as illustrated in Fig. 11.12. 

Photoelectron spectra have confirmed the expected trends in the frontier orbitals.The tetrafiuoro derivative 12.12 (R = F) is prepared by treatment of C6F5SNSNSiMc3 with CsF in acetonitrile (Scheme 12.2). Several difiuoro- and trifiuoro-benzodithiadiazines have also been prepared by these methods.In contrast to 12.12 (R = H), which has an essentially planar structure in the solid state,the dithiadiazine ring in the tetrafiuoro derivative is somewhat twisted. In the gas phase, on the other hand, electron diffraction studies show that 12.12 (R = F) is planar whereas 12.12 (R = H) is non-planar. ... 

The type of conjugation is also reflected in the frontier orbital profile, the charge distribution, and the permanent dipole moments. The results of semiempirical calculations on l-methylpyridinium-3-olate (16), Malloapeltine (17), Trigollenine (18), and Homarine (19) are presented in Scheme 7. Characteristically for the class of conjugated mesomeric betaines, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are distributed over the entire molecule as examplifled for l-methylpyridinium-3-olate. It was shown that 90% of the... 

The shifting of electrons as shown in the scheme should be taken as a simplified depiction only. A more thorough understanding follows from consideration of the frontier orbitals and their coefficients this may then permit a prediction of the regiochemical course of the cycloaddition. 

The frontier orbital theory [7-9] assumes that the stabihzation by the electron delocalization could control chemical reactions. The stabilization comes from the interactions between the occupied molecular orbitals of one molecule and the unoccupied molecular orbitals of another (Sect. 1.4). The strong interaction occurs when the energy gap is small (Sect. 1.3). The HOMO and the LUMO are the closest in energy to each other. The HOMO-LUMO interaction, especially the interaction between the HOMO of electron donors and the LUMO of electron acceptors, controls the chemical reactions (Scheme 20). The HOMO and the LUMO are termed the frontier orbitals. ... 

The amplitude of the frontier orbitals determines the selectivity. The most reactive atom in a molecule has the largest amplitude of the frontier orbitals. The frontier orbitals overlap each other to the greatest extent at the sites with the largest amphtudes. Reactions occur on the atoms in the electron donors and acceptors, where the HOMO and LUMO amplitudes are largest, respectively. Electrophiles prefer the a position of naphthalene, an electron donor, with the larger HOMO amplitude (Scheme 21). Nucleophiles attack the carbons of the carbonyl groups, an electron acceptor, with the larger LUMO amplitude (Scheme 7). 

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

Scheme 24 The symmetry-allowed frontier orbital interaction for the Diels-Alder reactions...

Scheme 25a,b The symmetry-forbidden (a) and -free (b) frontier orbital interactions for the dimerization of ethylenes... 

The frontier orbital interaction is forbidden by the symmetry for the dimerization of ethylenes throngh the rectangular transition state. The HOMO is symmetric and the LUMO is antisymmetric (Scheme 25a). The overlap integrals have the opposite signs at the reaction sites. The overlap between the frontier orbitals is zero even if each overlap between the atomic p-orbitals increases. It follows that the dimerization cannot occur throngh the fonr-membered ring transition states in a concerted and stereospecfic manner. 

The frontier orbital interaction can be free from the symmetry restriction. A pair of the reaction sites is close to each other while the other pair of the sites is far from each other (Scheme 25b). This is the geometry of the transition state leading to diradical intermediates. 

The frontier orbital interactions at other than reaction sites can determine the selectivity [14]. The interaction between the HOMO of cyclopentadiene and the LUMO of maleic anhydride is illustrated in Scheme 26. The HOMO of cyclopentadiene has the same phase property as butadiene (Scheme 18). The LUMO of maleic anhydride is an in-phase combined orbital of and transition state for the... 

A radical has a singly occupied molecular orbital (SOMO). This is the frontier orbital. The SOMO interacts with HOMO and the LUMO of closed-shell molecules to stabilize the transition state (Scheme 27). The radical can be a donor toward a monomer with low LUMO or an acceptor toward one with high HOMO. 

Scheme 27 Frontier orbital interaction in the radical reactions...

The alkene with the electron donating group has the HOMO (n) raised by the interaction with the occupied orbital of the substiment. The low-lying SOMO (n ) interacts with the HOMO of the alkene more effectively. The frontier orbital interaction is the interaction (Scheme 30b), which is impossible at the four-membered... 

Molecules have some occupied and some unoccupied orbitals. There occur diverse interactions (Scheme 1) when molecules undergo reactions. According to the frontier orbital theory (Sect 3 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume), the HOMO d) of an electron donor (D) and the LUMO (fl ) of an electron acceptor (A) play a predominant role in the chemical reactions (delocalization band in Scheme 2). The electron configuration D A where one electron transfers from dio a significantly mixes into the ground configuration DA where... 

Scheme 2 Change of the frontier orbital interactions with the power of donors and acceptors...

With the power of the donors and acceptors, changes occur in the important frontier orbital interactions (Scheme 2) and in the mechanism of chemical reactions. The continuous change forms a mechanistic spectrum composed of the delocalization band to pseudoexcitation band to the electron transfer band. 

Reduced nicotinamide-adenine dinucleotide (NADH) plays a vital role in the reduction of oxygen in the respiratory chain [139]. The biological activity of NADH and oxidized nicotinamideadenine dinucleotide (NAD ) is based on the ability of the nicotinamide group to undergo reversible oxidation-reduction reactions, where a hydride equivalent transfers between a pyridine nucleus in the coenzymes and a substrate (Scheme 29a). The prototype of the reaction is formulated by a simple process where a hydride equivalent transfers from an allylic position to an unsaturated bond (Scheme 29b). No bonds form between the n bonds where electrons delocalize or where the frontier orbitals localize. The simplified formula can be compared with the ene reaction of propene (Scheme 29c), where a bond forms between the n bonds. 

The n orbital amplitudes of ethene are identical on both carbons. Unsymmetrical substitutions polarize the n orbital. Electron acceptors or electrophiles attack the carbon with the larger r amplitude. The polarization of frontier orbitals is important for regioselectivities of reactions. Here, mechanism of the n orbital polarization of ethene by methyl substitution [4] is described (Scheme 5). 

The electrostatic mixing by the positive charge polarizes rin the same direction (Scheme 12b, cf. Scheme 8a), possibly more significantly than the overlap mixing. The n orbital is the frontier orbital. The proton attacks on C. The regioselectivity is reversed. 

Scheme 17 The polarized frontier orbitals determine the regioselectivity...

The most reactive site of the diene part is Cj of the cyclohexadienone ring with the alkoxy gronp. This corresponds to Cj of 2-alkoxybutadiene (Scheme 15), which has the largest HOMO amplitnde. The preferable frontier orbital interactions (Scheme 22) are in agreement with the reversed regioselectivities. 

Scheme 22 Preferable frontier orbital interactions reversing the regioselectivities...

The frontier orbital theory was developed for electrophilic aromatic substitution (Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). Application is successful to the ortho-para orientation (Scheme 23a) for the benzenes substituted with electron donating groups. The ortho and para positions have larger HOMO amplitudes. The meta orientation (Scheme 23b) for the electron accepting groups is under control of both HOMO and the next HOMO [25]. 

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