Frontier Molecular Orbital FMO Theory

According to frontier molecular orbital theory (FMO), the reactivity, regio-chemistry and stereochemistry of the Diels-Alder reaction are controlled by the suprafacial in phase interaction of the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied molecular orbital (LUMO) of the other. [17e, 41-43, 64] These orbitals are the closest in energy Scheme 1.14 illustrates the two dominant orbital interactions of a symmetry-allowed Diels-Alder cycloaddition. 

These relations highlight the fact that the formalism of DFT-based chemical reactivity built by Parr and coworkers, captures the essence of the pre DFT formulation of reactivity under frontier molecular orbital theory (FMO). Berkowitz showed that similar to FMO, DFT could also explain the orientation or stereoselectivity of a reaction [12]. In addition, DFT-based reactivity parameters are augmented by more global terms expressed in the softness. 

A fundamental understanding of the mechanistic and stereochemical aspects of the Diels-Alder reaction was unfolded during the 1970s. Several theoretical approaches are available nowadays from which Fukui s Frontier Molecular Orbital theory (FMO theory) is most frequently used because of its simplicity49- 53. 

According to the frontier molecular orbital theory (FMO) of chemical reactivity, the formation of a transition state is due to an interaction between the frontier orbitals, such as HOMO and LUMO of reacting species. In general, the important frontier orbitals for a nucleophile reacting with an electrophile are HOMO (nucleophile) and LUMO (electrophile). 

According to the frontier molecular orbital theory (FMO theory), the reactivity of a 1,3-dipole is inversely proportional to the energy difference between the frontier orbitals of a 1,3-dipole and a dipolarophile. The frontier orbital energies of the parent azomethine ylide 110 are calculated by a CNDO/2 method to be highest occupied molecular orbital (HOMO) =... 

A variety of molecular descriptors have been defined and used proceeding from frontier molecular orbital theory (FMO) of chemical reactivity [42]. This theory is based on the concept of the superdelocalizability, an index characterizing the affinity of occupied and unoccupied orbitals in chemical reactions. A distinction has been made between the electrophilic and the nucleophilic superdelocalizability (or acceptor and donor superdelocalizability), respectively. The former describes the interaction of... 

These reactivity trends clearly show that polar effects are involved in these radical substitution reactions. The transition state is thought to include a charge transfer 9) from the radical (electron donor) to the pyridinium ion (electron acceptor) [13], Frontier Molecular Orbital Theory (FMO) [14] has been applied to explain the reactivity differences which have been observed upon varying the substituents at the pyridinium ion and upon altering the nucleophilicity of the attacking radical. Moreover, FMO can be used to explain the regioselectivities obtained in these homolytic aromatic substitutions. The LUMO of the substituted pyridinium cation... 

The Bradsher reaction is formally a [4 + 2] Diels-Alder reaction. However, as a consequence of the aza cationic nature of the diene, this reaction proceeds by the inverse electron demand manifold. The classical Diels-Alder reaction employs the partnering of an electron-rich diene and an electron-deficient dienophile to provide the proper interaction of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) as prescribed by frontier molecular orbital theory (FMO) to generate the observed adducts. Thus FMO theory interprets this reaction proceeding via the HOMO of the diene with the LUMO of the dienophile. In the case of the inverse electron demand reaction, the electronics of the reaction are inverted. Therefore, in the Bradsher reaction, the electron-deficient aza cation diene s LUMO interacts with the HOMO of an electron rich dienophile. This mechanistic pathway provided a rationalization for the lack of reactivity of the electron-deficient tetracyanoethylene (TCNE), while electron-rich styrenes afforded the predicted product from reaction of 1 to generate 2. ... 

Throughout this book we have often referred to the importance of the HOMO and LUMO in understanding a molecule s properties. Fukui reasoned that these frontier molecular orbitals might play an especially important role in concerted, pericyclic reactions. We have also noted before that it is always favorable to mix filled molecular orbitals wi th empty molecular orbitals. Combining these ideas led to frontier molecular orbital (FMO) theory, an elegant analysis of the types of reactions of importance here. Quite simply, frontier molecular orbital theory states that if we can achieve a favorable mixing between the HOMO of one reactant and the LUMO of another reactant, a reaction is allowed. If we cannot, the reaction is forbidden. 

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

The importance of FMO theory hes in the fact that good results may be obtained even if the frontier molecular orbitals are calculated by rather simple, approximate quantum mechanical methods such as perturbation theory. Even simple additivity schemes have been developed for estimating the energies and the orbital coefficients of frontier molecular orbitals [6]. 

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

Aceording to Frontier Molecular Orbital (FMO) theory, thiophene s most reactive site can be identified by examining the shape of its highest-occupied molecular orbital (HOMO). Which atoms contribute to thiophene s HOMO Which atom(s) contributes the most Which nitration product should form preferentially ... 

According to Frontier Molecular Orbital (FMO) theory, Diels-Alder reaction between an electron-rich diene and an electron-poor dienophile involves interaction between the highest-occupied molecular orbital (HOMO) on the diene and the lowest-unoccupied molecular orbital (LUMO) on the dienophile. The better the HOMO/LUMO overlap and the smaller their energy difference, the more favorable the interaction and the faster the reaction. 

Frontier molecular orbital (FMO) theory 62) has provided new insights into chemical reactivity. This, and the simplicity of its application, has led to its widespread use, particularly in the treatment of pericyclic reactions 63). An FMO treatment depends on the energy of the highest occupied (HOMO) and lowest unoccupied molecular... 

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