Frontier Molecular Orbitals FMO

Highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) are frontier molecular orbitals. They are different for different olefins as well as depend upon species, i.e., whether it is cation, free radical or anion. For example  

As already discussed pericyclic reactions take place under thermal as well as photochemical conditions and stereochemistry of products generally differs under these two conditions. It is also well known that out of possible stereoisomers a particular stereomer is more active than other or one have activity and other does not. Hence, prediction about the fact that which stereoisomer will form under which condition is important for the preparation of particular isomer, which, is important from the point of view of its applications. There are three different approaches to predict conditions for a particular pericyclic reaction which are  

First method takes into account S3mametry properties of reactants and products second is based upon FMOs but in third forecasts can be made without considering symmetries of molecular orbitals. 

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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 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. ... 

Perfluoroalkyl groups adjacent to multiple bond systems lower the frontier molecular orbitals (FMOs) Therefore, cycloaddition reactions preferentially occur with electron-rich multiple-bond systems The preference of bis(trifluoromethyl)-substituted hetero-l,3-dienes for polar reacuons makes them excellent model compounds for developing new types of diene reactions deviating from the well documented Diels-Alder scheme (pathway 1) A systematic study of the reactions of diene (1 =2-3=4)-dienophile (5=6) combinations reveals new synthetic possibilities that have not yet been fully exploited as tools for preparative organic cherrustry (equation 25)... 

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. 

A theoretical study based on PM3 frontier molecular orbital (FMO) and potential energy surface (PES) analysis at the RHF/6-31-I-G level was performed to examine the reaction of l-amino-2-ethoxycarbonylpyridinium mesitylenesulfonate and acrylonitrile in the presence of Hiinig s base leading to the formation of 3-cyano-4-hydroxy-l,2-dihydropyrido[l,2-ft]pyridazi-nium inner salt (54) (99JOC9001). The calculations indicated that both the... 

One cannot discuss Lewis acid-catalyzed cycloaddition reactions in the present context without trying to understand the reaction course mechanistically, e.g. using a frontier molecular orbital (FMO) point of reasoning, or theoretical calculations of transition state structures. 

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). 

Apeloig and Kami (13) have also studied the effects of substituents on the reactivity of silenes by the frontier molecular orbital (FMO) approach. They have concluded that, concerning electronic factors, the polarity of the carbon-silicon double bond, and thus the coefficients of the frontier orbitals, play a more important role than the energies of these orbitals in controlling the reactivity of silenes. 

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... 

When ene-nitrile oxidoisoquinolium betaine 131 was heated as a dilute solution in toluene to 120 °C (Scheme 1.15), near quantitative conversion to the cycloadduct 133, resulting from the undesired regioselectivity, was observed. While the near complete conversion to cycloadduct 133 of oxidoisoquinolinium betaine 131 indeed demonstrated complete avoidance of the conjugate addition pathway in favor of cycloaddition, initial production of undesired isomeric cycloadduct 133 (instead of 136) was disappointing. Notably, cycloadduct 133 is expected to be less kinetically favored based on frontier molecular orbital (FMO) analysis (assuming dipole HOMO-controlled cycloaddition) of the putative transition state. This result stands in contrast to the cycloaddition of nitroalkene oxidoisoquinolinium betaine... 

Based on the foregoing discussion, one might suppose that the Fukui function is nothing more than a DFT-inspired restatement of frontier molecular orbital (FMO) theory. This is not quite true. Because DFT is, in principle, exact, the Fukui function includes effects—notably electron correlation and orbital relaxation—that are a priori neglected in an FMO approach. This is most clear when the electron density is expressed in terms of the occupied Kohn-Sham spin-orbitals [16],... 

Doyle et al. (39) expanded the rhodium-catalyzed generation of isomiinchnones from diazoacetacetamides and subsequent trapping with dipolarophiles (38). As shown in Scheme 10.12, in the case of diazoacetoacetyl urea (79) the derived isomtinchnone 80 reacts with methyl propiolate to give a 2 1 mixture of cycloadducts 81. The resulting regiochemistry is successfully rationalized using frontier molecular orbital (FMO) theory as being isomiinchnone-HOMO controlled. This result represents one of the few reactions in which the cycloadducts from isomiinchnones and alkynes are stable. 

The relative frontier molecular orbital (FMO) energies of the reagents are very important for the catalytic control of 1,3-dipolar cycloadditions. In order to control the stereochemical outcome of a reaction with a substoichiometric amount of a ligand-metal catalyst, it is desirable that a large rate acceleration is obtained in order to assure that the reaction only takes place in the sphere of the metal and the chiral ligand. The FMO considerations will be outlined in the following using nitrones as an example. 

Ease of dimerization (Scheme 3) is related to HOMO-LUMO splitting. Within the framework of the frontier molecular orbital (FMO) approximation, reducing the frontier orbital gap favors symmetry allowed cycloadditions (e.g., 99 - 97) by stabilizing the transition state. Since the... 

Frontier molecular orbital (FMO) theory has been successful in rationalizing the reactivity, electroselectivity, and regioselectivity of many heterocycles, including mesomeric betaines. To apply FMO theory, some knowledge of the frontier orbital coefficients and energies is necessary, and it is useful to draw some general conclusions about the frontier orbitals in mesomeric betaines. 

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