Molecular orbital frontier

Simple Approaches to Quantifying Chemical Reactivity 3.4.2.1 Frontier Molecular Orbital Theory... 

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]. 

Emphasis was put on providing a sound physicochemical basis for the modeling of the effects determining a reaction mechanism. Thus, methods were developed for the estimation of pXj-vahies, bond dissociation energies, heats of formation, frontier molecular orbital energies and coefficients, and stcric hindrance. 

HOMO and LLMO, also known as Frontier orbitals, are important in in tcrprcLitig results of a calculation (see Frontier Molecular Orbitals on page 141). You can use these m olecular orbiLals to comptiLe the lowest excited electronic singlet state of molecules and the ground states of radicals. 

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. ... 

Extended Huckel provides the approximate shape and energy ordering of molecular orbitals. It also yields the approximate form of an electron density map. This is the only requirement for many qualitative applications of quantum mechanics calculations, such as Frontier Orbital estimates of chemical reactivity (see Frontier Molecular Orbitals on page 141). 

The BDE theory does not explain all observed experimental results. Addition reactions are not adequately handled at all, mosdy owing to steric and electronic effects in the transition state. Thus it is important to consider both the reactivities of the radical and the intended coreactant or environment in any attempt to predict the course of a radical reaction (18). AppHcation of frontier molecular orbital theory may be more appropriate to explain certain reactions (19). 

According to one classification (15,16), symmetrical dinuclear PMDs can be divided into two classes, A and B, with respect to the symmetry of the frontier molecular orbital (MO). Thus, the lowest unoccupied MO (LUMO) of class-A dyes is antisymmetrical and the highest occupied MO (HOMO) is symmetrical, and the TT-system contains an odd number of TT-electron pairs. On the other hand, the frontier MO symmetry of class-B dyes is the opposite, and the molecule has an even number of TT-electron pairs. 

The problems associated with predicting regioselectivity in quinone Diels-Alder chemistry have been studied, and a mechanistic model based on frontier molecular orbital theory proposed (85). In certain cases of poor regioselectivity, eg, 2-methoxy-5-methyl-l,4-ben2oquinone with alkyl-substituted dienes, the use of Lewis acid catalysts is effective (86). 

Frontier molecular orbital theory correctly rationalizes the regioselectivity of most 1,3-dipolar cycloadditions (73JA7287). When nitrile ylides are used as 1,3-dipoles, the dipole... 

The frontier molecular orbital approach provides a description of the bonding interactions that occur in the 8 2 process. The orbitals involved are depicted in Fig. 

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)... 

The most important molecular- orbitals are the so-called frontier molecular- orbitals. These are the highest (energy) occupied molecular- orbital (HOMO), and lowest (energy) unoccupied molecular- orbital (LUMO). The following picture shows the LUMO surface for the hydrogen molecule, H2. The LUMO consists of two separate surfaces, a red... 

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 theory is closely related to various schemes of qualitative orbital theory where interactions between fragment MOs are considered. Ligand field theory, as commonly used in systems involving coordination to metal atoms, can be considered as a special case where only the d-orbitals on the metal and selected orbitals of the ligands are considered. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

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... 

Fig. 3.26 Frontier molecular orbital analysis for the Simmons-Smith cyclopropanation. [Dargel, T.K. Koch, W.J. Chem. Soc., Perkin Trans. 1996, 2, 877. Reproduced by pemiission of The Royal Society of Chemistry]...

Most reactions discussed can be classified into two types of [n s+iAs cycloadditions, the normal and inverse electron-demand cycloaddition reactions, based on the relative energies of the frontier molecular orbitals of the diene and the dieno-phile (Scheme 4.2) [4]. 

This chapter will try to cover some developments in the theoretical understanding of metal-catalyzed cycloaddition reactions. The reactions to be discussed below are related to the other chapters in this book in an attempt to obtain a coherent picture of the metal-catalyzed reactions discussed. The intention with this chapter is not to go into details of the theoretical methods used for the calculations - the reader must go to the original literature to obtain this information. The examples chosen are related to the different chapters, i.e. this chapter will cover carbo-Diels-Alder, hetero-Diels-Alder and 1,3-dipolar cycloaddition reactions. Each section will start with a description of the reactions considered, based on the frontier molecular orbital approach, in an attempt for the reader to understand the basis molecular orbital concepts for the reaction. 

Frontier-molecular-orbital Interactions for Carbo-Diels-Alder Reactions... 

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. 

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