FMO method

In the frozen MO approximation the last terms are zero and the Fukui functions are given directly by the contributions from the HOMO and LUMO. The preferred site of attack is therefore at the atom(s) with the largest MO coefficients in the HOMO/LUMO, in exact agreement with FMO theory. The Fukui function(s) may be considered as the equivalent (or generalization) of FMO methods within Density Functional Theory (Chapter 6). 

The fact that features in the total electron density are closely related to the shapes of the HOMO and LUMO provides a much better rationale of why FMO theory works as well as it does, than does the perturbation derivation. It should be noted, however, that improvements in the wave function do not necessarily lead to a better performance of the FMO method. Indeed the use of MOs from semi-empirical methods usually works better than data from ab initio wave functions. Furthermore it should be kept in mind that only the HOMO orbital converges to a specific shape and energy as the basis set is... 

Table 6.3 Selection rules for sigmatropic change by FMO method...

Ferraccioli and co-workers (131,132) employed the reaction of mtinchnones with N-(phenylsulfonyl)imines as a general synthesis of imidazoles (228) (Table 10.6). Regioselectivity is very high and was determined using NOE measurements. The authors utilize the perturbation MO treatment, which is less approximate than the FMO method, to predict correctly the observed regiochemistry. 

The structural requirements of the mesomeric betaines described in Section III endow these molecules with reactive -electron systems whose orbital symmetries are suitable for participation in a variety of pericyclic reactions. In particular, many betaines undergo 1,3-dipolar cycloaddition reactions giving stable adducts. Since these reactions are moderately exothermic, the transition state can be expected to occur early in the reaction and the magnitude of the frontier orbital interactions, as 1,3-dipole and 1,3-dipolarophile approach, can be expected to influence the energy of the transition state—and therefore the reaction rate and the structure of the product. This is the essence of frontier molecular orbital (EMO) theory, several accounts of which have been published. 16.317 application of the FMO method to the pericyclic reactions of mesomeric betaines has met with considerable success. The following section describes how the reactivity, electroselectivity, and regioselectivity of these molecules have been rationalized. 

The kinetic aspects of these reactions were inspected by the frontier molecular orbital (FMO) method for the 1,3-dipolar cycloaddition reactions of R Ns + R2NCO or R2N3 + R NCO affording the corresponding tetra-zolinone (97JHC113). Making use of the Klopman-Salem equation, from... 

A review of photo-cycloadditions of dienones and quinones has been published.41 The first example of a Lewis acid-catalysed 2 + 2-cycloaddition of styrene with naphthoquinone has been reported.42 FMO methods have been used to investigate the effect of substituents on the regiochemistry of the 2 + 2-photo-cycloaddition of a, fi-unsaturated carbonyl compounds with substituted alkenes.43 Evidence has been presented for the presence of a triplet exciplex intermediate in the photo-cycloaddition of 4,4-dimethylcyclohexenone to 1,1-diphenylethylene.44 The intramolecular 2-1-2-photo-cycloaddition of 2-acyloxy-3-hexenoylcyclohexenones (26) is highly diastereo-selective yielding the tricyclic adduct (27) (Scheme 10).45... 

Equation (12) is the mathematical basis of the FMO method and describes the energy change due to frontier orbital interactions when two molecules M and N interact (M + N - MN). AE mo is a measure of transition-state stabilization (or destabilization). The first term describes the interaction between the HOMO of molecule M and the LUMO of N whereas the second term describes the alternative interaction. ... 

For simple systems, the form of the HOMO and LUMO is not dijf cult to remember. For more complex systems, explicit calculations have to be made and the FMO method becomes more difficult to apply. 

The advantage of the FMO method is that it can be expressed quantitatively in terms of the magnitude of the coefficients involved, and hence can be used to predict regioselectivity (see Fig. 8.33). 

Another explanation has been proposed by K. Fukuii on the basis of frontier molecular orbitals (HOMO—LUMO) of the substrates this method is known as the frontier molecular orbitals (FMO) method. Alternatively, the PMO theory based on the Woodward—Hoffmann rule and Hiickel-Mobius method is also used to explain the results of pericyclic reactions. 

A similar analysis of such systems has led to the formulation of selection rules that state that if a sigmatropic reaction of the order [i,j] (for hydrogen migration i = 1) has i + j = 4n + 2, then thermal reaction is suprafacial and photochemical reaction will be antarafacial. However, for those cases in which i + j = 4n, the rales are reversed and the thermal reactions are antarafacial while the photochemical reaction will be suprafacial. The selection rules for the sigmatropic shift of hydrogen by FMO method are given in Table 3.1. 

TABLE 3.1 Selection rules for the sigmatropic shift of hydrogen by FMO method. 

The selection rules for the sigmatropic shift of carbon by FMO method are given in the Table 3.3, where n is zero or an integer. 

TABLE 4.2 Selection rules for cycloadditions and cycloreversions by FMO method. 

Applying FMO method, there are two possibilities in which the carbene can approach the olefin linear and nonlinear. In the linear approach, the plane of bonds of two substituents on carbene is perpendicular to that of the C—C bond of the olefin (Figure 5.2). However, this linear approach is ruled out as it creates an antibonding interaction. 

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