FMOs

D-fMO MO-Nonitol, 2,6-anhydro-3,S,7-trideoxy-l-C-([hydroxy-(tetrahydro-2-methoxy-5,6-dimethyl-4-methylene-2 H-pyran-2-yl) acetyl] amino)-5,5-di methyl-1, S,9-tri-0-rriethyl-, 2R-[2( j(,2[S (5-q], 5P,6P] -... 

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. 

FMO theory requires that a HOMO of one reactant has to be correlated with the LUMO of the other reactant. The decision between the two alternatives - i.e., from which reactant the HOMO should be taken - is made on the basis of which is the smaller energy difference in our case the HOMO of the electron rich diene, 3.1, has to be correlated with the LUMO of the electron-poor dienophile, 3.2. The smaller this HOMO-LUMO gap, the higher the reactivity will be. With the HOMO and LUMO fixed, the orbital coefficients of these two orbitals can explain the regios-electivity of the reaction, which strongly favors the formation of 3.3 over 3.4. 

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]. 

Figure 3-7. FMO trealirent of a) a Dlels-Alder reaction equation, b) correlation diagram, c) orbital coefficients,...

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. ... 

The FMO coefficients also allow cpralitative prediction of the kinetically controlled regioselectivity, which needs to be considered for asymmetric dienes in combination with asymmetric dienophiles (A and B in Scheme 1.1). There is a preference for formation of a o-bond between the termini with the most extreme orbital coefficients ... 

HOMO and LUMO energies FMO reactivity indices Refractivity Total energy Ionization potential Electron affinity Energy of protonation Orbital populations Frontier orbital densities Superdelocalizabilities... 

Saunders, C.S. and Lopata, V.J., Electron beam processing of advanced composites DREP Final Report (1994) Contract No. W7708-2-0001/01-XSA Department of National Defence Defence Research Establishment Pacific, FMO Victoria, Canada, 1994. 

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)... 

Perfluorinated and partially fluorinated substituents directly bonded to hetero multiple bond systems lower the energies of FMOs Consequently, they are highly reactive in H0MO (l,3-dipole)-LUMO (dipolarophile)-controlled [3+2] cycload-... 

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 ... 

Another way to assess thiophene s reactivity is to compare the intermediate ions formed by addition of N02. Examine the structures, charge distributions and electrostatic potential maps of thiophene+nitronium at C2 and thiophene+nitronium at C3. Draw all of the resonance contributors needed to describe these structures. Which, if either, better delocalizes the positive charge Compare the energies of the two intermediates. Which product should form preferentially if the reaction is under kinetic control Are these results consistent with FMO theory ... 

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. 

For the 2-1-2 pathway the FMO sum becomes (ab — ac) = a b — c) while for the 4 -I- 2 reaction it is (ab-I-ab) — a (2b). As (2b) > (b — c), it is clear that the 4 + 2 reaction has the largest stabilization, and therefore increases least in energy in the initial stages of the reaction (eq. (15.1), remembering that the steric repulsion will cause a net increase in energy). Consequently the 4 - - 2 reaction should have the lowest activation energy, and therefore occur easier than the 2-1-2. This is indeed what is observed, the Diels-Alder reaction occurs readily, but cyclobutane formation is not observed between non-polar dienes and dieneophiles. 

FMO theory was developed at a time when detailed calculations of reaction paths were infeasible. As many sophisticated computational models, and methods for actually locating the TS, have become widespread, the use of FMO arguments for predicting reactivity has declined. The primary goal of computational chemistry, however, is not tc... 

Figure 15.5 Correlation between reaction rates and FMO energy differences (AMI calculations)...

Figure 15.6 FMO rationalizes the stereochemistry of substituted Diels-Alder reactions...

The success of FMO theory is not because the neglected terms in the second-order perturbation expansion (eq. (15.1)) are especially small an actual calculation will reveal that they completely swamp the HOMO-LUMO contribution. The deeper reason is that the shapes of the HOMO and LUMO resemble features in the total electron density, which determines the reactivity. 

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... 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

The FMO approach shown in Figure 15.19 again indicates that the 4s - - 2s interaction should lead directly to formation of two new bonding a-bonds, i.e. this is an allowed reaction. The preference for a concerted 4s + 2s reaction is experimentally supported by observations which show that the stereochemistry of the diene and dieneophile is carried over to the product, e.g. a trans,frans-l,4-disubstituted diene... 

Figure 15.26 FMO interactions for allowed modes of [l,5]-metliyl shift in 1,3-hexadiene...

The theoretical rationalization described by FMO theory has to do with the value of the coefficients of the MO s on the atoms of the reactants. Atoms having p-orbitals of... 

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