FMO Approximation to Predict and Understand Chemical Reactivity
Let us consider an orbital diagram of two molecules which are in the process of undergoing a chemical reaction. One has a relatively high energy filled orbital (the highest occupied molecular orbital or HOMO). This will the donor molecule. The other has a relatively low energy unoccupied orbital (the lowest unoccupied molecular orbital or LUMO). This will be the acceptor molecule
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Interaction between the frontier molecular orbitals (HOMO of one partner and LUMO of the other) is an important (and often controlling) part of the total orbital interaction between two molecules.
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The interaction between HOMO and LUMO can only occur if the orbitals have the correct symmetry, i.e., if positive overlap can be achieved between HOMO and LUMO orbitals
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The strength of the interaction is directly related to the HOMO-LUMO energy separation. Thus, of the two HOMO-LUMO interactions which are in general possible, it is the one between the HOMO of the donor and LUMO of the acceptor which will tend to dominate. In general, the smaller the HOMO-LUMO separation, the stronger the interaction and the more favored the reaction becomes.
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The strength of interaction between HOMO and LUMO is a strong function of the orbital coefficients of the two orbitals at the contact points between the molecules, and the degree of orbital overlap that can be achieved at the transition state.
Analyzing a Cycloaddition by the FMO Approximation
1. Compare the two HOMO-LUMO energy separations of symmetry allowed interactions. Choose the one with the smallest energy separation. This will be the controlling HOMO-LUMO interaction. The energy separation is related to the rate of the cycloaddition - smaller energy difference means stronger interaction and a higher rate of cycloaddition.
2. Compare the orbital coefficients of the dominant HOMO-LUMO pair and align the large-HOMO with the large-LUMO orbital. This gives the regioselectivity
3. If the orbital coefficients for (2) are the same, then use the other HOMO-LUMO pair to predict regioselectivity.
Houk, K. N. J. Am. Chem. Soc. 1973, 95, 4092
