The frontier orbital description of cycloadditions

When an ionic cyclization reaction occurs, such as the lactonization at the head of this chapter, one important new bond is formed. It is enough to combine one full orbital with one empty orbital to make the new bond. But in a cycloaddition two new bonds are formed at the same time. We have to arrange for two filled p orbitals and two empty p orbitals to be available at the right place and with the right symmetry. See what happens if we draw the orbitals for the reaction above. We could try the HOMO (tc) of the alkene and the LUMO (k ) of the double bond in the anhydride. 

This combination is bonding at one end, but antibonding at the other so that no cylcoaddition reaction occurs. It obviously doesn t help to use the other HOMO/LUMO pair as they will have the same mismatched symmetry. 

Now see what happens when we replace the alkene with a diene. We shall again use the LUMO of the electron-poor anhydride. 

Now the symmetry is right because there is a node in the middle of the HOMO of the diene (the HOMO is 4 2 of the diene) just as there is in the LUMO of the dienophile. If we had tried the opposite arrangement, the LUMO of the diene and the HOMO of the dienophile, the symmetry would again be right. 

Now the LUMO of the diene has two nodes and gives the same symmetry as the HOMO of the dienophile, which has no nodes. So either combination is excellent. In fact most Diels-Alder reactions use electron-deficient dienophiles and electron-rich dienes so we prefer the first arrangement. The electron-deficient dienophile has a low-energy LUMO and the electron-rich diene has a high-energy HOMO so that this combination gives a better overlap in the transition state. The energy levels will be like this. 

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The frontier orbital description of cycloadditions 886 Radicals contain unpaired electrons 970... 

It is possible to give a frontier orbital description of a [3,3] -sigmatropic rearrangement but this is not a very satisfactory treatment because two reagents are not recognizing each other across space as they were in cycloadditions. There are three components in these reactions—two nonconjugated K bonds that do have to overlap across space and a O bond in the chain joining the two k bonds. 

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. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offulminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmarm mles [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4—6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

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