Perturbation theory molecular orbital

Coulson and H. C. Longuet-Higgins, Proc. R. Soc. London Ser. A, 192, 16 (1947) L. Salem, J. Am, Chem. Soc. 90, 543 (1968) M. J. S. Dewar and R. C. Dougherty, The PMO Theory of Organic Chemistry, Plenum Press, New York, 1975 G. Klopman, Chemical Reactivity and Reaction Paths, Wiley-Interscience, New York, 1974, Chapter 4. 

57 (1971) I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, New York, 1976 L. Salem, Electrons in Chemical Reactions, Wiley, New York, 1982, Chapter 6. 

Let us illustrate these ideas by returning to the comparisons of the reactivities of ethylene and formaldehyde toward a nucleophilic species and an electrophilic species. The interactions (perturbations) that arise as both a nucleophile and an electrophile approach are sketched in Fig. 1.28. 

IT MO energy levels for ethylene with a ir-donor substituent. 

An example of a 7r-acceptor group would be the formyl group, as in acrolein  

A general description of chemical reactivity has been given by Klopman [33]. It can be applied [2] to a simple Lewis acid-base reaction A - - B - AB. Klopman [33] and Jensen 

The first term is the coulombic attraction between the total net opposite charges Qr and Qs of the interacting atoms r and s of B and A at a distance Rrs- The second term is a second-order orbital perturbation due to the attractive interactions between the occupied orbitals on B (A) and the unoccupied orbitals on A(B). is the resonance integral between the AOs of r and. y, and Em (E ) is the energy of orbital m ( ) of B (A) in the field of A (B). The last term is a first-order orbital perturbation due to the repulsive interactions between the filled orbifals of A and B. 

The largest contribution to the double summation over orbital pairs in the second term will arise when the denominator is smallest. This occurs when the energies of the highest occupied MO (HOMO) of the base and the lowest unoccupied MO (LUMO) of the acid become closer. By considering only this contribution in the double summation (the so-called frontier orbitals approximation). Equation 1.38 simplifies to 

On the basis of Equation 1.39, the Lewis acid/base reactions can be divided into the categories of charge-controlled , those dominated by the first term, and orbital-controUed , those dominated by the second term. The factors determining the category are the following  

Recent examples of the application of Klopman s approach to molecular complexes are the partitioning of the binding energies of SO3 complexes with nitrogen bases [34] and of halogen-bonded complexes with diversified bases [35]. The results show that, for the Cl—L. . B complexes, the electrostatic (charge-controlled) bonding is predominant relative 

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This theory proves to be remarkably useful in rationalizing the whole set of general rules and mechanistic aspects described in the previous section as characteristic features of the Diels-Alder reaction. The application of perturbation molecular orbital theory as an approximate quantum mechanical method forms the theoretical basis of Fukui s FMO theory. Perturbation theory predicts a net stabilization for the intermolecular interaction between a diene and a dienophile as a consequence of the interaction of an occupied molecular orbital of one reaction partner with an unoccupied molecular orbital of the other reaction partner. 

Correlation of the effect of substituents on the rates of reactions with early transition states often is best accomplished in terms of perturbational molecular orbital theory, and polar effects can play a major role for such reactions [100, 101]. Essentially this theory states that energy differences between the highest occupied molecular orbital (HOMO) of one reactant and the lowest unoccupied molecular orbital (LUMO) of the other reactant are decisive in determining the reaction rate the smaller the difference in energy, the faster the predicted rate of reaction [102,103]. Since the HOMO of a free radical is the SOMO, the energy difference between the SOMO and the alkene HOMO and/or LUMO is of considerable importance in determining the rates of radical additions to alkenes [84],... 

Up to a few years ago chemical reactivity was discussed in term of reactivity indexes. These approaches, although valuable, will not be discussed here, since they have been frequently reviewed in the past40-44). Nor will we discuss the perturbation molecular orbital theory for reactants, which has been the subject of extensive reviews 45—47) Extensions of this method can be found in papers by Klopman 48 5°) and Dougherty 51). I shall now mention some methods which have not yet found wide popularity but seem very promising. I mean the criterion of maxi-... 

Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons AN transferred is given by Equation 3.14. 

B. Qualitative Model Perturbation Molecular Orbital Theory... 

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