Application of the frontier molecular orbital theory to the interpretation

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Olivier Henri-Rousseau and Fernand Texier lnstitut de Chimie Universite d'0ran Algerie

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Application of the Frontier Molecular Orbital Theory to the Interpretation of the hammett Correlations

The Hammett correlations (eqn. (1)) are generally explained using the concept of partial charge stabilization (I). log kj = log ho + pcj (1) However, this concept does not allow an explanation of the chemical reactivity; it is for instance of no use in the explanation of regioselectivity and reactivity observed in concerted cycloadditions (2); furthermore, it is not fundamental in physics. Repartition of charges is a consequence of variations in energy, through the variation principle. Our purpose is to show how a physical explanation of the Hammett relationship may be proposed in the framework of a frontier orbital method (3)which has provided a basis for explaining several aspects of chemical reactivity (4). General Concepts Used In Molecular Orbital Theory When two atomic orbitals (AO's) of different atoms overlap they lead to molecular orhitals (MO's). By using the superposition principle, the MO's may be written as linear combinations of AO's 9 For two overlapping AO's we have In agreement with the variational principle, coeffir~entso and b me those which lead m a minimum energ). k.' for the MO. The use of the variational principle leads to the set of simultaneous equations (3) when the overlap integral is neglected (5) o(E, - E) + bHij = 0 (3) oH;; + b(E, - E l = 0 E; and E j are the and rp, energies before interaction; Hij is the interaction Hamiltonian between q; and q,. The interaction leads to one stabilized bonding MO and one destabilized antibonding MO (see Fig. 1).The stabilization energy AE in this degree of approximation is equal to the destabilization AE*. a2 and b2 are the probabilities of finding the electrons described by J. either on the A 0 w or on qj; of course the normalization condition leads to a2 b2 = 1. By rearranging both eqns. (3) we obtain for the bonding MO

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lnteractlng MO's and Second-Order Perlurbatlon Energy When two mulecules are nppr