The Isolated Molecule Method

We must, at the outset, distinguish between the two kinds of change in coulomb integral that are applied in practice. 

Alternatively, perturbation formulae may be employed to derive the same results approximately, starting from the parent alternant hydrocarbons and using the polarizability coefficients. Thus, for example, 

The charges g, of equation (28) may be used as reactivity indices, either intuitively as relative measures of coulombic attraction or electron availability, or through equation (18), bearing in mind that in this case SS approximates the exact change A, as discussed in Section II. Since the leading term in (28) is unity, predictions of the active positions in derivatives can be made in terms of computed values of the tt, coefficients for the parent hydrocarbons. Moreover, changes with the same sign of Sa necessarily yield the same active positions, which, in practice, provides a theoretical explanation of orientation in benzene derivatives. 

Now the polarizability coefficients for alternant hydrocarbons have interesting analytical properties, like the secular equations themselves (Section III). These properties arise as special cases from a more general analysis which applies to the finite changes Aq, 

We select without proof, from the theory of Coulson and Longuet-Higgins (1947a,b), those formulae which relate to quantities used in the description of chemical reactivity, as follows  

---

B. Energy Level Diagrams and Parameter Variations The Isolated Molecule Method. ... 

Two main methods of approach are used in discussing the variation of E . These have been associated with different parts of the reaction path the isolated molecule method is usually assumed to refer to the initial stages of the reaction, and the localization method is generally associated with a transition state in the region of the maximum of the energy curve. Each method has its own reactivity indices these are defined in detail in later Sections, but at this point it is useful to list them, along with certain additional indices relating to models introduced more recently, and to indicate their applicability. 

The isolated-molecule method stems from the pioneering work of Wheland and Pauling (1935) on the orientation effects of substituents in benzene derivatives. It assumes that electrophilic and nucleophilic reagents attack preferentially at positions of high and low charge (qf) respectively, thus providing a more precise formulation of earlier... 

For this reason, and because it applies equally not only to the effect of substituents but also to the large changes Sa, at an attacked atom— and hence to the reactivity indices used in the isolated molecule method, the theory of finite changes will be briefly outlined. 

Most of these developments may be applied most directly within the framework of the isolated molecule method, in which the reactivity indices are the charges and self-polarizabilities of the unperturbed ground state of a given molecule calculations based on the localization model (e.g. Nesbet, 1962) have made less progress, and will not be considered. It is therefore natural to enquire whether indices similar to and tt,, in Hiickel theory can still be defined, and calculated more precisely, in self-consistent field theory. The obvious questions are... 

THE RANGE OF VALIDITY OF THE ISOLATED MOLECULE METHOD. GENERAL REMARKS... 

---