Quadratic Free-Energy Relationships QFER

The view that the ability of molecules to react rests ultimately ou their own structural properties has long been dear to chemists. Although the encounter of two molecules triggers unique features which neither molecule possess alone, notably an electron inflow to the reactive bonds up to a point of saturation, the notion that molecules contain all the information necessary to understand their reactivity has proved extremely useful. In the middle of the nineteenth century, Auguste Laurent expressed the idea that structure determines reactivity and is directly connected with crystalline form [1]. Chemical reactivity can be understood both as the ability of individual molecules to take part in various chemical reactions as well as the study of rates of such reactions, that is, equilibrium and rate processes. In this textbook, we will focus upon rate constants, conscious that their value for the understanding of chemical reactivity depends largely on our ability to relate them with reaction energies and molecular structure. 

Chemical reactivity depends on energy relationships along the reaction coordinate. While some features are specific for particular reactions, others are common to series of reactions, which in some sense constitute family of reactions. Those relations are the ones that allow the establishment of structure-reactivity relationships and can be classified into some broad categories. 

It is one of the fundamental assumptions of our chemical knowledge that like substances react similarly and that similar changes in structure produce similar changes in reactivity. This is a qualitative and intuitive notion, which can be addressed in a quantitative way in terms of chemical kinetics that is in terms of the rate constant k 

In an ideal situation one would wish that the changes in A in a series of chemical reactions would be dominated by the changes in a single structural factor. In such a case, other structural factors do not change along the reaction series, or such changes are not significant. Under such conditions we can say that these processes constitute a reaction family. 

Owing to the exponential dependence of the rate upon energy, the rate problem reduces mainly to the determination of the lowest energy barrier that has to be surmounted. The ISM model, which was presented in the previous chapter, points, in general terms, to some structural factors that control the barriers of chemical reactions and as a consequence the rate constants. These relevant factors are (i) reaction energy, AEP, AFfi or AG° (ii) the electrophilicity index of Parr, m, a measure of the electron inflow to the reactive bonds at the ttansition state, also characterised as a transition-state bond order (iii) when the potential energy curves for reactants and products can be represented adequately by harmonic oscillators, the relevant strucmral parameters are the force constants of reactive bonds, f and/p in reactants and products, respectively and (iv) equilibrium bond-lengths of reactive bonds, and Zp in reactants and products, respectively. 

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For reactions in solution, one tends to use Gibbs energy, G, instead of intemal energy, E. For this reason, eqs. (7.6) and (7.11) are called (Gihbs)free-energy relationships. In this particular case such equations represent quadratic free-energy relationships (QFER). 

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