Resonance integral heteroatoms

The resonance integral of the 7r-bond between the heteroatom and carbon is another possible parameter in the treatment of heteroatomic molecules. However, for nitrogen compounds more detailed calculations have suggested that this resonance integral is similar to that for a C—C bond and moreover the relative values of the reactivity Indices at different positions are not very sensitive to change in this parameter. 

Analogous theoretical calculations on conjugated systems involving heteroatoms are more difficult, because more numerous assumptions about the unknown Coulomb integrals and resonance integrals are needed. Conclusions about the relative basicity of two conjugated sites obtained from such calculations are therefore necessarily more tentative. 

For unsubstituted aromatic hydrocarbons all the carbon atoms are assigned the same Coulomb integral (a°) and all C—C bonds are assigned the same resonance integral 0°). In heteroaromatic molecules the approximate Coulomb integral for heteroatom ax is expressed as in Eq. (1) in terms of a0 and (3° and the electronegativity parameter h. 

In 1954 Sandorfyand Daudel15) published their C" approximation, a one-electron approximation which employs a linear combination of sp3 orbitals and borrows most of its simplifying features from the Htickel theory. The originality of this method lies essentially in the introduction of a resonance integral m/J between sp3 orbitals of the same carbon atom. Sandorfy 16> showed that the inductive effect due to a heteroatom can be reproduced by such a calculation. 

Discussions of heteroatoms in the SHM written in the heyday of that method present the heteroatom parameters in a slightly more complicated way, in terms of the coulomb and resonance integrals a and p, rather than as simple numbers. 

Theoreticians call any non-hydrogen atom a heavy atom, and any heavy atom other than carbon a heteroatom. In the Hiickel model, all carbon atoms are assumed to be the same. Consequently, their Coulomb and resonance integrals never change from a and If respectively. However, heteroatom X and carbon have different electronegativities, so we have to set ccx = a. Equally, the C-X and C-C bond strengths are different, so that Pcx X p. Thus, for heteroatoms, we employ the modified parameters... 

In analogy with the bond order-weighted edge adjacency matrix, a resonance-weighted edge adjacency matrix E was also proposed, replacing the bond orders with parameters kc-x used in the Hiickel matrix and related to the resonance integral Pc-x of the bond between the heteroatom X and the carbon atom by the relationship ... 

As a rule, a much better agreement can be obtained for compounds with heteroatoms because the additional parameters used in the calculations (the Coulomb integral of the heteroatoms, the resonance integral of the carbon-heteroatom bonds, etc.) can be adjusted to give a reasonable fit with experimental data. 

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