Bond order spin-orbit reduction

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

In addition to the conventional overlap energy term there is a second term that depends on the bond-order Pq and the repulsive integral between an electron in adsorbate orbital 0 and an electron in orbital I on the neighboring atom, is equal to /fjj, Ek).(2.282), and the second term in follows from the first term of (2.283a) when using definition Eq.(2.35c) for the bond-order Pi2 and the zero-differential overlap approximation Eq.(2.284). In section 2 Eq.(2.40b) related to Eq.(2.309) was derived. It was shown to lead to a reduction of the interaction energy of two electrons with different spins in the same orbital (see Eq.(2.42,II)). The result implies that Ucff is not independent of the bond-order. An improved expression for would be ... 

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