Electronic Energy and Heat of Formation

The bond energies of saturated and unsaturated homologues of hydrocarbons may be treated in some detail since they will give us some understanding of the correlation of bond energies in polyolefins. In saturated hydrocarbons with localized electrons it is reasonable to equate the energy of a bond with the energy of the 

One assumes that the wave functions are a solution of the equation H I j = E j (4.11) 

The system (4.14) of equations has a nontrivial solution only if the determinant of the quantities in brackets is zero. Since in principle the coefficients Hij and Sy are derivable from the electron wave functions the secular determinant of the system (4,14) may be solved to yield the energy eigenvalues Ej to E. The total electronic energy E of the molecule then is 

Following the treatment of Brown [6] it is assumed that the Coulomb integral, Hmm of an orbital j) depends only on the type of bond in which it resides, thus all C—H bond orbitals will be assigned the same value a of the Coulomb integral. 

The term is one half of the binding energy of an isolated C—H bond. The resonance integral, will be assumed to be zero unless m and n denote adjacent bonds. In 

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