Analysis of the MO Bond Energy

Rather than from the homogeneous system corresponding to the pseudosecular equation (2.77), it is convenient to obtain X for the lowest eigenvalue as the appropriate solution of the quadratic equation  

Equation (2.106) allows then for the MO description of the electric dipole moment /a of the bond. 

14Arising from the matrix formulation of the full 2x2 non-orthogonal eigenvalue problem 

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Analysis of the MO Bond Energy sp-hybridization Effects in First-row Hydrides... 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

W Another type of energy partitioning in MO theory was proposed by Clementi 86>. This kind of partitioning called Bond Energy Analysis" (BEA) was found to be particularly useful in larger molecular clusters 87-90) Since the individual contributions of BEA are not directly related to the quantities discussed in intermolecular perturbation theory, dementi s technique will not be used here (see Chapter V). 

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