Energies of MOs

Fig. 4.2 b. The change in energy of MO s in ethylene and butadiene along the reaction path... 

Other models, which have been developed independently, have features in common with the AOM. Kettle and his co-workers (39—42) have discussed molecular geometry using a perturbation treatment which places the relative energies of MO s in terms of squared overlap integrals, and the point bond model of Howald and Keeton (43) is essentially equivalent to the ex model. 

Thus, in summary, by using values of the various integrals (often called matrix elements) Hih Htj, S , the energies of MOs may be calculated in the LCAO-MO approximation without knowing the explicit form of the LCAO-MOs. After the energy values are known, it is possible to determine the coefficients, c,h and thus obtain the explicit expressions for the LCAO-MOs. 

In many instances it is helpful to plot the calculated energies of MOs as in Figure 7.1. The energy scale is vertical, and each orbital is represented as a short horizontal line placed at the position corresponding to the energy of the orbital. For doubly degenerate orbitals a pair of closely spaced lines is used. The occupation of the orbitals by electrons is indicated by placing small circles on the lines. 

FACTORS GOVERNING ENERGIES OF MOs SHMO THEORY Reference Energy and Energy Scale... 

Use the Inscribed Polygon Method to Determine the Relative Energies of MOs for Cyclic, Completely Conjugated Compounds... 

The balance of electrostatic and delocalization interactions in an isolated molecule may be perturbed by the influence of the solvent. In calculations based on Eq. 7, the analysis of solvation-energy terms suggested that the electrostatic contribution stabilizing the ap orientation of the acetal s ment is the conformationally dominant term. For example, in 2-methoxyoxane, the difference in energy of the (ap, ap) and (ap, sc) conformers in water, compared to that in the isolated molecule, caused by solute-solvent electrostatic interactions alone, amounts to 4 kJ.mor. Accordingly, the inter-and intra-molecular, electrostatic interactions operate in reverse directions in acetals. Whereas the intramolecular, electrostatic interactions are responsible, together with delocalization interactions, for the aiq)earance of the anomeric, reverse anomeric, and exo-anomeric effects, the solute-solvent electrostatic interactions lessen their im nitude, and may even cancel them. Of course, the solvent may also influence the electron distribution and energy of MO s in a molecule. In this way, the orbital interactions of lone-pairs and delocalization contributions to the anomeric effect may be scaled by the solvent, but this mechanism of the environmental effect is, in most cases, of only minor importance. 

Fig. 1. Energies of % MOs in (a) benzene, (b) a four-membered ring compound.

Its qualitative features are common to all energy level diagrams showing the energies of MO s formed between two atoms, each supplying one orbital. 

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