Energy levels molecular orbital theory

Higher level molecular orbital theory can provide quantitative information about orbital energies and how strongly a molecule holds its electrons. When one compares aromatic and nonaromatic species in this way, it is found that cyclic delocalization causes the TT electrons of benzene to be more strongly bound (more stable) than they would be if restricted to a system with alternating single and double bonds. 

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

The variation method is usually employed to determine an approximate value of the lowest eneigy state (the ground state) of a given atomic or molecular system. It can, furthermore, be extended to the calculation of energy levels of excited stales. It forms the basis of molecular orbital theory and that which is often referred to (incorrectly) as theoretical chemistry". 

The application of ab initio molecular orbital theory to suitable model systems has led to theoretical scales of substituent parameters, which may be compared with the experimental scales. Calculations (3-21G or 4-31G level) of energies or electron populations were made by Marriott and Topsom in 1984164. The results are well correlated with op (i.e. 07) for a small number of substituents whose op values on the various experimental scales (gas phase, non-polar solvents, polar solvents) are concordant. The nitro group is considered to be one of these, with values 0.65 in the gas phase, 0.65 in non-polar solvents and 0.67 in polar solvents. The regression equations are the basis of theoretical op values for about fifty substituents. The nitro group is well behaved and the derived theoretical value of op is 0.66. 

Molecular orbital theory is a semi-empirical method devoted to interpreting the energy-level structure of optical centers where the valence electron cannot be considered as belonging to a specific ion. In our ABe reference center, this would mean that the valence electrons are shared by A and B ions. The approach is based on the calculation of molecular orbitals (MO) of the ABe pseudo-molecule, V mo, from various trial combinations of the individual atomic orbitals, V a and of the A and B ions, respectively. The molecular orbitals V mo of the center ABe are conveniently written in the form... 

Figure 5.7 A schematic energy-level diagram for an octahedral ABg center within molecular orbital theory. This diagram is constructed from the atomic levels of A and B. The filled and half-filled states (two possible opposite spins for each state) correspond to A = Ti + and B = ions (reproduced with permission from Ballhausen and Gray, 1965).

The above discussion has considered the stabilization of complexes in terms of the crystal field theory. It is desirable to consider the same topic in terms of modern molecular orbital theory. Although the development and sophisticated consideration of the MO treatment is far beyond the scope of this chapter, an abbreviated, qualitative picture will be presented, focusing again on the energy levels of the highest occupied and lowest empty orbitals and again using the square planar d case. 

Concerning 1,4-dioxane 16, its inversion has been studied by using ab initio molecular orbital theory at the HF/6-31G and BLYP/6-31G levels. The chair conformation is the lowest in energy, followed by the two twist-boats. The transition state connecting the chair and the twist-boats is a half-chair structure, in which four atoms in the ring are planar <1997PCA3382>. 

By referring to the diagrams in Figure 3.1 it may be seen that the orbital <)), transforms as Gg+, and that the orbital < )2 transforms as ou+. That two molecular orbitals are produced from the two atomic orbitals is an important part of molecular orbital theory a law of conservation of orbital numbers- The two molecular orbitals differ in energy, both from each other and from the energy of the atomic level. To understand how this arises it is essential to consider the normalization of the orbitals. 

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