Numerical Application of MO Theory

Molecular orbital computations are currently used extensively for calculation of a range of molecular properties. The energy minimization process can provide detailed information about the most stable stmcture of the molecule. The total binding energy can be related to thermodynamic definitions of molecular energy. The calculations also provide the total electron density distribution, and properties that depend on electron distribution, such as dipole moments, can be obtained. The spatial distribution of orbitals, especially the HOMO and LUMO, provides the basis for reactivity assessment. We illustrate some of these applications below. In Chapter 3 we show how MO calculations can be applied to intermediates and transitions structures and thus help define reaction mechanisms. Numerical calculation of spectroscopic features including electronic, vibrational, and rotational energy levels, as well as NMR spectra is also possible. 

A common numerical application of MO calculations is to compare the stability of related compounds. For example, in the discussion of both resonance and qualitative MQ theory, we stated that stabilization results from attachment of conjugating substituents to double bonds. We might ask, How much stabilization One way to answer this question is to compare the total energy of the two compounds, but since they are not isomers, simple numerical comparison is not feasible. We discuss various ways to make the comparison, and some of the pitfalls, in Chapter 3, but one method is to use isodesmic reactions. These are hypothetical reactions in which the number of each kind of bond is the same on each side of the equation. For the case of substituents on double bonds the isodesmic reaction below estimates the added stabilization, since it is balanced with respect to bond types. Any extra stabilization owing to substituents will appear as an energy difference. 

The dipole moments of molecules depend on both the molecular dimensions and the electron distribution. For example, Z-l,2-dichloroethene has a dipole moment of 1.90 D, whereas, owing to its symmetrical structure, the E isomer has no molecular dipole. 

MO calculations of molecular dipoles involves summing the electron distribution in the filled orbitals. Although they calculating the order correctly, both HF/6-31G and MP2/6-31G calculations seem to overestimate the dipole moments of small polar molecules (Table 1.11). 

MO calculations can also be applied to reactions. The effect of substituents on the acidity i K ) of carboxylic acids is a well-studied area experimentally. Shields and co-workers used several of the ab initio protocols to calculate the aqueous acidity of some substituted carboxylic acids relative to acetic acid, which represented quite a challenging test of theory. The dissociation of a carboxylic acid involves formation of ions, and solvation is a major component of the free energy change. Furthermore, solvation introduces both enthalpy and entropy components. The calculations were approached using a thermodynamic cycle that includes the energies of solvation of the neutral acids and the anion. Since the calculation is relative to acetic acid, the energy of solvation of the proton cancels out. 

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