Methylene groups, molecular orbitals

A reactivity index suitable for use in Equation 1 was calculated by using the simple molecular orbital techniques described by the Pullmans (14). Many indexes may be deduced from this type of procedure. The one that seemed to have the most significance for the correlation was the energy of the highest occupied molecular orbital (HOMO). This index is a relative measure of the ability of an electron to be transferred to an acceptor molecule. The calculations were performed on the substituted phenol in the imidazoline structure. This simplification was made since it could be assumed that any perturbation caused by the imidazole would be insulated from the rest of the molecule by the methylene group. 

In the study of coupling constants a large lore has also been accumulated. The qualitative behavior of the H-H coupling constant in saturated methylene groups is predicted by molecular orbital theory,12 and the effects of electronegative element substitution, angle deformation, and adjacent ir-bonded groups observed experimentally confirm the theory. 

After twisting of the methylene groups begins (preceded or accompanied by stretching of the carbon-carbon a bond), the point group becomes Ca, only a two-fold axis being preserved. In this lower symmetry both Ai and Aa become A, and Bi and Ba both become B. This is a necessary requirement. As conrotatory twisting continues the two A orbitals combine and the two B orbitals combine to form the two new molecular orbitals which are the 7t orbitals of butadiene. 

Molecular orbitals, which we will also later use as group orbitals can be built from AOs in exactly the same way as MO-programs do, except that we can use the LCAO principle qualitatively to understand the AO-combination process. We will consider a simple example, methylene, CH2, in order to illustrate the principles involved. We can then use the MOs obtained as generic orbitals for the fragment or group AH2, where A can be any main group element, in order to explain the shapes of these molecules, and also as group orbitals in order to build the MOs of more complicated molecules like ethylene or cyclopropane. 

The final group orbitals that we will consider here are the 7C-orbitals prependicular to the CH2-plane. These MOs are formed as combinations of the pure carbon p-orbitals that form the Lowest L/noccupied Molecular Orbital (LUMO) of singlet methylene and the highest Singly Occupied Molecular Orbital (SOMO) of the triplet. 

Irreducible representations, or symmetry species, are ways to depict all possible properties (such as molecular orbitals or normal vibrations) of a molecule in terms of their symmetry properties. The symmetry properties are defined in terms of the behaviour of the property when the symmetry elements of the molecular point group are applied. Thus, for instance, the Och-MO of methylene (Fig. 5.12) is symmetrical with respect to rotation about the principal axis (it does not change) whereas the tCch2" MO is antisymmetrical (it changes its phase. Fig. 5.13). 

Figure 12.56 Molecular orbitals of a methylene group along with sign of contribution to the coupling constant from electronic excitations. The largest contributing transition (HOMO- LUMO) hcis a positive contribution to the...

B3LYP/6-31 lG(d) calculations have used frontier molecular orbitals, chemical potential, and Pearson s electrophilicity index co to study the reactions between allylic and aliphatic alcohols and ethylacetoacetate. All three methods predict the correct product substitution by the R group of the alcohol at the methylene carbon when the alcohol is electrophilic, and transesteriflcation of the ethylacetoacetate when the alcohol is nucleophilic. The results agree with the existing experimental evidence. 

The much more elaborate correspondence diagram for generation of TMM [14, Fig. 9] is displayed in Fig. 9.6. As in previous examples in which CH bonds occupy different planes in the reactant and product, the occupied acH orbitals are taken into account explicitly. They can be brought into correspondence by either a conrotation or a disrotation, respectively 02 -nd 62 in the axis convention adopted. The symmetry coordinates that have to be incorporated in the two reaction coordinates are illustrated schematically in Fig. 9.7 In one (a2) the extruded N2 molecule rotates about the symmetry axis as it departs and the methylene groups move into plane conrotatorily. In the other (62) if recedes above (or below) the molecular plane as the methylenes disrotate into plane. 

Comparison of compounds 1 + and 2 + shows that, despite the longer metal-metal distance, the forward electron transfer is faster across the phenylene spacer (k = 3.0 X 10 s ) than across the two methylene groups (k = 1.7 X 10 s ). This result can be related to the lower energy of the lowest unoccupied molecular orbital (LUMO) of the phenylene group, which facilitates electronic coupling. In the homogeneous family of compounds 2 +-4 +, the rate constant decreases exponentially with increasing metal-metal distance. 

Use the appropriate group orbitals and the QMOT rules in Table 1.7 to create the molecular orbitals of protonated formaldehyde (CH2=0H ), starting with methylene and OH. 

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