Methylene group orbitals

In many instances, the interaction of a neighboring methylene group or methyl group influences the characteristics of a functional group. The appropriate group orbitals of —CH2— and —CH3 are shown in Figures 3.19 and 3.20, respectively. 

Figure 3.19. Group orbitals for a tetracoordinated atom as a substituent interacting through a bonds. A methylene group is illustrated.

As discussed at the end of Chapter 3, one group orbital of a methyl or methylene group will always have the correct nodal characteristics to interact with an adjacent n orbital or with an adjacent spn orbital in fashion. The degree of interaction may be inferred from the energies of the orbitals, which may in turn be obtained by measurements of ionization potentials and application of Koopmans theorem. Thus, the methyl groups adjacent to the n bond in (Z)-2-butene (ionization potential IP = 9.12 eY [63]) raise the energy of the n orbital by 1.39 eV relative to that of ethylene (IP = 10.51 eV [87]). A similar effect is observed in cyclohexene [64]. 

While fewer data are available, the utility of DFT in computing the bond strengths between transition metals and hydrides, methyl groups, and methylene groups has also been demonstrated (Table 8.2). Because of the non-dynamical correlation problem associated with the partially filled metal d orbitals, such binding energies are usually very poorly predicted by MO theory methods, until quite high levels are used to account for electron correlation. 

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. 

Fig. 3.10 Combination of three methylene n-group orbitals in cyclopropane...

Whereas in allenes the AOs of the methylene hydrogen atoms may become part of the molecule s ir system, in planar ethylene, ketene (43), diazomethane (42), and butatriene (223) the methylene proton 1j AOs are always part of the molecular skeleton on the CH2 two-bond proton-proton couplings in these last cumulenes should be determined by electron populations of the H2CX units which are determined by the antisymmetric or symmetric group orbitals of the hydrogen 1j AOs ( sh I h ) (162). 

The methyl group was just a start. Let s now use the same procedure for the CH2 group. Our goals are the same as they were with CH3 define the group orbitals and examine how electron population leads to differing structures. Figure 1.9 shows the Walsh diagram for methylene, where we consider the relationship between the linear and bent forms. 

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. 

The methylene group carries an empty p orbital. Howr will the methyl group interact w ith this empty orbital Clearly the 7r-type orbitals of the methyl group (ttu in E, tt. in B) have the appropriate symmetry to mix with the p orbital. A typical orbital interaction diagram (for E) is shown in Fig. 37. Several conclusions emerge immediately from this diagram ... 

The vinyl cation (Fig. 40 and III.13) in which the empty p orbital on the positive center is coplanar with the terminal methylene group, is clearly another candidate for hyperconjugative donation. The in-plane orbital readily overlaps with the odd p orbital, with formation of two delocalized orbitals and an energy gain... 

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