Natural bond orbital vicinal interaction

In this section, we present a unified picture of the different electronic effects that combine to determine methyl rotor potentials in the S0, Sp and D0 electronic states of different substituted toluenes. Our approach is based on analysis of ab initio wavefunctions using the natural bond orbitals (NBOs)33 of Weinhold and cowork-ers. We will attempt to decompose the methyl torsional potential into two dominant contributions. The first is repulsive steric interactions, which are important only when an ortho substituent is present. The second is attractive donor-acceptor interactions between CH bond pairs and empty antibonding orbitals vicinal to the CH bonds. In the NBO basis, these attractive interactions dominate the barrier in ethane (1025 cm-1) and in 2-methylpropene (1010 cm-1) see Figure 3. By analogy, donor-acceptor attractions are important in toluenes whenever there is a substantial difference in bond order between the two ring CC bonds adjacent to the C-CH3 bond. Viewed the other way around, we can use the measured methyl rotor potential as a sensitive probe of local ring geometry. 

With accurate calculated barriers in hand, we return to the question of the underlying causes of methyl barriers in substituted toluenes. For simpler acyclic cases such as ethane and methanol, ab initio quantum mechanics yields the correct ground state conformer and remarkably accurate barrier heights as well.34-36 Analysis of the wavefunctions in terms of natural bond orbitals (NBOs)33 explains barriers to internal rotation in terms of attractive donor-acceptor (hyperconjuga-tive) interactions between doubly occupied aCH-bond orbitals or lone pairs and unoccupied vicinal antibonding orbitals. 

An analysis of the mechanism governing the couphng between the vicinal protons in ethane and fluoroethane has been studied by Contreras and co-workers by the developed by them method of natural bond orbital interactions between bonds and antibonds, cTin->a n. The authors have concluded that the main contribution to Jhh comes from the through space term while the introduction of a fluorine changes this term and yields a direct contribution to the coupling. 

Schleyer et al. combine Weinhold s natural bond orbital analysis with calculations using nonrelativistic and quasi-relativistic ECPs to analyze relativistic effects on the Pb—C and Pb—Pb rotational barriers. This work shows that, although relativity has a large effect on interactions between vicinal T—H and T —H bonds that control the barrier height, the effect is of similar magnitude for the minimum (eclipsed conformer) and transition state (staggered conformer), so that rotational barriers are not affected. 

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