Ethane internal rotation

Figure 1 Ethane internal rotation showing equilibrium (staggered, S) and barrier top (eclipsed, E) conformers...

Next come the dihedral angles (or torsions), and the contribution that each makes to the total intramolecular potential energy depends on the local symmetry. We distinguish between torsion where full internal rotation is chemically possible, and torsion where we would not normally expect full rotation. Full rotation about the C-C bond in ethane is normal behaviour at room temperature (although 1 have yet to tell you why), and the two CH3 groups would clearly need a threefold potential, such as... 

Thus the orbitals and r electrons lie in the outermost part of the valence shell of ethane. They should play a critical role in determining the chemical properties of the molecule. Some theories have ascribed the barrier to internal rotation to these orbitals. It should be noted that the existence of r electrons in ethane is not a novelty, and was first pointed out by Mullikcn in 1935. 

The potential function that governs internal rotation in ethane is represented in Fig. 6. The three equivalent minima correspond to equilibrium positions, that is, three identical molecular structures. The form of this potential function for an internal rotator with three-fold symmetry can be expressed as a Fourier series,... 

Methyl rotors pose relatively simple, fundamental questions about the nature of noncovalent interactions within molecules. The discovery in the late 1930s1 of the 1025 cm-1 potential energy barrier to internal rotation in ethane was surprising, since no covalent chemical bonds are formed or broken as methyl rotates. By now it is clear that the methyl torsional potential depends sensitively on the local chemical environment. The barrier is 690 cm-1 in propene,2 comparable to ethane,... 

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. 

The strikingly different characteristics of transition-metal hyperconjugative interactions are particularly apparent in their influence on internal rotation barriers. To illustrate, let us first consider ethane-like Os2H6, whose optimized staggered and eclipsed conformations (displaying conspicuous deviations from those of ethane) are shown in Fig. 4.81. 

The most famous rotational barrier is that in ethane, but because the molecule is nonpolar its barrier is obtained from thermodynamic or infrared data, rather than from microwave spectroscopy. Microwave spectroscopy has provided barrier heights for a few dozen molecules. For molecules with three equivalent potential minima in the internal-rotation potential-energy function, the barriers usually range from 1 to 4 kcal/ mole, except for very bulky substituents, where the barrier is higher. Interestingly, when the potential function has sixfold symmetry, the barrier is extremely low for example, CH3BF2 has a barrier of 14 cal/mole.14... 

Variation of the potential energy U(a) for torsional vibration a is the angle of internal rotation in a molecule like ethane. The energy levels above the potential maxima have been omitted. For -0°, 120°, and - 120°, we have the staggered form. 

Show that if the overlap between torsional-vibration wave functions corresponding to oscillation about different equilibrium configurations is neglected, the perturbation-theory secular equation (1.207) for internal rotation in ethane has the same form as the secular equation for the Hiickel MOs of the cyclopropenyl system, thereby justifying (5.96)-(5.98). Write down an expression (in terms of the Hamiltonian and the wave functions) for the energy splitting between sublevels of each torsional level. 

For most substituted ethanes, which have a low barrier to internal rotation ( 3 kcal/mole), the rate of internal rotation is sufficiently fast at room temperature (and well below room temperature) to give only a single peak for the nuclei exchanged by the internal rotation. 

The shape of the potential energy profile for internal rotation in 2,2-dimethylpropane more closely resembles that of ethane than that of butane. 

Preliminary approximate calculations of the transition state in C2H6 + IIO reaction, also executed by the Partial Reservation of Double-Centered Differential Overlap (PRDDO) method [29, 30] indicate the interaction between masked ethane conformation (with a calculated internal rotation barrier equal 1.3kJ/mol) and the HO radical approaching it in the C—C plane. The distance between C—C and O—O bond sites was taken as the reaction coordinate. It is found that planar structure (II) corresponds to the transition state in the C2H6 + H02 reaction. 

Ethane C2H8 — 2CH3. The models for the ethane molecule, C—C rupture complex, and H rupture complex are the molecule, complex 3, and complex 4, respectively, shown in Table I. For illustrative purposes and consistency with Sec. II, the 350 torsion model of ethane, rather than the internal rotation model, was used. The latter would be a better conceptual representation, but, in fact, for the relevant energies, to = 85 kcal. mole, there is little practical difference (cf. Sec. II-C,3). The calculated results which are obtained by combining the kt values, Figure 2, with the distribution function that is appropriate for the activation technique, Figure 8, are shown in Table XII. 

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