Barrier to Rotation in Ethane

We saw in Chapter 7 that rotation about the C-N bond in an amide is relatively slow at room temperature—the NMR spectrum of DMF clearly shows two methyl signals (p. 165). In Chapter 13 you learned that the rate of a chemical process is associated with an energy barrier (this holds both for reactions and simple bond rotations) the lower the rate, the higher the barrier. The energy barrier to the rotation about the C-N bond in an amide is usually about 80 kj mol-1, translating into a rate of about 0,1 s-1 at 20 °C. Rotation about single bonds is much faster than this at room temperature, but there is nonetheless a barrier to rotation in ethane, for example, of about 12 kj mol-1. 

Figure 8.4 Energy barriers to rotation in ethane (plot of energy versus angular rotation). Reprinted by permission from Macmillan Publishers Ltd Weinhold F. Nature. 2001, 411, 539. Figure 1.

Looking more globally at the potential surface, we encounter phenomena such as rotational barriers and inversion barriers. The barriers to rotation in ethane and many other compounds are described well by any of the basis sets so far considered (STO-3G, 3-21G, 6-31G ), even at the HF level. However, when the barriers are small, as in the case of methanol ( 1.1 kcal/mol), the HF method tends to overestimate A rot. 

It is difficult not to conclude however that some result do reflect higher barriers to rotation about single bonds in acyclic compounds. The barriers to rotation in hydrogen peroxide and hydrogen persulphide are 7.0 and 6.8 kcal/mol compared with a value of 2.9 kcal/mol for ethane 8), and these larger barriers seem to be reflected in the ring inversion barriers for the compounds 24—26. 65,87-89)... 

Although the barrier to rotation in //-butane is a little higher than in ethane, it is still low enough that—at ordinary temperatures, at least—interconversion of conformers is easy and rapid. Equilibrium exists, and favors a higher population of the more stable anti conformer the populations of the two gauche conformers—... 

Although the barriers to rotation in a butane molecule are larger than those of an ethane molecule (Section 4.8), they are still far too small to permit isolation of the gauche and anti conformations at normal temperatures. Only at extremely low temperatures would the molecules have insufficient energies to surmount these barriers. 

The barrier to rotation in 1,3-butadiene turns out to be 4—5 kcal/mol, only a bit larger than the barrier to rotation about the carbon—carbon bond in ethane. It is the s-trans form that is favored at equilibrium, by 2—3 kcal/mol. There is a simple steric effect favoring the s-trans conformation. In the s-cis conformation the two inside hydrogens are quite close to each other (make a model ) and in the s-trans conformation they are not. In order to make sense of these structures, we have to watch out not only for the locations of the double bonds, but for the positions of the hydrogens attached to them as well (Fig. 12.21b). 

Although semiempirical methods are usually parameterized using ground-state systems, these methods have often been successfully applied to the study of transition states and electronic excited states. Three examples of rotational barriers are of interest the rotation of a methyl group in ethane, around the double bond in ethylene, and about the partial double bond in the peptide linkage. In one of these, the barrier to rotation in the peptide linkage, the PM3 method does extremely poorly. 

In Eq. (2), the dihedral tenn includes parameters for the force constant, Ky, the periodicity or multiplicity, n and the phase, 8. The magnimde of Ky dictates the height of the barrier to rotation, such that Ky associated with a double bond would be significantly larger that that for a single bond. The periodicity, n, indicates the number of cycles per 360° rotation about the dihedral. In the case of an bond, as in ethane, n would... 

One of the frmdamental structural facets of organic chemistry, which has been explained most satisfactorily in MO terms, is the existence of a small barrier to rotation about single bonds. In ethane, for example, it is known that the staggered conformation is about 3kcal/mol more stable than the ecl sed conformation so that the eclipsed conformation represents a transition state for transformation of one staggered conformation into another by rotation. 

Despite what we ve just said, we actually don t observe perfectly free rotation in ethane. Experiments show that there is a small (12 kj/mol 2.9 kcal/mol) barrier to rotation and that some conformers are more stable than others. The lowest-energy, most stable conformer is the one in which all six C-H bonds are as far away from one another as possible—staggered when viewed end-on in a Newman projection. The highest-energy, least stable conformer is the one in which the six C-H bonds are as close as possible—eclipsed in a Newman projection. At any given instant, about 99% of ethane molecules have an approximately staggered conformation... 

Although essentially free rotation is possible around single bonds (Section 3.6), the same is not true of double bonds. For rotation to occur around a double bond, the -rrbond must break and re-form (Figure 6.2). Thus, the barrier to double-bond rotation must be at least as great as the strength of the 7r bond itself, an estimated 350 kj/mol (84 kcal/mol). Recall that the barrier to bond rotation in ethane is only 12 kj/mol. 

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,... 

The two representations shown here are actually two different conformers of ethane there will be an infinite number of such conformers, depending upon the amount of rotation about the C-C bond. Although there is fairly free rotation about this bond, there does exist a small energy barrier to rotation of about 12kJmol due to repulsion of the electrons in the C-H bonds. By inspecting the Newman projections, it can be predicted that this repulsion will be a minimum when the C-H bonds are positioned as far away from each other... 

Full 360° rotation leads to three identical staggered structures which are energy minima, and three identical eclipsed structures which are energy maxima. The difference in energy between eclipsed and staggered structures of ethane, termed the barrier to rotation, is known experimentally to be 2.9 kcal/mol (12 kJ/mol). Note, that any physical measurements on ethane pertain only to its staggered structure, or... 

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... 

When rotation occurs about a bond there are two sources of strain energy. The first arises from the nonbonded interactions between the atoms attached to the two atoms of the bond (1,4-interactions) and these interactions are automatically included in most molecular mechanics models. The second source arises from reorganization of the electron density about the bonded atoms, which alters the degree of orbital overlap. The values for the force constants can be determined if a frequency for rotation about a bond in a model compound can be determined. For instance, the bond rotation frequencies of ethane and ethylamine have been determined by microwave spectroscopy. From the temperature dependence of the frequencies, the barriers to rotation have been determined as 12.1 and 8.28 kJ mol-1, respectively1243. The contribution to this barrier that arises from the nonbonded 1,4-interactions is then calculated using the potential functions to be employed in the force field. 

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