Rotations in ethane

Step through the sequence of structures depicting bond rotation in ethane. Plot energy (vertical axis) vs. HCCP torsion angle (horizontal axis). Do the minima correspond to staggered structures Do the maxima correspond tc eclipsed structures If not, to what do they correspond ... 

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... 

Figure 3.7 A graph of potential energy versus bond rotation in ethane. The staggered conformers are 12 kJ/mol lower in energy than the eclipsed conformers.

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. 

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,... 

Actually this energy barrier creates hindrance in free rotation in the molecule. Therefore, strictly speaking there is not free rotation in ethane. But since this value is small we, may neglect it and regard that there is free rotation about C—C single bond in ethane. 

In this case, the geometrical coordinate connecting stable forms is not specified in detail (as in the previous two examples), but is referred to simply as the reaction coordinate . Also the energy maxima have been designated as transition states as an indication that their structures may not be simply described (as the energy maxima for rotation in ethane and /7-butane). 

In the case of bond rotation in ethane, the reactants and products are the same and the reaction is said to be thermoneutral . This is also the case for the overall ring-inversion motion in cyclohexane. 

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. 

Simple yet important mechanistic cases concern the computation of rotational barriers around single bonds. A timely case in point is the rotational barrier of ethane, an old yet much debated subject [27, 28]. While the notion of hindered rotation in ethane is often... 

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 7. Modeling the C-C rotation in ethane, (a) Only the right hand tetrahedron moves (b) the cycle starts with the eclipsed Dih rotamer (c) one of the six chiramers (see text) (d) the Did staggered rotamer.

Figure 9. (a) A sinusoidal potential is superimposed on Figure 8a. (b)TheC-C rotation in ethane presented in the plane of potential vs. symmetry measure of Did, Dih, and C3 ). 

The restricted Hamiltonian operator for the internal rotation in ethane, in a random conformation, may be easily written by taking into account ... 

Use Spartan View to step through the sequence of structures showing bond rotation in ethane and 2,2-dimethylpropane, and compute the energy difference between staggered and eclipsed conformations for each molecule. Which molecule has a larger energy difference, and why ... 

Figure 1.6 Torsion strain energy versus bond rotation in ethane...

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