Ethane , symmetry

The origin of a torsional barrier can be studied best in simple cases like ethane. Here, rotation about the central carbon-carbon bond results in three staggered and three eclipsed stationary points on the potential energy surface, at least when symmetry considerations are not taken into account. Quantum mechanically, the barrier of rotation is explained by anti-bonding interactions between the hydrogens attached to different carbon atoms. These interactions are small when the conformation of ethane is staggered, and reach a maximum value when the molecule approaches an eclipsed geometry. 

Figure 4-11 The Potential Energy Form for Ethane. The midpoint of the range of oj is m =0° and the end points are 180°. The end points and the minima are identical by molecular symmetry and correspond to the stable staggered form.

In the case of ethylene, because of 2-fold symmetry, odd terms drop out of the series, V3, V5,... = 0. In the case of ethane, because of 3-fold symmeti-y, even temis drop out, V2, V4,... = 0. Terms higher than three, even though permitted by symmetry, are usually quite small and force fields can often be limited to three torsional terms. Like cubic and quaitic terms modifying the basic quadratic approximation for stretching and bending, terms in the Fourier expansion of Ftors (to) beyond n = 3 have limited use in special cases, for example, in problems involving octahedrally bound complexes. In most cases we are left with the simple expression... 

All bonds between equal atoms are given zero values. Because of their symmetry, methane and ethane molecules are nonpolar. The principle of bond moments thus requires that the CH3 group moment equal one H—C moment. Hence the substitution of any aliphatic H by CH3 does not alter the dipole moment, and all saturated hydrocarbons have zero moments as long as the tetrahedral angles are maintained. 

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... 

We know from Section 1.5 that cr bonds are cylindrically symmetrical. In other words, the intersection of a plane cutting through a carbon-carbon singlebond orbital looks like a circle. Because of this cjdindrical symmetry rotation is possible around carbon-carbon bonds in open-chain molecules. In ethane, for instance, rotation around the C-C bond occurs freely, constantly changing the spatial relationships between the hydrogens on one carbon and those on the other (Figure 3.5),... 

The potential energy is often described in terms of an oscillating function like the one shown in Figure 10.9(a) where the minima correspond to the relative orientations in which the interactions are most favorable, and the maxima correspond to unfavorable orientations. In ethane, the minima would occur at the staggered conformation and the maxima at the eclipsed conformation. In symmetrical molecules like ethane, the potential function reflects the symmetry and has a number of equivalent maxima and minima. In less symmetric molecules, the function may be more complex and show a number of minima of various depths and maxima of various heights. For our purposes, we will consider only molecules with symmetric potential functions and designate the number of minima in a complete rotation as r. For molecules like ethane and H3C-CCI3, r = 3. 

Because of the small difference between the electronegativities of carbon and hydrogen, alkanes have very small dipole moments, so small that they are difficult to measure. For example, the dipole moment of isobutane is 0.132 and that of propane is 0.085 Of course, methane and ethane, because of their symmetry, have no dipole moments. Few organic molecules have dipole moments greater than 7 D. 

C09-0029. Use molecular symmetry to determine if ethane (C2 Hg) and ethanol (C2 H5 OH) have dipole moments. 

The threefold symmetry of rotation about the C—C bond of ethane disappears when substituents are introduced on both of the carbon... 

The wealth of information accessible by analyzing this type of PFG NMR data is reflected in Figure 3.1.1. This shows a representation of the (smoothed) propagators for ethane in zeolites NaCaA (a special type of nanoporous crystallite) at two different temperatures and for two different crystal sizes. Owing to their symmetry in space, it is sufficient to reproduce only one half of the propagators. In fact,... 

What are the symmetry groups of the possible conformations of the ethane molecule ... 

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,... 

One of the suitable examples of sizable molecules may be ethane. The trans form belongs to the symmetry D3(l. The HO s are degenerate leg MO, which are largely localized at C—Hbondsand have bonding character on these bonds. The mode of extension is indicated below 89.00). The LU is also localized at C—H bonds and antibonding. It is understood that most of the ionic and radical reactions of aliphatic hydrocarbons have some concern with the C—H bond. 

The donor and acceptor classes illustrated with hydrocarbons can be directly extended to include hetero-atoms. For example, the alcohol moiety q /H would be a 4e donor, of the same orbital symmetry as the ethane moiety Similarly the carbonyl... 

Metal salen complexes can adopt non-planar conformations as a result of the conformations of the ethane-1,2-diyl bridge. The conformations may have Cs or C2 symmetry, but the mixtures are racemic. Replacement of the ethylenediamine linker by chiral 1,2-diamines leads to chiral distortions and a C2 chiral symmetry of the complex due to the half-chair conformation of the 5-membered ring of the chelate. Depending on substitution at the axial positions of the salen complex, the symmetry may be reduced to Q, but as we have seen before in diphosphine complexes of rhodium (Chapter 4) and bisindenyl complexes of Group 4 metals (Chapter 10) substitution at either side leads to the same chiral complex. Figure 14.10 sketches the view from above the complex and a front view. 

Figure 3. Different conformations with different symmetries in ethane, H3C-CH3 (left) and 1,2-dichloroethane, CIH2C-CH2CI (right). ...

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