One of the most general structural features of saturated hydrocarbons is the preference for staggered versus eclipsed conformations. This preference is seen with the simplest hydrocarbon with a carbon-carbon bond—ethane. The staggered conformation is more stable than the eclipsed by 2.9 kcal/mol, as shown in Figure 1.33.102
The preference for the staggered conformation continues in larger acyclic and also cyclic hydrocarbons, and is a fundamental factor in the conformation of saturated hydrocarbons (see Section 2.2.1). The origin of this important structural feature has been the subject of ongoing analysis.103 We consider here the structural origin of the energy barrier. A first step in doing so is to decide if the barrier is the result of a destabilizing factor(s) in the eclipsed conformation or a stabilizing factor(s) in the staggered one. One destabilizing factor that can be ruled out is van der Waals repulsions. The van der Waals radii of the hydrogens are too small to make contact, even in the eclipsed conformation. However, there is a repulsion between the bonding electrons. This includes both electrostatic and quantum mechanical effects (exchange repulsion) resulting from the Pauli exclusion principle, which requires that occupied orbitals maintain maximum separation (see Section 1.1.2). There is also a contribution from nuclear-nuclear repulsion, since the hydrogen nuclei are closer together in the eclipsed conformation. The main candidate for a stabilizing interaction is delocal- ization (hyperconjugation). The staggered conformation optimizes the alignment of the and∗orbitals on adjacent carbon atoms.
Fig. 1.33. Potential energy as a function of rotation angle for ethane.
102 K. S. Pitzer,Disc. Faraday Soc.,10, 66 (1951); S. Weiss and G. E. Leroi,J. Chem. Phys.,48,962 (1968); E. Hirota, S. Saito, and Y. Endo,J. Chem. Phys.,71, 1183 (1979).
103 R. M. Pitzer,Acc. Chem. Res.,16, 207 (1983).
79
TOPIC 1.1 The Origin of the Rotational (Torsional) Barrier in Ethane and Other Small Molecules C
C C C
H
H H
H
The repulsive electronic interactions were emphasized in early efforts to under- stand the origin of the rotational barrier.104 In particular the character of the z, y,z, andy(see Figure 1.34) was emphasized.105The repulsive interactions among these orbitals are maximized in the eclipsed conformation.
Efforts have been made to dissect the contributing factors within an MO framework. The NPA method was applied to ethane. Hyperconjugation was found to contribute nearly 5 kcal/mol of stabilization to the staggered conformation, whereas electron-electron repulsion destabilized the eclipsed conformation by 2 kcal/mol.106 These two factors, which favor the staggered conformation, are partially canceled by other effects. The problem is complicated by adjustments in bond lengths and bond angles that minimize repulsive interactions. These deformations affect the shapes and energies of the orbitals. When the effects of molecular relaxation are incorporated into
π'z π'y
σx
πz πy
σ'
σ
Fig. 1.34. Molecular orbitals of ethane revealingcharacter ofz,y,z, andy orbitals. Only filled orbitals are shown.
104 J. P. Lowe,J. Am. Chem. Soc.,92, 3799 (1970); J. P. Lowe,Science,179, 527 (1973).
105 E. T. Knight and L. C. Allen,J. Am. Chem. Soc.,117, 4401 (1995).
106 J. K. Badenhoop and F. Weinhold,Int. J. Quantum Chem.,72, 269 (1999).
80
CHAPTER 1 Chemical Bonding and Molecular Structure
the analysis, the conclusion reached is that delocalization (hyperconjugation) is the principal factor favoring the staggered conformation.107
When methyl groups are added, as in butane, two additional conformations are possible. There are two staggered conformations, called anti and gauche, and two eclipsed conformations, one with methyl-methyl eclipsing and the other with two hydrogen-methyl alignments. In the methyl-methyl eclipsed conformation, van der Waals repulsions come into play. The barrier for this conformation increases to about 6 kcal/mol, as shown in Figure 1.35. We pursue the conformation of hydrocarbons further in Section 2.2.1.
Changing the atom bound to a methyl group from carbon to nitrogen to oxygen, as in going from ethane to methylamine to methanol, which results in shorter bonds, produces a regulardecreasein the rotational barrier from 2.9 to 2.0 to 1.1 kcal/mol, respectively. The NPA analysis was applied to a dissection of these barriers.108The contributions to differ- ences in energy between the eclipsed and staggered conformations were calculated for four factors. These are effects on the localized bondsELewis, hyperconjugationEdeloc, van der Waals repulsionsEsteric, and exchangeE2×2. The dominant stabilizing terms are theEdelocandE2×2, representing hyperconjugation and exchange, respectively, but
Fig. 1.35. Potential energy diagram for rotation about the C(2)−C(3) bond in butane.
107 V. Pophristic and L. Goodman,Nature,411, 565 (2001); F. Weinhold,Angew. Chem. Int. Ed. Engl., 42, 4188 (2003).
108 J. K. Badenhoop and F. Weinhold,Int. J. Quantum Chem.,72, 269 (1999).
81
TOPIC 1.2 Heteroatom Hyperconjugation (Anomeric Effect) in Acyclic Molecules
this analysis indicates that the overall barrier results from compensating trends in the four components. These results pertain to a fixed geometry and do not take into account bond angle and bond length adjustments in response to rotation.
CH3CH3 CH3NH2 CH3OH
ELewis −1423 −0766 −0440
Edeloc +4953 +2920 +1467
Esteric −0827 −0488 −1287
E2×2 +2009 +1483 +0475
Etotal +4712 +3149 +0215
The methanol rotational barrier was further explored, using the approach described above for ethane.109 The effect of changes in molecular structure that accompany rotation were included. The approach taken was to systematically compare the effect on the rotational barrier of each specific interaction, e.g., hyperconjugation and exchange repulsion, and to determine the effect on molecular geometry, i.e., bond lengths and angles. The analysis of electrostatic forces (nuclear-nuclear, electron-electron, and nuclear-electron) showed that it was the nuclear-electron forces that are most important in favoring the staggered conformation, whereas the other two actually favor the eclipsed conformation. The structural response to the eclipsed conformation is to lengthen the C−O bond, destabilizing the molecule. The more favorable nuclear- electron interaction in the staggered conformation is primarily a manifestation of hyperconjugation. In comparison with ethane, a major difference is the number of hyperconjugative interactions. The oxygen atom does not have any antibonding orbitals associated with its unshared electron pairs and these orbitals cannot act as acceptors.
The oxygen unshared electrons function only as donors to the adjacentantiC–H bonds The total number of hyperconjugative interactions is reduced from six in ethane to two in methanol.
six anti H-H combinations
two anti H-H combinations H
H H
H H
H
H
H H
O H
Topic 1.2. Heteroatom Hyperconjugation (Anomeric Effect) in Acyclic