Quantum chemical analysis of the energetics of the anti and gauche conformers of ethanol
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- Scheiner, S. & Seybold, P.G. Struct Chem (2009) 20: 43. doi:10.1007/s11224-008-9395-7
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Ethanol displays two stable conformers, the classic anti (or trans) form and a gauche conformation in which the hydroxyl hydrogen points toward one of the methyl hydrogens. Surprisingly, the two forms have nearly equal energies, and in the vapor phase the gauche form predominates because of its twofold degeneracy. An analysis of the energetics of these conformers based on natural bond orbital analysis helps to explain the apparently anomalous near degeneracy of these conformers.
KeywordsRotamersLone pairsNBOCharge transfer
Ethanol was among the first organic chemicals to be synthesized and remains today a classic organic chemical, an important industrial product, a key biofuel, and a molecule of astronomical interest . It has long been recognized that the ethanol molecule itself can exist in two stable rotameric forms, anti (or trans) and gauche, although in textbooks  and other venues  the molecule is almost always depicted in its paradigmatic anti form. Historically, because of instrumental and other experimental limitations, most early studies of ethanol focused almost exclusively on the anti conformer, although by the 1970s experimental studies confirmed the presence of the stable gauche form [4–6].
An early study by Barnes and Hallam  estimated the ratio of anti to gauche conformers at room temperature in the vapor phase to be roughly 2:1. However, a microwave study by Kakar and Quade , a far-IR study by Durig and Larsen , and a 1996 microwave study by Pearson et al.  have all indicated that the energy of the gauche form lies only about 40 cm−1 above that of the anti conformer, so that one might expect a preponderance of the gauche form at room temperature because of its two-fold degeneracy. An IR/VCD study has indeed reported a 42:58 anti/gauche ratio for the two conformers .
Difference in energy (gauche–anti) and geometric details calculated for ethanol by different methods
r(Ho−Hb1)a gauche (Å)
φ(CCOHo)a gauche (degs)
It is thus clear from both experimental and theoretical perspectives that the anti and gauche conformers of ethanol have very nearly equal energies. What is curious about this finding is that whereas in the anti form the hydroxyl hydrogen points symmetrically away from the methyl hydrogen atoms, thereby avoiding contact with these atoms, inspection of the gauche form shows that its –OH hydrogen is oriented directly toward one of the methyl hydrogens, an orientation that might be expected to have a notably unfavorable effect on the energy.
There have been attempts to rationalize this surprisingly small energy difference over the years. As one example, an early proposal  explained OH frequency shifts  by suggesting that an oxygen lone pair can delocalize into the CH σ* antibonding orbital when the two are anti to one another, thereby weakening the CH bond, and shifting its stretching frequency to the red. Despite the experimental and theoretical scrutiny that these forms have received over several decades, so far as we are aware no satisfactory explanation for the surprising near degeneracy of these two conformers and the geometry of the gauche form has been presented. Here, we examine the energetic influences prevailing in these conformers and suggest an explanation for their nearly equal energies and for the apparently counterintuitive geometry of the gauche form.
The calculations reported here were performed using Spartan06 (Wavefunction, Inc., 18401 Von Karman Ave., Suite 370, Irvine, CA 92612) and the Gaussian03 suite  of programs. Several different basis sets were applied, all of which were internal to the computer codes. Geometries were fully optimized, with no restrictions. Wave functions were analyzed using the NBO formalism of Reed et al.  [21, 22].
Differences in bond lengths and sums of E(2), between gauche and anti conformers (G–A), calculated at MP2 level
Taking the C–Ha2 bond as an example, in the anti-geometry there are three orbitals which transfer charge into its σ* orbital. There is an energy contribution of 2.64 kcal/mol arising from the C–Hb1 bonding orbital. Another 9.34 kcal/mol comes from the two O lone pair orbitals; of the latter sum, 8.40 kcal/mol, or 90%, is attributable to the O lone pair that is essentially a p-orbital, perpendicular to the C–O–Ho plane, and that nearly eclipses the C–Ha2 bond. Altogether, there is a total of 11.94 kcal/mol resulting from charge transfer into the C–Ha2 antibond in the anti configuration. Turning next to the gauche structure, there are again three orbitals that transfer charge into the C–Ha2 antibond. The C–Hb1 bonding orbital contributes 2.54 kcal/mol, not very different from its 2.64 in the anti structure. The O–H bond makes another contribution, in the amount of 2.46 kcal/mol. There is only one O lone pair (a sort of sp2 hybrid that eclipses the C–Ha2 bond) that contributes, in the amount of 3.62 kcal/mol. The total of these three contributions is 8.62 kcal/mol, smaller by 3.32 kcal/mol than in the case of the anti structure. It is this value that is reported as the last entry in Table 2, which lists the difference in E(2) between the gauche and anti structures for each bond.
What is perhaps apparent from the above discussion of the C–Ha2 antibonding orbital is that the contributing orbitals all lie roughly parallel to the bond in question. That is, in the context of the anti structure, the C–Hb1 bond is anti (180°) to the C–Ha2 bond, and the O lone pair that is the major contributor (p-orbital) is roughly parallel to C–Ha2. Likewise in the case of the gauche geometry, the bonds that are anti to C–Ha2 are C–Hb1 and O–Ho. Since one of the two O lone pairs is orthogonal to C–Ha2 in the gauche structure, charge transfer into its antibonding orbital is very severely diminished (by 61%). Considering the O–Ho bond as another example, it is not surprising that its contributors are the C–C bond in the anti conformer and C–Ha2 in the gauche conformer. This pattern in which the major components of charge transfer arise from orbitals that are coplanar to one another is in fact the dominating factor in the trends observed in both charge transfer and bond length.
Total charge transfer energy (E(2), kcal/mol) into indicated antibonds, arising from O lone pairs
In summary, then, one can explain the near degeneracy of the anti and gauche conformers by a compensatory effect. The anti structure is stabilized by charge transfer from the O lone pairs into the C–Ha1 and C–Ha2 bonds that are each trans to one of the lone pairs. Internal rotation into the gauche conformer retains the C–Ha1 interaction, and simply replaces the C–Ha2 charge transfer with a like process that involves the C–C bond. We note in passing that in related compounds additional influences may substantially shift the conformer equilibrium. In 2,2,2-trifluoroethanol, for example, where –OH···F attractions are present, calculations at the B3LYP/6–311++G** level show the gauche form to be more stable by 9 kJ/mol, and in 2,2,2-trichloroethanol the calculations show the gauche form to be more stable by 12 kJ/mol.