Structural Chemistry

, Volume 20, Issue 1, pp 43–48

Quantum chemical analysis of the energetics of the anti and gauche conformers of ethanol

Authors

    • Department of Chemistry and BiochemistryUtah State University
  • Paul G. Seybold
    • Departments of Chemistry and BiochemistryWright State University
Original Research

DOI: 10.1007/s11224-008-9395-7

Cite this article as:
Scheiner, S. & Seybold, P.G. Struct Chem (2009) 20: 43. doi:10.1007/s11224-008-9395-7

Abstract

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.

Keywords

RotamersLone pairsNBOCharge transfer

Introduction

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 [1]. 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 [2] and other venues [3] 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 [46].

An early study by Barnes and Hallam [7] 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 [8], a far-IR study by Durig and Larsen [9], and a 1996 microwave study by Pearson et al. [10] 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 [11].

Theoretical studies of the two conformers, although differing in specific details, have generally shown the two conformers to have closely comparable energies. Indeed, even changes in basis set or application of electron correlation can cause a reversal in the order [12], and vibrational effects can also play a major role [11]. For example, using a 4-21G basis set Van Alsenoy et al. [13] found the gauche form to be more stable by 0.15 kcal/mol. A study by Görbitz [12] using second-order Møller–Plesset perturbation theory (MP2) with a 6-311G** basis set also showed the gauche conformer to be slightly lower in energy. However, an MP4/6-31+G** calculation by Shaw et al. [11] found the anti form to be more stable by 0.52 kJ/mol. A more recent density functional theory B3LYP/6-311++G** study by Coussan et al. [14] places the anti conformer 0.42 kJ/mol lower in energy than the gauche conformer. Senent et al. [15] used Dunning’s correlation consistent triple zeta basis set with Møller–Plesset perturbation theory up to MP4 and obtained the anti form falling 19 cm−1 below the gauche form. Weibel et al. [16] have carried out a number of higher-level ab initio calculations including coupled cluster calculations, and found that both MP4 and CCSD(T) single-point calculations place the gauche form about 0.13 kcal/mol below the anti form. These workers also noted that the narrower potential well for the gauche torsion results in a zero-point energy larger by about 113–125 cm−1 for this form, which can reverse the order. Some representative calculated energies for the two conformers are given in Table 1.
Table 1

Difference in energy (gaucheanti) and geometric details calculated for ethanol by different methods

Level

ΔE (kJ/mol)

r(Ho−Hb1)a gauche (Å)

φ(CCOHo)a gauche (degs)

Refs.

HF 6-31G*

−0.45

2.548

63.8

b

HF 6-311+G**

−1.18

2.549

62.6

b

B3LYP/6-31G*

1.33

2.540

61.6

b

B3LYP/6-311G**

1.05

2.534

60.7

b

B3LYP/6-311++G**

−0.17

2.549

60.0

b

B3LYP/cc-pVTZ

0.13

2.543

60.4

b

MP2/6-31+G*

−0.72

2.534

60.9

b

MP2/6-311++G**

0.06

2.472

57.0

b

MP2/cc-pVTZ

−0.28

2.493

60.0

b

MP2/6-311++G(3df,3pd)

0.97

2.506

60.8

b

MP2/cc-pVQZ

1.03

2.496

60.0

b

MP2/aug-cc-pVQZ

1.04

2.500

60.0

b

MP4/6-31+G**

−0.52

  

c

CCSD(T)/6-311++G**

0.49

  

d

aAtomic labeling from Fig. 1

bThis work

cRef. [11]

dRef. [17]

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 [17] explained OH frequency shifts [18] 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.

Calculations

The calculations reported here were performed using Spartan06 (Wavefunction, Inc., 18401 Von Karman Ave., Suite 370, Irvine, CA 92612) and the Gaussian03 suite [19] 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. [20] [21, 22].

Results

It is sometimes thought that the gauche structure ought to be higher in energy than the anti rotamer by virtue of a closer contact between the hydroxyl H atom H0 and the methyl H labeled Hb1 in Fig. 1. However, this interatomic distance is about 2.5 Å in the optimized gauche structure, as indicated in Table 1. This relatively long interhydrogen distance, 0.1 Å greater than the sum of the van der Waals radii, would argue for only very minimal steric repulsion. Moreover, the closest –OH···H contacts are actually those with the Cα hydrogens, Ha1 and Ha2, for both the anti (2.34 Å, two contacts) and the gauche (2.35 Å, one contact) conformers.
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-008-9395-7/MediaObjects/11224_2008_9395_Fig1_HTML.gif
Fig. 1

Anti and gauche conformers of ethanol, showing atomic labeling used below

One might seek hints as to the near degeneracy of the two conformers in the details of the covalent bond lengths. The differences between gauche and anti bond lengths are reported in Table 2 using several different basis sets, all at the MP2 level. The positive entries in the first row indicate that the hydroxyl O–Ho bond is nearly 1 mÅ longer in the gauche conformer when compared to the anti value. Two of the largest differences occur for the C–C bond, which is about 6 mÅ longer in the gauche form, and the C–O, bond, which is 2–3 mÅ shorter. Within the subset of C–H bonds, the C–Ha2 bond shows the greatest change, about 5 mÅ shorter in gauche, followed by the 2.5 mÅ lengthening of C–Hb1. There are certain aspects of these trends which are intriguing. The change in the C–Hb1 bond length is certainly understandable in light of the much closer approach of Ho to this atom in the gauche arrangement. On the other hand, it is not obvious from the outset why the C–Ha2 bond should be so sensitive to C–OH rotation, as the Ho atom is not situated very close to Ha2 in either structure.
Table 2

Differences in bond lengths and sums of E(2), between gauche and anti conformers (G–A), calculated at MP2 level

 

Δra (mÅ)

ΔE(2)b

6-31+G**

6-311++G(3df,3pd)

cc-pVQZ

aug-cc-pVQZ

kcal/mol

O–Ho

0.7

0.8

0.6

0.7

1.14

C–O

−1.3

−3.0

−1.8

−3.0

−1.64

C–C

6.3

6.1

5.6

5.9

4.43

C–Hb1

2.5

2.6

2.5

2.7

0.27

C–Hb2

0.1

0.2

0.0

0.3

0.07

C–Hb3

0.5

1.0

1.0

1.0

0.16

C–Ha1

0.5

0.6

0.1

0.5

0.34

C–Ha2

−5.7

−5.0

−5.4

−5.0

−3.32

aGaucheanti

bComputed with aug-cc-pVQZ basis set

In order to obtain some insights into the underlying reasons for the changes in bond lengths, NBO analysis was carried out on the wave functions associated with the anti and gauche geometries. Of particular interest was the possibility of charge transfer into the antibonding orbitals of each of these bonds. The energetic consequence of such charge transfer is measured via E(2), the second-order perturbation theory component, which is defined as
$$ E_{ij}\left( 2\right) = q_{i} \left( {F_{ij}^{ 2} /\varepsilon_{j} - \varepsilon_{i} } \right), $$
(1)
where q refers to the donor orbital occupancy, Fij to the off-diagonal NBO Fock matrix element, and \( \varepsilon_{i} \) to the orbital eigenvalue. For each bond, the values of all charge transfers into the relevant antibonding orbital were added together to arrive at a total charge transfer energy for that particular bond.

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.

Indeed, the change in the total charge transfer energy, on going from anti to gauche, does appear to correlate quite well with the change in the length of each bond. This correlation is evident in Fig. 2 where the values of ΔE(2) in the last column of Table 2 for all the different bonds are compared with the bond length elongation or contraction in the preceding column of the table. In all cases, an increase of charge transfer into a given bond’s antibonding orbital correlates with an elongation, and a presumed weakening, of the bond while a lowering of transfer into the antibond shortens and strengthens this bond. The linear relationship is fair, with a correlation coefficient r = 0.863. The slope of the best-fit straight line is such that each 1 kcal/mol increase in charge transfer energy corresponds to an elongation of the pertinent bond by 1.15 mÅ.
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-008-9395-7/MediaObjects/11224_2008_9395_Fig2_HTML.gif
Fig. 2

Linear correlation between gauche-anti bond length differences and NBO charge transfer ΔE(2)

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.

Finally, we turn our attention to the fundamental distinctions between the anti and gauche structures, with respect to the idea that charge transfer, as described above, can help stabilize or destabilize the system. Bearing in mind that the lone pairs are better suited to release charge than are the covalent bonds, due to the constrained nature of the latter, we focus our attention on the orientation of the two O lone pairs, whose orientations are illustrated in Fig. 3 for the two configurations. The NBO localized description of the wave function provides for two different orbitals, which would fit into the general notion of sp2 hybridization of the O atom. Thus one lone pair, LP1, corresponds to the third sp2 orbital, lying in the C–O–Ho plane. LP2 represents the third p-orbital of O, which is perpendicular to the latter plane. The numbers displayed in Fig. 3 represent the charge transfer energy E(2) (in kcal/mol) from each lone pair to the indicated C–H or C–C antibond. The charge transfers associated with LP1 are fairly modest. The largest value, 3.62 kcal/mol, occurs for the C–Ha2 antibond in the gauche configuration. The size of this contribution may be attributed to the fact that this lone pair very nearly eclipses the C–Ha2 bond, i.e. the dihedral angle is 0°. The p-orbital, LP2, seems much more capable of transferring charge, with quantities in excess of 8 kcal/mol. Most importantly, these large degrees of transfer occur for those C–H and C–C bonds which are most closely aligned with the p-orbital. The charge transfers are equal to 8.40 kcal/mol for the C–Ha1 and C–Ha2 antibonds in the anti configuration, while there is no such transfer into C–C which is orthogonal to LP2. A similar pattern is evident for the gauche structure, where the C–Ha1 and C–C antibonds are now the recipients of charge transfer, while the orthogonal C–Ha2 antibond receives none. In summary then, the charge transfer from the O lone pairs is maximized by a roughly coplanar alignment with the recipient antibond.
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-008-9395-7/MediaObjects/11224_2008_9395_Fig3_HTML.gif
Fig. 3

Disposition of two localized lone pairs in the anti and gauche conformers. LP1 refers to sp2-type lone pair, and LP2 to p-orbital. The amount of charge transfer energy E(2) from the indicated lone pair to the labeled CH and CC antibonds are included, in kcal/mol

There has been some discussion in the literature as to whether the two hydroxyl O lone pairs are better described as the aforementioned sp2 hybrid and p-orbital, or as a pair of equivalent “rabbit ears” that would follow from an sp3-hybridization of the oxygen atom [23, 24]. In fact, the two descriptions are equivalent as one is related to the other by a unitary transformation of the total wave function. It follows that a rabbit-ear description ought to obey the same patterns of charge transfer as does the sp2 hybrid and p-orbital description. Figure 4 illustrates the sp3-disposition of lone pairs from which it may be observed that there is a lone pair anti to the C–Ha1 bond, for both the anti and gauche structures. Since the anti (or syn) arrangement of the charge-donating lone pair and the accepting antibond corresponds to a planar alignment, with a zero dihedral angle, it is hence not surprising to note from the first row of Table 3 that the charge transfer into the C–Ha1 antibond from the O lone pairs is about the same for both conformers. In the case of C–Ha2, however, this C–H bond is anti to a lone pair in the anti conformer, but there is no such anti lone pair in the gauche structure. There is consequently a strong diminution in the lone pair charge transfer, by a factor of nearly three, on going from anti to gauche, as documented in the second row of Table 3. The trend in the C–C bond is just the opposite, in that the lone pair transfer is much larger in the gauche structure, which is easily explained by the presence of an O lone pair anti to C–C in gauche, but not in the anti conformer. The dominating influence of the two O lone pairs is reinforced by inspection of Table 2 which reveals that it is the aforementioned C–C and C–Ha2 bonds that undergo by far the largest changes in both bond length and ΔE(2).
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-008-9395-7/MediaObjects/11224_2008_9395_Fig4_HTML.gif
Fig. 4

Disposition of two equivalent sp3 “rabbit ear” O lone pairs in the anti and gauche conformers

Table 3

Total charge transfer energy (E(2), kcal/mol) into indicated antibonds, arising from O lone pairs

Antibond

Anti

Gauche

CHa1

9.30

9.70

CHa2

9.30

3.62

C–C

1.20

9.23

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.

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