Gauche preference in 1,2-difluoroethane originates from both orbital and electrostatic stabilization interactions

Abstract

The origin of the gauche preference in 1,2-difluoroethane has been investigated by using an energy decomposition analysis (EDA). The EDA results show that favourable orbital interactions are not the sole source of stabilization in this conformer. Electrostatic interactions, too, are more attractive in the gauche than in the anti form. This finding opposes our traditional view of electrostatic interactions and their influence on conformational equilibria, but points out that they should be considered as an all-charge phenomenon, rather than partial interaction between pairs of bonds.

---

Introduction

It is often the case in chemistry that conformational preferences do not follow our intuition. For example, despite the expected strong electrostatic destabilization of the gauche conformer of 1,2-difluoroethane (DFE), due to the C–F bond dipolar repulsion, DFE prefers the gauche conformation over the anti by 0.5–1 kcal mol⁻¹, even in the gas phase.^1,2 On the other hand, 1,2-dichloroethane (DCE) and 1,2-dibromoethane (DBE), with weaker dipolar repulsion, prefer the anti conformation.^1,3 The tendency of vicinal highly electronegative substituents or lone pairs to adopt the gauche form has been termed as the “gauche effect” and rationalized as an influence of nucleus–electron attraction (V_ne) on the balance between attractive (V_ne) and repulsive effects (nucleus–nucleus and electron–electron repulsion, V_nn and V_ee, and kinetic energy of electrons, T).⁴ Epiotis⁵ offered an explanation in terms of attractive interactions between lone pairs, provided an antibonding orbital of appropriate symmetry is present in the molecule.

Currently, there are two main explanations for the “gauche effect” in DFE: bent bonds and hyperconjugation. According to the bent bond model, proposed by Wiberg and co-workers,⁶ the highly electronegative fluorine creates bond bending at the carbon nuclei, the sense of which weakens the C–C bond in anti conformer more than in gauche conformer (Fig. 1a).⁶ The bent bond model was questioned by the natural bond orbital (NBO) study of Goodman and co-workers,⁷ who calculated too small difference in the amount of orbital overlap between conformers to account for the observed gauche stabilization. More widely used hyperconjugation model invokes σ_C–H → σ^*_C–F charge transfer as a stabilizing factor in the gauche form. This type of orbital interaction is maximized when C–H and C–F bonds adopt antiperiplanar orientation (Fig. 1b).^3,7,8 However, the computational data have shown that the magnitude of σ_C–H → σ^*_C–X hyperconjugative interactions increase in the order X = F < Cl < Br.^3,8c,9 Obviously, other factors are involved, too. Thus, it was found that the σ_C–X → σ^*_C–X hyperconjugation (X = Cl, Br) contributes to the stabilization of anti DCE and DBE.^3,8c,9a In an interesting work, designed to test the hyperconjugation model in 2-substituted-1-fluoroethanes, Rablen et al.² concluded that it is the interplay of hyperconjugation, electrostatic and steric effects that influences conformational behaviour of the studied molecules.

Fig. 1 Bent bond model (a) and hyperconjugation model (b) used to explain the gauche preference in 1,2-difluoroethane.

Interestingly, the “gauche effect” in DFE was correctly predicted by dipolar and lone pair interactions of molecular mechanics, without invoking molecular orbital effects.¹⁰ A recent work of Freitas et al.¹¹ showed that ¹J_CF coupling constant in DFE is independant of hyperconjugation.

The fluorine “gauche effect” is also found in various fluorinated compounds having an electronegative or positively charged substituent in the β-position,^8b,12 with a significant potential for synthetic application.¹³ In the latter case (β-positively charged group), the gauche preference is attributed to both hyperconjugative and attractive electrostatic interactions.

Although, the “gauche effect” is found in many other molecules,^4,8a,14 DFE has been considered as a benchmark to understand its origin. Moreover, the F/F gauche preference influences conformational stability of extended and of polyfluorinated molecules, as well.¹⁵ Hence, in this study, the conformational preference in DFE is addressed from the standpoint of energy decomposition analysis (EDA), with an aim to get a further insight into its origin.

Computational methods

In the framework of EDA, DFE has been built from two CH₂F radicals. Total bonding energy ΔE between them consists of preparation energy ΔE_prep and interaction energy ΔE_int (eqn (1)).

ΔE = ΔE_prep + ΔE_int (1)

The ΔE_prep represents the amount of energy required to deform two CH₂F radicals from their equilibrium geometry to the one they adopt in DFE. The ΔE_int is the energy change occurring when these two prepared radicals interact to form the molecule. Localized molecular orbital EDA (LMOEDA) of Su and Li,¹⁶ implemented in the Gamess program package,¹⁷ allows a further decomposition of ΔE_int into five energy terms (eqn (2)).

ΔE_int = ΔE_es + ΔE_ex + ΔE_rep + ΔE_pol + ΔE_disp (2)

Electrostatic energy ΔE_es involves nucleus–nucleus and electron–electron repulsion, and nucleus–electron attraction between two prepared CH₂F radicals that adopt their positions in the final molecule. Total electrostatic energy is usually stabilizing (negative), since nucleus-electron attraction outweighs the two repulsive terms. Exchange energy ΔE_ex refers to the quantum-mechanical exchange of electrons. Repulsion energy ΔE_rep comes from partially overlapping electron densities of the two fragments. The first one is stabilizing, the second destabilizing. Taken together, they form the exchange repulsion¹⁸ or Pauli repulsion¹⁹ of other EDA schemes, which is a destabilizing (positive) energy term. Polarization energy ΔE_pol is an orbital relaxation energy which arises from a change in orbital shapes upon binding, including also empty-occupied orbital mixing within one fragment due to the presence of another one (polarization) and between two fragments (charge transfer). Dispersion energy ΔE_disp comes from electron correlation. Both ΔE_pol and ΔE_disp are stabilizing effects.

Geometry optimizations were done by using the Gaussian 09 program package,²⁰ at the DFT level using the B3LYP functional²¹ and 6-311+G** basis set.²²

Results and discussion

The optimized structural parameters of gauche and anti conformers of DFE are given in Table 1 (see the ESI† for absolute energies and x, y, z coordinates). They compare well with the experimental data.²³ Principal structural changes that accompany anti to gauche rotation are: (1) 0.014 Å C–C and 0.003 Å C–F bond shortening, (2) 0.003 Å C–H bond lengthening, which is anti to the C–F bond on the other carbon, (3) 2.9° CCF bond angle opening and (4) 1.6° CCH bond angle closing, which is anti to the C–F bond on the other carbon. The decrease/increase in the C–C/C–H bond lengths is consistent with the hyperconjugation model, but not a decrease in the C–F bond length. The above mentioned structural changes have significant consequences on the gauche/anti energy difference and particularly on the individual energy terms contributing to this difference, as will be discussed.

Table 1 Theoretically calculated and experimentally determined bond lengths (d/Å), bond angles (τ/°) and torsional angles (θ/°) of anti and gauche conformers of 1,2-difluoroethane (DFE) and differences between them (Δgauche–anti)

Conformation	Method	dCC	dCF	dCH^a	dCH^b	τCCF	τCCH^a	τCCH^b	θFCCF
a Gauche to the CF bond on the other carbon.b Anti to the CF bond on the other carbon.c From ref. 23a (infrared spectroscopy).d From ref. 23b (microwave spectroscopy).
Anti-DFE	B3LYP/6-311+G**	1.5184	1.3994	1.0922		108.04	111.24		180
	Experimental^c	1.501(4)	1.401(6)	1.094(2)		107.4(5)	111.4(2)
Gauche-DFE	B3LYP/6-311+G**	1.5046	1.3966	1.0930	1.0950	110.90	110.98	109.62	71.96
	Experimental^d	1.493(8)	1.390(3)	1.099(2)	1.093(5)	110.6(5)	108.4(6)	111.3(6)	71.0(3)
ΔGauche–anti	B3LYP/6-311+G**	−0.0138	−0.0028	0.0008	0.0028	2.86	−0.26	−1.62

---

The EDA was done at the UB3LYP/6-311+G** level. Effects of various structural changes that accompany anti → gauche rotation on the individual energy terms are presented in Table 2 (absolute values for various structures are given in Table S1 in the ESI†). First, rigid anti → gauche rotation will be examined. This means that only torsional angle changes from 180° in anti to 72° in gauche conformer. The total energy ΔE decreases by 0.48 kcal mol⁻¹, which is mainly due to the more favourable orbital interactions, that is ΔE_pol decreases (becomes more negative) by 0.65 kcal mol⁻¹. The exchange repulsion (or Pauli repulsion), ΔE_ex+rep, and ΔE_disp also contribute to the energy lowering by 0.15 kcal mol⁻¹ and 0.14 kcal mol⁻¹, respectively. A decrease in the repulsive term appears a bit counterintuitive, since the two fluorine atoms come closer to each other. However, it should be noted that this energy change refers to the total exchange repulsion. Moreover, small atomic volume of fluorine should not bring about strong repulsion. The electrostatic energy is raised by 0.46 kcal mol⁻¹, which is consistent with our intuitive prediction that two C–F bond dipoles repel each other in gauche conformer.

Table 2 Contribution of various energy terms to the structural changes accompanying anti → gauche rotation.^a Values are in kcal mol⁻¹

Structural change	ΔEes	ΔEex+rep	ΔEpol	ΔEdisp	ΔEint	ΔEprep	ΔE
a ΔEes = electrostatic energy, ΔEex+rep = exchange repulsion energy, ΔEpol = polarization energy, ΔEdisp = dispersion energy, ΔEint = interaction energy, ΔEprep = preparation energy, ΔE = total bonding energy.
Rigid anti → gauche rotation	0.46	−0.15	−0.65	−0.14	−0.48	0.00	−0.48
Effect of geometry relaxation after rigid rotation	−4.55	8.81	−5.00	−0.04	−0.78	0.36	−0.42
Flexible anti → gauche rotation	−4.09	8.66	−5.65	−0.18	−1.26	0.36	−0.90
Effect of all bonds relaxation after rigid rotation	−5.61	10.26	−4.24	−0.26	0.15	−0.16	−0.01
Effect of only C–C bond shortening	−5.33	9.74	−4.17	−0.27	−0.02	0.00	−0.02
Effect of C–H and C–F bond changes	−0.28	0.52	−0.07	0.01	0.17	−0.16	0.01
Effect of all angles relaxation after rigid rotation	1.06	−1.45	−0.76	0.22	−0.93	0.53	−0.40
Effect of CCF bond angles widening	2.08	−3.99	−0.33	0.27	−1.97	1.70	−0.27
Effect of CCH bond angles closing	−1.02	2.54	−0.43	−0.05	1.04	−1.18	−0.14

---

In the next step, we consider the effect of geometry relaxation, following the rigid rotation. It lowers the energy by additional 0.42 kcal mol⁻¹, resulting in the total gauche/anti energy difference of 0.90 kcal mol⁻¹. This additional energy decrease comes from a decrease in the interaction energy ΔE_int by 0.78 kcal mol⁻¹, while preparation energy ΔE_prep increases by 0.36 kcal mol⁻¹, due to further deformation of CH₂F fragments.²⁴ Now, let us see how geometry relaxation affects individual energy terms contributing to ΔE_int. The only energy that becomes more destabilizing is the Pauli repulsion, which increases by 8.81 kcal mol⁻¹. The ΔE_disp changes negligibly, while both orbital and electrostatic interactions become more stabilizing by 5.00 kcal mol⁻¹ and 4.55 kcal mol⁻¹, respectively.

The total effect of structural relaxation can be divided into two parts: effect of bond length changes and effect of bond angle changes (Table 2). Changes of all bond lengths have almost no effect on the total energy since ΔE_prep decreases by 0.16 kcal mol⁻¹, but ΔE_int increases by 0.15 kcal mol⁻¹. The insensitivity of the total energy on the bond length changes has also been found by Goodman et al.⁷ The only cause for ΔE_int becoming less stabilizing after bonds relaxation is the increase in the Pauli repulsion energy by 10.26 kcal mol⁻¹. All the remaining three energies, ΔE_disp, ΔE_pol and ΔE_es, strengthen bonding interactions between CH₂F groups by 0.26 kcal mol⁻¹, 4.24 kcal mol⁻¹ and 5.61 kcal mol⁻¹, respectively. The main effect is exerted by the C–C bond shortening (Table 2). Changes of C–H and C–F bond lengths have significantly smaller influence on individual energy terms. Thus, the increase in both orbital and electrostatic attractive interactions can be considered as a driving force for the C–C bond shortening. The slight C–H bond lengthening, which is anti to the C–F bond on the other carbon, can be viewed as a consequence of σ_C−H → σ^*_C–F hyperconjugative interaction. However, instead of being increased, too, due to hyperconjugation, the C–F bond length decreases slightly, thus enhancing the electrostatic attractive interactions by 0.31 kcal mol⁻¹ with almost no effect on the orbital interaction energy. Apparently, bond length changes increase attractive electrostatic interactions more than the repulsive ones, resulting in stronger electrostatic attraction.

Bond angles relaxation increases ΔE_prep by 0.53 kcal mol⁻¹, but makes ΔE_int more attractive by 0.93 kcal mol⁻¹, enhancing total bonding interactions by 0.40 kcal mol⁻¹ (Table 2). The main cause for this enhancement is the relief of Pauli repulsion by 1.45 kcal mol⁻¹, caused by the CCF bond angle expansion. There is also increase in orbital interactions by 0.76 kcal mol⁻¹ induced by both CCF and CCH bond angle changes. The ΔE_es and ΔE_disp, however, become less attractive by 1.06 kcal mol⁻¹ and 0.22 kcal mol⁻¹, respectively. Hence, the release of Pauli repulsion can be considered as major driving force for bond angle changes, and additional enhancement of orbital interactions as minor.

Overall, the 0.90 kcal mol⁻¹ stabilization of gauche conformer of DFE relative to anti does not arise solely from stronger orbital interactions (including hyperconjugation), as is widely accepted in the literature. Contrary to our intuitive predictions, gauche conformer is also stabilized by electrostatic interactions more than the anti conformer. This observation points out that electrostatic interactions should be considered as an all-charge phenomenon, not as a partial interaction between pairs of bonds. Stabilization of gauche conformer relative to anti by orbital and electrostatic interactions amount 5.65 kcal mol⁻¹ and 4.09 kcal mol⁻¹, respectively (Table 2). Additional stabilization is provided by dispersion interactions, with significantly smaller magnitude of 0.18 kcal mol⁻¹, as could be expected for weakly polarizable atoms. These stabilizing interactions are opposed mostly by an increased Pauli repulsion, ΔE_ex+rep = 8.66 kcal mol⁻¹, and to smaller extent by the energy required to further deform CH₂F groups upon anti → gauche rotation, ΔE_prep = 0.36 kcal mol⁻¹. The observed electrostatic stabilization of gauche conformer supports the significance of nucleus–electron attraction recognized earlier by Wolfe⁴ and is also somewhat consistent with the correct prediction of “gauche effect” in DFE by molecular mechanics.¹⁰ Although, according to the presented EDA, without either electrostatic or orbital stabilization interactions, anti conformer would be the preferred one.

Conclusions

In summary, the energy decomposition analysis of bonding interactions between two CH₂F radicals, making up difluoroethane (DFE), revealed that gauche preference in this molecule does not originate only from more favourable orbital interactions, as is widely accepted in the literature. Shorter C–C bond in gauche conformer also enhances attractive electrostatic interactions, making gauche conformer more electrostatically stabilized than anti conformer. Although opposing our traditional view of electrostatic interaction influence on conformational equilibria, this finding indicates that electrostatic interactions should be considered as an all-charge phenomenon, not partial interactions between bond pairs. In addition, structural changes accompanying the rotation should not be neglected.

Acknowledgements

Financial support from the Ministry of Education, Science and Technological Development of the Republic of Serbia to Grant no. 172020 is acknowledged.

References

1. E. L. Eliel, S. H. Wilen and L. N. Mander, in Stereochemistry of Organic Compounds, John Wiley & Sons, Inc., New York, 1994, pp. 606–615.
2. P. R. Rablen, R. W. Hoffmann, D. A. Hrovat and W. Thatcher Borden, J. Chem. Soc., Perkin Trans. 2, 1999, 1719–1726 and references therein.
3. F. R. Souza, M. P. Freitas and R. Rittner, J. Mol. Struct.: THEOCHEM, 2008, 863, 137–140.
4. S. Wolfe, Acc. Chem. Res., 1972, 5, 102–111.
5. N. D. Epiotis, J. Am. Chem. Soc., 1973, 95, 3087–3096.
6. (a) K. B. Wiberg, M. A. Murcko, K. E. Laidig and P. J. MacDougall, J. Phys. Chem., 1990, 94, 6956–6959; (b) K. B. Wiberg, Acc. Chem. Res., 1996, 29, 229–234.
7. L. Goodman, H. Gu and V. Pophristic, J. Phys. Chem. A, 2005, 109, 1223–1229.
8. (a) T. K. Brunck and F. Weinhold, J. Am. Chem. Soc., 1979, 101, 1700–1709; (b) D. Y. Buissonneaud, T. Van Mourik and D. O'Hagan, Tetrahedron, 2010, 66, 2196–2202; (c) For a comprehensive review on hyperconjugation, see: I. V. Alabugin, K. M. Gilmore and P. W. Peterson, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2011, 1, 109–141.
9. (a) C. Trindle, P. Crum and K. Daglas, J. Phys. Chem. A, 2003, 107, 6236–6242; (b) I. Fernández and G. Frenking, Chem.–Eur. J., 2006, 12, 3617–3629; (c) Z. Chen, C. Corminboeuf and Y. Mo, J. Phys. Chem. A, 2014, 118, 5743–5747.
10. V. G. S. Box and L. L. Box, J. Mol. Struct., 2003, 649, 117–132.
11. M. P. Freitas, M. Bühl and D. O'Hagan, Chem. Commun., 2012, 48, 2433–2435.
12. (a) L. E. Combettes, P. Clausen-Thue, M. A. King, B. Odell, A. L. Thompson, V. Gouverneur and T. D. W. Claridge, Chem.–Eur. J., 2012, 18, 13133–13141; (b) I. Humelnicu, E.-U. Würthwein and G. Haufe, Org. Biomol. Chem., 2012, 10, 2084–2093; (c) S. Samdal, H. Møllendal and J.-C. Guillemin, J. Phys. Chem. A, 2011, 115, 9192–9198; (d) C. Sparr, E. Salamanova, W. B. Schweizer, H. M. Senn and R. Gilmour, Chem.–Eur. J., 2011, 17, 8850–8857; (e) N. E. J. Gooseman, D. O'Hagan, M. J. G. Peach, A. M. Z. Slawin, D. J. Tozer and R. J. Young, Angew. Chem., Int. Ed., 2007, 46, 5904–5908; (f) C. R. S. Briggs, M. J. Allen, D. O'Hagan, D. J. Tozer, A. M. Z. Slawin, A. E. Goeta and J. A. K. Howard, Org. Biomol. Chem., 2004, 2, 732–740; (g) D. O'Hagan, C. Bilton, J. A. K. Howard, L. Knight and D. J. Tozer, J. Chem. Soc., Perkin Trans. 2, 2000, 605–607.
13. (a) Y. P. Rey, L. E. Zimmer, C. Sparr, E.-M. Tanzer, W. B. Schweizer, H. M. Senn, S. Lakhdar and R. Gilmour, Eur. J. Org. Chem., 2014, 1202–1211; (b) E. M. Tanzer, W. B. Schweizer, M.-O. Ebert and R. Gilmour, Chem.–Eur. J., 2012, 18, 2006–2013; (c) E. M. Tanzer, L. E. Zimmer, W. B. Schweizer and R. Gilmour, Chem.–Eur. J., 2012, 18, 11334–11342; (d) L. E. Zimmer, C. Sparr and R. Gilmour, Angew. Chem., Int. Ed., 2011, 50, 11860–11871.
14. H. Senderowitz and B. Fuchs, J. Mol. Struct.: THEOCHEM, 1997, 395–396, 123–155.
15. D. O'Hagan, J. Org. Chem., 2012, 77, 3689–3699.
16. P. Su and H. Li, J. Chem. Phys., 2009, 131, 014102.
17. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. J. Su, T. L. Windus, M. Dupuis and J. A. Montgomery Jr, J. Comput. Chem., 1993, 14, 1347–1363 ; Gamess (2013-R1 version) was used in this work.
18. (a) K. Kitaura and K. Morokuma, Int. J. Quantum Chem., 1976, 10, 325–340; (b) K. Morokuma, Acc. Chem. Res., 1977, 10, 294–300.
19. G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C. Fronseca Guerra, S. J. A. Van Gisbergen, J. G. Snijders and T. Ziegler, J. Comput. Chem., 2001, 22, 931–967.
20. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09 (Revision D.01), Gaussian, Inc., Wallingford CT, 2013.
21. (a) A. D. Becke, J. Chem. Phys., 1993, 98, 5648–5652; (b) C. Lee, W. Yang and R. G. Parr, Phys. Rev. B: Condens. Matter Mater. Phys., 1988, 37, 785–789.
22. J. B. Foresman and A. Frisch, in Exploring Chemistry with Electronic Structure Methods, Gaussian, Inc., 1996.
23. (a) N. C. Craig, A. Chen, K. Hwan Suh, S. Klee, G. C. Mellau, B. P. Winnewisser and M. Winnewisser, J. Am. Chem. Soc., 1997, 119, 4789–4790; (b) H. Takeo, C. Matsumura and Y. Morino, J. Chem. Phys., 1986, 84, 4205–4210.
24. The preparation energy of anti conformer, ΔE_prep = 11.70 kcal mol⁻¹ (Table S1 in the ESI.†), reflects difference in energy between two CH₂F radicals in their prepared state (geometry they have in anti-DFE) and their optimal geometry.

---

Footnote

† Electronic supplementary information (ESI) available: Absolute EDA values for various structures of DFE, absolute energies and x, y, z coordinates of the optimized anti and gauche form of DFE. See DOI: 10.1039/c4ra07909d

---