On the origin of the gauche effect. A quantum chemical study of 1,2-difluoroethane

31 January 1997

CHEMICAL

PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 265 (1997) 19-23

On the origin of the gauche effect. A quantum chemical study of 1,2-difluoroethane O. Engkvist",

G . K a r l s t r 6 m a, E - O . W i d m a r k b

a Department of Theoretical Chemistry, Chemical Centre, University of Lund, P.O. Box 124, S-221 O0 Lund, Sweden b IBM Sweden, P.O. Box 4104, S-203 12 Malm6, Sweden

Received 1 August 1996; in final form 23 October 1996

Abstract

The conformational equilibrium of 1,2-difluoroethane has been investigated using ab initio quantum chemical calculations at the SCF, MP2 and CCSD(T) levels, with ANO basis sets. The relative stability of the gauche-conformation of 1,2difluoroethane is found to be a consequence of the nodal structure of the singly occupied orbital in the CFH2 radical. It is also shown that the nodal structure of the singly occupied orbitals in the CFH biradical can explain the stability of the cis conformation of 1,2-difluoroethene.

1. I n t r o d u c t i o n

Theoretical conformation analysis has become a very important tool for understanding the relationship between structure and energy for organic molecules. Among the most studied systems are 1,2-disubstituted ethanes (XCH2CH2Y). If X and Y are small polar groups, one would expect that the molecule would prefer the anti conformation. However both experiment and theoretical investigations have shown that the molecules prefer the gauche conformation. This has been termed the gauche effect. Microwave [ 1 ], IR, Raman [ 2 - 4 ] , electron diffraction [5], N M R [6] and dipole moment measurements [7] all indicate that the gauche conformation o f 1,2-difluoroethane is more stable than the anti conformation in the gas phase. The most recent experimental investigations [6,4] suggest that the gauche conformation is approximately 0.8 kcal/mol more stable than the anti. This is in excellent accordance with several quantum chemical investigations [ 8 - 1 0 ]. The situation is simi-

lar for 1,2-difluoroethene, where a similar energy difference is reported between the cis and trans conformations [ 11,12,9]. The origin of this apparent attraction between the fluorine atoms is, however, not fully understood. In a recent work Wiberg et al. [9] associated the stability of the cis and anti conformations with bent C - C bonds. Empirically one can note that the C - C bond is somewhat shorter in the more stable gauche conformation of 1,2-difluoroethane than in the anti form, while the C - F bonds are longer for the gauche compared to the anti form [9]. For 1,2difluoroethene the opposite is true; the C - C bond is longer and the C - F bond is shorter in the more stable cis form. The stability of the conformations with small F - F distance becomes even more puzzling when one observes that the structural parameters like the dihedral angle and the C - C - F angles indicate a repulsive F - F interaction. One would expect that the F - F interaction would be dominated by a repulsive electrostatic interaction, as well as an exchange-repulsion. The only attractive interaction expected between the

0009-2614/97/$17.00 Copyright (~) 1997 Elsevier Science B.V. All rights reserved. PII S0009-2614(96)01385-1

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O. Engkvist et al./Chemical Physics Letters 265 (1997) 19-23

fluorine atoms is a dispersion interaction. However, quantum chemical calculations at the SCF level predict that the forms with short F-F distance are the most stable ones. This is remarkable since it is normally believed that the conformation of a molecule could be deduced from electrostatic, exchange-repulsion and dispersion interactions between the substituents. At the SCF level of approximation only the first two terms are present, and both the exchange-repulsion and the electrostatic term must favour the anti and trans forms of the studied molecules. In the gauche and cis forms there will be overlap of the electron clbuds of the fluorine atoms leading to larger exchange-repulsion and the electronegative fluorine atoms will also repel each other electrostatically in the gauche and cis forms. Thus one would expect, at least at the SCF level of approximation, that the anti and trans forms should be the most stable ones. However, all quantum chemical Hartree-Fock calculations performed with large basis sets suggest that the gauche and cis conformers are the most stable [8-10]. The purpose of this investigation is to look for an explanation of the observed anomalies in physical terms using high quality quantum chemical ab initio methods.

2. Calculations All the calculations in this report were performed with the MOLCAS-3 program package [ 13], except for the CCSD(T) calculations which was performed with the TITAN program [ 14]. The basis sets used were of ANO type in two different sizes: A smaller set of Pierloot et al. [ 15], denoted ANO-S, and a larger set of Widmark et al. [ 16] denoted ANO-L. For 1,2-difluoroethane, a full geometry optimization was performed at the HF level with an ANO-S type basis set, for carbon and fluorine a 10s6p3d basis set was contracted to 3s2pld and for hydrogen a 7s3p basis set was contracted to 2slp. Recently it has been observed that for 1,2difluoroethane the C - F bond length is the only geometry parameter which is significantly changed due to correlation effects [ 10]. Therefore, we only optimized the C - F bond length in both the gauche and anti forms at the MP2 level. For both conformers the bond was 0.03 A, longer at the MP2 level in agreement with a previous study [ 10]. The optimized structural

Table 1 Structural parameters for the gauche and anti conformer of 1,2difluoroethane optimized at the SCF level. The experimental geometry [18] is also included in the table. Bond lengths are given in A,, angles in deg Parameter

Trans

Gauche

Exp.

r (C-C) r (C-F) r(C-Ht) a r(C-Hg) a ACCF ACCHt a ACCHg a 7-b FCCF

1.516 1.403 1.088

1.507 1.401 1.090 1.089 110.4 110.8 109.6 70.8

1.493 1.390 1.099 1.093 110.6 108.4 113.3 71.0

107.9 111.0 180.0

a Ht and Hg denote hydrogen atoms in trans and gauche position with respect to the fluorine atom attached to the adjacent carbon atom. b Dihedral angle.

parameters together with the experimental geometry are given in Table 1. For 1,2-difluoroethane, geometry optimization at the MP2 level does not affect the energy difference between the anti and gauche conformers obtained with the HF geometries. However, in general, conformational energies obtained with geometry optimizations at the MP2 level and at the HF level can differ [ 17]. The agreement between our gauche structure and the experimental structure [ 18] is good. It is also noticed that our geometry for the gauche conformer is similar to the optimized geometry presented in Ref. [ 10]. In all correlated calculations, the I s orbitals on carbon and fluorine were frozen. To check the importance of third and higher order correlation contributions, CCSD(T) calculations were performed for the ANO-S basis set given in Table 2. The CCSD(T) calculations reduced the energy difference between the gauche and trans conformer by 0.15 kcal/mol. Accordingly, our best estimate of the energy difference favours the gauche conformer by 0.66 kcal/mol. These results are in good agreement with both previously published quantum chemical calculations [8-10] and experimental investigations [ 6,4]. At the HF level the gauche form is the most stable conformation. As was discussed in the introduction, this result is counterintuitive. In order to investigate the reason for this anomaly, an open shell restricted HF calculation was performed on the CFH2 radical. The geometry was taken from the anti conformation of 1,2-

O. Engkvist et al./Chemical Physics Letters 265 (1997) 19-23

21

Table 2 Energies for the trans and gauche conformer of 1,2-difluoroethaneat the SCF and MP2 levels with different type of basis sets. Absolute energies are given in hartree and relative energies in kcal/mol Method

Trans

Gauche

AE a

# b

SCF c SCF d SCF e SCF t SCF g MP2 J MP2 c MP2 f MP2_~

-276.8943533 --276.9984384 -277.0213568 -277.0494872 -277.0565142 -277.6658896 -277.7813766 -277.8100214 -277.8957186

-276.8937833 -276.9987971 -277.0217496 -277.0498456 -277.0569568 -277.6674882 -277.7826228 -277.8111374 -277.8970057

-0.36 0.23 0.25 0.22 0.28 1.00 0.78 h 0.70 0.81

4.2 3.5 3.2 3.2 3.2

exp. a d f h

0.8 ± 0.09 i

2.62 ± 0.18 J

b E = Etmns - Egauche. b Dipole m o m e n t i n D forthe gauche conformee c ANO-S C,F 10s6p3d/3s2p H 7s3p/2s. ANO-S C,F 1 0 s 6 p 3 d / 3 s 2 p l d H 7 s 3 p / 2 s l p . e ANO-S C,F 10s6p3d/4s3p2dH 7s3p/3s2p. ANO-L C,F 14s9p4d3f/4s3p2dH 8s4p3d/3s2p. g ANO-LC ,F 14s9p4d3f/4s3p2dlfH 8s4p3d/3s2pld. CCSD(T) calculations give an energy diffe~nce of 0.63 kcal/mol, i Re~ 141. J Re~ [7].

Fig. I. The wavefunction for the singly occupied orbital in the CFH2 radical. The two different greytones indicate the phase of the wavefunction. The carbon-carbon bond and the other carbon in 1,2-difluoroethane are also indicated in the figure. The geometry parameters of the radical are taken from the anti form of 1,2-difluoroethane.

difluoroethane and a 3 s 2 p l d A N O - S basis set on the fluorine and carbon, and 2 s l p basis set on hydrogen were employed. The singly occupied orbital is shown in Fig. 1. Fig. 1 shows that the overlap between the singly occupied orbitals on the two CFH2 radicals are larger if the F atoms are in a gauche position. Accordingly there is a stronger o'-bond in the gauche conformation,

leading to a lower energy for the gauche conformation compared to the trans conformation. Calculations of the overlap o f the two singly occupied orbitals for the gauche and anti conformer were also performed. The bond lengths and bond angles of the radicals were taken from the geometries o f their respective conformer. The C - C bond length was fixed at 1.516/~ for both conformers. The basis set used was a 3 s 2 p l d A N O - S basis set on fluorine and carbon and a 2 s l p basis set on hydrogen. The calculations o f the radicals were performed at the open shell restricted H F level. The overlap was 0.487 for the gauche conformer and 0.483 for the anti conformer indicating that the gauche conformer should be the most stable. If the fluorine was exchanged to a hydrogen the singly occupied orbital would be an sp 3 orbital centered at the carbon. The difference in shape between the singly occupied orbital in Fig. 1 and an sp 3 orbital on carbon is that the orbital in Fig. 1 must be orthogonal to the doubly occupied orbitals on the fluorine atom. Table 2 reveals that d functions are important for describing the electrostatics of the molecule. The H F dipole moments are overestimated by 1 D if d basis functions are absent on the carbons and fluorines. Since the overestimated dipole moment leads to a strongly repulsive electrostatic interaction between the two fluorine atoms, the trans conformation will be more stable than the gauche conformation with small basis sets. A similar study was also performed on 1,2-

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O. Engkvist et al./Chemical Physics Letters 265 (1997) 19-23

Fig. 2. The wavefunction for the singly occupied orbital in the CFH biradical that will form a o--bond in 1,2-difiuoroethene. The two different greytones indicate the phase of the wavefunction. The carbon-carbon bond and the other carbon in 1,2-difluoroethene are also indicated in the figure. The geometry parameters of the radical are taken from the cis form of 1,2-difluoroethene.

difluoroethene. The geometry was optimized at the HF level with the same ANO-S basis set as for 1,2-difluoroethane. Single point calculations at the MP2 level were performed with an ANO-L basis set for the cis and trans isomers. For C and F a 14s9p4d3f/4s3p2dlf basis set, and for H a 8s4p3d/3s2pld basis set were used. The calculations showed that the cis conformer was 1.1 kcal/mol more stable at the HF level and 1.3 kcal/mol more stable at the MP2 level. This result is also in accordance with previous experimental and theoretical investigations [ 11,12,9]. We also analyzed the CFH biradical. The orbital on the CFH biradical that forms a o--bond is plotted in Fig. 2 and the orbital that will form a zr-bond is plotted in Fig. 3. Again, note that if the fluorine atoms are in cis-positions the nodal structure of the singly occupied orbitals on the molecular fragments will give a larger overlap. Particularly it is observed that for 1,2-difluoroethene the main effect originates from the zr-orbital.

3. Conclusions An explanation for the gauche effect in 1,2difluoroethane and the cis effect in 1,2-difluoroethene has been proposed. Plots of the singly occupied orbitals on the CFH2 radical (with geometry parameters from the anti conformer of 1,2-difluoroethane) show that the largest overlap between the two CFH2 frag-

Fig. 3. The wavefunction for the singly occupied orbital in the CFH biradical that will form a ~'-bond in 1,2-difluoroethene seen from above the or-nodal plane. The two different greytones indicates the phase of the wavefunction. The carbon-carbon bond and the other carbon in 1,2-difluoroethene are also indicated in the figure. The geometry parameters of the radical are taken from the cis form of 1,2-difluoroethene.

ments in 1,2-difluoroethane will occur if the fluorine atoms are in the gauche position. The same effect occurs for 1,2-difluoroethene. The overlap between the singly occupied orbitals of the two CFH fragments (with geometry parameters from the cis conformer of 1,2-difluoroethene) will be larger in the cis conformer compared to the trans conformer. 1,2-difluoroethane illustrates that it is not always possible to predict the structure from electrostatic, exchange-repulsion and dispersion terms. References [ 1 I S.S. Butcher, R.A. Cohen and T.C. Rounds, J. Chem. Phys. 54 (1971) 4123. [21 W.C. Harris, J.R. Holtzclaw and V.F. Kalasinsky, J. Chem. Phys. 67 (1977) 3330. 13l P. Huber-W/ilchli and H.H. Giinthardt, Spectrochim. Acta 37A (1981) 285. I41 J.R. Durig, J. Liu, T.S. Little and V.E Kalasinsky, J. Phys. Chem. 96 (1992) 8224. 151 D. Friesen and K. Hedberg, J. Am. Chem. Soc. 102 (1980) 3987. [6] T. Hirano, S. Nonoyama, T. Miyajima, Y. Kurita, T. Kawamura and H. Sato, J. Chem. Soc., Chem. Commun. (1986) p 606. [7 ] A.R.H. Goodwin and G. Morrison, J. Phys. Chem. 96 (1992) 5521. 181 D.A. Dixon and B.E. Smart, J. Phys. Chem. 92 (1988) 2729. [9] K.B. Wiberg, M.A. Murcko, K.E. Laidig and P.J. MacDougall, J. Phys. Chem. 94 (1990) 18.

O. Engkvist et al./Chemical Physics Letters 265 (1997) 19-23 101 M.W. Wong, K.B. Wiberg and M.J. Frisch, J. Comput. Chem. 16 (1995) 385. 1 I I N.C. Craig, L.G. Piper and V.L. Wheeler, J. Phys. Chem. 75 (1971) 1453. 121 D.A. Dixon, B.E. Smart and T. Fukunaga, Chem. Phys. Lett. 125 (1986) 447. 131 K. Andersson, M.E Fiilscher, G. Karlstr~m, R. Lindh, Malmqvist, P.-/~.; J. Olsen, B.O. Roos, A.J. Sadlej, M.R.A. Blomberg, P.E.M. Siegbahn, V. Kell6, J. Noga, M. Urban and P.-O. Widmark, MOLCAS Version 3. Dept. of Theor. Chem., Chem. Center, Univ. of Lund, P.O.B. 124, S-221 00 Lund, Sweden, Lund (1994).

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[141 M.P. FiJlscher and A. RendeU, TITAN Coupled-cluster MOLCAS version 2. Dept. of Theor. Chem., Chem. Center, Univ. of Lund, P.O.B. 124, S-221 00 Lund, Sweden, Lund (1992). 1151 K. Pierloot, B. Dumez, P. Widmark and B.O. Roos, Theor. Chim. Acta 90 (1995) 87. [161 E-O. Widmark, E-A.. Malmqvist and B.O. Roos, Theor. Chim. Acta 77 (1990) 291. [17] M. Ramek, F.A. Momany, D.M. Miller and L. Sch~ifer, J. Mol. Struc. 375 (1996) 189. [ 18] H. Takeo, C. Matsumura and Y. Morion, J. Chem. Phys. 84 (1986) 4205.