Relative stability of 1,2-difluoroethylenes

Volume 45, number 2

CHEMICAL

PHYSICS

LETTERS

IS January 1977

RELATIVE STABILITY OF I ,24MFLUOROETHYLENES 3,s. BINKLEY and 3.A. POPLE Department of Chemistry. Carnegie-Mellon pittsburgi, &mnsyfvania ISZI3; USA

Utriversity.

Received 12 October 1976

The relative energy of cis- and rrans-i ,2~i~uoroethy~ene is investigated by ab initio molecular orbital theory. Hartree-Fock theory predicts the cis isomer to be most stable with the hugest basis set used. Some evidence is found for steric attraction between fluorine atoms. &f@er-Ptesset theory indicates that correlation energy corrections further increase the relative stabitity of the cis structure_

1. Introduction

C&-l ,~-di~uoroethy~ene (1) is known to be more stable than the fr~#zsisomer (2) [ 1,221. By studying the equilibrium constant over a temperature range and correcting for rotational and vibrational energies, Craig et al- [2,3] obtained a value of 1.08 + 0.12 kc&’ mole for the difference between electronic energies (i-e- difference between minima in the potential surface)_ This is the simplest example of a general effect, ‘known to apply to many 1.2-dihaloethylenes (for a review see ref. [4])_

2

22

The h&her stability of&s isomers is somewhat surprising as simple electrostatic arguments suggest that the tram form-should have lower energy, the negatively charged fluorine atoms then being further apart. This effect may be estimated quantitatively by a point charge model. If charges of -0.2 1 are place-;!

on each fluorine and +0.2 I on each carbon, the experiiental dipole moment [S] of the c& isomer (2-42 debye) is reproduced_ The Coulomb repuIsion between these negative point charges is lower in the @Q~Sthan in the cis isomer by about 1.2 kcaljmolelt follows that additional stabWing effects of the or-

dez of 2 kcaljmole must be present in the ci’s form. Several qualitative mechanisms have been proposed for this cis effect- Pitzer and Hollenberg [6f, in a st&dy of 1,2-dich~oroethy~enes, suggested thnt contributions from resonance structures of the type Cl-:CH-CH==Clf would tend to stabilize the cis isomer_ Since electron dc?ation from chlorine will occur in the x-orbital&, this explanation is equivalent to a proposed favorable interaction between the 5dipole moment of one CC1 bond and the (opposite) n-dipole moment of the other. This kind of mechaxi&n can only operate through correlated motion of the electrons, since only-total dipole interactions are significant if the electron distributions are averaged_ Another argument that has been put fonvard involves fluorine-fluorine overlap_ Epiotis [7], following earlier work by Hoffmann and Olofson [8], has suggested that f is preferentially s:abilized over 2 by interaction of the fluorine fone pair orbit& with both the X* and 0” antibonding orbit& of the carbon-carbon double bond- For the n-system, the antisymmetric combination of euorine 2pu orbitils 4 can donate some electrons to the vacant a* orbital of C=C but the symmetric combination 3 cannot. Consequently 4 is depopuIated relative to 3 and some

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CHEMICAL PHYSICS LETTERS

Volume 45, number 2

z-bonding results_ This is described as “steric attraction”. A similar argument applies to the iri-plane u-type lone pairs. The occupied orbital 6 can donate electrons to the vacant o* orbital of C=C but 5 cannot, leading to further fluorinefluorine bonding. net fluorine-fluorine

2

2

The purpose of this paper is to present the results of some ab initio molecular orbital studies of the reiative stability of 1 and 2. The pmary objective is to test whether theory does reproduce the experimental observation that 1 is m_orestable. Secondly, the results are examined to fmd whether they give support to the qualitative suggestions that have been put forward.

2. Methods and results Most of the calculations use the spin-restricted Hartree-Fock procedure (RI-IF) with doubly occupied molecular orbitals [9] _Correlation corrections

are made in-some cases using the second-order

M#.ler-

Plesset perturbation method (R%iP2) [lo,1 11 _ A series of basis sets [12] is employed to investigate the dependence of the results on the flexibility allowed for the molecular orbitals. These include the split-

valence 4-31G set, the 6-3 1G set which improves the description of inner shells, and the 6-31G* set which adds d-type polarization functions on non-hydrogen atoms. At a higher level, we have used a larger basis

15 January 1977

[13] =I* lllVOlvitlg a triple split for the valence functions. This may be denoted by 6-3 1 lG. Finally, sets of five d-functions (ad = 0.8) for carbon and fluorine have been added to 6-3 1lG to give a basis 6-3 1 lG*. The EU-IFmethod is explored through all these basis levels but present program limitations do not permit the Rh4P2 studies to be taken beyond 631G. A full set of computations has been carried out using fixed standard geometries 1143 (RCC = 1.34 A, R .,=1_33&RC~= 1.08 A, all angles 1200). These cannot give an exact description of the energy difference, since relaxation of geometrical parameters will allow some distortion to take place. However, it is reasonable to expect that the principal mechanisms determining the relative stability are operative at these assumed geometries. To test the possible influence of geometrical relaxation, full optimizations were carried out at the RHF/4-3 1G level. The calculated energies and di$ole moments are listed in table 1. Geometrical parameters optimized at RHF/4-3 1G are: cis: RCC = 1.302 a, RCF = 1.362 A, R,, = 1.063 a, CCF = 122.6O, CCH = 123.?; pans: RcC = 1.304 A, I?,, = 1.366 A, RcH = 1.066 A, CCF = 119.5”, CCH = 126”. These are in reasonable agreement with experimental values [S,lS].

* Note that the fluorinebasis, as reported in tabIe 3 of ref. [ 131, is incorrect.The third s-coefficient, d,, of the sp’ shell should be positive, not negative. That is, it should read +1.349192(+0).

Table 1 Total energies (hartree) and dipole moments (debye) a) Method

Energy (cisC!~F~H,)

Energy (tnzns-C2 F2 HZ )

Dipole c) (cisCz F2 Hz)

RHF/4-3 1G RHF/4-3 1G b) RHF/6-31G RHF/6-311G RHF/6-3 lG* RHF/6=311G*

-275.361429 -275.367447 -275.631147 -275.703713 -275.71?256 -275.788253

-275.363093

350

-275.632560 -275.704031 -275.717615 -275.787845

RMP2j4-3 1G RMP2/6-31G

-275.786100 -276.051041

-275.787224 -276.051873

a) At standard geometry.

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3.60 3.50 3.53 2.81 2.91

-275.369547

b) Geometry optimized at the RHF/4-31G IeveL

c) Experimstal

value

2.42 [S] .

CHEMICAL PHYSICS LETI’ERS

Volume 45, number 2

3_ Discussion The standard geometrical model results for the - Ecis are collected in table 2. The RHF/4-3 IG method incorrectly predicts the tram isomer to be more stable by 1.04 kcal/mole. However, there are two deficiencies of this level of theory which may contribute to the failure. In the first place, the 4-3 IG basis generally leads to excesenergy difference AE = E-

sive polarity in polar bonds; this is exemplified

by the

large RIIF/4-3

1G dipole moment. As a consequence, the electrostatic repulsion effect between the fluorines is exaggerated. Indeed, if the point charge model described in the introduction is used with the 4-. 31G dipole moment, the tpans isomer is favored by 3 kcal/mole. A second possible source of error in the 43 1G basis is inadequate description of fluorinefluorine overlap. If the steric attraction hypothesis is correct, the “outer tails” of the fluorine valence functions must play an important role. The 4-3 1G basis has only four primitive p-type gaussians per patomic orbital on fluorine and may be insufficiently diffuse for a good description of the overlap region_ That these deficiencies of RHF/4-3 1G theory do contribute to the erroneous prediction is partially confirmed by the RHF studies with higher levels of basis set. 6-3 1G has a more diffuse outer p-function than 43 1G and gives a lower AE of -0.89 kcal/mole. Fur-t&r extension of the basis set to 63 1 lG which increases the number of primitive p-type gaussians to five per valence p-atomic orbital leads to a substantial further change of AE to -0.20 kcal/mole. All of the sp basis sets give comparable excessive diTable 2

Relative energies a) (kcaI/mole) for Etrans - Bc.

at standard

geometry Basis

4-31G 6-3 1G 6311G 631G* 631 lG*

Method RHF

RMP2

-1.04 b) -0.89 -0-20 -0.23 i-O.26

-0.71 -0.52

pole moments so this trend is consistent with the importance of fluorine-~uo~ne overlap. The consequences of excessive polarity in the C--F bonds are partly eliminated if d-functions are added to the basis set. Going from RHF/6-3 1G to RHF/63 lG* reduces the theoretical dipole moment from 3.50 to 2.8 1 debye. This changes AE from -0.89 to -0.23 kcal/mole. Finally, if the larger 6-3 11G basis is used together with d-functions (RI-W/&31 lG*), AE changes sign and becomes -1-O-26 kcal/mole. The effects of sp-basis expansion and polarization functions are apparently nearly additive and, in combination, are sufficient to give a slight preferential stabilization to the cis isomer with Hartree-Fock wavefunctions. Some further evidence supporting the steric attraction hypothesis comes from the fluorine-fluorine overlap populations [16]_ Using the largest (6-3 1lG”) basis and separating overlap populations into (Tand ‘IT

(p,,) types, the values shown in table 3 are obtained. Since a positive overlap population between separate atoms is associated with bonding, these suggest a small amount of fluorine-fluorine

n-bonding in the

cis isomer. Thus the detailed electron distribution gives some support to the concept of steric attraction involving the n-type fluorine lone pair orbit&, 3 and 4, leading to some cyclic 6-electron “aromatic character”, It is worth noting that the n-overlap population increases threefold in going from 63 1G” to 6-3 1 lG* (table 3), indicating the importance of a good description of the outer part of the valence fluorine orbit&. Nevertheless, the magnitude of the overlap population remains fairly small and other contributory mechanisms cannot be ruled out. These seems to be no comparable evidence for steric attraction involving the o-type fluorine Ione pair orbitah 5 and 6_ Indeed, the F-F o-overlap population is larger in the tram isomer than in the cis. Actually fram F-F overlap occurs mainly in the C=C Table 3 fluorine-fluorine

t&C2 Fz H2 tronS-c2

a) Experimentalvalue +I.08 kc&/mob [3] _ b) Becomes -1.32 after geometry optimization,

15 January 1977

Fz H2

overlap populations (6-3 1 lG*) u

IT

Tota!

0.00038 1 a) 0.001391

0.00302’7 b) 0.300179

0.003408 0.001571

a) d.00028 1 with 6-3 1G*.

b) 0.00 1049 wi+&6-3 lG*.

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Volume 45, number 2

CHEhiICAL PHYSICS LETTERS

15 January 1977

region and cannot really be interpreted in terms of direct f?ubrine interaction. The Mdller-Plesset results for AE (table 2) indicate that the correlation energy is greater in the cis

(3) another part of this stabilization is due to a greater correlation energy in the cis isomer.

than in the trans isomer, thereby furtbcr stabilizing the former. The correlation contribution to AE is comparable with the 4-3 1G and 6-3 1G basis sets

Acknowledgement

(W.33 and +0.37 kcai/mole respectively). It is not possible at present to determine how this is modified if d-functions are added to the basis. However, if no further change is assumed and the 6-3 1G value of +0.37 added to the best Hartree-Pock value (i-O.26 from 6-3 1 IG”), a total estimate of AE of -l-O_63kcal/ mole is obtained, in fair agreement with the experimental value of +1.08 kcal/mole. It is not possible to separate correlation contributions which represent the Pitzer-Hollenberg resonance strucmres. Such effects are included approximately in the M$Uer-Plesset treatment and all that can be said is that &&esestudies indicate that correlation effects of some sort do make a significant positive contribution (i.e. favoring cisj to the total AE_ Finally, we consider how these conclusions may be modified if full geometry optimization is undertaken for each isomer. The only results relevant to this are at the RHF/43lG level and these show a slight negative change in A.!?’(i.e. favoring trons) from -1.04 kcal/mole (standard model) to - 1.32 kcal/ mole (optimized geometry). It is not clear at present whether this would still apply at higher.levels of theory. The change may be due, in part, to the rather long CF bonds predicted by the RHF/4-3lG method (0.02 to 0.03 A longer than experimental values). In summary, the results of this investigation provide evidence that (1) cjs-difluoroethylene is more stable than DZVZSdifluoroethylene at the Hartree-Fock level of theory, (2) part of the stabilization of the cis isomer is due to steric attraction between the fluorine atoms and

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This research was supported in part by the National Science Foundation under Grant CHE7.5.09808.

References [ 1] H-G. Viehe, Chem. Ber. 93 (1960) 1967. [2 ] NC. Craig and E.A. Entemann, J. Am. Chem. Sot. 83 (1961) 3047. [3] NC. Craig and J. Overend, J. Phys. Chem. 51 (1969) 1127. [4] NC. Craig, L.C. Piper and V.L. Wheeler, J. Phys. Chem. 75 (1971) 1453. [5] V.W. Laurie and D.T. Pence, J. Chem. Phys. 38 (1963) 2693. [6] KS. Pitzer and J-L. HoIIenberg, J. Am. Chem. Sot. 76 (1954) 1493. [7] N.D. Epiotis, J. Am. Chem. Sot. 95 (1973) 3007. [8] R. Hoffmann and R.A. Olofson, J. Am. Chem. Sot. 88 (1966) 943. [9] C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. [lo] Chr. MdIlerand MS. Pleas&, Phys. Rev. 46 (1934) 618. [ll] J.A. Pople, J.S. Binkley and R. Seeaer, Intern. J_ Quanturn Chem. IQS, to be published. R. Ditchfield, W.J. Hehre and J.A. Pople, J. Chem. Phys. 54 (1971) 724; W.J. Hehre, R. Ditchfield and J-A_ Pople, J. Chem. Phys. 56 (1972) 2257; P-C. Hariharan and J.A. Pople, Chem. Phys. Letters 16 . (1972) 217. J.A. PopIe and J.S. Binkley, Mol. Phys. 29 (1975) 599. J-A. Pople and M. Gordon, J. Am. Chem. Sot. 89 (1967) 4253_ E.J.M. van Shaick, F-C_ Mijlhoff, G. Renes and H.J.

G&e, J. Mol. Struct. 21 (1974) 17; J.L. Caries Jr., R.R. Karl Jr. and S.H. Bauer, J. Chem. Sot. Faraday Trans. II 70 (1974) 177. R.S. IMuIIiken,J. Chem. Phys. 23 (1955) 1833,1841, 2338,2343.