Ab Initio Study on the Structural Properties of Hexafluorocyclobutene

Adam W. Van Wynsberghe, Sean A. Peebles, Rebecca A. Peebles, and Robert ... Heather E. Robertson, Vincent Murtagh, Axel Heppeler, and Carole Morrison...
0 downloads 0 Views 527KB Size
Download PDF
J. Phys. Chem. 1995, 99, 173-176

173

Ab Initio Study on the Structural Properties of Hexafluorocyclobutene, 3,3,4,4-Tetrafluorocyclobutene,and Cyclobutene: The Remarkable Length of the C(3)- C(4) Bond? Roland H. Hertwig,” Wolfram Koch,*t$and Zvonimir B. MaksiCs Institut fur Organische Chemie, Technische Universitat Berlin, Strasse des 17.Juni 135, 0-10623 Berlin, Germany, and Ruder BoSkoviC Institute, BijeniEka 54, HR-41001 Zagreb, and Faculty of Science and Mathematics, University of Zagreb, MaruliCev trg 19, HR-41001 Zagreb, Republic of Croatia Received: August 4, 1994; In Final Form: October 13, 1994@

The equilibrium geometries of hexafluorocyclobutene, 3,3,4,4-tetrafluorocyclobutene,and cyclobutene are determined employing quantum chemical calculations at the MP2/6-3 1+G* and LDA+BP/TZP levels of theory and compared to the structural parameters determined experimentally by microwave spectroscopy and electron diffraction techniques. The theoretical results are in better overall agreement with the latter set of experimental data and substantiate the experimental finding of a remarkably long C(3)-C(4) bond in hexafluorocyclobutene. The origins of the structural changes upon fluorination are discussed on the basis of qualitative concepts such as rehybridization, Coulombic interaction, hyperconjugation, and n-back-bonding.

Introduction Halogenated hydrocarbons have fascinated organic chemists for a long time since they provide a serious challenge for both experimentalists and theoreticians. From a practical point of view these compounds play an important role as anesthetics, fire-retarding materials, propellants, refrigerants, etc. Some of them, such as freon, represent environmental hazards. On the other hand their scientific appeal is given by the high electronegativity of fluorine, which may not only stretch the covalent bonding to its ionic limit but also extends its 0-acceptor and n-donor effects to the bonds in the vicinity of the C-F bond. Recently, considerable experimental efforts have been focused on the structural features of highly fluorinated small ring^*^^^^ which in several cases led to controversial results, depending on the experimental methods applied. A striking example is provided by hexafluorocyclobutene, where microwave (MW)2 and electron diffraction (ED)4techniques gave structures which could not be reconciled within the experimental errors. In particular the C-C single bonds adjacent and opposite to the double bond are significantly shorter (by 0.02 and 0.03 A, respectively) when determined by MW spectroscopy2as compared to the ED datae4 These discrepancies are so large that both results cannot be correct at the same time, and yet, both methods have been applied lege artis. This indicates a conflict of considerable interest and importance. Modem methods of computationalquantum chemistry may prove useful in resolving this dilemma. Hence, we decided to perform a theoretical investigation at elaborate levels of theory on hexafluorocyclobutene (l), 3,3,4,4-tetrafluorocyclobutene(2) and the parent hydrocarbon, cyclobutene (3) (Figure l), hoping that theory will offer new insights which help to discriminate between the MW and ED data. Computational Details The systems we are interested in are characterized by small, strained rings and the presence of fluorine. Thus, the use of Dedicated to Prof. Martin Klessinger on the occasion of his 60th birthday. Technische Universiat Berlin. E-mail: [email protected] 8 Ruder BoSkoviC Institute and University of Zagreb. E-mail: [email protected] Abstract published in Advance ACS Abstracts, December 1, 1994.

*

@

0022-3654/95/2099-0173$09.00/0

X

1: XtY=F

X

2: XsH, YeF

3: XzYsH

Figure 1. Atom numbering in species 1-3.

polarized one-particle basis sets with extra diffuse functions to describe the lone-pair specific interactions is mandatory. In addition, electron correlation effects can be expected of significant importance for a proper theoretical description. We therefore employed the ab initio Hartree-Fock (HF) as well as the valence electron correlated MP2 schemes using the standard 6-31+G* basis set. For 2 and 3 we also used more flexible basis sets with larger sp and polarization expansion^.^ In a recent papep we have shown that also gradient-corrected density functional methods are capable of capturing large parts of (dynamical and nondynamical) correlation energy in hydrocarbons and that these methods lead to results which are frequently superior to conventional HF or MP2 calculations. Thus, we additionally investigated the structures of 1-3 using approximate density functional theory.’ The local Slater functional for exchange8and the local correlation functional parametrized on the homogeneous electron gas by Vosko, Wilk, and Nusairg were supplemented by nonlocal functionals for exchange and correlation due to Beckelo and Perdew,” respectively. This level is commonly known as LDA+BP. The basis set for constructingthe Kohn-Sham orbitals consisted of a Slater-typeorbital basis set of triple-c plus polarization quality (TZP). The 1s electrons of C and F were treated in the frozen core approximation. The ab initio MO calculations were performed 0 1995 American Chemical Society

Hertwig et al.

174 J. Phys. Chem., Vol. 99, No. 1, 1995

TABLE 1: Optimized Geometries for Hexafluorocyclobutene (l),Bond Lengths in Angstroms, Bond Angles in Degrees, Point Group Symmetry CZ, parameter

exptl (ED)"

r[C(l)-C(2)] r[C(2)-C(3)] r[C(3)-C(4)] r [ W )-Fl r[C(3)-Fl a[C(l)C(2)C(3)] a[C(2)C(3)C(4)] a[C(2)C(3)Fj a[C(4)C(3)F] a[C(4)C(l)F] atFC(3)Fl

1.326(22) 1.502(5) 1.583(10) 1.313(10) 1.347(5) 94.9(5) 85.1(5) 117.1(5) 114.5(4) 129.8(13) 107.6(5)

exptl HFI Mpu LDA+BP/ (MW)b 6-31+G* 6-31+G* TZP 1.333(6) 1.478(6) 1.552(6) 1.311' 1.35Sd 94.3(2) 85.7(2) 117.W 115.3c 131.lC 106.0(5)

1.316 1.494 1.550 1.295 1.326 94.5 85.5 116.4 115.0 130.3 107.6

1.349 1.496 1.564 1.324 1.360 94.1 85.9 116.4 114.8 130.8 107.7

1.344 1.502 1.584 1.311 1.352 94.6 85.4 116.3 114.9 130.1 108.0

Reference 4. Reference 2. No error bars given in ref 2. Assumed value, not determined in the MW experiment; see ref 2. using Gaussian 92,12 while the DFT-based calculations were carried out employing the ADF ~r0gram.l~ All geometries were optimized using analytical gradients imposing Cz, point group symmetry.

Results and Discussion Our theoretically predicted structural parameters for hexafluorocyclobutene are compared to the available experimental information in Table 1. The HF/6-31+G* results for 1 show good agreement with the MW structure; in particular, the length of the C(3)-C(4) bond is 1.550 A, only 0.002 shorter than the microwave number. However, the underestimation of the other bond distances is much higher, in line with the known trend that bond distances are computed too short at the HF 1 e ~ e l . lOnce ~ valence electron correlation is taken into account through the second-order Moller-Plesset scheme, the expected overall increase in bond lengths is observed. The MP2/63 l+G*-computed equilibrium geometry of 1 is, however, not sufficient for an unambiguous discrimination between the MW and ED results; the calculated structural parameters are in between the two sets of data. This is particularly noteworthy for the C(3)-C(4) bond distance, where the largest deviation between the two experimental geometries is observed. At the MP2/6-31+G* level it amounts to 1.564 A, while the MW and ED data are 1.552 f0.006 and 1.583 f0.010 A, re~pective1y.l~ For the other critical bond, the C(2)-C(3) single bond, the MP2/ 6-31+G*-computed distance of 1.496 8, is, however, in much better agreement with the ED (1.502 f 0.05 A) than with the MW (1.478 f0.006 A) result. The MP2 scheme accounts only for a certain part of the dynamical electron correlation; effects based on an inadequacy of the single-determinant approach (nondynamical correlation) are not covered at all. On the other hand, approximate density functional theory does in principle include both effects implicitly through the functionals used.' However, it is unfortunately impossible to predict to what extent electron correlation is actually described in such methods. The LDA+BP/TZP-optimized geometry of hexafluorocyclobutene is very similar to the MP2/6-31+G* one, with two exceptions: The C(1)-F distance is predicted to be significantly shorter at this level (1.307 A as compared to 1.324 A at MP2/6-31+G*) and is in much better agreement with both the MW (1.311 A, no error bars given) and ED (1.313 f 0.010 A) C(1)-F bond distance. The other exception concerns the C(3)-C(4) bond, which is computed as 1.584 A, in remarkable agreement with the ED result of 1.583 A. Interestingly, MP2/6-31+G* and LDA+BP/TZP are in agreement with each other in assigning a bond distance of 1.349 and 1.344 A for the carbon-carbon double bond, while the two experimental data are also mutually

TABLE 2: Optimized Geometries for 3,3,4,4-Tetrafluorocyclobutene(2), Bond Lengths in Angstroms, Selected Bond Angles in Degrees, Point Group Symmetry CZ, exptl HF/ MP2/ MP2/ LDA+BP/ (Mw)" 6-31+G* 6-31+G* 6311+G(2d)

parameter r[C(l)-C(2)] r[C(2)-C(3)] r[C(3)-C(4)] r[C(l)-H] r[C(3)-FI a[C(l)C(2)C(3)] a[C(2)C(3)C(4)]

1.349(6) 1.501(6) 1.539(6) 1.079(6) 1.358(6) 93.6(2) 86.3(2)

1.326 1.501 1.547 1.072 1.322 94.2 85.8

1.353 1.501 1.560 1.084 1.366 94.0 86.0

1.347 1.502 1.562 1.083 1.353 94.1 85.9

TZP

1.349 1.513 1.581 1.091 1.356 94.6 85.4

Reference 3.

TABLE 3: Optimized Geometries for Cyclobutene (31, Bond Lengths in Angstroms, Selected Bond Angles in Degrees, Point Group Symmetry CZ, MP21 HF/ MP2/ 6-311G- LDA+BP/ (MW)" 6-31+G* 6-31+G* (2df,2p) TZP

exptl

parameter r[C(l)-C(2)] r[C(2)-C(3)] r[C(3)-C(4)] r[C(l)-Hl r[C(3)-Hl a[C(l)C(2)C(3)] a[C(2)C(3)C(4)]

1.342(4) 1.517(3) 1.566(3) 1.083(3) 1.094(5) 94.2(3) 85.8(2)

1.326 1.516 1.563 1.076 1.086 94.5 85.5

1.351 1.515 1.567 1.087 1.096 94.1 85.9

1.343 1.512 1.564 1.081 1.089 94.2 85.8

1.344 1.521 1.577 1.093 1.104 94.4 85.6

Reference 16. consistent but give shorter distances of 1.326 f 0.022 (ED) and 1.333 f 0.006 8, (MW). However, if the experimental uncertainties of 0.022 (ED) and 0.006 A ( M W ) are considered, the difference between the theoretical and experimental data is much less severe and the LDA+BP/TZP data are within experimental range for the ED and only slightly above that for the MW results. Overall, the LDA+BP/TZP geometry is in excellent accord with the ED structure of 1; in particular, the predictions for the critical C-C single-bond lengths perfectly match the ED data. It is important to stress that Hedberg and Hedberd have employed rotational MW constants of Kuczkowski and co-workers2in a refined analysis of their ED data which led to rao (ED+MW) bond lengths. These are, however, only marginally different from the ED r, values when the thermal averaging effect is properly taken into account. It would therefore appear that the ED r, and rao (EDSMW) bond distances are closer to the equilibrium distances re corresponding to the minimum on the potential energy hypersurface than the pure ro (MW)estimates. This finding is of some relevance and should give impetus for further investigations along these lines. We note in passing that all theoretical and experimental methods discussed here provide an accurate and mutually consistent description of the molecular shape (bond angles), in spite of the inconsistencies in reproducing their size (bond lengths). In order to provide a better understanding of the accuracy of the computed structural parameters and to enable a qualitative discussion of the structure-determining effects, we also determined the equilibrium geometries of 3,3,4,4-tetrafluorocyclobutene, 2 (Table 2), and cyclobutene itself, 3 (Table 3). Unfortunately, for these two species no accurate ED data are available16 and comparison can only be made to their MW structures.17 The general picture is very similar to the discussion above. For 2, at HF/6-31+G* the double-bond length is underestimated, while the C(2)-C(3) distance is reproduced very accurately. The single bond opposite to the double bond is, however, already at this uncorrelated level too long (1.547 A) compared to the experimental MW number (1.539 ic 0.006 A). At the MP2/6-31+G* level a significant lengthening of the C-C double bond and the C-C single bond opposite to it

Remarkable Length of the C(3)-C(4) Bond is observed, while the C(2)-C(3) bond distance remains unchanged compared to the uncorrelated HF result. The agreement with the MW data is very good with the notable exception of the C(3)-C(4) bond, which is 0.021 8, longer than determined in the microwave experiment. To check whether a further increase of the basis set will influence this parameter, we repeated the optimization with the larger 6-311+G* and 6-3 1lSG(2d) basis sets,I8 which was not possible for 1 due to the size of the system. Such MP2 optimizations with large basis sets give usually very accurate geometries, as demonstrated recently by Simandiras et al.19 As documented in Table 2, the changes in geometry upon increase of the basis set are only marginal. Of particular importance in the current context is that the C(3)-C(4) bond distance gets even a bit longer when the desription of the one-particle problem is improved. At our highest level, MP2/6-311+G(2d), this bond length is predicted as 1.562 A, compared to 1.539 =k 0.006 8, determined experimentally. All other parameters are, on the other hand, in perfect harmony with the MW data. The DFT-based calculations show slightly longer bonds for the two single bonds; the most important deviation from the MP2 data occurs for the C(3)-C(4) bond, which is computed as 1.581 A, only slightly shorter than 1. For the pure hydrocarbon, 3, very good agreement is found between the computed data and the MW results, irrespective of the theoretical level employed. In particular, no significant deviations for the C(3)-C(4) bond are observed, even though at LDAfBPmZP this bond distance is computed to be some 0.01 8, longer than at the MP2 level and experimentally observed. Also for 3 we checked the basis set dependence of the MP2 data by employing a variety of larger basis sets, but no‘significant changes could be observed, even with the very large 6-31 1G(2df,2p) basis setz0 (Table 3). These findings can be summarized as follows: Compared to the microwave data, in the case of the fluorinated compounds 1 and 2, the calculations always predict C(3)-C(4) bond lengths that are significantly longer, with the LDA-kBP level showing the most pronounced effect. It is hard to decide whether the DFT approach or the conventional ab initio MO scheme gives the more reliable results; nevertheless, since the DFT data are in such a remarkable accord with the electron diffraction data of 1, we tend to assign the highest degree of confidence to them. In any case, all our calculations indicate that the MW experiments apparently systematically underestimate the C(3)-C(4) bond distance in the fluorinated compounds. Analyzing the trend in the structural properties with increasing fluorine substitution, one sees that the C(3)-C(4) bond distance increases slightly, the C(2)-(C3) distance decreases, while the doublebond length remains essentially unaltered. How can these effects be rationalized? The most popular interpretation of structural properties in fluorohydrocarbons is based on rehyb r i d i z a t i ~ n ~and . ~ ~Coulombic repulsions.z2~z3The latter is certainly of importance and leads to a lengthening of the single bonds. However, whether Coulombic interactions alone are sufficient to overjcompensate the rehybridization effect in the C(3)-C(4) bond is questionable. A shift of s-character from the C-F bonds into the carbocyclic C-C bonds should result in a significant shortening of the distal C(3)-C(4) bond. That such a rehybridization is indeed present is evidenced by the sharpening of the F-C-F angle to some 107’ in spite of the repulsion between the fluorine atoms. Apparently, there is an additional effect which is responsible for the significant lengthening of this C-C single bond. It is conceivable that this is a consequence of the lone pair n-back-bonding of the fluorine atoms: Each fluorine has a lone-pair properly oriented for a conjugative interaction with the unoccupied orbitals of a1

J. Phys. Chem., Vol. 99, No. I, 1995 175 MO 17 L l l M O t l rLmRB

H

ONEBOHRIS

I

I c _ .

I

.

.__.

I

I.--. ..

‘

I

1

1

I1

I

MO 18 LllMO+l PLTORB

I.

ONE BOHR IS

H

,_---_

,

Figure 2. Contour plots of MO 17 (al) and MO 18 (bz) of cyclobutene, computed from the STO-3Gwave function with increments of 0.05 bohP2.

and b2 symmetry of the cyclobutene ring, involving the in-plane p-orbitals of the carbon atoms. In this context, the two most relevant virtual orbitals of cyclobutene (MO 17 (al), LUh40+1, and MO 18 (b2), LUM0+2), computed from a STO-3G wave function, are depicted in Figure 2. These orbitals, which have almost degenerate orbital energies, are predominantly antibonding in the C(2)-C(3) bonds (MO 17) and in the C(3)-C(4) ring-bond (MOlS), while the contribution to the C(I)-C(Z) bond is bonding in MO 17 and slightly antibonding in MO 18. It is evident that MO 18 is better oriented for an effective overlap with the in-plane p-orbitals on fluorine, which may explain why only the C(3)-C(4) bond is lengthened. The presence of the

Hertwig et al.

176 J. Phys. Chem., Vol. 99, No. I, 1995 two additional fluorines in 1 leads to a lowering of the virtual orbital energies, thus making them more apt for the n-backbonding compared to 2, and indeed, the C(3)-C(4) bond is slightly longer in hexafluorocyclobutene than in 3,3,4,4-tetrafluorocyclobutene. On the other hand, the C-C single bond adjacent to the double bond is shorter in 1 since both atoms C(2) and C(3) are experiencing a rehybridization, thereby shifting some more s-character into this bond. The picture is, however, not complete without considering the hyperconjugative interaction between the double bond and the CFZgroups. This should lead to a weakening of the double bond and a strengthening of the adjacent single bonds. Analysis of the n-bond orders shows that they are somewhat diminished in 1 as compared to the parent compound, 3. Since hardly any effect is seen for the double bond, it seems that Coulombic repulsion, hyperconjugation, and n-back-bonding practically cancel the rehybridization effect in 1, whereas the adjacent single bonds do indeed show the expected trend. More specifically, rehybridization prevails in determining the C(2)-C(3) bond distance, while Coulombic repulsion and n-back-bonding of the fluorine atoms are the dominating effects for the C(3)-C(4) bond length. These examples illustrate nicely that multiple fluorination has many faces and that its full description requires a balanced treatment of the various effects. The resulting geometries are the result of a subtle interplay between rehybridization, Coulombic interaction, hyperconjugation, and n-back-bonding.

Conclusion High-level quantum chemical calculations, employing the MP2/6-31+G* and LDASBPITUP schemes, respectively, have been employed to study the equilibrium structue of hexafluorocyclobutene, 3,3,4,4-tetrafluorocyclobutene,and cyclobutene. For hexafluorocyclobutene two different experimental investigations on the structural parameters are available, using either electron diffraction or microwave spectroscopy techniques, which differ significantly in the assignment of the bond distance between C(2)-C(3) and C(3)-C(4). The present calculations, particularly at the approximate density functional level, indicate that the microwave experiments seem to underestimate these bond distances and that the structure obtained by electron diffraction is probably closer to the true equilibrium geometry of hexafluorocyclobutene. The origins of the structural changes upon fluorination are traced back to the subtle interplay between rehybridization, Coulombic interaction, hyperconjugation, and n-back-bonding.

Acknowledgment. The work in Berlin was supported by the Fonds der chemischen Industrie and the Gesellschaft von Freunden der TU Berlin. We are grateful to J. Natterer for helpful discussions and assistance with some of the calculations. Part of this work has been done while Z.B.M. visited the Organisch-Chemische Institut, Westfdische Wilhelms-Univer-

sitlit, Miinster, Germany. He thanks the International Office of the KFA Julich for financial support and Prof. M. Klessinger for hospitality.

References and Notes (1) See for example: Liebman, J. F., Greenberg, A., Dolbier, W. R., Jr., Eds. Fluorine Containing Compounds; VCH: New York, 1988. (2) Xu,L. W.; Klausner, M. E.; Andrews, A. M.; Kuczkowski, R. L. J. Phys. Chem. 1993, 97, 10346. (3) Andrews, A. M.; Maruca, S . L.; Hillig, K. W., II; Kuczkowski, R. L.; Craig, N. C. J. Phys. Chem. 1991,95,7714 and references cited therein. (4) Hedberg, L.; Hedberg, K. J . Phys. Chem.1993,97,10349. CsaSz&, A. G.; Hedberg, K. J. Chem. Phys. 1990,94, 3525. ( 5 ) For a competent description of the methods and basis sets used, see the following excellent discussions: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A Initio Molecular Orbital Theory; Wiley: New York, 1986. (6) Hertwig, R. H.; Holthausen, M. C.; Koch, W.; MaksiC, Z. B. Angew. Chem., Int. Ed. Engl. 1994, 33, 1192; Int. J. Quantum Chem., in press. (7) Ziegler, T. Chem. Rev. 1991, 91, 651. (8) Slater, J. C. Phys. Rev. 1951, 81, 285. (9) Vosko, S. J.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (10) Becke, A. D. J . Chem. Phys. 1986, 84, 4524. (11) Perdew, J. P. Phys. Rev. B . 1986, 33, 8822. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replodge, E. S.; Gomperts, R.; Andres, J. L.; Ragavachaxi, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Pople, J. A. Gaussian 92DFT, Revision F2; Gaussian Inc.: Pittsburgh, PA, 1993. (13) te Velde, G.; Baerends, E. J.; ADF, version 1.02; Dept. of Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, 1993. (14) See for example the following discussion: Bartlett, R. J.; Stanton J. F. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH: New York, 1994; Vol. V, Chapter 2. (15) It should be noted that Hedberg and Hedberg in ref 4 quote an MP2/6-31G* calculation on 1which yields a C(3)-C(4) distance of 1.553 A. Thus, it is obvious that the inclusion of diffuse functions in the basis set has a significant effect (0.011 A) on this bond length. (16) For cyclobutene an ED structure has been reported Goldish, E.; Hedberg, K.; Schomaker, V. J. Am. Chem. SOC. 1956,78,2714. They report a double-bond length of 1.325 i 0.046 8, and a distance for both single bonds on the order of 1.537 f 0.010 A and add that the two single bonds differ by no more than 0.06 A. Due to the large uncertainities in these data, they are not included in the present discussion. (17) MW study on 3,3,4,4-tetrafluorocyclobutene:see ref 3. On cyclobutene: Bak, B.; Led, J.; Nygaard, L.; Rastrup-Anderson, J.; Sorensen, G. 0. J. Mol. Struct. 1969, 3, 369. (18) For a general discussion on the size and quality of the basis sets used, see: Feller, D.; Davidson, E. R. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH: New York, 1990; Vol. I, Chapter 1. (19) Simandiras, E. D.; Handy, N. C.; Amos, R. D. Chem. Phys. Lett. 1987, 133, 324. (20) This basis set does not include diffuse functions. It is known that these are of no importance for a proper decription of pure hydrocarbon compounds such as 3 since neither weakly bound electrons nor lone-pairs are present in these systems. See, for example Frisch, M. J.; Pople, J. A.; Binkley, J. S.J. Chem. Phys. 1984, 80,3265. (21) Bemett, W. A. J . Org. Chem. 1969, 34, 1772. (22) Cooper, D. L.; Wright, S. C.; Allen, N. L.; Winterton, N. J . Fluor. Chem. 1990,47,489. (23) Wiberg, K. B.; Rablen, P. R. J. Am. Chem. SOC.1993, I15, 614.

Jp942037+