Theoretical study on the stability of hexafluoro dewar benzene

Journal of Molecular Structure (Theochem), 136 (1986) 111-119 Elsevier Science Pubhshers B.V., Amsterdam - Printed in The Netherlands

THEORETICAL STUDY ON THE STABILITY OF HEXAFLUORO DEWAR BENZENE

K. KANDA* and A. IMAMURA Department of Chemistry, Faculty of Science, Hiroshima University, Higashisenda-machi, Naka-ku, Hiroshima 730 (Japan) (Received 31 May 1985)

ABSTRACT Ab initio calculations were carried out on benzene, Dewar benzene and their perfiuoro derivatives. Full geometry optimization was performed for the above molecules, and vibrational analysis was also carried out for the Dewar isomers. The mechanism of stabilization by fluorine substitution is discussed. It is suggested that the vibrational relaxation of the resultant molecule is important for the prevent&ion of the decomposition of a molecule with such a highly strained carbon skeleton. INTRODUCTION

On account of the lack of evidence to the contrary from ortho-di-substituted benzene derivatives and other theoretical and experimental sources, there is nowadays no doubt that the benzene molecule has the Kekule structure which is a planar six-membered carbon ring. Many other structures of benzene, however, were suggested before and after Kekule’s proposal. Though many of them do not have any theoretical basis, some were actually synthesized as the valence isomers of benzene. These are Dewar benzene (bicyclobenzvalene (tricyclo[3.1.0.02*6] hex-3-ene), and [ 22.01 hexa-2,5-diene), prismane (tetracyclo[2.2.0.02*6.035] hexane). The above isomers have nonplanar and highly distorted structures, so they are unstable and are likely to isomerize to normal benzene or non-aromatic molecules. The first synthesis of a benzene valence isomer was performed in 1962 by van Tamelen and Pappas [ 11. They prepared 1,2,5-tri-tert-butylbicyclo[2.2.0] hexadiene by the photochemical isomerization of 1,2,5-tri-tert-butylbenzene, which has a large steric repulsion between its ortho substituents. More recently, it was confirmed that of the above isomers and fulvene was formed in the liquid phase from non-substituted benzene a mixture by UV irradiation [2]. In 1966, the photoisomerization of hexafluorobenzene was reported [3, 41, that is, the hexafluoro Dewar benzene was formed in the vapor phase at room temperature. Furthermore, many perfluoro aromatic compounds were utilized for the synthesis of their valence isomers [5, 61; for example, hexakis(trifluoromethyl)benzene gives its benzvalene-type 0166-1280/86/$03.50

o 1986 Elsevier Science Publishers B.V.

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isomer under irradiation with a high pressure mercury lamp, and gives its Dewar benzene and prismane isomers with a low pressure mercury lamp [7, 81. Many theoretical [9-133 and experimental [14-161 studies have been reported for benzene valence isomers and their derivatives. As stated above, fluorine substitution plays an important role in the syntheses of benzene valence isomers. The purpose of this paper is to clarify the nature of the effect of fluorine; thus the isomerization reaction from hexafluorobenzene to its Dewar structure is discussed in which steric repulsion between substituents is not present. Ab initio calculations on benzene, Dewar benzene, and their fluorides are also reported, as is the full geometry optimization and vibrational analysis for the Dewar benzenes. METHODOF CALCULATIONS The geometry optimization was performed by the ab initio closed-shell SCF method with the energy gradient technique using the lMS version of the GAUSSIAN 80 program [ 171. The 4-31G basis set [ 181 was used with standard scale factors. For benzene and hexafluorobenzene, Deb symmetry was kept during the optimization, so there were two geometrical parameters. Dewar benzene and its fluoride with C?, symmetry had nine parameters. Free optimizations were accomplished for all parameters. The vibrational analysis was done for Dewar benzene and its fluoride using the GAMESS program [19] to perform the numerical differentiation of the energy gradient. The STO-3G basis set [20] was used to obtain the second derivatives of the potential energy at the 4-31G optimized geometries. RESULTSAND DISCUSSION The 4-31G optimized geometries for benzene, Dewar benzene, and their fluorides are summarized in Table 1 with experimental data [21]. In this table T is the dihedral angle between the two cyclobutene rings of Dewar benzene, and D is the angle between the cyclobutene plane and the C-X (X=H, F) bond. The negative values of D mean that the angle is in the direction indicated by the arrow in Fig. 1. For benzene and hexafluorobenzene the calculated internuclear distances, except for the C-F bond, are shorter than the experimental values in accordance with the general tendency of the Hartree-Fock method. This trend is also true for Dewar benzene and its fluoride except for the C(l)-C(2) bond lengths which are a little longer than the experimental values. The reason for the elongation of the C-F bond may relate to the fact that the Hartree-Fock approximation fails to give a low enough energy value for bonding in the fluorine molecule Fz. Although the positions of hydrogen atoms in Dewar benzene are not clear experimentally, the angles that were obtained by the present calculations are near the experimental values. For the non-substituted Dewar benzene, the C-C distance is elongated in

113 TABLE 1 Dewar benzene,

Optimized structures of benzene, dngstrijms and angles in degrees.)

C,F,

C,H, (X = H) Calc. Benzene C-C C-X

1.384 1.072

Dewar benzene C(1)+(4) C(l)+(2) C(2)+(3) C(l)-X(1) C(2)-X(2) X(l)C(l)C(Q) X(2)C(2)c(3)

1.582 1.534 1.326 1.077 1.069 122.3 133.5

Angle !P Angle Da

116.7 -2.5

and their fluorides (Distances in

(X = F)

Calc.

Ex~.~

1.396 1.083 1.62 1.53 1.34 -

177 -

EXp.b

1.372 1.346

1.397 1.321

1.557 1.512 1.316 1.366 1.332 120.6 134.0

1.598 1.505 1.366 1.328 1.319 118.7 133.6

120.1 -7.0

121.8 -7.5

aSee Fig. 1. T is the dihedral angle between two cyclobutene rings; D is the angle between the C&X bond and the cyclobutene ring plane, and its direction in Fig. 1 means the value is negative. bFtef. 21.

the C(l)-C(Z) bond corresponding to the decrease of the formal bond order and the shorting of the C(2)+(3) double bond. The bond length between bridge-head carbons (C(1) and C(4)) implies that this is nearly a single bond. The changes in C-H bond lengths by the isomerization of benzene to Dewar benzene are small for both C(l )-H(l) and C(2)-H(2). For the fluorinated benzene, however, the C-F bond lengths change slightly, which does not correspond to the experimental values. This difference may be an error arising from the Hartree-Fock-Roothaan approximation. A comparison between non-substituted and fluorinated benzenes shows that the carbon skeletons shrink upon fluorination especially in the Dewar benzene form, while the bond angles, including the two dihedral angles T and D, do not change significantly. It can, therefore, be supposed that the two Dewar benzenes have approximately the same angular distortions.

Dewar Benzene

Fig. 1. Structures of benzene and Dewar benzene.

y‘D

114 TABLE 2 Total energies (a.u.)

Benzene Dewar benzene A E (kcal mol-’ )

-230.3778 -230.2169 101.0

-822.6880 -822.5471 88.4

Table 2 summarizes the total calculated energies for the optimized structures of the molecules and gives the energy differences between the isomers. The positive values of AE mean that this isomerization reaction is endothermic. Thermodynamically the fluorinated Dewar benzene is more stable than the non-substituted Dewar benzene because AE of the former is about 13 kcal mol’ smaller than that of the latter. This fact, however, does not definitely mean that hexafluoro Dewar benzene can be more easily synthesized since the whole reaction path must be considered. Figure 2 shows a schematic energy profile of the isomerization from benzene to the Dewar isomer. The solid line corresponds to the non-substituted benzene, and the broken line to the fluorinated one. If the two reaction paths have shapes similar to each other, the low heat of isomerization to Dewar benzene may mean that the product is easily isomerized back to the reactant. Unfortunately, transition state structures of these compounds were not determined in this work, but the experimental energy profile has been reported for hexamethyl benzene and hexakis(trifluoromethyl)benzene by LemaI and Dunlap [ 161. The trifluoromethyl group, like fluorine itself, has an electronwithdrawing power. The heat of isomerization of perfluoromethyl Dewar benzene is 28.0 kcal mol-’ and that of hexamethyl Dewar benzene is 59.5 kcal mol-‘. These values are smaller than those of molecules studied here, because a steric repulsion between methyl groups is present in their planar structures. In contrast to the existence of an isomerization energy difference between the above methyl and trifluoromethyl derivatives, the activation energy from hexakis(trifluoromethyl)Dewar benzene to the corresponding planar benzene is 37.4 kcal mol-‘, which is nearly equal to that of the

Benzene

Dewar Benzene

Fig. 2. Schematic energy profile along the reaction path of the isomerization from benzene to Dewar benzene.

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hexamethyl compound, 36.4 kcal mol-‘. So whilst the barrier heights for the molecules studied here are not known exactly, it can be assumed that they are not very different from each other. Haller investigated the kinetics of the photoisomerization from hexafluorobenzene to its Dewar isomer experimentally. He suggested the following mechanism: A+hv+A*

(1)

A*+X

(2)

A*-+D,

(3)

D,+A

(4)

D,+M-+D

(5)

D,+A+D

(6)

where A and D are the reactant and product, respectively, and the asterisk corresponds to an electronically excited state. The subscript n refers to vibrational excitation, X is a decomposed product, and M is the added foreign gas which can remove vibrational excess energy from “hot” Dewar benzene. Since a higher partial pressure of the vibrational quencher M causes a higher quantum yield of Dewar benzene, and since non-substituted benzene isomerizes only in liquid phase and not in vapor phase, the relaxation of the vibrational energy of the Dewar isomer is essential to the ease of formation of product in the synthesis of the fluorinated valence isomer. The normal mode vibration frequencies of Dewar benzene and its fluoride, calculated with the STO-3G basis set, are shown in Table 3. The 4-31G optimized geometries were used throughout the vibrational analysis. All the frequncies of hexafluoro Dewar benzene are generally much lower than those of non-substituted Dewar benzene, but a mode-by-mode comparison of these two derivatives is not appropriate because of the large differences of displacement vectors in the vibrations. The fluorine nucleus is about nineteen times as heavy as a proton, and it has the same order of magnitude of atomic weight as a carbon nucleus. Thus the six-membered ring of carbons in the fluorinated Dewar benzene moves much more than that of the unsubstituted Dewar benzene, even if the two Dewar benzenes studied here have the same force field. For non-substituted Dewar benzene, the six highest frequencies (laI, Za,, la,, lbI, lbz, and 2bz), whose wave numbers are about 3800 cm-‘, correspond to the carbon-hydrogen stretching modes, while those of hexafluoro Dewar benzene (1700-2200 cm-‘) correspond to the stretching between carbon and fluorine. The 2aI and the 2bz vibrations of both molecules, which are the bridge-head C-X stretching modes, have lower frequencies than the other C-X stretching modes. This means that the bridge-head carbons are more saturated in nature than the other four carbons, as indicated

116 TABLE 3 Normal mode vibrations of Dewar Benzene and its derivative (cm-‘)

a1

V-h

C,F,

1 2 3 4 5 6 7 8 9

3883 3771 1920 1423 1215 1133 1024 898 405

2204 1691 1372 1184 695 616 272 225 120

1 2 3 4 5 6 7

3834 1585 1392 1140 1063 937 381

1718 1437 862 643 465 267 79

‘AH,

W,

b,

1 2 3 4 5 6

3881 1890 1469 1264 1171 781

2193 1565 1036 488 321 233

b,

1 2 3 4 5 6 7 8

3835 3760 1537 1354 1121 1109 995 587

1712 1635 1057 901 750 585 285 149

by the formal chemical formula. Though the minimal STO-3G basis set used in this study is empirically known to give higher frequencies (sometimes about 30%) at the Hartree-Fock level than the experimental values [22], the relative ordering is expected to be qualitatively correct. For medium frequencies in the range 800-2000 cm-l for the hydride and 200-1500 cm-’ for the fluoride derivative, the vibrations are not pure stretching or pure bending, so the assignment is very difficult. Since these molecules have ring structures, the stretching between carbons and the bending of carbon valence bonds mix with each other. The vibrations related to the movement of the carbon skeleton are slightly decreased by the fluorine substitution of protons; for example, the 3aI vibration of 1920 cm-’ in Dewar benzene corresponds to the 1372 cm-’ vibration in the hexafluoro compound. The lowest frequencies of each symmetry correspond to the C-X bond bending with respect to the cyclobutene plane. In this group of vibrations only hydrogen or fluorine nuclei move, and the ratios of wavenumbers for hydride to that of fluoride are about four. This factor corresponds approximately to the square root of the mass of fluorine (~4.4). Thus, from the vibrational analysis point of view, the substitution effect is mainly due to the increase in the reduced mass of vibration. From the point of view of radiationless electronic transition processes [23], the low frequencies for hexafluoro Dewar benzene are expected to produce an increase in the state density of vibronic excited states of this Dewar benzene. Thus, if both molecules have approximately the same Franck-Condon factor, the rate of

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reaction (3) may become much faster than that for unsubstituted benzene. Furthermore, the lower frequency of the vibrations results in lower energy differences of these vibronic excited states and may accelerate the intramolecular vibronic relaxation. Consequently it can reasonably be expected that hexafluoro Dewar benzene is formed faster through reaction (3) than nonsubstituted benzene and is stabilized by the radiationless transition to its ground state as well as the vibronic relaxation. The Mulliken population analysis and calculated dipole moments are shown in Table 4. The charges on the carbons of nonsubstituted benzene are not large in absolute values and this is also the case for Dewar benzene. Those of the perfluoride derivative, however, are large and have opposite signs, and the C-F bond has a large ionic character as expected. Furthermore, in isomerization, the electrons flow to the bridge-head carbon and thus the atomic charges decrease. For hydrogen and fluorine large differences in atomic charge are not found through the isomerization process. Since there is no large difference between the structures of these Dewar benzene derivatives, this large ionic character of the C-F bonds is the cause of the large dipole moment of hexafluoro Dewar benzene (Table 4). Furthermore, the atomic charges on the carbons of hexafluoro Dewar benzene are very positive which produces two effects: first, the decrease of electron repulsion in the distorted sixmembered ring contributes to the thermodynamic stability of hexafluoro Dewar benzene as indicated in Table 2; and second, this tendency protects the highly strained carbon skeleton from the attack of electrophiles. The C-C bond population in benzene is 1.042, and this should correspond to one and a half bonds of the conjugated R-system. For those of Dewar benzene, the C(2)-C(3) bond, which is formally a double bond, increases in population, whereas the C(1)+(2) bond decreases in population. The C(l)-C(4) bond which is formed by the isomerization has almost the same population as the C(1)+(2) single bond. In contrast with this, the C-H bond populations do not change significantly through the isomerization. For the fluoride, the C-C and the C-F bond populations decrease to about half of those of the hydride. This means that the electron density around the carbon nucleus flows to fluorine, resulting in the large ionic character of the C-F bond. It is noteworthy that, for hexafluoro Dewar benzene, the bond population between the bridge-head carbons (C(1) and C(4)) is nearly zero. The 4-31G basis set used for the population analysis has diffuse basis functions so that above character may be underestimated, but it should be expected that this bond is qualitatively much weaker than the usual one. The other bond populations are about half the values of the hydride as is the case for perfluoro benzene. The calculated dipole moments of Dewar benzene derivatives are given in the last row of Table 4. The fluoride has a large dipole moment than the hydride and so in the condensed phase (i.e., the liquid or a gas at high pressure) the hexafluoro Dewar benzene is likely to form a weak complex with foreign molecules or itself. Therefore the energy transfer, as in reactions (5)

118 TABLE 4 Atomic charges, bond populations

and dipole moments

of benzene and Dewar benzene

Atomic charge Benzene C X

-0.19 +0.19

+ 0.40 -0.40

Dewar benzene C(l) C(2) X(l) X(2)

-0.28 4.14 +0.18 +0.19

+0.26 + 0.46 -0.39 -0.39

Bond population Benzene C(l)_C(2) C(lkX(l)

1.042 0.772

0.472 0.488

Dewar benzene C(lkq4) C(l)-c(2) C(2W3) C(l)_X(l) (x2)-X(2)

0.564 0.662 1.326 0.760 0.746

-0.060 0.388 0.726 0.340 0.432

Dipole momenta Dewar benzene aWhen the dipole is as indicated moments given in Debye.

-0.058

-0.847

in Fig. 1, the value is defined

to be negative.

Dipole

and (6), is easier than for nonsubstituted benzene. Furthermore, at the longer distances, at which the reaction complex with M or A is not formed, the van der Waals interaction is increased by the large dipole moment. Since the six C-F bonds with their large ionic character can be regarded as a cluster of electronic dipoles, the dipole moment temporarily formed by vibration becomes larger than in the case of nonsubstituted Dewar benzene. Thus, the vibronic relaxation reactions (5 and 6) are more likely to occur in the fluoride because of the large intermolecular interaction. CONCLUSION

The stability of perfluoro benzene derivatives have been studied. The reasons for the stabilization of perfluoro molecules can be considered as follows. First, hexafluoro Dewar benzene is thermodynamically more stable than normal Dewar benzene (Fig. 2) due to the decrease of electron repulsion in

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the six-membered carbon ring caused by the electron withdrawing power of fluorine. Furthermore, this withdrawing power protects the highly strained carbon skeleton from attack by electrophiles. Second, it is important that the much lower vibrational frequencies of hexafluoro Dewar benzene (relative to Dewar benzene) enhance the radiationless transition from electronically excited benzen to Dewar benzene, and promotes the inter- and intra-molecular vibrational relaxation. The above mechanism of stabilization by fluorination can also be expected to be the case for the other benzene valence isomers which have highly strained carbon skeletons. ACKNOWLEDGEMENT

The authors are grateful to Prof. D. Munch for reading the manuscript and correcting the English. All calculations were carried out at the Computer Center of Institute for Molecular Science and at the Data Processing Center of Kyoto University with HITAC M-200H and FACOM M-382 computers, respectively. The authors also thank the Information Processing Center of Hiroshima University for permission to use the N-l network facility. REFERENCES 1 2 3 4 5 6 7 8

E. E. van Tamelen and S. P. Pappas, J. Am. Chem. Sot., 84 (1962) 3789. H. R. Ward and J. S. Wiihnok, J. Am. Chem. Sot., 90 (1968) 1086. I. J. Hailer, J. Am. Chem. Sot., 88 (1966) 2070; J. Chem. Phys., 47 (1967) 1117. G. Camoggi, F. Gozzo and G. Cevidaili, Chem. Commun., (1966) 313. E. E. van Tamelen, Act. Chem. Res., 5 (1972) 186. Y. Kobayashi and I. Kumadaki, Act. Chem. Res., 14 (1981) 76. D. M. Lemal, J. V. Staros and V. Austel, J. Am. Chem. Sot., 91 (1969) 3373. M. G. Barlow, R. N. Haszeldine and R. Hubbard, J. Chem. Sot., Chem. Commun., (1969) 202; J. Chem. Sot. C, (1970) 1232. 9 D. Bryce-Smith and H. C. Longuet-Higgins, Chem. Commun., (1966) 593. 10 R. E. Christoffersen, J. Am. Chem. Sot,, 93 (1971) 4104. 11 M. D. Newton, J. M. Schuhnan and M. M. Manus, J. Am. Chem. Sot., 96 (1974) 17. 12 M. Tsuda, S. Oikawa and K. Kimura, Int. J. Quantum Chem., 18 (1980) 157. 13 S. Gikawa, M. Tsuda, Y. Okamura and T. Urabe, J. Am. Chem. Sot., 106 (1984) 6751. 14 D. Bryce-Smith and A. Gilbert, Tetrahedron, 32 (1976) 1309. 15 R. Breslow, J. Napierski and A. H. Schmidt, J. Am. Chem. Sot., 94 (1972) 5906. 16 D. M. Lemal and L. H. Duniap, Jr., J. Am. Chem. Sot., 94 (1972) 6562. 17 J. A. Pople, J. S. Binkley, R. A. Whiteside, R. Kriihnam, R. Seeger, D. J. Defrees, H. B. Schleegel, S. Topiol and L. R. Kahn, Program Library GAUSSIAN 80 (No. 482), Computer Center of the Institute for Molecular Science, 1984; QCPE, 13 (1981) 406,437. 18 R. Ditchfield, R. F. Hehre and J. A. Pople, J. Chem. Phys., 54 (1971) 724. 19 M. Dupuis, D. Sprangler and J. J. Wedoiski, Program Library GAMESS (No. 481), Computer Center of the Institute for Molecular Science, 1984; NRCC QGOl GAMESS. 20 W. J. Hehre, R. F. Stewart and J. A. Pople, J. Chem. Phys., 51 (1969) 2657. 21 H. J. Calomon, E. Hirota, K. Kuchitsu, W. J. Lafferty, A. G. Maki and C. S. Pote, Structure Data of Free Polyatomic Molecules, New Series, Group II, Vol. 7, LandoltBoernstein, Berlin, 1976. 22 (a) P. Carsky and M. Urban, Lect. Notes Chem., 16 (1980) 145; (b) S. Iwata, in K. Ohno and K. Morokuma (Eds.), Quantum Chemistry Literature Data Base, Elsevier, Amsterdam, 1982. 23 M. Bixon and J. Jortner, J. Chem. Phys., 48 (1968) 715.