14958
J. Phys. Chem. 1996, 100, 14958-14961
Conformational Isomerization of 1,2-Difluoroethane in Solid Argon: Cage-Modified Reaction Barriers Alexander V. Benderskii and Charles A. Wight* Department of Chemistry, UniVersity of Utah, Salt Lake City, Utah 84112 ReceiVed: May 24, 1996X
Thermally induced rotational isomerization of trans-1,2-difluoroethane into the more stable gauche conformer in Ar matrices was studied over the temperature range 30-36 K by infrared spectroscopy. Photochemical generation of 1,2-difluoroethane in the matrix by two different mechanisms forms the product in singly and doubly substitutional argon lattice sites. Only the more stable doubly substitutional site is populated by the ordinary vapor deposition technique. At 33 K, the first-order rate constant for isomerization in the single site is 1.0 × 10-5 s-1 whereas the corresponding value for the double site is 5 × 10-3 s-1. Measurements of the temperature-dependent isomerization rates show that the activation energies for molecules in single and double sites are 15.0 ( 1.5 and 9.7 ( 0.8 kJ/mol, respectively. The latter value is close to a recent estimate of the gas phase reaction barrier (8.86 kJ/mol). This study provides an important example of how a reaction barrier is significantly modified by a solid-state environment. Computer simulations have been performed to calculate the cage-induced changes to the gas phase potential energy surface for this reaction. The calculations are in a good agreement with the experimental results.
Introduction In the condensed phase, the rate of chemical reaction is modified by the local environment of the reaction system. In many cases, distributions of local environments lead to complicated multiexponential kinetics with a distribution of reaction rates. In this paper we describe a simple example of this effect in which the reactant is prepared in only two distinctly different local geometries. The resulting effect on the reaction rates has been characterized quantitatively. Reactions of small impurity molecules isolated in rare gas solids are convenient model systems of solid-state chemical mechanisms,1 in particular for studying the effects of local condensed phase environment because the possible local geometries of the solid around the impurity are few and can be well characterized. Stable and unstable confomers of many simple organic molecules have been trapped in rare gas matrices and studied using vibrational spectroscopy.2-4 A review by Barnes5 lists some 50 molecules that have been characterized in this way. However, there are relatively few studies of conformational isomerization reactions, and most of these have emphasized infrared-induced photochemistry. Pimentel and coworkers6,7 were the first to observe infrared-induced isomerization of HONO in a nitrogen matrix at 20 K. Later, the infrared-induced cis-trans isomerization of but-3-en-2-one in solid argon was reported by Krantz et al.8 Photolysis in the visible and ultraviolet regions can also induce conformational isomerization, as was demonstrated for HONO and N2O3 in nitrogen matrices.9 In a number of cases, thermally activated interconversion can be observed in the cryogenic matrix. Examples include rotamers of aldehyde-ketene COH(CH)3CO in Ar at 30 K,10 chair-twist boat conformers of cyclohexane at 70 K,11 and rotamers of methanol,12 ethylene glycol,13 and 2-haloethanols14,15 in inert low-temperature matrices. Effects of IR irradiation on the rotamer interconversion of 1,2-difluoroethane (DFE) in solid argon matrices were observed and studied by Gu¨nthard and co-workers.16,17 A nonequilibrium mixture of trans and gauche conformers was prepared by X
Abstract published in AdVance ACS Abstracts, August 15, 1996.
S0022-3654(96)01519-5 CCC: $12.00
molecular beam deposition from a heated Knudsen cell,18,19 and the IR spectra were analyzed to characterize the enthalpy difference between conformers and estimate the barrier for internal rotation.20 Extensive computer modeling was also performed to better understand the vibrational spectra and the structure of the sites.21-23 Spectroscopic studies on the gas phase DFE concluded that the gauche conformer is energetically more stable by 3.35 kJ/mol (280 cm-1).24 Measured frequencies of hindered rotor transitions for the gauche and trans forms were used to construct a potential energy function for internal rotation in the form of a six-term Fourier cosine series. The trans to gauche barrier of the resulting potential function is 8.86 kJ/mol. In this paper we report direct kinetic measurements of thermally activated conversion of trans- to gauche-DFE at 3036 K. In a previous study,25 we demonstrated that DFE is formed by two different photochemical mechanisms in an argon matrix containing ethene and fluorine. Direct UV photolysis of C2H4:F2 complexes at 14 K forms DFE in doubly substitutional sites, whereas the diffusion-limited reaction of individual F atoms with isolated C2H4 molecules at 25 K forms DFE in singly subsitutional sites. This photochemical method produces approximately equal amounts of trans- and gauche-DFE in both types of sites. The molecules in single sites have slightly blueshifted infrared bands, which allows the two species to be distinguished on the basis of their spectra. Comparison of the kinetics and activation barriers for the two sites with the gas phase value reveals the influence of the local environment on the potential barrier for this reaction. Simple potential energy calculations based on pairwise additive interactions have been carried out to better understand the geometry of the local environment for the two sites and how it affects the potential function for the internal rotation of DFE. Experimental Section Sample preparation starts with vapor deposition of triple mixture F2:C2H4:Ar (1:1:1000) onto a surface of a CsI window mounted on a cold tip of a closed-cycle helium refrigerator (APD Cryogenics Model DE-202E). The assembly is mounted © 1996 American Chemical Society
Isomerization of 1,2-Difluoroethane in Solid Argon in an ultrahigh-vacuum (UHV) cell evacuated to 5 × 10-8 Torr by a Varian Turbo-V60 turbomolecular pump, which minimizes sample contamination during kinetic experiments that may last several days each. The sample temperature was maintained using a Lakeshore Cryotronics Model 330 temperature controller and a resistance wire heater. In order to minimize reaction in the gas mixture during sample preparation, ethene (Aldrich, 99.5%) and fluorine (Spectra Gases, 10% in Ar) were mixed with argon (Spectra gases, 99.999%) in separate manifolds prior to deposition. The deposition lines merge before entering the UHV cell. Parts of the manifold in contact with fluorine are made of stainless steel and were passivated with F2:Ar (1:10) mixture prior to each experiment. Prepared matrices were photolyzed by the third harmonic (355 nm) of a Nd:YAG laser (Continuum Model Surelite) at a repetition frequency of 10 Hz and average intensity 5-10 mW/ cm2. Photodissociation of F2 molecules results in formation of various products in the matrix including trans- and gaucheDFE, as described in our previous publication.25 Typically, a 60 min photolysis at 26 K converts 10% of the initial reactants into DFE. This forms 1017 molecules/cm2 of approximately equal amounts of trans- and gauche-DFE conformers (peak IR adsorbance 0.005-0.05, base 10). The probe IR beam of a Mattson RS1000 FTIR spectrometer is passed through the UHV cell to a cooled HgCdTe detector. The stationary configuration of the setup allows detection of impurities in the matrices at absorption intensities as low as 0.001 (base 10) with good signal-to-noise ratio. Spectra were recorded at 0.5 and 0.25 cm-1 resolution. Control experiments were performed to ensure that the probe IR beam does not induce any changes in the samples. After the samples were photolyzed, the temperature was ramped to the desired value in the region 30-36 K, and kinetics of thermally induced transformations were recorded. The time resolution is limited by the warming rate of the sample (about 30 s) and the time required for acquisition of each spectrum (5 min). Experimental Results Laser photolysis of 1:1:1000 solid mixtures of F2:C2H4:Ar generates DFE molecules in both the trans and gauche conformations. At 26-28 K, two different mechanisms form DFE in distinct argon lattice sites, as shown in the infrared spectra presented in Figure 1A. The size of the lattice site (single or double) depends on the size of the original occupant of the site prior to photolysis. Direct photolysis of F2:C2H4 binary complexes (which comprise about 5% of the total reactant concentration in 1:1:1000 samples) forms 1,2-difluoroethane in a doubly substituted site. The corresponding infrared bands of the trans and gauche conformers are indicated by the label DFE(2) in Figure 1A. Formation of 1,2-difluoroethane conformers in singly substituted sites is accomplished by successive addition of two F atoms to isolated ethene molecules. These bands are indicated by the label DFE(1). The mechanisms were established by noting that DFE(1) is only formed at temperatures above 20 K where F atoms diffuse through solid argon on a laboratory time scale.25 The infrared spectrum clearly shows that the DFE(1) bands are blue-shifted by 2-3 cm-1 relative to DFE(2). The band positions are listed in Table 1. The positions of the DFE(2) bands coincide with those reported by Huber-Wa¨lchli and Gu¨nthard,19 who prepared samples by direct molecular beam codeposition of difluoroethane and argon. We performed a single control experiment in which a room temperature mixture of 1,2-difluoroethane and argon was deposited through an
J. Phys. Chem., Vol. 100, No. 36, 1996 14959
Figure 1. Partial infrared spectrum of 1,2-difluoroethane formed in singly and doubly substitutional argon lattice sites, indicated by DFE(1) and DFE(2), respectively: (A) after UV laser photolysis of a 1:1: 1000 mixture of F2:C2H4:Ar at 25 K; (B) after annealing to 30 K for 2 h, and (C) after annealing to 35 K for 5 h.
Figure 2. Kinetic curves of trans-gauche interconversion for 1,2difluoroethane in a doubly substitutional site at 32 K. The squares represent the integrated infrared band intensity for trans conformer (1047.5 cm-1). Triangles and diamonds represent the growth in infrared bands of the gauche conformer (1070.2 and 1096.0 cm-1, respectively). The solid curves are kinetic fits to the data yielding a first-order rate constant k ) (1.37 ( 0.15) × 10-3 s-1.
TABLE 1: Observed Infrared Frequencies (cm-1) of Photoproduced 1,2-Difluoroethane in Solid Argon DFE(1)
DFE(2)
assignment
861.3 893.6 1053.0 1071.8 1099.0 1455.8
858.6 890.1 1047.5 1070.2 1096.0 1454.0
gauche C-C stretch gauche CH2 rock trans-C-F stretch gauche C-F stretch gauche C-F stretch gauche CH2 deformation
effusive source. We observed infrared bands attributed to the more stable gauche-DFE(2) conformer; we did not observe trans-DFE(2), although this was observed in the earlier study in which the DFE source was heated. More importantly, there was no evidence for formation of either conformer in a singly substitutional site by direct vapor deposition, either in our work or in the previous studies.18-20 Both DFE(1) and DFE(2) undergo thermally induced transgauche conversion, as shown in Figure 1. After annealing the sample at 30 K for 5 h, trans-DFE(2) bands disappear and gauche-DFE(2) increase in intensity. Subsequent annealing of the same sample to 35 K for 30 h results in disappearance of the DFE(2) trans bands and growth of gauche-DFE(1). Kinetic curves of the thermally activated trans-gauche conversion for DFE(1) and DFE(2) are shown in Figures 2 and 3. For the trans conformer, the integrated band intensity is
14960 J. Phys. Chem., Vol. 100, No. 36, 1996
Figure 3. Kinetic curves of trans-gauche interconversion for 1,2difluoroethane in a singly substitutional site at 35 K. The squares represent the integrated infrared band intensity for trans conformer (1053.0 cm-1). Triangles and diamonds represent the growth in infrared bands of the gauhe conformer (1071.8 and 1099.0 cm-1, respectively). The solid curves are kinetic fits to the data yielding a first-order rate constant k ) (0.97 ( 0.1) × 10-4 s-1.
Benderskii and Wight
Figure 5. Potential energy for the internal rotation of 1,2-difluoroethane about its C-C bond. Triangles represent calculated potentials for DFE(1); squares are calculated for DFE(2). Open symbols represent calculations in which the lattice was fixed during C-C bond rotation (starting from the relaxed trans geometry), whereas solid symbols correspond to calculations in which the lattice was relaxed at each stage of C-C bond rotation. The dashed curve is the gas phase potential from ref 24.
angles, developed earlier by Raff.27 The torsional potential for rotation about the C-C bond was represented by a six term Fourier cosine series 6
V(φ) ) ∑1/2Vn[1 - cos(nφ)] n)1
Figure 4. Arrhenius plot of the temperature dependence of the interconversion rate constants. Least-squares linear fits yield activation energies for conformational isomerization of 15.0 ( 1.5 and 9.7 ( 0.8 kJ/mol for DFE(1) and DFE(2), respectively.
shown as a function of time at constant sample temperature. For the gauche conformer, the initial band intensity has been subtracted from each point so that only the growth in the integrated band intensities are shown. Solid curves represent single exponential fits with the same rate constant for all three bands in the C-F stretching region (one trans and two gauche). The kinetics of trans-gauche conversion were measured at seven different temperatures, and Arrhenius plots were constructed, as shown in Figure 4. The apparent activation energies for isomerization of DFE(1) and DFE(2) are 15.0 ( 1.5 and 9.7 ( 0.8 kJ/mol, respectively. Computer Simulations Simple potential energy calculations were performed in order to better understand the nature of the lattice sites corresponding to DFE(1) and DFE(2) and the influence of the cage on the reaction barrier. The system consisted of a single DFE molecule at the center of a roughly spherical cluster of 1506 Ar atoms arranged in a face-centered-cubic lattice. The innermost 430 Ar atoms were mobile and formed a globular mass approximately 3.1 nm in diameter around the DFE. The remaining 1076 atoms formed a frozen outer shell (spherical layer with outside diameter of 4.8 nm). The lattice-lattice and impuritylattice interactions were modeled by Morse pairwise additive atom-atom potentials used by Raff.26 The internal vibrational modes of DFE were represented by a set of Morse potentials to represent chemical bonds and harmonic potentials for bending
in which the coefficients Vn were determined on the basis of far-infrared and low-frequency Raman spectra of gaseous DFE.24 Each calculation was begun by placing a trans-1,2-DFE molecule in an interstitial or substitutional (single, double, or triple) site in the center of the cluster of argon atoms arranged in a perfect fcc lattice. This geometry was then allowed to relax to a local minimum by means of a damped trajectory method in which the velocities of each particle are reset to zero at each step in the trajectory. The doubly substitutional site of DFE(2) was found to be the most stable, as measured by the total potential energy of the system. The single substitutional site corresponding to DFE(1) was higher by only 2 kJ/mol. Triple substitutional and interstitial sites were found to be considerably higher in energy, by 25 and 45 kJ/mol, respectively. Similar calculations performed for the ethene molecule indicate that the most stable site is singly substitutional; doubly substitutional and interstitial sites lie 10 and 30 kJ/mol higher in energy, respectively. These results strongly support the assignments of the DFE(1) and DFE(2) bands to singly and doubly subsititutional sites, which were previously based only on the experimentally observed blue shift of the DFE(1) bands.25 Figure 5 shows that the total potential energy of the system as a function of the internal rotation coordinate for the doubly and singly substitutional sites. In the first set of calculations, the potential was determined by rotation of one CH2F group starting from the equilibrium configuration of the lattice around trans-DFE. The surrounding Ar atoms were fixed during the rotation. Upper limits for the potential barrier to internal rotation obtained from this procedure were 16.2 kJ/mol for DFE(1) and 12.6 kJ/mol for DFE(2). A second set of calculations was performed in which the lattice was allowed to relax to the nearest local minimum (via the damped trajectory method) after each step in rotation about the C-C bond. The resulting potential energy curve (also shown in Figure 5) follows quite closely that of gas phase potential for DFE, indicating that local rearrangements of the surrounding argon atoms can accommodate essentially all rotational configurations of DFE regardless of cage size. The calculated barriers, 8.2 kJ/mol for DFE(1) and 9.1 kJ/mol for DFE(2), are close to the gas phase value of 8.86 kJ/mol.24 In
Isomerization of 1,2-Difluoroethane in Solid Argon the singly substitutional site, the complicated interactions with the lattice actually reduce the barrier along the minimum-energy path for internal rotation. This is in qualitative agreement with the more elaborate consistent force field calculations carried out by Gu¨nthard and co-workers.22 Discussion The most important methodological aspect of this work is that we have exploited a photochemical technique for in situ generation of DFE in two well-defined lattice sites. Direct UV laser photolysis of C2H4:F2 complexes forms DFE(2) in a double substitutional site. This is the lowest energy site of DFE, and conformational isomerization is essentially unhindered by the surrounding lattice. This is confirmed by the close agreement between the measured activation energy for DFE(2) and the gas phase potential derived from spectroscopic data. Conversely, formation of DFE(1) occurs by successive addition two F atoms by diffusion-limited reaction to an isolated ethene molecule in a singly substitutional site. In this much smaller lattice cage, interaction of the CH2F groups with the surrounding argon atoms raises the activation energy by more than 50%. By most standards, the 5 kJ/mol difference in activation energies is quite modest. However, at 30 K the effect is to lower the rate of trans-gauche conversion by 3 orders of magnitude. Comparison of the experimental data with the computer simulations reveals a consistent and logical physical interpretation of our results. The simulations suggest that if internal rotation about the C-C bond is slower than the lattice relaxation time, then the barrier to the isomerization reaction should be essentially the same as the gas phase value, regardless of whether the DFE is in a single or double lattice site. However, the barriers for rotation in unrelaxed lattices are in better agreement with the experimentally determined activation energies. On this basis, we tentatively conclude that the transition from trans to gauche is sudden in comparison with the argon lattice relaxation time. This conclusion is supported by the fact that the characteristic frequency of the hindered rotation about the C-C bond (120 cm-1) is twice the Debye lattice frequency of argon (60 cm-1).28 However, we hasten to point out that, at the naively simple level of our calculations, the agreement with experiment might result from fortuitous choice of the pairwise interaction potentials. In our opinion, more sophisticated calculations than the ones reported here could only be justified if a considerable effort were made to formulate a more accurate model of the inter- and intramolecular potential energy surface. Perhaps the single most significant aspect of this work is that we have experimentally measured the temperature dependence of reaction rates for molecules prepared in two distinct and wellcharacterized lattice sites in the solid state. Although it is
J. Phys. Chem., Vol. 100, No. 36, 1996 14961 intuitively obvious that the size of a lattice cage should have some effect on the rate of reaction, well-documented experimental studies that quantify such an effect are quite rare. It is our hope that this modest beginning will inspire additional studies such that the complicated nature of solid-state reactions will one day be understood at a level that compares with gas phase reactive dynamics. Acknowledgment. This research is supported by the National Science Foundation under Grant CHE-9300367. References and Notes (1) Pimentel, G. C. J. Am. Chem. Soc. 1957, 80, 62. (2) Barnes, A. J.; Hallam, H. E. Trans. Faraday Soc. 1970, 66, 1932. (3) Hallam, H. E. In Vibrational Spectra of Trapped Species; Wiley: New York, 1973. (4) Barnes, A. J.; Whittle, G. C. In Molecular Spectroscopy of Dense Phases; Grossman, M., Elkomoss, S. G., Ringeissen, J., Eds.; Elsevier: Amsterdam, 1976; p 373. (5) Barnes, A. J. In Matrix Isolation Spectroscopy; Barnes, A. J., Orville-Thomas, W. J., Mu¨ller, A., Gaufres, R., Eds.; Reidel: Boston, 1981; p 531. (6) Baldeschwieler, J. D.; Pimentel, G. C. J. Chem. Phys. 1960, 33, 1008. (7) Hall, R. T.; Pimentel, G. C. J. Chem. Phys. 1963, 38, 1889. (8) Krantz, A.; Goldfarb, T. D.; Lin, C. Y. J. Am. Chem. Soc. 1972, 94, 4022. (9) Varetti, E. L.; Pimentel, G. C. J. Chem. Phys. 1971, 55, 3813. (10) Chapman, O. L.; McIntosh, C. L.; Pacansky, J. J. Am. Chem. Soc. 1973, 95, 244. (11) Squillacote, M.; Sheridan, R. S.; Chapman, O. L.; Anet, F. A. L. J. Am. Chem. Soc. 1975, 97, 3244. (12) Serralach, A., Meyer, R. J. Mol. Spectrosc. 1976, 60, 246. (13) Frei, H.; Ha, T. K.; Meyer, R.; Gu¨nthard, Hs. H. Chem. Phys. 1977, 25, 271. (14) Pertilla¨, M.; Murto, J.; Kivinen, A.; Turunen, K. Spectrochim. Acta 1978, 34A, 9. Pertilla¨, M.; Murto, J.; Nalonen, L. Spectrochim. Acta 1978, 34A, 469. (15) Pourcin, J.; Davidovics, G.; Bodot, H.; Abouaf-Marguin, L.; Gauthier-Roy, B. Chem. Phys. Lett. 1980, 74, 147. (16) Dubs, M.; Ermanni, L.; Gu¨nthard, Hs. H. J. Mol. Spectrosc. 1982, 91, 458. (17) Felder, P.; Gu¨nthard, Hs. H. Chem. Phys. 1984, 85, 1. (18) Hu¨ber-Wa¨lchli, P. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 10. (19) Hu¨ber-Wa¨lchli, P.; Gu¨nthard, Hs. H. Chem. Phys. Lett. 1975, 30, 347. (20) Hu¨ber-Wa¨lchli, P.; Gu¨nthard, Hs. H. Spectrochim. Acta 1981, 37, 285. (21) Gunde, R.; Gu¨nthard, Hs. H. Chem. Phys. 1987, 111, 339. (22) Gunde, R.; Ha, T.-K.; Gu¨nthard, Hs. H. Chem. Phys. 1990, 145, 37. (23) Gunde, R.; Heller, H. J.; Ha, T.-K.; Gu¨nthard, Hs. H. J. Phys. Chem. 1991, 95, 2802. (24) Durig, J. R.; Liu, J.; Little, T. S.; Kalasinsky, V. F. J. Phys. Chem. 1992, 96, 8224. (25) Misochko, E. Ya.; Benderskii, A. V.; Wight, C. A. J. Phys. Chem. 1996, 100, 4496. (26) Raff, L. M. J. Chem. Phys. 1991, 95, 8901. (27) Raff, L. M. J. Chem. Phys. 1987, 91, 3266. (28) Pollack, G. L. ReV. Mod. Phys. 1964, 36, 748.
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