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J. Phys. Chem. A 2010, 114, 794–803
Unimolecular HCl and HF Elimination Reactions of 1,2-Dichloroethane, 1,2-Difluoroethane, and 1,2-Chlorofluoroethane: Assignment of Threshold Energies Juliana R. Duncan,† Sarah A. Solaka,† D. W. Setser,‡ and Bert E. Holmes*,† Department of Chemistry, UniVersity of North Carolina at AsheVille, One UniVersity Heights, AsheVille, North Carolina 28804-8511, and Department of Chemistry, Kansas State UniVersity, Manhattan, Kansas 66506 ReceiVed: September 2, 2009; ReVised Manuscript ReceiVed: December 1, 2009
The recombination of CH2Cl and CH2F radicals generates vibrationally excited CH2ClCH2Cl, CH2FCH2F, and CH2ClCH2F molecules with about 90 kcal mol-1 of energy in a room temperature bath gas. New experimental data for CH2ClCH2F have been obtained that are combined with previously published studies for C2H4Cl2 and C2H4F2 to define reliable rate constants of 3.0 × 108 (C2H4F2), 2.4 × 108 (C2H4Cl2), and 1.9 × 108 (CH2ClCH2F) s-1 for HCl and HF elimination. The product branching ratio for CH2ClCH2F is approximately 1. These experimental rate constants are compared to calculated statistical rate constants (RRKM) to assign threshold energies for HF and HCl elimination. The calculated rate constants are based on transitionstate models obtained from calculations of electronic structures; the energy levels of the asymmetric, hindered, internal rotation were directly included in the state counting to obtain a more realistic measure for the density of internal states for the molecules. The assigned threshold energies for C2H4F2 and C2H4Cl2 are both 63 ( 2 kcal mol-1. The threshold energies for CH2ClCH2F are 65 ( 2 (HCl) and 63 ( 2 (HF) kcal mol-1. These threshold energies are 5-7 kcal mol-1 higher than the corresponding values for C2H5Cl or C2H5F, and β-substitution of F or Cl atoms raises threshold energies for HF or HCl elimination reactions. The treatment presented here for obtaining the densities of states and the entropy of activation from models with asymmetric internal rotations with high barriers can be used to judge the validity of using a symmetric internal-rotor approximation for other cases. Finally, threshold energies for the 1,2-fluorochloroethanes are compared to those of the 1,1-fluorochloroethanes to illustrate substituent effects on the relative energies of the isomeric transition states. I. Introduction The HX or HY unimolecular elimination reactions of CH2XCH2Y (X, Y ) F, Cl, Br) molecules have been investigated by both thermal and chemical activation experiments.1–14 However, the threshold energies (E0) have not been established with confidence, which has hindered the development of a comprehensive understanding for the effect of halogen substitution on threshold energies for HX elimination reactions. For similar levels of internal energy, the chemical activation rate constants for CH2XCH2X molecules formed by recombination of CH2X radicals are an order of magnitude smaller than for C2H5X molecules formed by recombination of CH3 and CH2X radicals. This could be a consequence of higher threshold energies and/or higher densities of states for the CH2XCH2X molecules. Accurate evaluation of the density of states (or the pre-exponential factor for thermal activation) has been difficult because of the complex nature of the torsional degree of freedom with two conformers and different barrier heights for internal rotation. In addition to HX(Y) elimination reactions, the possibility of unimolecular X-Y interchange in 1,2-dihaloalkanes is of current interest,15–18 and the CH2XCH2Y class of molecules is the simplest representative for this category of reaction. In the present work we have obtained new data for HF and HCl elimination reactions of CH2ClCH2F formed by recombination of CH2F and CH2Cl radicals at room temperature. Rate * Corresponding author. † University of North Carolina at Asheville. ‡ Kansas State University.
constants from these data for CH2ClCH2F and rate constants from previously published data for C2H4F21–7 and C2H4Cl29–12 are interpreted with RRKM theory based upon electronic structure calculations8,19,20 to obtain threshold energies. The internal rotational modes of all three molecules recently have been characterized21–27 and the energy states have been enumerated from zero to above the highest barrier.27 That work will be utilized to obtain more accurate evaluation of the densities of molecular states, which are required for the RRKM calculations (and for the thermal pre-exponential factor). The availability of the energy levels for this complex torsional motion with different barrier heights, as well as the change in the reduced moment with rotation, presents the opportunity to compare the density of states from a reliable calculation to other approximations, which would be necessary if an enumeration of energy levels did not exist. Our main objectives are to characterize the reactions of CH2ClCH2F and assign threshold energies, E0, for all three molecules. In addition, these E0 values will be compared to those for CH3CHF2, CH3CHCl2, and CH3CHClF; the 1,1-isomers have lower E0 for HCl elimination processes than the 1,2-isomers. Chemical and thermal activation studies of CH2FCH2F are the most self-consistent of the three molecules.1–7 In fact, apparent agreement exists for E0 ) 62 ( 2 kcal mol, which is 4 kcal mol-1 higher than for C2H5F. Experimental data for CH2FCH2F activated by recombination of CH2F radicals have been published from several laboratories, and the rate constants are in agreement. However, the original models chosen for the transition state and for the molecule certainly can be improved
10.1021/jp908483m 2010 American Chemical Society Published on Web 12/29/2009
Unimolecular HCl and HF Elimination Reactions by modern calculations of structures, and the apparent agreement between thermal and chemical activation rate constants for a common E0 may be somewhat fortuitous. Recent calculations by Rajakumar, and Arunan8 favor a 3-4 kcal mol-1 higher E0 for CH2FCH2F relative to C2H5F. Conventional thermal activation studies of CH2ClCH2Cl have been affected by heterogeneous and free-radical reactions. A recent shock-tube study14 over a relatively small temperature range reported that the activation energies for C2H5Cl and CH2ClCH2Cl were nearly the same (to within (2 kcal mol-1). Chemical activation data9–12 for CH2ClCH2Cl formed by recombination of CH2Cl radicals are extensive and include systematic studies in various bath gases, as well as deuterium kinetic-isotope effects. The conclusion from the early work was that the E0 for CH2ClCH2Cl had to be several kcal mol-1 higher than that for C2H5Cl in order to match the RRKM and experimental rate constants. The density of states for the molecule was evaluated with vibrational or free-rotor models of the torsional mode in those rate constant calculations. However, C2H4Cl2 has the highest barrier (gauche-to-gauche) to internal rotation of the three molecules, and a correct accounting for the density of states to obtain a more reliable rate constant is desirable. Electronic structure calculations8 suggest that E0(CH2ClCH2Cl) is 3-4 kcal mol-1 higher than E0 for (C2H5Cl). Thermal activation studies13 of CH2ClCH2F reported that the rates for HCl and HF elimination were equal to within the experimental uncertainty. The derived E0(HCl), which was 3 kcal mol-1 higher than E0(HF), is about 5 kcal mol-1 higher than for C2H5Cl; however, E0(HF) was similar to the threshold energy for C2H5F. The chemical activation data are limited to a report6,7 using CH2ClCH2 + F2 as the activation reaction, and the results may not be reliable. Electronic structure calculations8 have not resolved the question of whether E0(HF) is lower or higher than E0(HCl). Therefore, we initiated a chemical activation study using (CH2F)2CO and CH2ClI as photolytic sources of CH2F and CH2Cl radicals at room temperature. These data give individual rate constants for the two channels of CH2ClCH2F. Arunan and co-workers8,14 have published results from calculations of the structures for all three reactions. We augmented those results with density functional theory (DFT) calculations using the B3PW91/6-31G(d′,p′) method to be consistent with our former work.16–18,20 This method usually gives close accord with experimentally assigned threshold energies for HF elimination,16,17,20 but the E0(HCl) values are frequently underestimated. The calculated structures for the molecules and transition states by the B3PW91/6-31G(d′,p′) method agree with the DFT(B3LYP/6311++G**) calculations of Arunan and co-workers,8 and both are in good accord with experimental characterization of the structures and frequencies of the molecules. These calculations plus recent treatments of the hindered internal rotations of these molecules provide a sound basis for calculation of the RRKM rate constants and assignment of E0 values.27 The mechanism for HX elimination from 1,2-dihaloethanes has always been assumed to be 1,2-HX elimination by analogy to the C2H5X reactions10 for which the 1,2-HX mechanism was established by deuterium labeling. The enthalpy of formation of the CH2FCH carbene is now known31 to be 42 kcal mol-1. The threshold energy for 1,1-HX elimination must be equal to or greater than the enthalpy of reaction, which is 85 and 89 kcal/mol for CH2FCH2F(-HF) and CH2ClCH2F(-HCl), respectively. These lower limits are substantially larger than than
J. Phys. Chem. A, Vol. 114, No. 2, 2010 795 the range of threshold energies mentioned above, and the mechanism for the 1,2-dihaloethanes can be safely taken to be 1,2-HX elimination. The carbene structures are stabilized if the halogen atom is located on the carbene carbon atom; thus, the enthalpy of formation of CH3CF is 20 kcal mol-1 lower than for CH2FCH. This explains why 1,1-HX elimination becomes a minor competiting reaction for 1,1-dihaloalkanes. II. Experimental Methods The CH2F and CH2Cl radicals were generated at room temperature by the photolysis of (CH2F)2CO and CH2ClI gases in quartz vessels with an Oriel high pressure 200 W Hg or a 500 W Hg-Xe lamp. Quartz vessels were used to obtain the necessary short wavelength light needed to dissociate the ketone. All gas handling was done in glass, grease-free, high-vacuum lines, and a MKS-270 electronic manometer was used to measure pressures. The (CH2F)2CO and CH2ClI were obtained from SynQuest and Acros, respectively. The first sample of (CH2F)2CO, which was purchased in 2004, contained diethyl ether as an impurity; the second sample obtained in 2009 was free of ether. The recombination of CH2F and CH2Cl radicals generates vibrationally excited C2H4ClF*, C2H4Cl2*, and C2H4F2* molecules.
CH2F + CH2Cl f CH2FCH2Cl*
(1a)
f CH2FCH2F*
(1b)
f CH2ClCH2Cl*
(1c)
These molecules eliminate HCl or HF unless stabilized by collision with bath-gas molecules, M.
CH2FCH2Cl* f C2H3F + HCl
(2a)
f C2H3Cl + HF
(2b)
+ M f CH2FCH2Cl CH2FCH2F* f C2H3F + HF + M f CH2FCH2F CH2ClCH2Cl* f C2H3Cl + HCl + M f CH2ClCH2Cl
(2c) (3a) (3b) (4a) (4b)
Since reactions 2a and 3a both generate C2H3F and reactions 2b and 4a both generate C2H3Cl, a way to separate the decomposition products of reactions 2, 3, and 4 is needed to measure the rate constants of (2a) and (2b). Two different series of experiments were done to achieve this objective. In one series of experiments, a 35-40-fold excess of (CH2F)2CO over CH2ClI with added SF6 to obtain higher pressures was photolyzed in clean quartz vessels for 5-6 min. The typical composition was 4.2 µmol of (CH2F)2CO, 0.11 µmol of CH2ClI, and 6.2 µmol of SF6 in vessels ranging in volume from 7.186 to 32.70 cm3 resulting in a pressure range from 27 to 6.0 Torr. The photodecomposition of (CH2F)2CO yielded a high concentration of CH2F radicals that subsequently abstract I atoms from CH2ClI to yield CH2Cl radicals. The main recombination products are CH2FCH2F* and CH2FCH2Cl*. As the pressures were reduced, the decomposition of C2H4F2* (3a) and C2H4ClF* (2a + 2b) were observed. Plots of C2H3Cl/ C2H4ClF could be constructed to assign the rate constant for reaction 2b. The yield of C2H4Cl2* was small but still measurable, and the C2H3Cl from 4a was subtracted from the total measured amount of C2H3Cl. The ratio of C2H3F/C2H4F2 could be measured, and it provided a monitor for successful experiments. Further details are provided in the results section.
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TABLE 1: Comparison of Experimental and Calculated Rate Constants and the Threshold Energy Barriers experimental rate constants s-1
〈E〉, kcal/mol
molecule
bath gas
Torr
CH2FCH2Cla
(CH2F)2CO and SF6
(-HF) 7.0 ( 0.9
(1.1 ( 0.3) × 108
91.0
CH2ICl
(-HCl) 5.3 ( 0.5
(0.82 ( 0.25) × 108
91.0
CH2FCH2Fb
(CH2F)2CO
18.0 ( 2.0
(3.0 ( 0.6) × 108
92.1
CH2ClCH2Clc
cyclo-C4F8
13.5 ( 1.3
(2.4 ( 0.5) × 108
90.0
k〈E〉d, s-1
E0, kcal/mole
× × × × × × × × × ×
64 63 62 65 64 63 63 62 64 63
0.9 1.3 1.8 1.4 2.0 2.8 3.5 4.9 2.9 4.2
108 108 108 108 108 108 108 108 108 108
This work with T ) 298 K. The collision diameters and ε/k values were 5.5 Å; 350 K for C2H4ClF, 5.1 Å; 400 K for CH2ICl, and 5.0 Å; 502 K for (CH2F)2CO. b Taken from ref 1 as the average of results from CH2FCOCH2F and CH2FCl as efficient bath gases; the collision cross sections are specified in that work; see also refs 2 and 3. c Taken from ref 9 with cyclo-C4F8 as the bath gas; the collision cross sections are given in that work. d Based upon the calculations using the direct count of quantum levels of the hindered rotor. If the overall rotation about the long axis of the molecule and transition state is included with the internal modes as active, the calculated rate constants are smaller by a factor of 1.5 and the lower values of E0 would be preferred. e The listed E0 values are for calculations with 18 internal modes as active with the three overall rotations as adiabatic; see footnote d and the text. a
Another series of experiments were done with a 25-30-fold excess of CH2ClI relative to (CH2F)2CO plus added Hg2I2 to scavenge28 the I and I2. Typical experiments utilized 6.2 µmol of CH2ICl and 0.23 µmol of (CH2F)2CO in vessels ranging in size from 7.186 to 32.70 cm3 resulting in a pressure range from 17 to 3.7 Torr. Since the CH2Cl radicals are in large excess, CH2FCH2Cl* and CH2ClCH2Cl* are the main recombination products. As the pressure was reduced, reactions 2a and 4a were observed and C2H3F/CH2FCH2Cl ratios vs pressure could be obtained that were free of contributions from (3a). Although the pressure regime was not optimum to study reaction 4, the C2H3Cl/C2H4Cl2 ratio was useful to monitor the experiments. Authentic samples were available for identification of all components from reactions 2-4. Products were identified and measured by gas chromatography with both flame-ionization and mass-spectrometric detectors. The quantitative measurement of product ratios was accomplished with a Shimadzu GC-14A gas chromatograph using a 105 m Restek RTX-VGC column. The temperature program consisted of holding the starting temperature at 30 °C for 20 min, followed by increasing the temperature at a rate of 7.5 °C per min until the final temperature of 180 °C was attained. The retention times (minutes) were CH2dCHF (8.2), CH2dCHCl (11.2), CH2FCH2F (13.2), CH2ClCH2F (24.4), and CH2ClCH2Cl (34.6). The reagents, (CH2F)2CO and CH2ClI, were eluted at 37.2 and 38.0 min, respectively. One ketone sample contained some diethyl ether, which was eluted 0.4 min after the C2H4ClF, and care had to be taken to account for any overlap with the C2H4ClF peak. Response factors for the GC-FID were measured from preprepared mixtures that were replicas of the photolyzed samples. The calibration factors for the C2H3F/CH2ClCH2F and C2H3Cl/ CH2ClCH2F ratios were 1.27 ( 0.10 and 1.16 ( 0.04, respectively. These factors convert the measured ratios of peak areas to ratios of concentration. The experimental methods that were employed to study C2H4Cl2* and C2H4F2* are described in the original papers. The CH2F radicals usually were generated by photolysis of (CH2F)2CO.1–6 The CH2Cl radicals usually were generated by secondary reactions following the photolytic production of CH2 radicals9–12 and, in general, there were more complications from secondary reactions than when using CH2ClI as a radical source. III. Experimental Results A. Experimental Rate Constants. The experimental rate constants are summarized in Table 1. The rate constants for
C2H4Cl2* and C2H4F2* have been measured systematically in several bath gases in an effort to understand collisional deactivation. We have selected data from bath gases that were the most efficient, i.e., the average energy lost per collision was 10-12 kcal mol-1 according to a simple stepladder model. Such rate constants are 10-15% larger than those for unit deactivation, which is within the uncertainty of the assignment of collision cross sections in the calculation of the bimolecular collision rate constants, kM for (2c), (3b), and (4b). Therefore, no adjustments to the reported rate constants were made to obtain unit deactivation rate constants. In the demonstration of the utility of mercury(I) iodide for the generation of radicals from photolysis of iodine containing precursor molecules, Holmes and co-workers28 used CH2ClI to prepare CH2ClCH2Cl molecules; the D/S vs pressure plot gave a high pressure rate constant of 15 Torr. Collision diameters of 5.1 Å for CH2ClI and 5.5 Å for C2H4Cl2 with ε/k values of 400 (CH2ClI) and 350 (C2H4Cl2) give a rate constant of 2.4 × 108 s-1. This value is in agreement with the rate constant for cyclo-C4F8 as the bath gas in Table 1. This comparison shows that the CH2ClI bath gas is efficient and that no adjustments are needed for rate constants measured with CH2ClI, CH3I, or other iodides as bath gases,15–17 i.e., the rate constants from the D/S vs 1/P plots need no adjustment to unit deactivation, based on some assumed model. In the series of experiments using excess CH2ClI with (CH2F)2CO, data were obtained to measure the rate constant for HCl elimination from CH2ClCH2F. The yield of C2H4F2 was sufficiently small that it did not contribute to the observed yield of C2H3F. The rate constant based upon the 17 points in Figure 1 give 5.3 ( 0.5 Torr. The data in the plot have more scatter than desirable due to the low and variable yields of CH2ClCH2F and C2H3F; the sum of these products was in the ratio of 0.01 to 0.005 relative to C2H4Cl2 plus C2H3Cl. The small negative intercept implies that some CHFdCH2 could have been consumed during the photolysis and the rate constant may be a lower limit. The CH2dCHCl/C2H4Cl2 ratio from reaction 4 also was measured in this series of experiments, and the results are consistent with the D/S plots shown in refs 9 and 28. In the series of experiments with excess (CH2F)2CO, the rate constant for HF elimination from CH2ClCH2F was measured. Due to the low vapor pressure of the ketone, SF6 was used as an additional bath gas. The rate of reaction of the CH2F radicals with CH2ClI is very rapid and, even for the 35:1 ratio of ketone to iodide, the concentration of CH2Cl radicals was enough to
Unimolecular HCl and HF Elimination Reactions
J. Phys. Chem. A, Vol. 114, No. 2, 2010 797
CH2FCH2F + CH2ClCH2Cl f 2CH2FCH2Cl
(5)
8
According to MP2 and DFT calculations for several basis sets, the enthalpy change is 0 ( 1 kcal mol-1 for (5), as would be expected. Combining this information with the experimental enthalpies of formation gives ∆H°f(CH2FCH2Cl) ) -69.1 kcal mol-1 and D(CF2F-CH2Cl) ) 90.4 kcal mol-1 at 298 K; the uncertainty is probably (3 kcal mol-1. This assignment for ∆H°f(CH2FCH2Cl) is supported by WI calculations,34 which give -71.1 kcal mol-1. The average vibrational energies of the molecules formed at room temperature are given by eq 6. 〈E〉
Figure 1. Plot of CH2dCHF/CH2FCH2Cl (b) and CH2dCHCl/ CH2FCH2Cl (0) vs pressure-1 from the CH2ClCH2F system. The slopes and intercepts from the plots are 5.3 ( 0.5 and -0.20 ( 0.08 for HCl elimination and 7.0 ( 0.8 and -0.07 ( 0.10 for HF elimination; the correlation coefficients are 0.94 for both plots.
yield a measurable amount of C2H4Cl2. Therefore, a correction to the measured yield of C2H3Cl was necessary to obtain the component just from (2b). For this purpose a C2H4Cl2* rate constant of 17 Torr was used with the observed C2H4Cl2 to calculate the C2H3Cl from reaction 4a, which was subtracted from the observed total amount of C2H3Cl. The typical adjustment was a subtraction of 15% from the observed yield of CH2dCHCl. The resulting plot of CH2dCHCl/CH2FCH2Cl vs 1/P is shown in Figure 1; the slope of the plot gives a rate constant of 7.0 ( 0.8 Torr. The least-squares line does pass through the origin, which suggests that the correction for the contribution from (3a) was appropriate. The rate constants in pressure units were converted to s-1 using the collision cross sections given in the footnotes of Table 1. The combined uncertainty of the experimental measurements and the cross sections give error limits of (30% for the rate constants in s-1 units for CH2ClCH2F. The uncertainty in the rate constants in s-1 units for CH2ClCH2Cl and CH2FCH2F were increased to (20%. As would be expected, the total rate constants for the three dihaloethanes formed by radical recombination are similar. Within the experimental uncertainty of the difficult experiments for C2H4ClF, the product branching ratio for HCl vs HF elimination seems to be unity. B. Thermochemistry. The average energies of the three molecules formed in reaction 1 depend upon D(CH2X-CH2Y), which are obtained from enthalpies of formation for the components of the reactions. The enthalpies of formation of CH2ClCH2Cl and CH2FCH2F are established as -31.5 ( 0.829 and -106.830,31 kcal mol-1, respectively, at 298 K. The ∆H°f(CH2Cl) and ∆H°f(CH2F) at 298 K are 28.032 and -7.633,31 kcal mol-1, respectively. These values lead to D298(CH2Cl-CH2Cl) ) 89.3 and D298(CH2F-CH2F) ) 91.6 kcal mol-1 with uncertainties of (2 kcal mol-1. The experimental enthalpy of formation of C2H4ClF seems not to have been reported. However, the computed results8,14 for the total electronic energies of C2H4F2, C2H4Cl2, and C2H4ClF can be used to evaluate the enthalpy change for reaction 5, which then can be combined with experimental ∆H°f(C2H4Cl2) and ∆H°f(C2H4Cl2) to obtain ∆H°f(CH2FCH2Cl).
) D0(CH2X-CH2Y) + 3RT + 〈Ev(CH2X)〉 + 〈Ev(CH2Y)〉 (6)
The last two terms are the thermal vibrational energies of CH2Cl or CH2F, which are very small at 298 K. Converting the bond dissociation energies at 298 to 0 K and adding the 〈Ev〉 terms gives 〈E〉 ) 92.1, 91.0, and 90.0 kcal mol-1 for C2H4F2, C2H4ClF, and C2H4Cl2, respectively. These assignments for 〈E(C2H4F2)〉 and 〈E(C2H4Cl2)〉 are nearly the same as those used in the early chemical activation studies.1–7 IV. Computation of Rate Constants A. Statistical Rate Constants. The standard method for obtaining statistical rate constants at a given energy, E, is eq 7.
kE ) s† /h(I† /I)1/2(ΣP†(E - E0) /N†(E)) †
(7)
The (I /I) term is the ratio of the product of the three overall moments of inertia for the transition state and molecule, s† is the reaction path degeneracy, ∑P†(E - E0) is the sum of vibrational states for the transition state, and N*(E) is the density of states for the molecule at energy E. Since the energy distribution for the molecules formed by recombination of the radicals at room temperature is narrow, E can be associated with 〈E〉. After selection of models for the molecule and transition state, E0 can be assigned by matching k〈E〉 to kexpt. Raff and co-workers35 explored computational models for F-atom dissociation from C2H4F2 in an effort to find criteria for rapid internal vibrational energy redistribution (IVR). Although their model for C2H4F2 did exhibit slow IVR rates, the experimental behavior of the actual 1,2-dihaloethane molecules with 90 kcal mol-1 of vibrational energy with unimolecular lifetimes of several nanoseconds for HF or HCl elimination do follow statistical behavior, and eq 7 is applicable. In fact, the elimination processes satisfy several of the criteria suggested by Raff for judging whether reactions would be expected to follow statistical behavior. The most serious question for these molecules is how to treat the torsional motion, which gives trans and gauche conformers with different overall moments of inertia and different reduced moments of inertia for internal rotation. We have chosen to calculate N*(E) by treating the torsional motion as an asymmetric, hindered, internal rotation. This raises the question of a possible coupling of the torsional motion and the overall rotation about the long axis of the molecule. Including one overall rotation as an active mode would add one more degree of freedom to the 18 internal modes. This possibility reduces the magnitude of the rate constant by about 50%, vide infra, which would reduce the assignment of the E0 values by about 1 kcal mol-1. Structures and vibrational frequencies of the molecules and transition states were obtained by electronic structure calculations using density functional theory with the B3PW91/6-31G(d′,p′) method using the Gaussian code.36 Some calculations also were done with the B3LYP/
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TABLE 2: Densities of States at 90 kcal mol-1 and Thermal Partition Function at 1000 K for the Torsional Motion internal rotation V (kcal/mol)a,b molecule
calcd
CH2FCH2Cl
4.5 7.8 3.4 8.0 5.4 9.8
CH2FCH2F CH2ClCH2Cl
densities (1010 states/cm-1) and partition functions at 1000 K
exptl vibrationc free rotord HIR(S)d HIR(A)e (5.8) (5.1) (2.9) (5.7) (5.2) (9.2)
0.40 5.8 0.16 5.5 1.1 6.5
1.5 38.7 0.56 33.7 4.4 46.1
0.97 14.6 0.39 14.0 2.9 17.3
1.0 14.7 0.43 16.0 2.7 12.3
a The trans conformers are more stable than the gauche by 0.82 ( 0.17 and by 1.0-1.5 kcal mol-1 for CH2FCH2Cl22 and CH2ClCH2Cl,23 respectively. The gauche conformer is more stable21 by 0.80 ( 0.9 kcal mol-1 for C2H4F2.. b The heights of the two barriers measured from the lowest energy conformer. The values in parentheses are experimentally based values22,23 or high level calculations (for C2H4Cl2).23 The numbers in the first column are from the potentials used by Wong, Thom, and Field.27 c Calculated using the average torsional frequency of the two conformers. d Calculation for a symmetric rotor using the average value from the two conformers for Ired and the average of the two barriers for V. The partition functions were calculated by Pitzer’s methods. e Direct count calculation using the specific energy levels27a of the asymmetric rotor; the first line is the density, and the second line is the partition function.
6-31G(d′,p′) method for comparison of calculated threshold energies. Our results are very similar to those published by Arunan and co-workers8,14 who explored several computational methods. The calculations of the sums and densities were done using the Multiwell code supplied by Professor Barker.37 B. Model for Hindered Internal Rotation of CH2XCH2Y Molecules. The unscaled calculated vibrational frequencies are satisfactory for use in eq 7 after a decision is made about how to treat the torsional motion of CH2XCH2Y molecules. The trans conformer is more stable (by 1-2 kcal mol-1) for C2H4Cl223,24,26 and CH2FCH2Cl;22 however, the gauche conformer is more stable for C2H4F221,27 by 0.8 kcal mol-1. The potential for the torsional motion has three barriers; the gauche f gauche barrier in which the X and Y atoms pass each other has a barrier of 8-10 kcal mol-1. The trans f gauche barriers are 3-6 kcal mol-1; see Table 2 for more detail. Since the gauche f gauche barrier is so high, most investigators have treated the torsional mode as a harmonic vibration of the most stable conformer in the calculation of the density of states needed for the RRKM rate constant. This approximation provides a lower limit to the density of states, and it avoids the problem of the change in overall rotational moments of inertia with internal rotation.27 A free-rotor model provides the upper limit to the density of states, but the torsional motion of CH2XCH2Y molecules is not a free rotor or even a hindered rotor with three similar barrier heights. Recently, Wong, Thom, and Field27,28 published a method for the calculation of effective moments of inertia for largeamplitude low-frequency internal motions. Their calculations also can provide the energy levels associated with such motions. The torsional motions of C2H4F2, C2H4Cl2, and C2H4ClF were among the examples that Wong et al.27 treated, and they generously provided us with a listing of the energy levels associated with these molecules. We combined those energy levels with the direct count of the number of vibrational states associated with the other 17 vibrational modes to calculate the sums and densities of these three molecules. The potential functions used by Wong et al. as models are not necessarily the very best functions for these molecules, although their results do closely resemble a different type of calculation for the lower levels of C2H4Cl2 by Chung-Phillips.26 Wong’s potential for
C2H4F2 also seems realistic relative to the experimentally based potential.21 Only the potential function C2H4ClF could be questionable. According to the experimental analysis based upon assignments of several low torsional levels of each C2H4FCl22 conformer, the g f g and t f g barriers are both about 5 kcal mol-1. However, calculations predict that the g f g barrier22,27 for C2H4ClF should resemble those for C2H4F2 and C2H4Cl2. We adopted the energy levels from the model of Wong et al. to calculate the density of states for C2H4ClF. The densities of states for the vibrational model, the freerotor model, and a symmetric hindered-rotor model with a barrier height equal to the average of the two barriers used by Wong et al. are compared to the direct count result in Table 2 at an energy of 90 kcal mol-1. The average of the Ired for the two conformers was used in the free-rotor and symmetric-rotor calculation. As would be expected, the density of states increases with the number of Cl atoms for all models. The lower limit, the vibrational model, and the upper limit, the free-rotor model, to the densities differ by a factor of approximately 4. The best result, the direct count, lies about midway between the two limits. The symmetric hindered-rotor model with the average barrier gives a density that is close to the direct count for C2H4F2 and C2H4ClF, but it overestimates the density for C2H4Cl2 by 10%. Nevertheless, the symmetric barrier approximation provides a reasonably good approximation for the density of states at 90 kcal mol-1 of excitation, even for these C2H4XY molecules with high and unequal barriers. Except for C2H4Cl2, the symmetric-rotor approximation also provides a good estimate for the thermal partition function. The direct-count partition function at 1000 K actually decreases in the C2H4F2, C2H4ClF, C2H4Cl2 series, because of the complex energy-level structure below the potential barriers.27 C. Transition States and Threshold Energies. Following the initial work of Toto, Pritchard, and Kirtman,19 many investigators have applied different computational methods to explore the four-centered transition state for HX elimination reactions.8,14,20,38 Although the threshold energies depend upon the computational method, the structure and frequencies of the transition states are quite similar for all methods. The calculated thermal and chemical activation rate constants from these transition-state models are in accord with experimental results for several test reactions, providing that the torsional motions are treated as hindered internal rotations.20 We have found that the DFT calculation with the B3PW91/6-31G(d′,p′) method gives threshold energies that are in close agreement with experimentally assigned values for HF elimination from several fluoroalkanes.17,18,20 We used that method in this work so that comparison could be made to previous results for C2H5Cl and C2H5F.20 A table is provided in Supporting Information for the molecular and transition-state models of the three systems, which enables a comparison to the calculations of Arunan.8,14 The differences in the transition state structures for HCl and HF elimination are displayed by drawings presented in the Discussion. These differences also can be summarized by the thermal activation pre-exponential factors, which are 3.7 × 1013, 11.6 × 1013, 2.1 × 1013, and 4.5 × 1013 s-1 for C2H4F2, C2H4Cl2, C2H4ClF(HF), and C2H4ClF(HCl), respectively, in partition function form at 1000 K. These values include reaction path degeneracy, which are 4, 4, 2 and 2, respectively. The 2-fold larger pre-exponential factors for HCl elimination vs HF elimination are typical for all electronic structure calculations.8,16,20 The calculated rate constants at the specified energy are matched with experimental results in Table 1. The preferred threshold energies would be 63 kcal mol-1 for C2H4F2 and 64
Unimolecular HCl and HF Elimination Reactions kcal mol-1 for C2H4Cl2 based on rate constants calculated with 18 internal degrees of freedom. If one overall rotation is included in the active degrees of freedom, the calculated rate constants are reduced by a factor of 1.5 and the preferred E0 would be 62 and 63 kcal mol-1. The experimental rate constants have been measured several times, and the uncertainty should be better than (20%; however, the calculated rate constants have an uncertainty of 50%. Thus, the most reasonable choice for these two E0 values is 63 ( 2 kcal mol-1. Given the possibility of an active overall rotation in the calculation of kE, the selected E0 values for C2H4ClF are 63 kcal mol-1 for HF elimination and 65 kcal mol-1 for HCl elimination. The data in Figure 1 for C2H4ClF are less reliable than the extensive studies of the other two molecules, and the overall uncertainty in the E0 for C2H4ClF may be (3 kcal mol-1. Within the combined uncertainty of the calculated kE and experimental data, the two channels have the same E0. These experimentally based threshold energies can be compared to our calculated values by the B3PW91/6-31G(d′,p′) method, which are 61.3 and 58.2 kcal mol-1 for C2H4F2 and C2H4Cl2, respectively, and 60.6 and 58.0 kcal mol-1 for HF and HCl elimination from C2H4FCl. The threshold energies from the B3LYP/6-311++G** calculation8 were systematically lower, 58.0, 55.5, 57.4, and 56.0 kcal mol-1 for the reactions listed in the same order as in the preceding sentence. All calculated E0 values are quoted relative to the most stable conformer of the molecule. Calculations of the structures and threshold energies also were done for CH3CHF2, CH3CHCl2, and CH3CHClF. The calculated threshold energies with B3PW91/6-31G(d′,p′) are 63.2 (CH3CHF2), 51.1 (CH3CHCl2), 62.7 (HF, CH3CHClF), and 50.1 (HCl, CH3CHClF) kcal mol-1. Chemical activation data39 exist for CH3CHF2, and the rate constant is (12 ( 4) × 108 s-1 for molecules with 96 kcal mol-1 of energy formed by CH3 + CHF2. This rate constant is 4 times larger than the rate constant for CH2FCH2F. We used models from the DFT calculations, see Supporting Information, with a hindered internal rotation for the methyl torsion to calculate a rate constant that matched the experimental value. The required E0 was 62 kcal mol-1, which is in accord with the previous assignment.39 The consensus value for E0 from thermal experiments40 is 62 ( 2 kcal mol-1. V. Discussion A. Threshold Energies and Pre-exponential Factors for CH2XCH2Y. The current assignment of E0 ) 62-63 kcal mol-1 for C2H4F2 is in agreement with the value from the early work.1–3 The increase in ∑P†(E - E0) for the modern transition state is partly balanced by the higher N*(E) from the direct count of states for the hindered rotor versus the previously used vibrational model. The Arrhenius expression from a thermal activation study4 over the 734-820 K range and pressures equal to or greater than 100 Torr was k(T) ) (2.7 ( 1.2) × 1013 exp[-(62900 ( 900)/RT] s-1, which corresponds to E0 ) 60.8 kcal mol-1. Our transition-state model gives an Arrhenius rate constant of 10.8 × 1013 exp[-(65200/RT)] s-1 at 800 K for E0 ) 63 kcal mol-1. The large pre-exponential factor is a consequence of the reaction path degeneracy of 4; the actual entropies of the molecule and transition state are nearly equal. The upper range for the experimental pre-exponential factor is still a factor of 2 smaller than the value calculated from the model; however, the temperature range of the thermal study is rather narrow and the uncertainty in the pre-exponential factor may be larger than (1.6. Our calculation of the pre-exponential
J. Phys. Chem. A, Vol. 114, No. 2, 2010 799 factor used the exact sum for the partition function of the internal rotation. The consequences of more approximate calculations can be gauged from the results in Table 2. The E0 required to match the kexpt of C2H4Cl2 is 63-64 kcal mol-1. This value is even higher than the earlier estimate9–12 of 59-60 kcal mol-1, which was 4-5 kcal mol-1 higher than the E0 for C2H5Cl. In this case, the ∑P†(E - E0) for the modern transition state increased more than N*(E), because the HCl elimination transition state has more lower frequencies, relative to the molecule, than does the HF transition state. This conclusion is not in agreement with the only thermal study (1070-1175 K) of the reaction,14 which reported k(T) ) (9.6 ( 6.3) × 1013 exp[-(57800 ( 2000)/RT] s-1. This activation energy would correspond to an E0 of 55 ( 2 kcal mol-1. The pre-exponential factor is 4 times smaller than our model, which gives 45 × 1013 s-1 at 1000 K. However, the activation energy and the pre-exponential factor are strongly correlated, so if the experimental Ea increases, the experimental pre-exponential factor also increases. The shock tube experiments were done in 10-15 atm of Ar, and the rate constants presumably were at their high pressure limit. The experimental difficulty with thermal studies of C2H4Cl2 is the propensity for abstraction of an H-atom followed by the decomposition of the CHClCH2Cl radical to give CH2dCHCl and a Cl atom, which subsequently continues the chain. Given the numerous measurements of the chemical activation rate constant, and the more exact calculation for kE in this study, E0 g 62 kcal mol-1 for C2H4Cl2 seems certain. The threshold energies for C2H4ClF correspond to E0(HF) and E0(HCl) ) 63 and 65 kcal mol-1, respectively, which are similar to those for C2H4Cl2 and C2H4F2. The surprising feature is that E0(HCl) is slightly higher than E0(HF). Although the experimental rate constants are nearly the same, the sums of states for the HCl transition state are two times higher than the HF transition state, which then forces a higher E0(HCl). Results from a bulb pyrolysis study13a over the 715-760 K range gave k(HF) ) (2.2 ( 1.6) × 1013 exp[-(60000 ( 1000)/RT] s-1 and k(HCl) ) (5.0 ( 3.0) × 1013 exp[-(62500 ( 1100)/RT] s-1. The HCl channel, but not the HF channel, was sensitive to radical inhibitors, and the quoted k(HCl) was from studies with added 1-butene. These Arrhenius parameters also agree with those from higher temperature shock-tube experiments in the same study, although the methodology for assignment of the temperature in the shock tube experiments has been severely criticized;13b nevertheless, the ratio of the HCl to HF elimination rates was close to unity in both sets of experiments. The activation energies from the pyrolysis work correspond to E0 values of about 58.5 and 60.5 kcal mol-1 with HCl elimination higher than HF elimination. Our models give Arrhenius preexponential factors at 740 K of 5.7 × 1013 (HF) and 12 × 1013 (HCl) s-1, which are factors of 2-3 larger than the upper range of the experimental values. Rajakumar and Arunan8 also noted that the calculated pre-exponential factors from all models were systematically larger than the experimental values. The essential question is whether the threshold energies assigned from the chemical activation rate constants are reliable? For these three molecules the 〈E〉 are established. Although the experiments were difficult for C2H4ClF, the rate constants should be within (50% of the true values and the uncertainty of the others should be within (30%. The assigned values for HF elimination are about 2 kcal mol-1 higher than the DFT calculated values, which normally are close to the experimental values. This suggests that, although the experimentally derived values may be upper limits, they should be reliable to within
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Figure 2. Thermochemical summary for the molecules and transition states for each C2H4XY pair. The majority of the energy values are based upon experimental measurements; see text. However, the E0(HF) for CH3CHFCl and the E0(interchange) for CH2FCH2Cl are calculated values.
(2 kcal mol-1. The DFT calculated E0(HCl) are usually 2-3 kcal mol-1 lower than experimental values, and the calculations imply that E0(HCl) ≈ E0(HF). We conclude that the E0 for CH2XCH2Y molecules are higher than those for CH3CH2X molecules. B. Comparison with CH3CHXY Reactions. The CH3CHXY and CH2XCH2Y series provides three pairs of isomeric molecules, products, and transition states (the † symbol will be used to represent the transition state structure). We wish to illustrate similarities and differences among the transition states based on thermochemistry using experimental and computational, when necessary, results rather than the more common approach based upon changes in the partial charges on atoms in the polar transition state. Although information about the CH3CHXY series is less well established than that for the CH2XCH2Y series, threshold energies can be chosen with confidence. The thermochemistry is summarized in Figure 2. The most stable isomeric molecule is the reference energy for each pair. For convenience of discussion, the carbon atoms in the transition states will be identified by subscripts, e.g., CF and CH in the top set of two structures in Figure 2. The minor contribution of 1,1-HX(HY) elimination to the 1,1-C2H4XY reactions is not relevant. The enthalpies of formation of CH2FCH2F and CH3CHF2 are known,30,31 and the latter is more stable by 14 kcal mol-1. The
E0(HF) from CH3CHF2 has been established as 62 ( 2 kcal mol-1 by both thermal and chemical activation experiments, as previously discussed. The relative energies of the two transitionstate structures in Figure 2A just follow the pattern of their parent molecules; the greater stability of the CH3CHF2 type structures arises from the cumulative effect of their larger D(H-C2H3F2), D(CH3-CHF2), and D(F-CHFCH3) relative to CH2FCH2F. One question can be posed; why is E0(HF) 4-5 kcal mol-1 higher for C2H4F2 than for C2H5F? One possible explanation is that the C-H bond energy is lower in the CHF group than in the CH2 group of the transition states relative to the respective molecules. At least this is the case for D(HsCFdCH2) vs D(HsCHdCHF).31 The energy diagram for the formation of CH2dCF2 from the CH3CF3 and CH2FCHF2 pair is similar to the diagram in Figure 2A; the difference in energy of the molecules, 21 kcal mol-1, is maintained in the transition state, since the threshold energy is 68 ( 2 kcal mol-1 for both reactions. Since computed energies must be utilized, in part, for Figure 2C, it is worth noting that the relative energies in Figure 2A are also supported by electronic structure calculations. The situation for the C2H4Cl2 pair is very different from that of the C2H4F2 pair; the molecules have virtually the same energy,29 but the energy of the transition states differs by about 10 kcal mol-1. Thermal activation studies41 give E0(HCl) ) 52
Unimolecular HCl and HF Elimination Reactions
Figure 3. Calculated structures at the B3PW91/6-31G(d′,p′) level for the eight transition states for HCl and HF elimination. The number below each structure is the calculated threshold energy based on the lowest energy conformer of the molecule. Calculations also were done with the B3LYP/6-31G(d′,p′); method; the E0 values in kcal mol-1 were CH2FCH2F (61.5), CH3CHF2 (63.5), CH2ClCH2Cl (57.1), CH3CHCl2 (49.6), and CH2FCH2Cl (HF, 61.0; HCl, 56.7), CH3CHClF (HF, 63.1; HCl, 48.7). The E0(HF) values are nearly the same as for the B3PW91 calculation, but the E0(HCl) values are about 2 kcal mol-1 lower, and both computational methods give lower values for E0(HCl) than the experimental results. Arunan’s calculations8 by the B3LYP method with a larger basis set gave even lower threshold energies than with the 6-31G(d′,p′) basis set.
kcal mol-1 for CH3CHCl2. The chemical activation results42 are not definitive, but E0(HCl) has to be significantly less than for C2H5Cl, which is 55 kcal mol-1. Thus, the position of the Cl atom affects the relative energies of the transition states, but not the energy of CH3CHCl2 versus CH2ClCH2Cl (CH2dCCl2 is more stable than cis- and trans-CHCldCHCl by 5.4 and 2.9 kcal mol-1, respectively).29 This trend for the energy difference in the transition states was verified by electronic structure calculations, which gave an energy difference of 6.5 kcal mol-1 for the transition states. The question becomes why is the
J. Phys. Chem. A, Vol. 114, No. 2, 2010 801 CH3CHCl2† structure more stable than the CH2ClCH2Cl† structure? One possible thermochemical explanation is the higher C-Cl bond energy when the Cl atom is attached to the CCl atom rather than to the CH atom because of the greater sp2 nature of the CCl atom. This possibility is supported by the structures shown in Figure 3 because the C-Cl bond length is shorter for the CH3CHCl2† case. Figure 2C is more complex than Figure 2A or Figure 2B because two sets of products and five transition states exist, if Cl/F interchange reaction is included. The two product channels differ in energy by only 1 kcal mol-1, but CH3CHFCl is more stable by 6 kcal mol-1 than CH2ClCH2F.43 The threshold energy for HCl elimination from CH3CHFCl has been reported as 54 kcal mol-1 from a thermal study.44 A chemical activation study45 of CH3CF2Cl found that HCl elimination is 25 times more important than HF elimination, and threshold energies of 55 and 69 kcal mol-1 were assigned with uncertainties of (2 kcal mol-1. The E0(HF) value given in Figure 2C for CH3CHFCl is based upon these experimental data and electronic structure calculations of this work. The E0(HCl) and E0(HF) for CH2ClCH2F are from our experiments; the E0(Cl/F) for interchange is our calculated value. Just as for the C2H4Cl2 pair, the transition states for HCl elimination differ in energy by more than 10 kcal mol-1 with the structure having the F atom on CCl being more stable. In contrast, the position of the Cl atom does not strongly affect the energies of the transition states for HF elimination from CH3CHFCl and CH2FCH2Cl; e.g., their relative energies are the same as for the two molecules. As a generalization, an out-of-ring F atom acts as in the same way as a Cl atom for HCl elimination and an out-of-ring Cl atom acts as a F atom for HF elimination.45 In conclusion, we note that Cl/F interchange is competitive with HF and HCl elimination from CH2FCH2Cl; this is a general result for 1,2-dihaloethanes. The structures and E0 values from the B3PW91/6-31G(d′,p′) calculations for the eight transition states are presented in Figure 3 to aid in understanding the trends just discussed. Because of the 10 kcal mol-1 increase in bond energy of C-H, -F, -Cl bonds with sp2 hybridization, attention is directed to the degree of sp2 and sp3 character of the carbon atoms, which is identified by the angle between the extension of the CXsCH axis and the plane defined by the three atoms, e.g., CH2 or CHX. As points of reference, 55° and 0° correspond to 100% sp3 and sp2, respectively. The striking aspect about the four HF elimination transition states is their overall similarity with nearly the same bond lengths and angles. The average angles between the CXsCH axis and the triangular planes are CH ) 28 ( 1° and CF ) 13 ( 1°; the location of the out-of-ring halogen atom has little effect on these angles. The Cl atom in C2H4ClF* seems to have the same influence as the out-of-ring F atom in C2H4F2*. The calculated E0 values are all similar with an average of 62.0 ( 1.0 kcal mol-1, although placing the Cl or F atom on CF does raise E0 by 2 kcal mol-1. This trend is not matched by the experimental assignments of E0; however, the predicted changes are within the experimental uncertainties. It should be remembered that the calculated E0(HCl) values generally tend to be 2-3 kcal mol-1 below the experimental values. The most obvious aspect of the structures for HCl elimination is the nearly pure sp2 nature of CCl for all four examples. In contrast, the deviation from planarity around CH varies (from 22.6° to 34.1° for C2H4Cl2†) with greater sp3 nature for H2CH than for FHCH or ClHCH. The more stable structures, by ≈10 kcal mol-1, have the out-of-ring F or Cl atom on CCl, and these structures have appreciably (0.21 and 0.15 Å) longer
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in-ring Cl-CCl bond lengths, and shorter (0.04 and 0.03 Å) outof-ring Cl- or F-CCl bonds than structures with the out-of-ring F or Cl atom on CH. The in-ring C-H and H-Cl distances are slightly shorter and longer, respectively, when the out-of-ring halogen atom is on CCl. However, the reduction in the CCl-F bond length vs that for CH-F indicates the donation of some electron density for the CCl-F case. It seems that the 10 kcal mol-1 greater stability of CH3CHCl2† and CH3CHClF† is associated with the stronger bonding for ClHCCl and FHCCl vs H2CCl for the sp2 environment. The difference in the E0 for HCl elimination from 1,1-C2H4Cl2 and 1,2-C2H2Cl2 has long been associated with the mesomeric effect of physical organic chemistry. We can investigate this point of view by examining the partial charges on the atoms in the transition states. The partial charges for CH2ClCH2Cl† and CH3CHCl2†, respectively, are CCl ) 0.074 and 0.16, CH ) -0.043 and -0.083, H in-ring ) 0.38 and 0.30, Cl in-ring ) -0.55 and -0.60, Cl out-of-ring ) -0.19 and -0.076, the outof-ring single H atom is 0.10 and 0.16 and the out-of-ring double H atoms are each 0.13 and 0.076. The Cl atom in CH3CHCl2† does donate electron density but not to CCl, rather the electron density goes to CH and to the in-ring H and Cl atoms. The outof-ring H atom on CCl also donates some electron density. In summary, the changes in partial charges are complex. These changes in electron density correlate with the changes of bond lengths. The net substituent effect of the Cl atom in CH2ClCH2Cl versus CH3CHCl2 is strikingly similar to that for CH3 in n-propyl chloride versus isopropyl chloride. An energy diagram like those in Figure 2 shows that CH3CHClCH3† is 9 kcal/mol more stable that CH3CH2CH2Cl†. The CH3 group donates electron density when it is located on the CCl position, even though the positive charge on CCl is quite small. The similarity between the effect of the CH3 group and Cl atom is remarkable. The change in partial charges is more extreme for the C2H4FCl structures, because of the strong polarity of the C-F bond. For example, the charge on CH changes from 0.42 to -0.10 and that for CCl changes from 0.06 to 0.68 when the F-atom moves from CH to CCl, even though the charge on the Fatom stays constant as -0.60. However, the reduction in the CCl-F bond length vs that for CH-F indicates the donation of some electron density for the CCl-F case. It seems that the 10 kcal mol-1 greater stability of CH3CHCl2† and CH3CHClF† is associated with the stronger bonding for ClHCCl and FHCCl vs H2CCl for the sp2 environment. The partial charges mentioned above were obtained by the atoms-in-molecules (AIM)46 approach. VI. Conclusions Rate constants for CH2ClCH2Cl, CH2FCH2F, and CH2FCH2Cl molecules formed with approximately 90 kcal mol-1 of internal energy by radical recombination have been interpreted by RRKM calculations to assign threshold energies for HCl and HF elimination reactions. Vibrational frequencies and moments of inertia were obtained from electronic structure calculations using DFT with the B3PW91/6-31G(d′,p′) method. The quantum levels associated with the asymmetric internal rotor with high barriers of these molecules were combined with the other vibrational states to obtain the density of states for the molecules. These densities were compared to the results from an approximation in which the internal rotor was treated as a pseudosymmetric rotor with a barrier equal to the average of the two actual barriers; the approximation is satisfactory at energies of 90 kcal mol-1. Since the overall rotational moments also change with the torsional motion, calculations were done
Duncan et al. with one overall rotation as active; i.e., the number of active degrees of freedom was increased to 19. Within the combined experimental and computational uncertainty, the assigned threshold energies, which are between 62 and 65 kcal mol-1, are nearly the same, and HCl elimination has the same or slightly larger threshold energy than HF elimination for these 1,2fluorochloroethanes. Comparison was made to the relative energies of the transition-state structures of the isomeric CH3CHXY and CH2XCH2Y pairs. For HF elimination, the relative energies of the transition states followed the relative energies of the parent molecules. However, for HCl elimination the CH3CHCl2 and CH3CHFCl transition states are more stable than those of CH2ClCH2Cl and CH2FCH2Cl by nearly 10 kcal mol-1. These energy differences were discussed in terms of the development of sp2 character of the carbon atom from which the halogen atom is departing. Acknowledgment. Financial support for this work was provided by the US National Science Foundation under Grants CHE-0647582. Professor George Heard is thanked for helpful discussions about the DFT and AIM calculations. We wish to thank Dr. Bryan M. Wong for providing the listings of energy levels for the internal rotations of CH2ClCH2Cl, CH2FCH2F, and CH2FCH2Cl. His cooperation was of great assistance to our work. D.W.S. also wishes to acknowledge helpful discussions with Professors Arunan and Chung-Phillips. Supporting Information Available: Tables of vibrational frequencies, overall moments of inertia, and the reduced moments of inertia for the internal rotors for models of the transition states and molecules for the CH2ClCH2Cl, CH2FCH2F, CH2FCH2Cl, and CH3CHF2 systems calcualted using B3PW91/ 6-31G(d′,p′). The geometric means of the molecular frequencies that were used in the calculation of the unimolecular rate constants are also listed. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Richmond, G.; Setser, D. W. J. Phys. Chem. 1980, 84, 2699. (2) Chang, H. W.; Setser, D. W. J. Am. Chem. Soc. 1969, 91, 7648. (3) Kerr, J. A.; Timlin, D. M. Trans. Faraday Soc. 1971, 67, 1376. (4) Kerr, J. A.; Timlin, D. M. Int. J. Chem. Kinet. 1971, 3, 427. (5) Pritchard, G. O.; Venugpalan, M.; Graham, T. F. J. Phys. Chem. 1964, 68, 1786. (6) (a) Kerr, J. A.; Kirk, A. W.; O’Grady, B. V.; Phillips, D. C.; Trotman-Dickenson, A. F. Discuss. Faraday Soc. 1967, 44, 263. (b) Cadman, P.; Kirk, A. W.; Trotman-Dickenson, A. F. Faraday Trans. 1 1976, 72, 996. (7) Pritchard, G. O.; Thommarson, R. L. J. Phys. Chem. 1967, 71, 1074 The rate constants reported in this work for C2H4F2 seem to be too high by a factor of 2-3. (8) Rajakumar, B.; Arunan, E. Phys. Chem. Chem. Phys. 2003, 5, 3897. (9) (a) Setser, D. W.; Siefert, E. E. J. Chem. Phys. 1972, 57, 3613– 3623. (b) Clark, W. G.; Setser, D. W.; Siefert, E. E. J. Phys. Chem. 1970, 74, 1670. (10) Dees, K.; Setser, D. W. J. Chem. Phys. 1968, 49, 1193. (11) Setser, D. W. J. Am. Chem. Soc. 1968, 90, 582. (12) Hassler, J. C.; Setser, D. W. J. Chem. Phys. 1966, 45, 3246. Hassler, J. C.; Setser, D. W. J. Phys. Chem. 1967, 71, 1364. (13) (a) Cadman, P.; Day, M.; Trotman-Dickenson, A. F. J. Chem. Soc. A 1971, 1356. (b) Okada, K.; Tschuikow-Roux, E.; Evans, P. J. J. Phys. Chem. 1980, 84, 467. Tsang, W. Int. J. Chem. Kinet. 1973, 5, 643 These papers provide a critique of the methodology of the shock-tube experiments in ref 13a. (14) Rajakumar, B.; Reddy, K. P. J.; Arunan, E. J. Phys. Chem. A 2002, 106, 8366. (15) (a) Burgin, M. O.; Heard, G. L.; Martell, J. M.; Holmes, B. E. J. Phys. Chem. A 2001, 105, 615. (b) Heard, G. L.; Holmes, B. E. J. Phys. Chem. A 2001, 105, 1622. (16) (a) Burgin, M. O.; Simmons, J. G., Jr.; Heard, G. L.; Setser, D. W.; Holmes, B. E. J. Phys. Chem. A 2007, 111, 2283. (b) Beaver, M. R.;
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