J. Phys. Chem. 1995, 99, 13402-13411
13402
Ab Initio Studies of Reactions of Hydroxyl Radicals with Fluorinated Ethanes Jaime M. Martell+ and Russell J. Boyd* Department of Chemistry, Dalhousie University, Halijbx, Nova Scotia, Canada B3H 4J3 Received: February 22, 1995; In Final Form: June 30, 1995@
Geometries for transition states in the reactions of OH radicals with molecules in the series C2HnF6-n, n = 1-5, have been optimized at the HF/6-31G(d) and MP2/6-31G(d,p) levels of theory. Vibrational frequency analyses were also performed at both levels of theory. Total energies have been calculated for the reactants, transition states, and products of the reactions at the MP2/6-3 11G(d,p)//HF/6-3 lG(d,p) level for all species, at the MP2/6-3 1lG(d,p)/iMP2/6-3 lG(d,p) level for all reactants and products, and transition states containing up to three fluorines, and at Gaussian-2 theory level for reactants and products with up to two fluorines and transition states with one fluorine. These calculations were performed for the abstraction of each inequivalent hydrogen from the most stable conformer of each molecule in the series. Activation entropies, classical barrier heights, with and without zero-point energy corrections at the MP2/6-3 lG(d,p) level, and enthalpies of reaction with zero-point and thermal energy corrections to 25 “C have been calculated. Energy values are affected by the degree and position of fluorine substitution. Trends throughout the series, and differences in the levels of theory, are discussed. In all cases an earlier transition state occurs when electron correlation is included in the geometry optimization. Evidence is seen for an intramolecular hydrogen bond between the hydroxyl hydrogen and a ,&fluorine positioned gauche to the hydrogen being abstracted.
Introduction Hydroxyl radicals are the most likely initiators of tropospheric degradation for the hydrochlorofluorocarbon (HCFC) and hydrofluorocarbon (HFC) classes of chlorofluorocarbon (CFC) replacement compounds. I In the HFC class several fluorinated ethanes have been investigated, and in particular CF3-CH2F (HFC-134a) has been chosen for use in home refrigeration units. Since the reactions of OH with hydrofluorinated ethanes (HFEs) are potentially of great significance in atmospheric chemistry, it is desirable to increase the knowledge base on them. To the best of our knowledge, there have been no published ab initio studies of these reactions. To date, experimental studies of these reactions have included the determination of rate coefficients for reactions of OH with C Z H ~ FCHF2-CH3,4-6 ,~.~ CF3-CH3,3*7 CF3-CH2F,4-6*ss9CHFZ-CHF~,~ and CF~-CHFZ.~-’Cohen and Benson used conventional transition state theory to extrapolate rate coefficients,I0 and derived empirical correlations for the activation energy and entropy,” for reactions of OH with several haloalkanes, including CzHsF, CHF2-CH3, CHzF-CHzF, CF3CH3, CHF2-CH2F, CF3-CH2F, CHF2-CHF2, and CS-CHFz. Experimental determination of transition state geometries and vibrational frequencies is not possible at present. In a recent paperI2 we presented results from a study on the prototype reaction of C2H6 with OH, including (among other values) the transition state geometry and frequencies, the activation barrier, and reaction enthalpy. Here we present the transition state geometries and vibrational frequencies, activation entropies, and results of energy calculations, including total and zero-point energies, classical barrier heights, and enthalpies of reaction, for the full series of H m s , C2HnF6-n,n = 1-5. Computational Methods Ab initio MO calculations were carried out with the Gaussian 9013 and Gaussian 92/DFTI4 program packages. Fully optimized geometries and harmonic vibrational frequencies for the ‘Walter C. Sumner Fellow and NSERC Predoctoral Scholar. Abstract published in Advance ACS Abstracts, August 15, 1995. @
transition state (TS) of each reaction were calculated at unrestricted Hartree-Fock (HF) and second-order M@ller-Plesset perturbation theory (MP2) with the 6-31G(d) and 6-31G(d,p)I5 basis sets, respectively, using analytical gradient methods.I6 Energies were calculated using MP2 and MP4 theory with the 6-31 lG(d,p)” basis set. In addition, energies for transition state species containing one fluorine and ground state species with one or two fluorines were calculated using Gaussian-2 (G2) theory,’* modified by using the optimized geometries and frequencies calculated at the MP2/6-3 lG(d,p) level of theory, rather than the MP2/6-31G(d) and HF/6-3 1G(d) levels, respectively, as in the original G2 method. The zero-point vibrational energies (ZPEs) taken from the frequency analyses were scaled by factors of 0.9135 and 0.9646 for the HF and MP2 frequencies, respectively, as recommended by Pople et al.I9 to compensate for systematic overestimation. The ZPEs have been adjusted to neglect the contribution from one loosely bound mode corresponding to a free rotation of the OH group. Results and Discussion The optimized geometries and vibrational frequencies for the 15 transition states which occur when OH abstracts an inequivalent hydrogen atom from the most stable conformer for each of the eight molecules in the series C2HnF6-n,n = 1-5 have been calculated. The HFl6-3 1G(d) optimized geometries are presented in Figure 1, and the MP2/6-31G(d,p) optimized geometries are presented in Figure 2. Key structural parameters at both levels of theory are given in Table 1, with complete geometrical parameters given in Table A of the supporting information. All the structures are asymmetrical except for CHs-CFzH OH, which has C, symmetry at HFl6-31G(d), but again has Cl symmetry at MP2/6-31G(d,p). As with the parent C2H6 OH reaction,I2 and other reactions where hydrogen is abstracted by hydroxyl,20,2’the MP2 geometries indicate a relatively early transition state, with the breaking bond stretched by only a small amount from its equilibrium value and the forming bond still relatively long, while the HF geometries show a long C-H bond and a short 0 - H one. The
+ +
0022-365419512099-13402$09.00/0 0 1995 American Chemical Society
Reactions of Hydroxyl Radicals with Fluorinated Ethanes
J. Phys. Chem., Vol. 99, No. 36, 1995 13403
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Figure 1. HF/6-31G(d) optimized transition states for the following reactions: la, CH3-CHzF OH; lb, CH2F-CH3 OH t; IC,CHzF-CH3 + OH g; Id, CHzF-CHP + OH t; le, CHP-CH2F OH g; lf, CHF2-CH3 OH g,t; lg, CHFZ-CH~ OH g,g; lh, CH3-CF2H OH; li, CF3-CH3 + OH; lj, CHFZ-CHZF + OH g,t; lk, CHFZ-CHZF OH g,g; 11, CHZF-CHF2 OH; lm, CF3-CH2F OH; In, CHF2-CHF2 OH; lo, CF3-CHFz OH. The designations t and g refer to the abstracted H being trans or gauche to a /3-F, respectively.
+
+
+
other major difference in the two levels of theory is the greater deviation from linearity for the C-H-0 angle at the reaction center seen with MP2 theory. Many of the trends seen in the geometrical parameters are similar to those noted previously for the series C Z H " F ~ -n~ = , 0-6,22,23 and C Z H , F ~ - n~ ,= 0-5.23 The C-C bond lengths have two opposing trends, decreasing with increasing fluorine substitution for less than three fluorines, reaching a minimum for CF3-CH3 -tOH, and then increasing to reach a maximum for CF3-CHF2 OH. There is also a tendency to shorter lengths when there is more than one fluorine on a given carbon, indicative of a geminal effect. The lengths are slightly shorter
+
+
+
+
+
+
+
+
at the MP2 level, except for CH2F-CHF2 OH, where it is 0.001 A longer. For the C-H bond being broken (Cl-Hl), bond lengths are shorter when there are more fluorines on the a-vs P-carbon and for conformers where there is a @-fluorinetrans rather than gauche to the abstracted hydro en. The HF-MP2 difference is fairly constant (0.106-0.1 13 , with most values in the range 0.107-0.109 A). For species with two or less fluorines, this value tends to be larger for trans and shorter for gauche conformers. For the 0-H bond being formed, H1-0 lengths are longer when there are more fluorines on the a- vs B-carbon and for
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13404 J. Phys. Chem., Vol. 99, No. 36, 1995
Martell and Boyd
tu
+ +
+
Figure 2. MP2/6-31G(d,p)optimized transition states for the following reactions: Za, CH3-CH2F OH; Zb, CH2F-CH3 OH t; Zc, CH2FOH g,t; Zg, CHF2-CH3 OH g,g; Zh,CH3-CF2H OH; CH3 + OH g; Zd, CHZF-CH2F + OH t; Ze, CHZF-CH2F OH g; Zf,CHF2-CH3 Zi, CF3-CH3 OH; Zj, CHFrCH2F OH g,t; Zk, CHFrCH2F OH g,g; 21, CH2F-CHF2 OH. The designations t and g refer to the abstracted H being trans or gauche to a P-F, respectively.
+
+
+
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conformers where there is a /?-fluorine trans rather than gauche to the abstracted hydrogen. These trends are complementary to those for C1-H1 and indicate an earlier TS in these instances. There is a general tendency to shorter lengths with increasing fluorine substitution. There is a large variation in the MP2HF difference (0.068-0.108 A), with larger differences seen for trans vs gauche conformers, and a general trend to smaller differences when the number of p-fluorines is two or more greater than the number of a-fluorines. The bond length in the hydroxyl moiety (0-H2) is remarkably constant throughout the series, having variations of only about 0.001 A at both levels of theory. The Ca-Ha (Cl-H3 or Cl-H4) bond lengths have little variability, ranging from 1.077 to 1.081 A at HF and 1.083 to 1.089 8, at MP2 theory. Lengths become shorter with increasing substitution, particularly on the ,&carbon, consistent with an inductive effect, as seen in the C-H bond dissociation energ i e ~ . *The ~ MP2-HF differences have a range of 0.004-0.009 A, with larger values in cases where there is an a-fluorine. The Ca-Fa bond lengths decrease with increasing substitution, especially when there is another a-fluorine. As with the
+
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reactants and products,23inclusion of electron correlation with MP2 theory gives significantly longer bond lengths (by 0.0280.036 A). The trends in Cb-Hp bond lengths are somewhat dependent on the theory used. In the HF structures, the variability in lengths (1.077-1.086 A) is slightly more than was the case at the a-center. The lengths tend to be shorter when there are p-fluorines and longer when the hydrogen is in position 5. The latter trend is also seen at the MP2 level, but not the former. The MP2-HF difference ranges from 0.002 to 0.009 A, with the smallest values seen when there are no /?-fluorines. The Cp-Fp bond lengths are highly variable, ranging from 1.311 to 1.375 8, and 1.346 to 1.404 8, at the HF and MP2 levels, respectively. At both levels the lengths decrease with increasing fluorine substitution, especially on the /?-carbon, but the correlation is not as strong at MP2. The MP2-HF difference is usually smaller when the fluorine is in position 5 , where it will be eclipsing the SOMO of the resultant radical, or when it is trans to the abstracted hydrogen. The C-H-0 angle varies more than any other through the series. Greater deviations from linearity are seen with MP2
J. Phys. Chem., Vol. 99, No. 36, 1995 13405
Reactions of Hydroxyl Radicals with Fluorinated Ethanes
TABLE 1: Key Structural Parameters for the TS of Each Reaction at Two Levels of Theow paramete+ HF/6-31G(d) MP2/6-3 lG(d,p) parameteP HF/6-3 1G(d)
+ OH
CH3-CH2F Cl-HI H1-0
1.299 1.210
1.190 1.314
171.4 2.896
157.8 2.525
Cl-HI H1-0
1.313 1.201
1.200 1.292
174.1 4.949
165.1 4.740
C1-HI H1-0
1.316 1.194
1.210 1.273
C 1-H1-0 H2. * *F6
166.0 2.515
157.1 2.193
Cl-HI H1-0
1.309 1.199
1.198 1.298
CH~F-CHZF OH t Cl-H1-0 H2. * -F4
171.6 2.971
158.5 2.641
C1-H1 H1-0
1.314 1.191
1.206 1.285
CH~F-CHZF OH g Cl-HI-0 H2. * -F7
167.9 2.340
157.9 2.195
Cl-HI H1-0
1.323 1.184
1.216 1.259
CHFZ-CH~ OH g,t C 1-H1-0 H2** *F7
167.8 2.697
158.1 2.340
C1-H1 H1-0
1.327 1.181
1.220 1.252
169.8 2.587
161.1 2.262
Cl-H1 H1-0
1.303 1.197
1.194 1.305
178.9 2.357
162.0 2.682
Cl-HI H1-0
1.331 1.173
1.223 1.241
171.9 2.739
163.1 2.41 1
C1-H1 H1-0
1.318 1.184
CHF2-CH2F 1.206 1.277
C1-H1-0 H2. * .F4
167.7 2.869
157.7 2.625
Cl-HI H1-0
1.322 1.179
CHFZ-CH~F OH g,g 1.212 Cl-H1-0 1.267 H2. * *F7
171.6 2.638
162.4 2.279
Cl-HI H1-0
1.319 1.179
1.212 1.273
-
169.4 2.679
158.1 2.262
Cl-HI H1-0
1.337 1.173
C1-HI-0 H2. .F4
171.9 3.015
Cl-HI H1-0
1.321 1.176
C1-H1 H1-0
1.332 1.162
+
CH2F-CH3
C1 -Hl-O H2. * *F4 OH t C1-HI-0 H 2 *F5
MP2/6-31G(d,p)
+ OH g
CH2F-CH3
+
+
+
CHS-CHj
+ OH g,g
Cl-H1-0 H2** *F7
+ OH
CH3-CF2H
C1-HI-0 H2** *F4
CF3-CH3
+ OH
C1-HI-0 H 2 * *F6
+ OH g,t +
CH2F-CHF2
+ OH
~
Cl-HI-0 H2. .F7
CF3-CH2F
CHFz-CHF2
+ OH
+ OH
C 1-H1-0 H2* *F4
CF3-CHF2
174.6 3.155
+ OH Cl-H1-0 H2. * *F3
172.2 2.955
Bond lengths in angstroms, angles in degrees. Atom-numbering system as in Figures 1 and 2. t and g refer to the abstracted H being trans or gauche to a P-F, respectively. theory, with the difference being larger when the number of a-fluorines is greater than the number at the /?-carbon. The H-0-H angle tends to be smaller when there are a-fluorines; the same situation gives rise to a larger difference in values at the two levels of theory. The magnitudes of the H-C-H angles decrease in the order Ha-C1-Ha > Hp-C2-Hp > H,-Cl-HI, where H, can be H3 or H5, and Hp can be H5, H6, or H7. The Ha-C1-H1 angles are about 2" larger at the MP2 level. For cases of R-CH3 OH, where there are two such angles, the largest magnitude is for the case where H, is closest to H1, with a particularly large difference seen when H, and H1 are eclipsed or nearly so. The Ha-C1-H, angles are about 1" larger at the HF level. At both levels of theory the magnitude increases with increasing fluorine substitution. This trend is also seen for Hp-C2-Hp angles, which are all within f l " of the
+
tetrahedral value, and only very small differences are seen between the two levels of theory. The magnitudes of the F-C-H angles also decrease in the order F,-Cl-H, > Fp-C2-Hp > Fa-C1-H1. For cases of R-CHF2 OH, the smaller value is seen for Fa closest to H1, with the exception of CHK-CHF2 OH. The F,-Cl-H, angles tend to increase with increasing fluorine substitution, and the MP2 value is higher, by 5 lo, except for CH3-CHzF -I-OH, where it is 0.1" smaller. Similar trends are observed for FaC 1-Ha angles, but the angles are larger at the HF level, with no exceptions. The magnitudes of the Fp-C2-Hp angles show little variation between the two levels of theory, being within f0.5"in all cases, and usually within f0.2". Also given in Table 1 are H2-Fx distances, where Fx is the closest fluorine to H2, the hydroxyl hydrogen. This gives an indication of the degree of intramolecular hydrogen bonding in
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13406 J. Phys. Chem., Vol. 99, No. 36, I995 the TS. Strong t h e ~ r e t i c a land ~ ~ e ~ p e r i m e n t a evidence l~~ for H-F intramolecular hydrogen bonding has been reported previously. Hydrogen bonding can occur when the interatomic distance from the hydrogen to the electronegative donor atom is significantly less than the sum of their effective van der Waals radii. These values are 1.2 8, for hydrogen and 1.35 8, for fluorine,26 so in the present case an intramolecular hydrogen bond can be deemed to be present if the H2-Fx distance is less than 2.5 8,. In all cases, except CH3-CHF2 OH, where the two levels of theory give different point groups, this distance is shorter at the MP2 level, consistent with giving a more accurate geometry description when polar bonds are present.27 Regardless of the level of theory, shorter distances are seen when at least one /?-fluorine is gauche to the abstracted hydrogen, in which case the incoming hydroxyl is oriented to take advantage of an intramolecular hydrogen bond, usually such that H2 is closer to /?- rather than a-fluorines. Exceptions occur for some of the more highly substituted species, where multiple /?-fluorines appear to have a canceling effect. In these cases, particularly when the /?-group is CF3, the H2-Fa distances of about 3 8, do not indicate hydrogen bonding. For the OH group to form a hydrogen bond to a trans /?-fluorine, a rotation of the ethane would first have to occur, and this is not energetically favorable. Even where hydrogen bonding is occurring, the interatomic distance is only about 0.3 A less than the sum of the van der Waals radii, so the energetic advantage should be small. Vibrational frequencies are presented in Table B of the supporting information. The modes are ordered by increasing wavenumber at the HF level and approximate type of mode, with the order of the MP2 frequencies adjusted to match the same type at the HF level. In some cases the types of mode do not match, due to differences both from the level of theory the frequencies are calculated at and in the optimized geometries. The assignment of modes is complicated by the lack of symmetry; many modes are strongly coupled, and most include compensating motions in the H-0-(H) fragment. Many modes which consist primarily of motion of one carbon group also contain smaller motions of the other group. The reduced masses are often less than expected due to the couplings and compensating motions. The hydrogen being abstracted is in some cases still considered as being in the ethane and in other cases as being in the product water molecule. This ambiguity, and the differing amounts of bond-breaking at the TS at the two levels of theory, often leads to different modes occurring at the two levels. Another effect is that it is difficult to ascertain a priori which modes to expect. Assignments are made based on those atoms with the largest mass-weighted motions, by inspection of the normal coordinate vectors; the descriptions can only be considered as approximate. In this context “symmetric” and “degenerate” should be interpreted loosely. For cases where equivalent groups are at both carbons, a and /? designations are used to distinguish the motions. If no designations appear in these cases, the motion occurs in both groups. There are six additional degrees of freedom in the TS as compared to the parent ethane. One C-H stretching mode in the reactant becomes the reaction coordinate, and one bending mode usually becomes either a C-H-0 bend or a C-C-0 skeletal bend, although it is retained in some cases where the hydrogen remains tightly bound to the carbon. The six additional modes consist of what is essentially a rotation of the OH group, an R-OH torsion, two H-0-H bends, an 0-H stretch, and a TS symmetrical stretch. Of the 24 degrees of freedom in each TS, eight are in the H20 fragment, including the C-H-0 or C-C-0 bend. For
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Martell and Boyd a CX3 group (X = H or F), there are three stretches, three deformations, and two rocking motions; a CX2 group has two stretches and four bends, normally one each of a rock, wag, scissors, and twist; a CX group has one stretch and one bend.28 In the case of a (HF)C-H group at the a-carbon, these numbers of degrees of freedom are not additive, so it is not clear which motions to expect. In general the frequencies are lower at the MP2 level (as expected since the systematic overestimation of ab initio frequencies is lower using MP2 vs HF theory29),except for some of the low-frequency modes which have different ordering at the two levels of theory or where the degree of coupling between modes is more severe at one level. In all cases the reaction coordinate is almost exclusively a motion of the hydrogen atom being abstracted away from the carbon atom and toward the oxygen. The magnitude of the vibration is always much lower at MP2 theory, consistent with the TS lying further out into the entrance channel. For each TS there is one mode which corresponds to essentially a free rotation of the incoming OH group. As explained previously,’2 it is not reasonable to include this mode in the zero-point energy (ZPE), and the ZPEs presented below are adjusted accordingly. This frequency is consistently higher, thus giving a greater adjustment, at the MP2 level. Vibrational consequences of hydrogen bonding include spectacular shifts of the stretching frequencies, particularly the A-H mode (where A is the atom directly bonded to the hydrogen), and coupling of this mode to various other vibrat i o n ~ . There ~ ~ is little evidence of coupling of the 0-H stretching frequency for cases where the H2-Fx distance indicates hydrogen bonding and only a slight decrease in the 0 - H stretching frequency at the MP2 level. Thus, the evidence from the vibrational frequencies is that any intramolecular hydrogen bonding is of a small magnitude. Unscaled ZPEs and standard entropies at 25 “C are given in Table 2. The unscaled ZPEs are lower at the MP2 level, as expected since HF theory systematically overestimated vibrational frequencies by -lo%, while MP2 frequencies are only -5% too high.I9 As with the total energies, ZPEs decrease with increasing fluorine substitution, as expected due to the larger reduced masses of the vibrations. Again, values tend to be lower for maximum substitution on one carbon, but there are no consistent trends for the a vs /? and gauche vs trans substitution pattems. The standard entropies are also generally lower at the MP2 level. They provide further evidence of intramolecular hydrogen bonding. An additional bonding interaction should reduce entropy. This is manifested in the standard entropies in two manners. First, for species where inequivalent hydrogens can be abstracted, lower entropies are seen for the TS where the H-F distances suggest an intramolecular hydrogen bond. Second, in these instances, the difference in the entropy values between the two levels of theory is more pronounced, consistent with MP2 giving a shorter H-F distance (see above) and thus a stronger hydrogen bond. Standard entropies of activation, A$,,,, can be calculated directly from the ab initio standard entropies of the TS and reactants or experimentally from the Arrhenius pre-exponential factor, A, through the relation
R Ah AS+ = - l n ( E ) n where R is the universal gas constant, n is the molecularity of the reaction, h is Planck’s constant, k is Boltzmann’s constant, and T is the absolute temperature. Entropies of activation at
J. Phys. Chem., Vol. 99, No. 36, 1995 13407
Reactions of Hydroxyl Radicals with Fluorinated Ethanes TABLE 2: Zero-Point Energies and Entropies, at Two Levels of Theory" speciesb
+ + + + + + + + + + + + + + +
ZPE//HF/6-3 1G(d)
ZPE//MP2/6-3 lG(d,p)
&.,//HF/6-3 1G(d)
$5.clIMP2/6-3 lG(d,p)
320.5 1 323.70 330.06 315.32 344.83 337.41 335.48 336.03 353.70 35 1.60 359.37 357.28 357.24 377.24 386.52 392.74
311.90 321.69 328.15 309.98 345.16 332.35 330.72 330.54 341.76 348.07 360.99 353.29 351.21
177.87 226.46 261.83 276.45 278.38 282.51 298.93 311.86 309.08 328.17
178.09 226.60 262.56 277.69 279.81 284.95 301.28 315.21 312.72 332.56
188.23 252.72 268.88 272.22 290.45 290.32 285.61 303.93 307.52 307.47 320.16 322.18 336.38
188.64 252.64 269.54 272.25 29 1.73 290.94 287.71 305.27 310.18 309.43 323.93 325.72 340.7 1
TS
CH3-CH3 OH CH3-CH2F OH CHzF-CH3 OH t CHZF-CH~ OH g CH2F-CH:F OH t CHZF-CH~F OH g CHF2-CH3 OH g,t CHFz-CH3 OH g,g CHj-CHF? OH CF3-CH3 OH CHF2-CH2F OH g,t CHF2-CH2F OH g,g CHzF-CHF2 + OH CF3-CH2F OH CHFz-CHFz OH CFj-CHF? OH
85.415d 78.463d 78.643d 78.765d 7 1.4966 7 1.50gd 70.884d 70.747d 70.543d 6 1.940d 63.652d 63.476d 63.404d 54.674d 55.3596 46.564d
OH CH3-CH3 CHzF-CH3 CHzF-CHzF Cz CHFz-CH3 CF3-CH3 CHF2-CHzF CI CF3-CHzF CHF2-CHF2 C z h CF3-CHF2
9.106 79.760' 73.141' 66.294' 65.524' 56.882' 58.550' 49.872' 50.592' 41.862'
H2O CH3-CHz CH3-CHF CHzF-CHz CI CHzF-CHF CHFz-CHz C1 CH3-CFz CF3-CHz CHF2-CHF CH2F-CF2 C, CF3-CHF CHFz-CFz C, CF3-CF2
22.977 63.352f 61.722f 56.814' 5 1.229 49.490' 50.932f 40.759 43.400' 44.209 34.737f 36.297f 27.443f
83.263c,d 76.316d 76.05gd 76.491d 68.842d 68.953d 68.467d 68.270d 68.076d 59.5976 60.935d 60.832d 60.867d
Reactants 8.758' 77.565' 70.524 63.232 62.798 54.260 55.456 46.968 47.438 38.924
Products 21.898' 61.43 l'.d 55.938 54.869 48.935 47.515 48.937 39.016 48.935 41.884 32.597 33.789 25.298
Zero-point energies in millihartrees, entropies in J mol-' K-I. Some values have been reported previously, as indicated, but are included here (in some cases with an extra digit), for completeness. t and g refer to the abstracted H being trans or gauche to a P-F, respectively. Symmetry point groups are given where necessary to identify conformers. Reference 12. Internal rotation mode removed; see ref 12 for details. Reference 22. f Reference 23. the two levels of theory used in the geometry optimizations and frequency analyses, and from experiment, at 25 "C,are given in Table 3. The experimental A$,,, values are more negative than the ab initio ones, by a factor of about 4. This discrepancy is greater than can be explained by errors in the calculated and/ or measured values. If there is curvature in the Arrhenius plot as a result of tunneling, the extrapolated A value will be lower than for a linear plot. This will lead to a lower, or more negative, A$5oc value, as is the case here. The magnitude of the effect suggests that tunneling is significant, as would be expected for hydrogen abstraction reactions. Total energies at three levels of theory and experimental heats of f ~ r m a t i o n ~ l are - ~ ' given in Table 4. Some of the energies have been reported previously, 12,22.23.42-45 but are included here for completeness. Additional total energies required for the G2 method are given in Table 5. As expected, the energies decrease with increasing level of theory, in terms of both level of electron correlation and basis set size. The lowest energies are obtained with the MP4/6-311G(2df,p) level, the lowest energies using the MP2 method (and second lowest overall) are obtained with the 6-3 11 G(3df,2p) basis set, the largest one used, and the lowest energies obtained using the 6-3 1lG(d,p) basis set are
+
with the QCISD(T) method, which gives the greatest degree of electron correlation. The MP2/6-3 1lG(d,p) energies for the TS are lower when the HF geometries are used, while the MP2 geometries give lower energies for the reactants and products. This is an indication of the MF'2 geometries being more accurate, since the TS is a maximum in one direction on the potential energy surface, so any deviation from the true maximum will give a lower energy. The lower TS energies of the HJ? geometries are probably due to the TS being located too late on the reaction coordinate, as indicated by the geometry results above. At every level of theory, total energies for species with the same number of fluorines are lower when as many as possible are on the same carbon, consistent with the geminal effect, and preferably on the a-carbon for the radicals and TS, since the electronegative fluorine atoms will prefer to be attached to the relatively more electropositive a-carbon. For the TS there is a secondary preference for lower energy where there is a p-fluorine gauche rather than trans to the hydrogen being abstracted. This can be attributed to a stabilization from an intramolecular H-bond, as evidenced by the short H-F distances in these instances. The effect decreases both with increasing level of theory and with increasing substitution by fluorine and
Martell and Boyd
13408 J . Phys. Chem., Vol. 99, No. 36, 1995 TABLE 3: Activation Entropies, in J mol-' K-' reaction" ~
MP2/6-3 1 lG(d,~)/MF/6-3 1G(d)
MP2/6-3 1 lG(d,p)//MP2/6-3 lG(d,p)
-83.8
-92.8 -119.0 -112.5 - 130.7 -121.2 -127.4 -116.1 - 1 10.6 -123.4 -115.0 -118.4 -126.1 -128.2
+ + + + + + + + + + + + + + + +
~~
experimentalb
~
CH?-CH? OH CH;-CH;F OH CH2F-CH3 OH t CH2F-CH3 OH g CHFz-CH, OH g,t CHF2-CH3 OH g,g OH CH3-CHF2 CH~F-CHZF OH t CH2F-CH2F OH g OH CF3-CH3 CHF2-CHzF OH g,t OH g,g CHF2-CH2F CH2F-CHF2 OH OH CF3-CH2F CHFz-CHFz OH CF3-CHF2 OH
- 1 16.0
-109.6 - 124.4 -120.8 -120.2 - 102.6 -109.5 - 1 16.9 -108.8 - 111.4 -119.5 -119.6 -1 12.5 - 100.4 -113.3
-471.9' -483.1' -480.0' It
-485.U
-489.18 -481.49 -496.g
a t and g refer to the abstracted H being trans or gauche to a P-F, respectively. " refers to the value being equivalent to the one immediately above since experiment does not distinguish inequivalent hydrogens in a common substrate. Reference 50. Reference 2. e Reference 5. /Reference I. g Reference 9.
TABLE 4: Total Energies at Various Levels of Theory and Experimental Heats of Formationa speciesb
+ + + + + + + + + + +
MP2/6-3 1lG(d,p)//HF/6-3 1G(d) MP2/6-3 11G(d,p)//MP2/6-3lG(d,p) MP4/6-3 1lG(d,p)//MP2/6-3 lG(d,p)
CH3-CH3 OH OH CH3-CH2F CH2F-CH3 OH t CH2F-CH3 OH g CH2F-CHlF OH t CHlF-CH2F OH g CHF2-CH3 OH g,t OH g,g CHFz-CH, CH3-CHF2 OH CFj-CH3 OH CHF2-CH2F OH g,t CHF2-CH2F + OH g,g OH CHzF-CHFz OH CF3-CH2F CHF?-CHF;, + OH OH CF3-CHF2
-155.134932 -254.201 068 -254.200 600 -254.204 199 -353.268 913 -353.210 023 -353.281 614 -353.287 103 -353.292 542 -452.378 924 -452.349 411 -452.349 958 -452.351 272 -551.438 967 -55 1.421 478 -650.515 898
OH CH3-CH3 CH2F-CH3 CHzF-CHzF C2 CHF2-CH3 CFj-CHl CHFz-CHzF CI CF3-CH2F CHFI-CHF~ C z h CF,-CHF*
-15.512 -19.570 -118.638 -211.102 -217.125 -376.820 -316.185 -415.811 -475.866 -515.954
H20 CH3-CH2 CH3-CHF CHzF-CHz Ci CH2F-CHF CHF2-CH2 CI CH3-CFz CF3-CH2 CHFz-CHF CH2F-CF2 C, CF3-CHF CHF2-CF2 C, CF3-CFz
-16.263 585 -18.902 140' -111.975 512f -171.967 9069 -217.038 424h -277.052 1939 -217.061 0 2 9 -316.145 2489 -316.1 18 799h -316.1 19 083' -475.208 852h -415.191 254' -574.285 606
+
+ +
AHf.298
ref
38.95 -83.8 -263.2 -4433 -500.8 -145.6 -664.8 -904.21 -8843 -1104.6
31 32 33 44 33 33 34 44 45 33
TS
831 654d 856' 617' 742' 167' 952' 015' 528' 378'
-155.130 -254.201 -254.197 -254.201 -353.264 -353.265 -353.285 -353.284 -353.286 -452.311 -452.345 -452.346 -452.346
898' 626 664 156 341 152 409 965 939 420 585 300 596
-155.190 -254.264 -254.259 -254.263 -353.329 -353.331 -353.349 -353.348 -353.351
331' 01 1 131 085 561 002 222 728 564
Reactants -75.512 -19.510 -178.639 -211.103 -271.126 -316.821 -316.186 -415.818 -415.861 -514.956
819' 139' 255e 348' 464' 14Ie 986' 430' 848' 045'
-15.588 -79.614 -118.685 -211.152 -211.114
329' 234' 358r 149 39Y
-16.276 -78.944 -118.019 -178.012 -277.085 -277.099 -211.106
272' 350' 618 454 944 007 853
Products -76.263 894' -18.902 838' -117.975 170' -171.968 344' -211.039 136' -277.052 965' -211.061 373' -316.146 393' -316.1 19 666' -376.1 19 197' -415.210 073' -415.198 160' -514.286 901'
-241.82 31 111.2 35 -11.5 36
-302.5 -511.1
37 38
-680.1
39
-891.2
40
Total energies in hartrees, heats of formation in kT mol-'. Some values have been reported previously, as indicated, but are included here (in some cases with an extra digit), for completeness. t and g refer to the abstracted H being trans or gauche to a P-F, respectively. Symmetry point groups are given where necessary to identify conformers. Reference 12. Reference 22. e Reference 23. f Reference 42. 9 Reference 43. Reference 44. Reference 45. Calculated by the triatomic additivity method of ref 41. a
in all cases is less than 10 W mol-', in line with the geometric and vibrational evidence that only a weak hydrogen bond occurs.
Classical barrier heights, with (A&*) and without (VB) ZPE corrections, at various levels of theory are given in Table 6.
Reactions of Hydroxyl Radicals with Fluorinated Ethanes
J. Phys. Chem., Vol. 99, No. 36, 1995 13409
TABLE 5: Total Energies at Additional Levels of Theory Required for G2 Method, in hartrees“ QCISD(T)/ Species’VG2 energy‘ MP2/6-31 l+G(d,p) MP2/6-3 11G(2df,p) MP2/6-3 11+G(3df,2p) MP4/6-3 1 l+G(d,p) MP4/6-3 1 1G(2df,p) 6-3 1lG(d,p) CH3-CH2F OH -254.422 705 OH t CH2F-CH3 -254.418 710 OH g CH2F-CH3 -254.420 453
-254.216 714
-254.321 429
TS -254.351 680
-254.280 235
-254.390 511
-254.261 226
-254.213 508
-254.311 238
-254.354 520
-254.276 611
-254.385 980
-254.232 325
-254.215 674
-254.321 181
-254.356 846
-254.278 684
-254.389 761
-254.265 631
CH2F-CH3 -178.782 113 CH2F-CH2F C? -277.932 684 CHF2-CH3 -217.953 302
-118.648 012
-118.724 112
Reactants -178.149 351
-118.694 743
-178.775 024
-178.685 266
-217.719 834
-271.838 134
-277.873 724
-211.169 697
-271.893 478
-217.150 697
-277.140 330
-271.861 834
-277.894 829
-217.189 372
-271.916 516
-271.172 646
CH3-CHF -178.124 225 CHIF-CH? CI -178.118 806 CHzF-CHF -271.274 298 CHFz-CH2 CI -217.286 952 CHj-CF2 -217.292 801
- 117.984 552
-178.060 864
Products -178.083 417
-178.029 031
-178.109 094
-118.020453
-117.978 043
-118.053 161
-178.076 199
-118.022 744
-178.101 511
-178.013 192
-271.055 820
-271.113 478
-271.207 171
-277.103 728
-277.226 944
-271.085 512
-271.061 120
-217.187 499
-217.219 417
-271.1 14 942
-277.240 391
-277.098 054
-211.074 986
-271.196 458
-277.221 268
-211.121 591
-217.248 812
-217.105 922
+
+ +
a All values given are single-point energies at the MP2/6-31G(d,p) geometries given here for TS and in ref 23 for reactants and products. The MP4/6-31 lG(d,p) and MP2/6-311G(d,p) single-point energies are given in Table 4; ZPEs, in Table 2. Values for CH3-CH3 OH, OH, and H 2 0 are given in ref 12. t and g refer to the abstracted H being trans or gauche to a p-F, respectively. Symmetry point groups are given where necessary to identify conformers. Scaled ZPEs included. To obtain energy without ZPE correction, subtract the MP2/6-31G(d,p) ZPE listed in Table 2 multiplied by the scaling factor of 0.9646.
+
Calculations using HF geometries give the lowest barriers of the unextrapolated methods, as a result of the TS energies being lower, while reactant energies are higher, at this level of theory (see above). Barriers calculated from the MP2 geometries decrease slightly when the MP4 vs MP2 method is employed (a trend noted previously in other reaction series, e.g., sN2 reactions of halogens with methyl halides46), with larger decreases seen when the G2 method is used. Barriers tend to decrease with increasing fluorine substitution on the a-carbon, but increase with increasing /?-substitution. In cases of inequivalent hydrogens being abstracted, the lower barrier occurs when the hydrogen is gauche to a /?-fluorine. These two trends result from the TS energy trends noted above. Comparing calculated barriers to those obtained from experiment is not straightforward. The term “activation energy” can apply to a series of related concepts.47 The calculated barriers presented here represent the differences between TS and reactants in potential energy ( VB) and potential energy plus ZPE (&os). Corrections for JCV dT will yield AET*. For bimolecular gas reactions, AET*is likely to be less than AEo*, because of a loss of translational degrees of freedom and a decrease in CV on a~tivation.~’It is often assumed that the Arrhenius activation energy, EA, can be obtained from Tolman’s theorem by adding RT to &T*. However, this is true only for reactions which exactly obey activated complex theory with a temperature independent K , which will not be the case here where tunneling will be important since a proton is being t r a n ~ f e r r e d . ~ ~ Therefore, the experimental barrier heights (EA) quoted in Table 6 cannot be directly compared to the calculated barriers. Furthermore, the EA values often have large uncertainties, and values for the same reaction obtained by different groups often have large discrepancies, possibly due to reactive impurities, secondary losses of OH, and unanticipated heterogeneous p r o c e s s e ~ . ~Also, . ~ ~ experiment cannot distinguish inequivalent hydrogens in a common substrate, as has been done in the
calculations. This is not necessarily a problem, as the channel with the lowest barrier will likely dominate. For example, for C2H5F OH the next lowest barrier is 5.9 kJ mol-’ higher at the G2 level, so the reaction through this TS is 10.8 times slower at room temperature. Thus, the error in assigning the total rate constant to the lowest barrier path is probably smaller than the errors either in the ab initio calculations or in the measurements. Using this approximation, excellent agreement is seen between the experimental and G2 values for this reaction, assuming there is only a slight difference in the EA and AEo* values. As a base for comparison, for the reaction of OH with unsubstituted ethane, EA is 9.1 kJ mol-’,50 whereas AEo* is 9.3 kJ mol-’ from a fit to experimental data,I2 so all other things being equal, EA should deviate only slightly from AEo* through the series. Therefore, comparison of calculated A&* values with experimental EA ones, while not being definitive, should be a reasonable approximation. While the G2 results show good agreement with experiment, overall the qualitative trends in the experimental barriers, both absolute and relative, are reproduced at each level of theory. Reaction enthalpies, including ZPE and thermal corrections to 298.15 K, are given in Table 7. Here, more dramatic effects are seen with different levels of theory. Inclusion of electron correlation in the geometry optimization has varying effects on enthalpy, while higher order correlation corrections (MP4 vs MP2) to the energies lower the magnitude of the enthalpy change. The reactions are about 20 kJ mol-’ more exothermic at G2 vs MP4 theory. Trends through the reaction series are not as consistent as for barrier heights. Reactions are more exothermic when fluorines are on the a- rather than /?-carbon, since this situation lowers the energy of the product ethyl radical. Exceptions occur for the reaction of fluoroethane, at the MP2/ 6-3 1lG(d,p)//MP2/6-3 lG(d,p) level, and trifluoroethane, at the MP2/6-3 1lG(d,p)//HF/6-3 1G(d) level, where the conformers with an extra fluorine on the @-carbonresult in slightly greater
+
Martell and Boyd
13410 J. Phys. Chem., Vol. 99, No. 36, 1995
TABLE 6: Classical Barriers (VdA&*P at Various Levels of Theory and Experimental Activation Energies, in kl/mol reactionb
MP2/6-31 lG(d,p)// HF/6-31G(d)
MP2/6-31 lG(d,p)// MP2/6-3 lG(d,p)
MP4/6-31 lG(d,p)// MP2/6-3 lG(d,p)
22.6 14.3 12.1 3.1 29.1 20.5 19.7 11.3 28.8 19.8 30.1 20.8 15.8 6.0 17.0 7.7 14.3 5.0 37.0 27.3 24.4 14.8 23.2 13.2 19.7 9.5 28.6 18.3 31.2 20.8 29.7 19.1
33.4 26.0 27.6 20.1 40.0 31.8 28.8 21.8 36.6 28.8 37.7 29.4 32.6 23.8 31.2 23.2 27.5 19.8 43.6 34.9 37.5 29.2 34.8 27.0 35.6 26.4
32.6 24.7 26.2 18.7 36.6 28.5 27.8 20.8 35.4 27.6 36.7 28.4 29.3 20.5 28.7 20.7 24.9 17.2
+ OH CH3-CH2F + OH CH2F-CH3 + OH t CH2F-CH3 + OH g CHF2-CH3 + OH g,t CHF2-CH3 + OH g,g CH3-CH3
+ OH CHzF-CHzF + OH t CH2F-CH2F + OH g CF3-CH3 + OH CHF2-CH2F + OH g,t CH3-CHF2
CHFz-CH2F
+ OH g,g
+ OH + OH
CH2F-CHF2 CF3-CH2F
CHF2-CHF2 CF3-CHF2
+ OH
+ OH
G2
experimental EA^
20.1 12.4d 15.5 8.0 26.5 18.3 21.0 13.9
9.1' 6.2f
11.49
18.3h
14.5' 14.0' 14.1h
ZPEs scaled by 0.9135 at HF/6-31G(d) and 0.9646 at MP2/6-31G(d,p). t and g refer to the abstracted H being trans or gauche to a P-F, respectively. " refers to the EA value being equivalent to the one immediately above since experiment does not distinguish inequivalent hydrogens in a common substrate. Reference 12. e Reference 50. /Reference 2. g Reference 5. * Reference 7. Reference 9.
TABLE 7: Reaction Enthalpies (A&S) at Various Levels of Theory, in kJ/mol reaction
+ + + + + + + + + + +
CH3-CH3 OH OH CH3-CH2F OH CH2F-CH3 OH CHF2-CH3 CH3-CHF2 + OH CH2F-CH2F OH CF3-CH3 OH CHFZ-CH~F OH OH CH2F-CHF2 CF3-CH2F OH CHF2-CHF2 OH OH CF3-CHF2
MP2/6-31 lG(d,p)//HF/6-31G(d) MP2/6-31 lG(d,p)//MP2/6-31G(d,p) MP4/6-31 lG(d,p)//MP2/6-31G(d,p) -64.8 -65.8 -57.2 -49.1 -68.8 -74.6 -45.7 -63.9 -62.6 -61.2 -68.9 -57.9
-7 1.O -74.7 -77.4 -50.2 -68.7 -72.1 -46.8 -44.2 -62.4 -63.1 -56.0 -57.4
-58.4 -60.9 -44.8 -37.2 -54.2 -58.8
G2
expt"
-72.6' -77.6 -64.6 -55.4 -70.8 -76.3
-79.8 -89.1 -82.5 -52.3 -57.3 -67.4
Calculated from the heats of formation given in Table 4. In ref 12, this value is reported as AHo.
exothermicities. Reactions are less exothermic when as many fluorines as possible are on one carbon, as a result of the geminal effect being greater in the reactants than in the products. An exception occurs for the reaction of tetrafluoroethane, where CFs-CH2F OH is more exothermic at the MP2/6-31 lG(d,p)/ NP2/6-31G(d,p) level. These exceptions are probably due to the inability of MP2 theory to adequately describe electron correlation. The G2 values give the best agreement with experiment, although perhaps not as good as expected given this method has an average absolute deviation from experiment of atomization energies of 39 first-row compounds of 3.85 kJ mol-' l 8 (and also performs remarkably well in calculating ionization energies, electron affinities, and proton affinities5') and calculation of reaction enthalpies is usually considered to give more accurate results than for atomization energies. A possible source of error is that while the same quantity is being measured by
+
both experiment and theory, the theoretical value is from the most stable conformers of reactants to the most stable conformers of products, while the experimental value is for a statistical average of all possible conformers in reactants and products. Conclusions Many of the trends seen in the optimized TS geometries are similar to those noted previously in the ethane and ethyl radical series. Variations in geometrical parameters are greater near the reaction center. Inclusion of electron correlation in the geometry optimizations gives slightly shorter C-C and C-H bonds, significantly longer C-F bonds, greater deviations from linearity in the C-H-0 angles, and greater &-Cl-Hl angles. The HF optimized geometries have greater H-0-H and XaCl-Ha angles, with the remaining types of angles having about the same magnitude at the two levels of theory. Increasing
Reactions of Hydroxyl Radicals with Fluorinated Ethanes fluorine substitution tends to decrease bond lengths and increase bond angles. The incoming hydroxyl group will take advantage of an intramolecular hydrogen bond to a ,&fluorine, but not at the expense of having to go through a rotational barrier. The relative lengths of the C-H bond being broken and the 0 - H bond being formed and the relative magnitudes of the imaginary frequency of the TS both point to an earlier TS at the MP2 level of theory. Standard entropy and total energy results confirm weak intramolecular hydrogen bonds in the transition states where the abstracted hydrogen is gauche to a @-,fluorine, as was suggested by the optimized geometries. Comparison of calculated barrier heights with experiment is difficult, but the trends are at least qualitatively correct. Calculated reaction enthalpies give fairly good agreement with experiment; the G2 method gives the best results, although not as good as expected, but again, direct comparison of theory and experiment is difficult. Total and zero-point energies, and, as a result, barrier height and reaction enthalpies, are affected by substitution pattems. Thus, barrier heights decrease with increasing a-fluorine substitution, but decrease with increasing @-fluorine substitution and when the hydrogen being abstracted is gauche to a /I-fluorine, in which case the TS is stabilized by an intramolecular hydrogen bond. The reaction exothermicity tends to increase when fluorines are on the a- rather than @-carbon and decreases when as many fluorines as possible are on one carbon. Acknowledgment. Financial support for this work was provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada. We are grateful for the technical advice provided by Doug Fox of Gaussian, Inc., and for useful suggestions from Zheng Shi. We also thank Xabier Lopez for completing some of the larger calculations, and Philip Pacey for fruitful discussions. We thank an anonymous referee for suggestions which improved the manuscript.
SupportingInformation Available: Geometrical parameters and vibrational frequencies for the TS of each reaction at two levels of theory (30 pages). Ordering information can be found on any current masthead page. References and Notes (1) Makide, Y.; Rowland, F. S. Proc. Natl. Acad. Sci. U.S.A. 1981,
78, 5933.
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1
JP950504X
