United States Environmental Protection Agency Atmospheric Sciences Research Laboratory Research Triangle Park NC 27711 Research and Development EPA/600/S3-86/072 Apr. 1987 &EPA Project Summary Structure-Reactivity Relationships for Predicting Environmentally Hazardous Chemicals Norman Cohen A method previously developed for extrapolating rate coefficients by con- ventional transition-state theory was applied to reactions of hydroxyl (OH) radicals with 10 halomethanes and 18 haloethanes. For each reagent, the entropy of activation AS* was calcu- lated. That value, together with an ex- perimental value of the rate of reaction at 298 K, k(298), was used to calculate k(T) at higher temperatures. The calcu- lated values for all the haloalkanes dif- fered from experimental values by no more than 25%, except that of (OH + CHCI3), for which the possibility of ex- perimental errors was considered. Those calculations were then used to develop a simpler, approximate scheme that can be applied to any haloalkane. For a-hydrogen abstraction reactions, AS*(298) can be fitted, with a maximum error of 1.4 and an average error of 0.3 cal mor1 K~1 (entropy units, or eu), by AS*(298) = -2.2 In M -18.0 + R In nH where M = molecular weight of the haloalkane and nH = the number of abstractable a-hydrogen atoms. The activation energy at 298 K, E(298). can be fitted, with an average error of 0.3 and a maximum error of 1.1 kcal/mol, by E(298)/R=2100-85nF-51nc1 - 950nCH3 - 600cH2X - 650nCHx2 - 250nCX3 where the n, indicate the number of H atoms on CH4 replaced with the in- dicated substituents, and X is either Cl or F. The above relations for AS*(298) and E(298) are used to generate a "universal" rate coefficient expression that depends only on the molecular weight and the number of abstractable H atoms in the reagent haloalkane: k(T) = nH 10" M-1 T1 6 exp[-[E(298)/R-450]/T] where E(298)/R is given by the pre- ceding equation. For most reagents, this expression predicts rate coefficients within a factor of 3 of experimental data and provides a useful predictive tool if no reliable data are available. This Project Summary was developed by EPA's Atmospheric Sciences Re- search Laboratory, Research Triangle Park, NC, to announce key findings of the research project that Is fully docu- mented In a separate report of the same title (see Project Report ordering In- formation at back). Introduction The aim of this research has been to develop the means for predicting reac- tivities of potential man-made pollutants in the stratosphere and troposphere. Although it is possible to measure re- activities in the laboratory, the number of possible species of concern is enormous, and the cost of studying each one in detail would be prohibitive. The assess- ment of the atmospheric fate of pollutants can, for the most part, be satisfied by a procedure that enables prediction of re- activities to within a factor of 3 to 5, without requiring the higher accuracy attainable by elaborate laboratory measurements. ------- Consideration of the important oxidizing species in the atmosphere and their rela- tive reactivities leads to the conclusion that for almost all reagents, the species that determines the lifetime of an atmo- spheric pollutant is the hydroxyl (OH) radical. Consequently, any program con- cerned with predicting reactivities of potential pollutants should concern itself first with the reactions of OH radicals. For this reason, the work under this con- tract focused on OH reactions. The initial efforts proceeded in two phases: The first addressed the problem of calculating in detail the temperature dependence of the reaction rate coef- ficients; the second explored the pos- sibility of developing simplified procedures for estimating, with sufficient accuracy, the rate coefficients of OH reactions at any temperature. The second phase re- quired estimating both the entropy of activation (AS*), and, with more dif- ficulty, the energy of activation (E). These two parameters determine the rate of reaction at any temperature, in accordance with the general equation k(T) = C exp(ASVR) exp(-Ea/RT) (1) Finally, the problem of developing a universal rate coefficient expression that can predict with reliability the rate coefficients, at various temperatures, for reactions of OH radicals with im- portant atmospheric pollutants was addressed. Procedure Transition-State Theory Calculations The procedure follows our previous studies. Here, the general reaction is XN ,0, XYZCH + OH - Y--C--H' 'H- Z' XYZC + HOH where X, Y, and Z are each either H, C1, F, CH3, or a halomethyl radical. The principal problem is how to calculate the entropy of the activated complex, S*. The calculation involves using the haloalkane reagent RH itself as a model compound, then making suitable corrections to the various degrees of freedom as indicated below. The entropy S* is then given by S* = SS,H + AS, + Av + ASr + .,, AS,r + ASe + AS<, + ASn ' ' where the AS terms represent the cor- rections required in replacing the pro- perties (translation, vibration, rotation, internal rotation, electronic, symmetry, optical isomerism, respectively) of the model compound by those of the acti- vated complex. It was assumed that the C-H, H-O, and 0-H bond lengths and C-H-0 and H-O-H bond angles are approximately the same as those calculated by Walch and Dunning1 for the reaction of (OH + CH4): 1.2, 1.3, 1.0 A and 160° and 110°, respectively. From this information, the product of moments of inertia of the complex I* can be calculated, whence AS, = R In (l*/l), where I is the product of the moments of inertia of the reagent RH. AS, is given by (3/2) R ln(M'/M). The electronic degeneracy of the activated complex is assumed to be 2, whence AS8 = R In 2 - 1.38 eu (entropy units, or cal mol"1 K'1). AS0 = R Info/a"), where a abd at are the external symmetry num- bers of the alkane and complex, respec- tively, calculated assuming rigid rotation. ASn = R In (nt/n), where n and n* are the numbers of optical isomers in the alkane and complex, respectively. Only the vibrational frequencies and internal rota- tions of the activated complex remain to be determined. Vibrational Frequencies For each halomethane XYZCH, where X, Y, and Z are either H, Cl, or F, we estimated the vibrational frequencies in the activated complex by using those in the molecule XYZCF as guides, on the assumption that the C-H-OH portion of the activated complex is similar to the C- F portion of a real molecule. The vibra- tional-frequency changes in the activated complexes for all the halomethanes are summarized in the full report. For the haloethanes, it was not possible to examine each reaction in detail because there are more frequencies, fewer mode identifications, and fewer molecules for which detailed spectra are available. In- stead, the vibrational frequencies of CH3CH3, CH3CH2F, CH3CHF2, and CH3CF3 were compared, the change in the first pair representing the reaction of OH with all haloethanes with only /3-hydrogen atoms (i.e., no H atoms on the same C atom as F or Cl atoms), and the changes between the second and third pairs repre- senting reactions with a-H atoms. Because the experimental data indicate that a reaction with haloethanes con- taining only /?-H atoms is at least an order of magnitude slower than for haloethanes with some a-H atoms, it was assumed that in those reagents con taining both a- and y-H atoms, the re action with the /J-H atoms could bi neglected. In both kinds of reactions, i was assumed that the newly formed C H-( and H-O-H bonds have the same value: that were used in the halomethane re actions (1000cm1 each). Internal Rotations The properties of the internal rotation; must be evaluated accurately, because considerable entropy is associated witr these two degrees of freedom. The moments of inertia for the internal rota- tions are calculated by the procedure 01 Herschbach et al.2 The entropy of free rotation is given by Sf = R(ln 0 + 1/2), where Q = 0.35(lrT)'/2/a for lr, the reduced moment of inertia, in dalton-A. Here o is the symmetry of the internal rotation, which is 1 for most of the reagents considered in this report but 3 for rotation about the C-H bond in CH4, CHC13, and CHF3. For rotation about the C-H bond, Q «= 6.2/a for all halomethanes and 1.8 for CH4. For rotation about the 0-H bond, Q » 5.9 for all halomethanes and 5.1 for CH4. The corrections to the entropy due to the barrier to rotation, S( - Sh> are interpolated from tables developed by Pitzer and coworkers where SH = entropy of hindered rotation. For all the haloethanes, the reduced moment of inertia lr for rotation about the C-H bond is approximately 1.1 dalton-A, which makes the partition function Q equal to 6.5, and the entropy of free rotation Sf, 4.7 eu. For rotation about the H-O bond, I, = 0.95, Q = 6.0, and Si = 4.6 eu. Unlike the halomethanes, the halo- ethanes already have one internal rota- tion — about the C-C bond. In a previous study involving transition-state theory calculations for reactions of oxygen (0) atoms with alkanes, reasonable agree- ment with experiment was obtained by assuming that the barrier to internal rota- tion was lowered by 1 kcal/mol in the activated complex. The same assumption was made here. The contributions to AS* are shown in the full report. There is a qualitative difference between the re- actions abstracting a-H atoms and those abstracting /3-H atoms, because the OH adduct makes a much greater change in the moment of inertia of a CH3 group than it does when added to a halomethyl group. 'Walch, S. P., and T H Dunning, Jr J. Chem. Phys , 72:1303, 1980. 2 Herschbach, D R., H S Johnston, K S Pitzer, and R F. Powell. J. Chem Phys., 25 736, 1956 ------- Empirical Correlations The results of the detailed transition- state theory calculations outlined above were used to establish simple empirical correlations between activation entropy and activation energy for an arbitrary (OH + haloalkane) reaction with readily deter- mined molecular parameters. The fol- lowing procedure generates simple, approximate expressions for ASt(298) and for E(298) without requiring more information than the molecular weight of the reacting haloalkane and its gross structural details. Entropy of Activation The entropy of the activated complex, S*, is calculated from the entropy of the reacting haloalkane RH by a series of corrections terms: S* = SttH + AS, + ASV + ASr + AS,r + .01 ASe + AS0 + ASn IJ' where the AS terms represent the cor- rections required in replacing the pro- perties (translation, vibration, rotation, internal rotation, electronic, symmetry, optical isomerism, respectively) of the haloalkane by those of the activated complex. The translational contribution AS, is given by (3/2)R In(MVM); therefore, it will decrease to zero as the mass M of the reagent RH increases (since M* = M + MOH). The rotational contribution AS, is given by (1/2)R ln[(la'blc)*/(lalblc)]. where the three I factors are the principal moments of inertia. Each I depends approximately on M; hence ASr too will decrease to zero as the size of the reagent haloalkane (and hence its mole- cular weight) increases. The vibrational contribution, ASV, is the sum of contribu- tions from each vibrational mode, each of which varies approximately with vibra- tional frequency. In this procedure, several vibrational modes, all of comparable frequencies in different reagents, are replaced by other modes in the activated complexes, for which the frequencies are comparable for different reactions. A similar argument, though somewhat weaker, can be made for internal rota- tions. The remaining three terms on the right-hand side of Eq. (3) are independent of mass. These arguments suggested that there might be some correlation between AS*(298) and M, a suggestion borne out by graphic display of the data. Activation Energy Previously, workers attempted to cor- relate activation energies with bond dis- sociation energies (BDEs) of the dis- sociating bond. This approach was tried with moderate success for (OH + halome- thane) reactions. However, the same could not be done profitably for the haloethanes because BDEs are known for very few of the compounds. Instead, an empirical correlation was made of the activation energies with a set of six struc- tural parameters; each parameter de- scribes the correction to the activation energy of CH4 that must be made as H atoms are substituted by F, Cl, CH3, CH2X, CHX2, or CX3, where X = F or Cl. (At present there are temperature- dependent rate data for only one bro- minated haloalkane; hence, attention was confined to fluorinated and chlorinated compounds until more data become available.) In other words, E(298)/R = E(CH4)/R - aFnF - aC1nC1 - aCH3nCH3 - acH2Xr>CH2X - aCHx2ncHX2 - acx3ncx3 (4) The calculated activation energies for all halomethanes and haloethanes (except CHF3 and CHsCFs, which pose unique problems), which are derived from the experimental values of k(298), were used in deriving the values of the various a,. The results of this effort are given in the following section. Results and Discussion Transition-State Theory Calculations OH + Haloalkanes Transition-state theory calculations were carried out using the vibrational- frequency changes and the entropies of activation listed in the full report. There it was shown that the temperature ex- ponents n for all the a-hydrogen abstrac- tions are 1.6 to 1.7, whereas for the three ^-hydrogen abstraction reactions n = 1.1. For the halomethanes, two models were used for each reaction: one with hindered internal rotation, and one with free internal rotation. The two models were otherwise identical. On the average, the free internal rotation model appears to give slightly better agreement with the data. For all but one reagent, agreement with experimental data is within the ex- perimental uncertainties, and discrep- ancies between experimental and cal- culated rate coefficients are no greater than 25%. The single puzzling exception is CHCI3, for which both models greatly underpre- dict the activation energy and hence the rate coefficients at T > 300 K. To obtain agreement with the data requires a greatly increased AS*(298) — from -28.7 to —25.3 eu — for the free internal rotation case. One way to achieve this is by lowering the four low-frequency vibra- tions in the activated complex to 150 cm"1. However, there is no a priori reason for making the frequencies of this one complex so much lower than those of all the others. The discrepancy between the calculated and experimental values of k(T) for this halomethane suggests either that k(300) is really larger than the measured value or, more likely, that at higher tempera- tures (400-500 K), another process re- moving OH radicals is occurring. Because of the possible serious consequences for the applications of the thermochemical approach to conventional transition-state theory as we have been using it, we recommend that the (OH + CHCI3) re- action rate be carefully remeasured over a temperature range sufficiently wide to eliminate any doubts concerning both the absolute value of the rate coefficients and the activation energy. Empirical Correlations Activation Entropies In the full report, AS*(298) for the free internal rotation model is plotted against the molecular weight M of the reacting haloalkane for all the a-hydrogen ab- stractions. The least-squares fit through all the points is described by AS*(298) (eu/H atom) = -2.2 In M -18.0 or AS'(298) = -2.2 In M- 18.0 + RlnnH where S is in eu (entropy units, or cal mol"1 K"1), M is in daltons, and nH is the number of abstractable a-H atoms. This expression fits all the data with a maxi- mum error of 1.4 eu and an average error of 0.3 eu. [The values of AS* for CH3CC13, CH3CF3, and CH3CF2CI, which have only 0-H atoms, are all 2 to 3 eu larger than Eq. (2) predicts.] When M becomes large enough (approximately 220 daltons), the contributions to AS, and ASr will be close to zero, and AS*(298) per H atom should reach a minimum value of —-30.3 eu. (5a) (5b) Activation Energies Using the approach outlined above, a least-squares fitting program was applied to activation energies for 28 (OH + haloalkane) reactions to solve for the parameters a, of Eq. (4). The derived ------- values, based on E(CH4)/R = 2100 at 298 K, are: a, = 85 aCH2x = 600 aa = 515 aCHx2 = 650 aCH3 = 950 aCX3 = 250 The values of E(298)/R predicted with Eq. (4) are compared with the experi- mentally derived values in the full report. The discrepancy between predicted and derived values is never worse than 570, i.e., an error in E of 1.1 kcal/mol, and in most casts is considerably smaller: The average error is 150, i.e., 0.3 kcal/mol. This approach to calculating the en- ergetics of a reaction is not novel: It relies on what is essentially a bond additivity argument. Heicklen3 explored a similar approach to predicting BDEs, from which he predicted rate coefficients for reactions of OH radicals with a wide variety of organics. The difference here is the use of the approach directly for calculating activation energies, rather than BDEs. This shortcut circumvents the problem of the uncertainties in many BDEs — gen- erally 1 to 2 kcal/mol. These uncertainties may introduce errors into the bond additivity expressions for predicting un- measured BDEs and hence in activation energies. Since the correlation factor in the equation relating activation energies with BDEs is approximately 0.4, a 2- kcal/mol error in BDE imparts an error to k(298) of a factor of 3.8. A "Universal" Rate Coefficient Expression Equation (4) for E(298)/R and Eq. (5) for AS*(298) can be substituted in the general expression for k(T) from transi- tion-state theory to yield a general rate coefficient expression for (OH + halo- alkanes) that depends only on the molecular weight of the reagent and the number of various substituents. We can force a T1 5pre-exponential tempera- ture dependence to agree with the results of the calculations. The A factor is determined by requiring the expres- sion to yield the proper values of k(298) and E(298). The result is k(T) = nH 106 s M-' T15 exp(-B/T) (6) where M is in daltons and T is in kelvins. The pre-exponential factors have been modified slightly to round off the ex- ponent of the molecular-weight factor M. 3Heicklen, J. Int. J. Chem. Kinet, 13 651, 1981 The term B is calculated from E(298)/R obtained from Eq. (4): B = [E(298)/R - 450]. The rate coefficients resulting from Eq. (6) are shown for several typical re- actions in figures given in the full report. [Equation (6) does not apply to halo- ethanes with only /3-hydrogens.] For CH2CICHCI2 and CH2FCHF2, Eq. (6) was applied separately to the two different kinds of H atoms and the results summed together. In general, the rate coefficients calculated by Eq. (6) disagree with experi- mental data (where they exist) by less than a factor of 3. Conclusions Four principal conclusions emerge from the present study. The first is that a reasonable set of assumptions can be applied consistently to all but one of the reactions considered here to obtain transition-state models that lead to cal- culated rate coefficients in good agree- ment with experimental data. This is true even though the A factors at 298 K are not in particularly good agreement with experimental values. The good agreement is a result of the tendency of activation entropies and energies to compensate one another. The second conclusion is that one of the reactions — that of (OH + CHCI3) — is anomalous. Either the experimental data are flawed or there is something unusual about the dynamics of this reaction, re- quiring a qualitatively different activated complex to obtain agreement between calculations and experiments. A new ex- perimental investigation is recommended. Third, the above two conclusions to- gether demonstrate that, while one might be able to tailor a model for the activated complex to force reasonable agreement with a particular set of experimental data for one reaction, simultaneous agreement with data for several homologous re- actions is by no means a fortuitous achievement. The greater constraints imposed by treating an entire family of reactions together rather than a single reaction give greater confidence that the model and the resulting calculations are physically meaningful. Finally, we used the calculations just discussed as a guide for generating empirical expressions for AS*(298) and E(298) for a-hydrogen abstraction re- actions of OH radicals from fluorinated and chlorinated methanes and ethanes. The calculated entropies and energies of activation were then applied to generate a "universal" rate coefficient that depends only on the molecular weight and the number of abstractable a-hydrogen atoms of the reagent haloalkane. This expression predicts rate coefficients within a factor of about 3 of the experimental data for all 26 reactions for which data were available (and generally much better), and offers promise as a predictive tool when no reliable experimental data are available. ------- Norman Cohen is with Aerospace Corporation, EIS eg undo, CA 90245. Bruce W. Gay, Jr.. is the EPA Project Officer (see below). The complete report, entitled "Structure-Reactivity Relationships for Predicting Environmentally Hazardous Chemicals," (Order No. PB87-140 497/AS; Cost: $9.95, subject to change) will be available only from: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 Telephone: 703-487-4650 The EPA Project Officer can be contacted at: Atmospheric Sciences Research Laboratory U.S. Environmental Protection Agency Research Triangle Park, NC 27711 United States Environmental Protection Agency Center for Environmental Research Information Cincinnati OH 45268 Official Business Penalty for Private Use $300 EPA/600/S3-86/072 OCOC329 PS *G£NCr ------- |