AN AB INITIO-BASED SCREENING TOOL FOR THE 

ATMOSPHERIC LlFETIMES OF HALON REPLACEMENTS 

Robert E. Huie, Florent Louis, Carlos A. Gonralez, and Michael J. Kurylo 

National Institute olStandards & Technology 

INTRODUCTION 

The decision to phase out the use of halons due to their role in stratospheric ozone loss has led to 

accelerated efforts to find “environmentally friendly” replacements. Thus, the need has arisen for 

an efficient means to evaluate the large suite of proposed alternatives for environmental acceptability. In particular, this means obtaining one of the most important pieces of information 

relating to the atmospheric fate of volatile species: the reactivity towards the hydroxyl radical. 

The reaction with tropospheric OH typically controls the atmospheric lifetime of many substances and is thus a starting point in the evaluation of its acceptability. Carrying out laboratory 

measurements on all the proposed replacements is an expensive proposition. made worse by the 

fact that many of the compounds would havc to be synthesized and provided in sufficient purity 

for kinetic measurements. Clearly, the development of screening tools capable of predicting the 

properties important in assessing environmental persistence would be beneficial to this proce 

STATEMENT OF THE PROBLEM 

Over the years. various structure-activity relationships have been used to estimate rate constants 

for chemical reactions, including those of the hydroxyl radical. These usually require a substantial amount of data on a suite of chemicals to provide reliable predictions for similar compounds. 

The magnitude and difficulty of this task is illustrated by the results of studies on hydrofluoroethers. Normally, it has been assumed that the presence of an ether linkage decreases the bond 

strength of adjacent C-H bonds and, thus, increases their reactivity. In comparing fluoroalkanes 

and the corresponding fluoroethers, however, both activation and deactivation are observed 

(Figure 1) [I]. An analysis of these results has not revealed any consistent pattern, suggesting 

that experimental kinetic studies for many morc fluoroethers would need to be conducted. 

Rather than taking this brute force approach, we have decided to explore the possibility ofapplying fundamental theory to the problem of predicting reactivity. We initiated a systematic study of 

the application of uh initio electronic structure calculations combined with transition state theory 

to the kinetics of hydrogen-atom abstractions by hydroxyl radicals. The objectivc was to devclop 

efficient and reliable computational chemistry “screening tools” useful in predicting the fate of 

halon replacements once they are released into the atmosphere. 

DEVELOPMENT OF THE METHODOLOGY 

The initial study [2] focused on the reaction: OH + CHZBr2 + HzO + CHBrz 

Dibrornomethane was chosen because (a) reliable experimental kinetic data are available and 

(b) because bromine is an important elcment in fire suppression. Further, thc relatively large 

electronic system associated with the bromine atom makes this a stringent test of the proposed 

quantum chemical methodologies. 

Ilalan Option\ Tcchnicnl Working Confcrcncc 2-4 May 2000 87 
, CHpO-CH3 t 

10''~ 

Figure 1. Graph of the relationship between the reactivity of OH towards 

fluoroalkanes and fluoroethers [ 11. 

Ab initio calculations were carried out with M@ller-Plesset second and fourth order perturbation 

theory (MP2 and MP4), and the coupled cluster method, in the space of singles, doubles and 

triple electronic excitations, CCSD(T). Full geometry optimization and vibrational frequency 

calculations at the MP2 level were performed on reactants, products, and the transition state 

using the 6-31 lG(d,p) and 6-31 IG(2d,2p) basis sets. The geometry parameters optimized at the 

MP2/ 6-31 IG(2d,2p) level of theory were used in single-point energy calculations with 

increasing basis set sizes, from 6-31 1G(2d,2p) to 6-31 I++G(3df,3pd) at both the MP2 and 

MP4(SDTQ) levels of theory. Canonical transition state theory was used to predict the rate 

constants as a function of the temperature (250-400 K) making use of the expression: 

where: QTS (T), QoH(T) and Q"lk(T) are the total partition functions for the transition state, 

hydroxyl radical, and the haloalkane at temperature T; AE is the activation energy including 

thermal corrections to the internal energy and zero-point energy: kg is Boltzman's constant; and 

h is Planck's constant. T(T) in the equation indicates the corresponding tunneling correction at 

temperature T. 

Three different expressions were tested for the tunneling correction: the closed-form approximation by Wigner: and calculations based on the symmetrical and unsymmetrical Eckart 

potentials. These three expressions were then applied in two different ways to obtain r(T). The 

first approach is the normal way in which these corrections are calculated, making use of the 

88 Halon Options Technical Working Conference 2-4 May 2000 
imaginary frequency, VI. calculated at the same level of theory as the forward and reverse 

reaction barriers. In the second approach, the reaction path was calculated by the intrinsic 

reaction coordinate (IRC) algorithm and fit to the Eckart potential in the region of the transition 

state. In this case, vi was an adjustable parameter in the fit. The results of these fits for the 

reaction of OH with CHIBrz are shown in Figures 2 and 3 [3-61. 

2.5 3.0 3.5 4.0 

IOOOIT, K~’ 

Figure 2. Temperature dependence of the 

rate constants for the reaction of 

CHzBrz with OH computed at 

PMP4 (SDTQ)/6-3 1 I ++G 

(3df,3pd)//MP2/6-3 I IG(2dJp) 

using the imaginary frequency 

computed at the MP2/6-3 I 1 G 

(2d.2~) level. Solid line: Wigner 

tunneling correction; short dashed 

line: symmetrical Eckart tunneling 

correction; and dash-dotted line: 

unsymmetrical Eckart tunneling 

correction [2]. 

3.0 3.5 4.0 

t. 

2.5 

1000/T, K-‘ 

Figure 3. Temperature dependence of the rate 

constants for the reaction of CH2BrZ 

with OH computed at PMP4 (SDTQ)/ 

(2d,2p). Solid line: Wigner tunneling 

correction; short dashed line: symmetrical Eckart tunneling correction; 

and dash-dotted line: unsymmetrical 

Eckart tunneling correction. In all 

cases, the imaginary frequency was 

obtained by the fitting of the Eckart 

function to the results of the MP2/6- 

31 IG (2d,2p) IRC [2]. 

6-3 1 I ++G (3df, 3pd)//MP2/ 6-3 1 I G 

1t is clear that calculations with the unsymmetrical Eckart treatment for tunneling not only do not 

reproduce the magnitude of the rate constants well, they do not even reproduce the shape of the 

Arrhenius plot. Interestingly, the best fits are obtained when the Wigner correction is utilized. 

Although excellent agreement with experiment is obtained when the imaginary frequency was 

derived from a fit to the IRC, reasonable agreement, within a factor of two, was obtained when vi 

was obtained directly from the transition state calculations. This is a considerably less expensive 

approach and will be employed in the suhsequcnt calculations. 

In the second phase of the project, kinetic parameters were calculated for a series of 12 partially 

halogenated methanes for which reliable experimental data exist [7]. Following the results for 

dibromomethane, geometry optimization and vibrational frequency calculations were perfomied 

for reactants, transition states, and products at the MP2/6-31 lG(2d.2~) level of theory. SingleHalon Options Technical Working Cr,nlcrcncc 2-4 May XKIO 89 
point energy calculations were carried out at the PMP4(SDTQ) level with both 6-31 1G (3df,2p), 

and 6-31 I++G(3df,3pd) basis sets. Then, canonical transition state theory with Wigner's tunneling correction was used to predict the rate constants as function of temperature. The results of 

these calculations at 298 K are presented in Figure 4. 

10-15 10-14 10-13 lo"2 

kexp (298 K), cm3 molecule-' s" 

Figure 4. Comparison of experimental and calculated rate constants. Open symbols, PMP4 

(SDTQ)/6-31 lG(3df,2p); closed symbols, PMP4(SDTQ)/6-3 1 l++G(3df,3pd). 

Circles, monosubstituted; triangles, disubstituted; squares, trisubstituted. 

Interestingly, the rate constants calculated with the smaller basis set were found to be in better 

agreement with experimental values than those calculated with the larger basis set. The Afactors computed at both levels of theory are very close, and they are found to be within a factor 

of 1 .O - 2.5 of the values reported in the literature. As with the rate constants at 298 K, the values 

of E& computed with the smaller basis set are closer to the experimental values (max. deviation 

= 15.6%, average deviation of 9.4%) when compared to the corresponding En's computed with 

the larger basis sets (max. deviation = 5 1.4%, average deviation = 19.4%). Overall, these results 

suggest that PMP4(SDTQ)/6-3 I lG(3df,2p)//MP2/6-3 1 1 G(2d,2p) is a good compromise between 

accuracy and computational expense in the theoretical treatment of hydrogen abstraction reactions between OH radicals and halomethanes, possibly as a result of a systematic cancellation of 

errors between the convergence rate of the perturbation theory and the size of the basis sets used. 

APPLICATION OF THE METHODOLOGY 

In the third phase of the project, we have calculated rate constants for a series of brominecontaining halomethanes for which experimental data do not exist [8]. These calculations have 

resulted in the following rate constants at 298 K: 

90 Halon Option\ Technicdl Working Conference 2-4 May Zoo0 
Bromoalkane k x cm3 s-' 

CHzFBr 3.0 

CHFBrz 10.0 

CHFClBr 6.8 

CHCIzBr 26 

CHClBrz 35 

In general, we consider these rate constants to be accurate to within a factor of 2 to 3. although it 

was apparent from the set of 12 halomethanes originally tested that the level of agreement with 

measurements worsened with increasing reactivity. From the point of view of a screening tool, 

this is not a problem since these reactions are already quite fast and hence environmental 

persistence is diminished. 

Finally, the reason we started this project was the difriculty in rationalizing the behavior ofthe 

hydrofluoroethers by simple structure-activity concepts. Therefore, we have carried out some 

preliminary calculations on the reactions of three selected ethers and their corresponding alkanes. 

These calculations are not yet complete in that we have not yet applied hindered rotor corrections 

to the transition state partition functions, nor have we taken into account all possible rotational 

conformers. Yet the calculations are sufficient to ascertain if this level of theory will correctly 

predict the observed reactivity patterns. Below we present the ratio of the rate constants for the 

alkane relative to those of the ethers at 298K: 

EthaneiEther Theorv Exveriment 

CHICF~ICHIOCFI 14.3 10.0 

CHF~CF~ICHF~OCF-I 0.3 0.2 

CHFzCHFz/CHF:OCHF2 0.2 0.4 

These results demonstrate that this basic approach is a viable method of predicting the reactivity 

of new functional groups towards the hydroxyl radical and thus can form a component of a 

screening tool for the environmental acceptability of proposed fire suppressants. 

CONCLUSIONS 

These studies have been quite successful, and we have been able to demonstrate that a relatively 

reasoliable level of theory is sufficient to predict rate constants to ii degree of accuracy sufficient 

for a screening tool. These full transition state calculations are still difficult, however, for larger 

systems. Therefore, we have been exploring additional strategies for the prediction of rate 

constants. Since the thermodynamics are far easier to calculate than reaction kinetics, we have 

begun looking into applying the simple relationship between rate constant and reaction enthalpy 

and the rate constant embodied in the Evans-Polanyi equation. We have found that there is a 

simple quadratic relationship between the logarithm of the rate constant and the calculated 

reaction enthalpy for the haloniethanes. It remains to be seen if we can make this concept work 

beyond a simple homologous series. 

Halon Option5 Technical Worhing Conlcrcncc 3-4 May 2000 9 1 
ACKNOWLEDGMENT 

We thank Drs. Marc Nyden and Vladimir Orkin of NIST for helpful conversations. This work 

was supported by the Upper Atmosphere Research Program of the National Aeronautics and 

Space Administration and by the Next-Generation Fire Suppression Technology Program, funded 

by the Department of Defense Strategic Environmental Research and Development Program 

under MIPR number W74RDV73243630. 

REFERENCES 

1. Orkin, V.L., Villenave, E., Huie, R. E., and Kurylo, M.J., “Atmospheric Lifetimes and Global 

Warming Potentials of Hydrofluoroethers: Reactivity Toward OH, UV Spectra, and IR 

Absorption Cross Sections,” J. Phys. Chem. A 103,9770-9779, 1999. 

2. Louis, F., Gonzalez, C., Huie, R.E., and Kurylo, M.J., “An Ab Inirio Study of the Reaction of 

Halomethanes with the Hydroxyl Radical. Part 1: CH2Br2,”J. Phys Chem. A 104, 2931- 

2938,2000. 

3. Zhang, D.Q., Zhong, J.X., and Qiu, L.X., “Kinetics of the Reaction of Hydroxyl Radicals 

with CH2Br2 and Its Implication in the Atmosphere,”J. Atmos. Chem. 27, 209-215, 1997. 

4. DeMore, W.B., “Experimental and Estimated Rate Constants for the Reactions of Hydroxyl 

Radicals with Several Halocarbons,” J. Atmos. Chem. 100,58 13-5820, 1996. 

5. Orlando, J.J., Tyndall, G.S., Wallington, T.J., and Dill, M., “Atmospheric Chemistry of 

CH2Br2: Rate Coefficients for Its Reaction with CI Atoms and OH and the Chemistry of the 

CHBrzO Radical,” Int. J. Chem. Kinet. 28, 433-442, 1996. 

6. Mellouki, A., Talukdar, R.K., Schmoltner, A-M, Gierczak, T., Mills, M.J., Solomon, S., and 

Ravishankara, A.R., “Atmospheric Lifetimes and Ozone Depletion Potentials of Methyl 

Bromide (CH3Br) and Dibromomethane (CH2Br2).” Geophys. Res. Left. 19,2059-2062, 

1992. 

7. Louis, F., Gonzalez, C., Huie, R.E., and Kurylo, M.J., “An Ah Initio Study of the Kinetics of 

the Reactions of Halomethanes with the Hydroxyl Radical. Part 2: A Comparison between 

Theoretical and Experimental Values of the Kinetic Parameters for 12 Partially Halogenated 

Substituted Methanes,”J. Phys Chem. A, accepted, April 2000. 

8. Louis, F., Gonzalez, C., Huie, R.E., and Kurylo, M.J., “An Ab Znitio Study of the Kinetics of 

the Reactions of Halomethanes with the Hydroxyl Radical. Part 3. Reactivity Trends and 

Kinetics Parameter Predictions for the Potential Halon Replacements CHzFBr, CHFBr2, 

CHFCIBr, CHCIzBr, and CHCIBr2,”J. Phys. Chem. A, submitted, May 2000. 

92 Halon Options Technical Working Conference 2-4 May 2000 

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