DFT Study of Trichloroethene Reaction with Permanganate in

Mar 7, 2011 - The mechanism of the environmentally important reaction between permanganate anion and trichloroethene (TCE) has been studied theoretica...
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DFT Study of Trichloroethene Reaction with Permanganate in Aqueous Solution Pawez Adamczyk, Agnieszka Dybala-Defratyka, and Piotr Paneth* Institute of Applied Radiation Chemistry, Faculty of Chemistry, Technical University of Lodz, Zeromskiego 116, 90-924 Lodz, Poland

bS Supporting Information ABSTRACT: The mechanism of the environmentally important reaction between permanganate anion and trichloroethene (TCE) has been studied theoretically using modern DFT functional. It has been shown that IEFPCM/M05-2X/aug-cc-pVDZ theory level yields activation parameters and carbon isotopic fractionation factor in excellent agreement with the experimental data. Obtained results indicate that this reaction proceeds via the 3 þ 2 mechanism with a very early transition state, in which the new C-O bonds are formed only in about 20%. An alternative, stepwise mechanism that involves initial formation of a single new C-O bond and a C-Mn bond, followed by rearrangement to the permanganate-TCE adduct, has been found to be more energetically demanding and in disagreement with the experimental isotopic fractionation.

’ INTRODUCTION Chloroethylenes, such as trichloroethylene (TCE), are among the most important environmental contaminants.1 TCE, which is commonly used as an industrial solvent2 in cleaning machinery, is widely released into subsurface groundwater by a significant number of companies in the EU and the USA,3,4 which makes it the most frequently detected environmental pollutant in water.5 Suspicion of TCE being a human carcinogen6 and also other possible effects on human health such as an impact on the female reproductive functions7 or possible association with congenital heart defects8-12 have made degradation of TCE extremely important. Additionally, in groundwater TCE can undergo an anaerobic enzymatic reductive dechlorination to cis-dichloroethylene (cDCE), which is also considered a possible human carcinogen,6 and vinyl chloride (VC), which is a known human carcinogen.13 Degradation of TCE as well as other chlorinated aliphatic compounds can be carried out in several ways, including chemical and biological approaches, which can be divided into two groups - reductive dehalogenation14-17 and oxidation, which can be further divided into pure chemical oxidation18 and photochemical oxidation.19,20 Chemical oxidation of groundwater subsurface pollutants is usually performed by injections of a chemical oxidant such as permanganate, hydroxyl peroxide, ozone, or persulfate, alone or in combination with other adjuvants.14-16,18-24 Among various treatments of TCE, chemical oxidation with permanganate is most common due to its effectiveness, rapidity, selectivity (in contrast to e.g. hydroxyl peroxide), wide pH range, and relatively low cost.24 The overall mechanism of permanganate oxidation of ethylene and some of its derivatives is well studied25,26 although some controversy regarding the mechanism in the case of TCE remains (see Discussion for details).18 Most frequently it is considered r 2011 American Chemical Society

to be a complex mechanism with the first step, formation of the cyclic hypomanganate ester via the 3 þ 2 electrocyclic addition of permanganate to the carbon-carbon double bond (illustrated by the upper part of Figure 1), being ratedetermining. Environmental importance of the degradation of TCE prompted us to use this reaction as a model for finding a level of theory adequate for predicting reactivity of environmentally important dechlorinations. Herein we report Density Functional Theory (DFT) calculations of the mechanism of the reaction between TCE and permanganate (Figure 1) carried out with the aim of finding a robust, widely applicable method for modeling dehalogenation processes. As the reference points we used experimental data on the Gibbs free energy of activation for this reaction18,27 and carbon isotopic fractionation.28,29 After establishing the adequate theory level we have applied it to learn details of the mechanism of TCE transformation.

’ METHODS AND RESULTS Calculations were carried out using two versions of the Gaussian package (G09, rev.A.0230 and Gaussian03-MN-GFM31) and Jaguar ver.7.6 program of the Schrodinger package32 with various combinations of B3LYP,33-35 CAM-B3LYP,36 MPW1K,37 M05,38 M052X,39,40 M06,40,41 M06-2X,40,41 M06-L,42 M08-HX,43 M08SO,43 LC-wPBE,44-48 LC-TPSS,48,49 MP2,50 and B2PLYP51 levels of theory and IEFPCM52 with UA053 and UFF54 atom radii, PBF,55-57 and SMD58 continuum solvent models of water. The majority of calculations were carried out using the 6-31G,59-61 Received: September 24, 2010 Accepted: February 22, 2011 Revised: February 16, 2011 Published: March 07, 2011 3006

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Figure 1. Mechanism of the 3 þ 2 (top) and 2 þ 2 (bottom) paths of electrocyclic addition of permanganate anion to TCE.

basis set augmented with a single set of diffuse functions,62 a set of d functions on nonhydrogenic atoms, and a set of p functions on hydrogen atoms;63 6-31þG(d,p), however 6-311þþG (d,p),64-66 def2-TZVPP,67 aug-cc-pVDZ,68-71 and aug-cc-pVTZ72 basis sets were also tested. Geometry optimizations were carried out using default convergence criteria. Vibrational analysis was performed to confirm that the obtained structures are stationary points on the potential energy surface and correspond to either a local minimum (3n-6 real normal modes of vibrations) or a transition state (exactly one imaginary frequency), to calculate free energies of activation (after inclusion of thermal and ZPE contributions), and to calculate isotopic fractionation factors. In all cases full optimizations were carried out. IRC73 calculations confirmed that the transition state structures correspond to the reaction presented in Figure 1. Carbon 13C isotopic fractionation factors, ε (%), were obtained, based on the rule of geometric mean,74 from the kinetic isotope effects calculated for both carbon atoms using complete Bigeleisen equation75 as implemented in the ISOEFF program.76 The obtained results of activation free energies and isotopic fractionations with different combinations of functionals, solvent models, and basis sets are presented in Table S1 in the Supporting Information. Figure 2 illustrates the transition state structure and provides the atom numbering scheme. Details of geometric data of the obtained transition state structures, which include values of bond lengths, the dihedral angle defining the twist of the oxygen atom O8 toward the hydrogen atom of the permanganate anion, and the imaginary frequencies are provided in Tables S2 and S3 of the Supporting Information.

’ DISCUSSION One of the most rapidly developing techniques in studies of environmentally important reactions is compound specific isotopic analysis (CSIA).77-79 The reaction between the permanganate anion and TCE has been studied by carbon CSIA at different reaction conditions. In the first report28 an experiment with a significant headspace was described. This experimental condition allowed for partition of TCE between solution and the gas phase, leading to a too low value of the carbon fractionation factor of -21.4 %. Later studies29 were carried out with no headspace and two different conditions with excess and limited permanganate supply. Similar values in both experiments have been obtained. We have adopted the more precise value

Figure 2. Transition state structure of the 3 þ 2 reaction mechanism.

of -25.1 ( 0.4 % for comparison with the values calculated theoretically. Since no temperature has been indicated we have assumed that the experiments were carried out at room temperature and used it in calculations of the kinetic isotope effects, KIE, that are related to isotopic fractionation factors, ε, by eq 1.80 ε ¼ ð1=KIE - 1Þ 3 1000

ð1Þ

CSIA analysis averages isotopic composition of atoms of a particular element present in the studied compound and since TCE contains two carbon atoms, their averaged theoretical ε are given in Table S1 (see the Supporting Information). The higher the position in this table of the results obtained at different theory levels, the smaller their absolute deviation from the experimental data. Out of the studied theory levels only those reported in the first three rows are within the reported confidence interval. It should be kept in mind though that theoretical values calculated from the Bigeleisen equations are obtained within the conventional transition state theory with harmonic normal modes and rigid rotor approximations. Typically, frequencies are scaled to account for anharmonicity. In terms of isotope effects, frequency scaling leads to lowering of their theoretical values; however, tunneling correction, which was shown to be important even for heavy atoms,81 tends to increase their values and these two effects nearly cancel out. For example, the value of -24.93% obtained from the unscaled frequencies at the PCM/B3LYP/6-31þG(d, p) level changes to -24.45% when the scaling factor82 for this theory level is used but reaches -24.96 % when tunneling is also included via the one-dimensional Wigner correction.83 We consider theoretical results that are within 1% (2SD) of the experimental value as acceptable; such results were obtained for theory levels reported in the first six rows of Table S1. Because of the importance of the studied reaction in bioremediation, its energetics has also been studied in detail. The values of the enthalpy and entropy of activation reported in 3007

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Environmental Science & Technology literature18 allow to estimate the Gibbs free energy of activation to be equal 10.3 kcal/mol. Since no estimation of errors has been provided, we consider the value of 0.9 kcal/mol reported in earlier studies of this reaction energetics84 as a fair estimation of the standard deviation. Only six values obtained theoretically are within the experimental uncertainty ((2SD). It should be noted, however, that several factors hidden in technical details of the calculations may influence the results. The energy in solution may be calculated with the solute’s electrostatic potential selfconsistent with the solvent reaction field85 or not. Furthermore, Wheeler and Houk showed recently86 that meta-GGA functionals are prone to grid errors. For example, changing the grid for DFT calculations from fine (default) to ultrafine increases ΔG‡ by about 0.2-0.3 kcal/mol and lowers ε by about 1%. Out of the six theory levels that yielded acceptable carbon isotopic fractionation factors, only three (PCM/M05-2X/augcc-pVDZ, PCM/M05-2X/aug-cc-pVTZ, and PCM/M08-SO/631þG(d,p)) predicted correctly the free energy of activation. Out of these, wide availability of the M05-2X functional in programs for quantum-mechanical calculations compared to M08-SO, and the cost of calculations, we have selected the PCM/M05-2X/aug-cc-pVDZ level for interpreting the mechanism of the reaction between TCE and permanganate. Before we move to detailed analysis of the mechanism, in the following paragraphs we comment on the performance of other theory levels tested in this study. Apart from several popular DFT methods we have tested three post-Hartree-Fock levels; CCSD, MP2, and B2PLYP. Both MP-based methods, MP2 and B2PLYP, gave wrong imaginary frequencies of 1346i and 1063i cm-1, respectively (see Table S2 in the Supporting Information), heavily overestimating the contribution of the hydrogen atom to this vibration. Poor performance of the MP2 level for reactions considered herein has been evidenced earlier in the literature.26 Furthermore, B2PLYP (and M05) predicted formation of the two C-O bonds not to be concerted. At the B2PLYP level the formation of the C1-O7 bond is significantly more advanced in the transition state than that of the C2-O8 bond, the difference in length is nearly 0.24 Å. The corresponding difference at the M05 level of theory approaches 0.12 Å also indicating lack of synchronicity in the formation of these new bonds. Other theory levels give the difference between these bonds not exceeding 0.04 Å. CCSD, on the other hand, heavily underestimates isotopic fractionation factor (see Table S1). It should be kept in mind that these theory levels converge slowly with basis sets and those used here might be too small. The use of large basis sets (CBS-type) with these levels, on the other hand, makes their applicability limited due to the computational requirements.87 Good performance of the PBF solvent model in predicting activation parameters has been noticed. Results of free energies of activation are collected in Table S1. In several cases these values are substantially larger than the experimental value. This is the case when a DFT method yielded a hydrogen-bonded complex of the reactants, as illustrated by the structure presented on the right in Figure S1 in the Supporting Information, rather than the proximity complex that leads to reaction. B3LYP, CAM-B3LYP, MPW1K, LC-WPBE, and LCTPSS functionals optimized structures of the reactants were hydrogen-bonded structures. The same result was obtained with the M05-2X functional when calculations did not involve any solvent model. We have evaluated that the hydrogen bonded complex is stabilized over the proximity complex by about 3 kcal/ mol in the case of B3LYP calculations for which both types of

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complexes were obtained. Typical proximity complex obtained in the remaining calculations is illustrated by the structure on the left side of Figure S1. Both structures in this figure are shown with the plane containing TCE atoms perpendicular to the plane of the page. It is interesting to note that M05-2X outperforms newer functionals from the same family and also M05 and M06 methods that are recommended for systems containing transition metals. We have, however, arrived at a similar conclusion earlier when studying spectral properties of iridium complexes.88 We now move our discussion to the mechanism of the reaction between TCE and permanganate. The chemical nature of the reaction is illustrated by Figure 1 as it emerges from the calculations at the selected PCM/M05-2X/aug-cc-pVDZ theory level. The reaction proceeds with a moderate activation barrier of less than 10 kcal/mol and a very large heat of reaction, with the adduct being more stable than the reactants by more than 100 kcal/mol. This huge exothermicity causes that the transition state is very early; formation of the two C-O bonds is practically concerted with the bonds lengths equal to 2.17 and 2.15 Å that correspond to the Wiberg bond orders89 of the forming C-O bonds of 0.22 and 0.24 for C1-O7 and C2-O8, respectively. At the same time partial atomic charges obtained from the NPA analysis90 indicate that there is practically no charge transfer from the permanganate anion to TCE in the transition state. The dihedral angle, Φ, defined by atoms Mn-O7-C1-C reflects asymmetry of the transition state induced by the presence of one hydrogen atom in the TCE molecule. This angle changes from the value of 42.4 degrees in the proximity complex to 19.5 degrees in the transition state and -32.6 degrees in the product. It has been postulated in the literature18 that the reaction between TCE and permanganate proceeds via the 2 þ 2 attack as illustrated in the bottom part of Figure 1 based on the assumption that this arrangement better explains interactions of electron-rich permanganate with carbon-carbon double bond91 and the predictions of a lower barrier92 than that of the 3 þ 2 reaction. We have studied this reaction path on the selected theory level and have found that it in fact corresponds to a stepwise formation of the C-O bonds. In agreement with literature, the transition state corresponding to rearrangement to the TCE-permanganate adduct is lower in energy than the one obtained for the concerted 3 þ 2 mechanism by about 11 kcal/ mol. This transition state structure is illustrated by the structure TS2 on the right side of Figure S2 in the Supporting Information. The imaginary frequency of 243i cm-1 that characterizes this transition state corresponds to the formation of the C2-O8 bond. Further calculation using IRC73 protocol disclosed, however, that this step is preceded by an initial formation of the C1O7 bond and that the transition state TS1 of this step (given on the left side of Figure S2) corresponds to the free energy of activation of 27.2 kcal/mol, much higher than experimentally observed (see Figure 3). The imaginary frequency of 774i cm-1 corresponds to the formation of the C-O bond. Calculated carbon isotope fractionation factors for both these transition states are equal to -16.9 and -21.9, respectively, indicating that this mechanism is not supported by experimental observations. In summary, very good results for both activation parameters and isotopic fractionation factors are simultaneously obtained with the M05-2X and M08-SO functionals with DZ-quality basis sets and the PCM continuum solvent model. Since the latter is not widely available, we have used the former in studies of the reaction of permanganate with TCE. Our results support recent communications from other laboratories that dispersion 3008

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Figure 3. Energy diagram of the TCE-permanganate reaction paths.

corrected Truhlar’s functional M05-2X yields good results in systems containing an alkene coordinated to a transition metal93 and in E2 or SN2 reactions of X- þ CH3CH2X (X = F, Cl).94 This theory level can thus be used for studying a whole range of environmental transformation reactions. Results obtained at the PCM/M05-2X/aug-cc-pVDZ level of theory for the 3 þ 2 reaction between permanganate anion and TCE indicate that this reaction proceeds via a very early transition state in which the new C-O bonds are formed only in about 20%. The alternative mechanism involving stepwise formation of the two C-O bonds is not supported by the experimental results; calculated overall barrier is much higher and predicted carbon isotopic fractionation is much smaller than observed.

’ ASSOCIATED CONTENT

bS

Supporting Information. Tables reporting activation free energies (kcal/mol) and carbon isotopic fractionations (%), key geometrical parameters of the calculated transition state structures of the 3 þ 2 reaction at all studied levels of theory, structures of proximity complexes and transitions states of the 2 þ 2 reaction, and the Cartesian coordinates for transition states for both mechanisms. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Phone: þ48 42 631 3199. E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the EU grant isoSoil, FP7-212781 (2009-2012) and the grant from the Polish Ministry of Science and Higher Education 1130/7.PRUE/2009/7. Access to supercomputing facilities at ICM, PCCS, and Cyfronet (Poland) and MSI (U.S.A.) is gratefully acknowledged. ’ REFERENCES (1) ATSDR (Agency for Toxic Substances and Disease Registry) 2007 CERCLA Priority List of Hazardous Substances, U.S. Department of Health and Human Services, Agency for Toxic Substances and

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