ARTICLE pubs.acs.org/est
Reactivity of Aqueous Phase Hydroxyl Radical with Halogenated Carboxylate Anions: Experimental and Theoretical Studies Daisuke Minakata,†,* Weihua Song,‡ and John Crittenden† †
School of Civil and Environmental Engineering, Georgia Institute of Technology, 800 West Peachtree Street, Suite 400 FH, Atlanta, Georgia 30332, United States ‡ Department of Environmental Science and Engineering, Fudan University, Shanghai 200433, P. R. China
bS Supporting Information ABSTRACT: With concerns about emerging contaminants increasing, advanced oxidation processes have become attractive technologies because of potential mineralization of these contaminants via radical involved reactions that are induced by highly reactive hydroxyl radical. Considering the expensive and time-consuming experimental studies of degradation intermediates and byproduct, there is a need to develop a firstprinciples computer-based kinetic model that predict reaction pathways and associated reaction rate constants. In this study, we measured temperature-dependent hydroxyl radical reaction rate constants for a series of haloacetate ions and obtained their Arrhenius kinetic parameters. We found a linear correlation between these reaction rate constants and theoretically calculated aqueous-phase free energies of activation. To understand the quantitative effects on entropy of solvation due to solvent water molecules, we calculate each portion of the entropic energies that contribute to the overall aqueous phase entropy of activation; cavity formation is a dominant portion. For the series of reactions of hydroxyl radical with carboxylate ions, the increase in the entropy of activation during the solvation process is approximately 1015 cal mol1K1 because of interactions with solvent water molecules and the transition state. Finally, charge distribution analysis for the aqueous-phase reactions of hydroxyl radical with acetate/haloacetate ions reveals that in the aqueous phase, the degree of polarizability at the transition state is less substantial than those that are in the gaseous phase resulting in a high charge density. In the presence of electronegative halogenated functional groups, the transition state is less polarized and hydrogen bonding interactions are expected to be weaker.
’ INTRODUCTION Advanced oxidation processes (AOPs) are attractive and promising technologies for the control of emerging contaminants.13 At ambient temperature and atmospheric pressure, AOPs produce a highly reactive electrophile, hydroxyl radical (HO•),4,5 which rapidly and nonselectively reacts with most electron-rich sites on organic contaminants. This potentially leads to complete mineralization of emerging contaminants. The reactivity of a number of contaminants has been extensively studied6 using electron pulse radiolysis techniques,7,8 and the degradation pathways of certain organic compounds have been experimentally investigated.911 However, the complicated, radical-involved reaction mechanisms make experimental studies of AOPs very expensive. In addition, it is timeconsuming to study the numerous chemicals that are commercially available.12 Accordingly, there is a need to develop a first-principles computer-based kinetic model that assesses the efficacy of AOPs. Pfaendtner and Broadbelt (2008)13 recently created a computer-based mechanistic model of condensed-phase auto-oxidation of hydrocarbons. However, an automated kinetic model has not yet to be developed for aqueous-phase AOPs. The automated kinetic model enumerates three major modules: (1) reaction pathway generator; (2) reaction rate constant predictor, and r 2011 American Chemical Society
(3) ordinary differential equations (ODEs) solver. We previously developed an automated reaction pathway generator for aqueous phase AOPs.14 For reaction rate constant predictors, a group contribution method (GCM) predicts HO• reaction rate constants for a wide range of organic compounds,15 and linear free energy relationships (LFERs) can be used for predicting HO• reaction rate constants for neutral aliphatic compounds and alkenes.16 Once the rate constant predictor module is completed, with toxicity estimators, the DGEAR algorithm17 will enable us to solve ODEs of concentrations of each species for target compounds, and intermediate and byproduct. We have successfully applied the DGEAR method to solving ODEs for the ultraviolet/hydrogen peroxide kinetic model.1821 When AOPs are applied at approximately neutral pH, acids that are major intermediates and byproduct22 are deprotonated. In particular, haloacetate ions are of serious concern2325 due to their widespread use in industry, adverse human health and ecological Received: March 25, 2011 Accepted: June 9, 2011 Revised: May 30, 2011 Published: June 21, 2011 6057
dx.doi.org/10.1021/es200978f | Environ. Sci. Technol. 2011, 45, 6057–6065
Environmental Science & Technology
ARTICLE
effects, chlorine and bromine disinfection byproducts, and metabolites of halogenated organics in biological systems. Many emerging contaminants are halogenated compounds and produce haloacetate ions in the aqueous phase AOPs. The lower reactivity of those compounds with HO•6 significantly affect the overall performance of AOPs. However, the detailed reactivity is incompletely understood.2628 For example, no temperature effects on rate constants have been examined. In molecular modeling of ionized compounds, the magnitudes of the solvation free energies are much larger than those for the neutral compounds.2931 In particular, the polarizability that results from the charge distribution at the transition state significantly changes the dipole moment and thus affects the solvation process.32 The large electrostatic contribution includes short-range and nonbulk electrostatics as well as cavitation, exchange repulsion, dispersion, and disruption or formation of the nearby solvent structure.30 Accordingly, entropy changes that arise from these solvent structure effects may be significant.33 In this study, temperature-dependent aqueous phase HO• reaction rate constants are measured to obtain the thermochemical properties of a series of haloacetate ions. Ab initio quantum mechanical approaches are used to simulate the HO• reactions with carboxylate ions and to calculate the aqueous phase free energies of activation.
’ ACTIVATED-COMPLEX THEORY Activated-complex theory (ACT) (or transition state theory34) treats a transition state as a chemical species in thermal equilibrium with its surroundings. Although the free energy and other equilibrium properties of a transition state cannot be measured directly, the order of magnitude of vibration frequencies (1012 s1) may enable us to find an activated complex in thermodynamic equilibrium with unreacted species.35 Accordingly, the kinetic reaction rate constant for a given elementary reaction may relate linearly to the free energy change in the transition from reactants to transition states and, after putting natural logarithms on both sides, may be expressed as follows: ln kH ¼ FΔGact rxn + σ
ð1Þ
where kH is the reaction rate constant for the hydrogen-atom abstraction reaction from one C—H bond by HO•, M1s1; F denotes a coefficient for the difference in the free energy of activation; σ is a coefficient; and ΔGact aq is the aqueous phase standard free energy of activation, kcal/mol. If there are equivalent H atoms, nH, that contribute to the same extent to the overall reaction rate, k, then kH is obtained from k/nH. The coefficient F accounts for the transmission coefficient and the frequency of transition-state dissociation to form products (i.e., kBT/h where kB is the Boltzmann constant, h is the Planck constant and T is temperature, K). Under the thermodynamic equilibrium assumption between reactants and transition states, thermodynamic parameters in the aqueous phase can be obtained36 using the following eqs 24: act Ea ¼ ΔHaq + RT
ΔSact ekB T aq exp A¼ h R
where Ea and A are the experimentally obtained Arrhenius activation energy, kcal/mol, and frequency factor, M1s1, act respectively; ΔHact aq and ΔSaq are the standard enthalpy and entropy of activation, kcal/mol, respectively; R is a gas constant (=1.98 cal K1 mol1); and e is a constant (=2.71). In the following sections, we compare experimentally obtained and theoretically calculated thermochemical properties (described above). To distinguish these, we will use the superscripts “exp” and “calc”. Approaches
’ EXPERIMENTAL SECTION In the past several decades, electron-pulse radiolysis7 has been used for measuring the uni/bimolecular reaction rate constants of various reactions that are induced by radical compounds; the details are described elsewhere.6 The Supporting Information (SI) provides details about the linear accelerator (Figure SI-1 of SI) used in the electron-pulse radiolysis as well as the setup and experimental procedures. ’ THEORETICAL SECTION Ab initio molecular orbital and density functional theory (DFT)-based quantum mechanical calculations were performed using Gaussian 09.37 The Berny geometry optimization algorithm38 using GEDIIS39 in redundant internal coordinates optimized the geometry of reactants, complex compounds, and products. Transition states were found as first-order saddle points on the potential energy surface. The quadratic synchronous transit method (QST)40,41 was used to locate many of the transition states. All transition states were verified by a single negative frequency, which indicates the saddle point. Anharmonicity from hindered rotors and basis set superposition error (BSSE) were neglected due to their minor contributions.15,42 The effect of tunneling was included using Wigner’s equation.43 The universal solvation model, SMD,30 was used as the aqueous phase implicit polarizable continuum model. SMD includes two components: (1) the bulk electrostatic contribution that results from a self-consistent reaction field treatment and (2) the contribution that arises from short-range interactions between the solute and solvent molecules in the first solvation shell. The SMD-Coulomb atomic radii and the van der Waals surface were used for cavity formation using the GePol algorithms on default settings.44 The theoretically calculated aqueous phase standard free energy of activation, ΔGact aq,calc, at a given temperature, T, is the sum of standard state gaseous phase free energy of activation, ΔGact gas,calc, 45 and the solvation free energy of activation, ΔGact solv,calc . act act ΔGact aq, calc ¼ ΔGgas, calc + ΔGsolv, calc
ΔGact aq,calc is obtained by subtracting the free energies of the reactants from the transition state free energy, and it contains an extra portion of free energy, Gextra, that is written as:
ð2Þ !
act act ΔGact aq ¼ ΔHaq TΔSaq
ð3Þ ð4Þ
ð5Þ
Gextra ¼ RTln γðTÞ
ð6Þ
γ(T) is a transmission coefficient that represents the effect of tunneling at temperature T at the transition state. Equation 6 was successfully used to determine the tunneling effect.15,16,46 The free energy change associated with moving from a gaseous phase at 1 atm to an aqueous phase concentration of 1 M (i.e., 1.89 kcal/mol47) was included. The solvent cage effect (i.e., a 2.96 kcal/mol decrease 6058
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
Cl3CCOO
Br2HCCOO
3
4
6059
F2HCCOO
ICH2COO
HCOO
6
7
8
Br3CCOO
Cl2HCCOO
2
5
C1CH2COO
1
no.
(2.12 ( 0.08) 10
(2.39 ( 0.23) 108
(3.19 ( 0.13) 108
40.0
50.0
(1.24 ( 0.03) 10
(1.44 ( 0.05) 108
(2.21 ( 0.04) 108
30.0
40.0
50.0
(3.02 ( 0.12) 10
(3.70 ( 0.28) 108
(4.77 ( 0.10) 108
30.6
40.0
51.0
(1.24 ( 0.06) 1010
50.0
Elliot et al, 1990 Elliot and Simons, 1994
3.8 109
1994
Chin and Wine,
Ervens et al, 2003
this study
this study
this study
this study
this study
this study
this study
reference
4.3 109
3.1 109
(2.4 ( 0.4) 109
(7.54 ( 0.16) 109
40.0
25.0
(5.48 ( 0.28) 10
30.0
9
(4.65 ( 0.16) 109
(1.10 ( 1.08) 108
40.0
22.5
(5.99 ( 0.99) 107
(7.41 ( 1.40) 107
(3.82 ( 0.17) 108
50.0
23.0
(3.07 ( 0.12) 108
40.0
30.0
(1.68 ( 0.07) 108
(2.62 ( 0.10) 108
23.0
30.6
8
(2.09 ( 0.07) 108
23.0
8
(6.21 ( 0.04) 107
22.5
8
30.0
(2.91 ( 0.06) 108
50.0
(1.50 ( 0.11) 108
(2.68 ( 0.07) 108
40.0
22.5
(1.81 ( 0.10) 10
(2.35 ( 0.06) 108
8
23.0
k, M s
30.0
temp, °C
1 1
8.5 (2.03)
4 (0.96)
10 (2.39)
(2.15 ( 1.19)
9( 5
(6.72 ( 0.03)
28.1 ( 0.11
(6.63 ( 0.62)
27.7 ( 2.61
(5.45 ( 0.03)
22.8 ( 0.14
(5.41 ( 0.03)
22.7 ( 0.13
(8.00 ( 0.23)
33.5 ( 0.98
(4.79 ( 0.10)
20.3 ( 0.3
(3.17 ( 0.20)
13.3 ( 0.8
(kcal/mol)
Ea, kJ/mol
10
(11.87 ( 0.44)
49.7 ( 1.83
(cal•K/mol)
ΔSactaq,exp J 3 K/mol
(2.48 ( 0.51)
10.4 ( 2.14
55 (13.1) 40 (9.55)
1.3 1011
37 (8.84)
(10.7 ( 0.96)
45 ( 4
(6.33 ( 0.07)
26.5 ( 0.31
2.2 1010
2.0 1011
(7.9 ( 0.7) 1010
(4.09 ( 1.55) 1014
(2.56 ( 1.37)
(4.66 ( 4.62) 1012 10.7 ( 5.72
(4.28 ( 0.21)
(1.96 ( 0.20) 1012 17.9 ( 0.88
(4.04 ( 0.02)
(2.21 ( 0.02) 1012 16.9 ( 0.07
(5.93 ( 1.74) 1013
(6.61 ( 0.10)
(6.03 ( 0.30) 1011 27.7 ( 0.40
(4.30 ( 1.06) 10
A, M s
1 1
6 (1.43)
1.5 (0.48)
7.5 (1.79)
(1.67 ( 0.96)
7(4
(6.11 ( 0.03)
25.6 ( 0.11
(6.04 ( 3.34)
25.3 ( 14.0
(4.85 ( 0.04)
20.3 ( 0.15
(4.82 ( 0.03)
20.2 ( 0.13
(7.40 ( 0.23)
31.0 ( 0.98
(4.25 ( 0.07)
17.8 ( 0.28
(2.58 ( 0.19)
10.8 ( 0.81
(kcal/mol)
ΔHactaq,exp kJ/mol
18.1 (4.3)
18.0 (4.3)
18.5 (4.4)
(4.8 ( 3.1)
20 ( 13
(4.23 ( 0.002)
17.7 ( 0.01
(6.80 ( 2.94)
28.5 ( 12.3
(6.14 ( 0.03)
25.7 ( 0.12
(6.02 ( 0.03)
25.2 ( 0.11
(6.66 ( 0.08)
27.9 ( 0.34
(6.21 ( 0.04)
26.0 ( 0.16
(6.11 ( 0.06)
25.6 ( 0.26
(kcal/mol)
ΔGactaq,exp kJ/mol
10.8 (2.57)
n.a.
36.8 (8.8)
53.2 (12.7)
22.6 (5.4)
97.1 (23.2)
na
31.0 (7.4)
(kcal/mol)
ΔGactaq,exp kJ/mol
Table 1. Experimentally Obtained Temperature-Dependent Reaction Rate Constants and Literature-Reported Rate Constants, Calculated Thermochemical Properties, And Theoretically Calculated Free Energies of Activation for a Series of Reactions of HO• with Carboxylate Ions
Environmental Science & Technology ARTICLE
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
30.0 (7.15) 22.2 (5.31) 8.28 (1.98) 46.8 (11.2) 6.1 1010 10.8 ( 0.35 (2.57 ( 0.08) Martin et al, 2008 22.2 15 CH3CH(OH)COO
(7 ( 2) 108 25.0 14 CH3COCOO
(7.77 ( 0.50) 108
n.a.
28.2 (6.73) 23 ( 7 (5.5 ( 1.7) 17 ( 3 (4.06 ( 0.72) 21 ( 2 (5.02 ( 0.48) Ervens et al, 2003
19 ( 4 (4.54 ( 0.96)
(1.3 ( 0.1) 1012
19 ( 5 (4.5 ( 1.2)
15.1 (3.60) 23 ( 12 (5.5 ( 2.9) 9 ( 4(2.15 ( 0.96)
34 ( 7(8.12 ( 1.67) 48 ( 3 (11.5 ( 0.72) (6.0 ( 0.4) 1015 36 ( 8(8.60 ( 1.91) Ervens et al, 2003 (2.6 ( 0.9) 10 25.0 13 CHOCOO
(5.O ( 0.4) 1010 11 ( 5(2.93 ( 1.19) Ervens et al, 2003 (5.0 ( 0.5) 108 25.0
9
12 —OOC(CH2)2COO-
11 HOOCCH2COO
ARTICLE
48 ( 4 (11.5 ( 0.96)
30 ( 17(7.2 ( 4.1) 9 ( 4(2.15 ( 0.96)
13.0(3.11)
25.7(6.15)
22 ( 7 (5.3 ( 1.7) 13 ( 3(3.10 ( 0.72)
72 ( 9 (17.2 ( 2.15) 11 ( 5(2.93 ( 1.19)
(3.2 ( 0.2) 1011 15 ( 4 (3.58 ( 0.96) Ervens et al, 2003
Ervens et al, 2003 25.0
(6 ( 1) 10
7
(7.2 ( 0.4) 108 25.0
9
10 CH3CH2COO
(3.2 ( 0.4) 109
33 ( 2 (7.88 ( 0.48)
31.1 (7.44) 28 (6.7) 13 (3.10) 53 (12.7) 2.8 1010
(kcal/mol)
Ea, kJ/mol
15 (3.58) 1984
Chin and Wine, 7.0 107 25.0 CH3COO
ΔGactaq,exp kJ/mol
(kcal/mol) (cal•K/mol) no.
Table 1. Continued
temp, °C
k, M1s1
reference
(kcal/mol)
A, M1s1
ΔSactaq,exp J 3 K/mol
ΔHactaq,exp kJ/mol
(kcal/mol)
ΔGactaq,exp kJ/mol
Environmental Science & Technology
in free energy for a bimolecular reaction at 298 K) was included according to the corrections proposed by Okuno (1997)48 and taking into account the free volume (FV) theory .35 These corrections are consistent with those obtained independently by Ardura et al. (2005)49 and have been used successfully by other authors. The Gaussian-4 theory (G4)50 using the SMD30 solvation model was used for calculating ΔGact aq,calc . The G4 theory includes the geometry optimization at the B3LYP/6-31G(2df,p), 0.9854 of a scaled factor for the zero-point energy (ZPE) frequency calculations as well as several combinations of high-level complementary singlepoint energy calculations. The geometry optimization does not include diffuse functions. Although the inclusion of diffuse functions for ionized compounds is recommended,44 others have speculated that their use often decreases accuracy due to outlying charge in the SMD model.51 Therefore, we used the default method for G4 to conduct the geometry optimization.
’ RESULTS AND DISCUSSION Experimental Section. The temperature-dependent rate constants, Arrhenius parameters, and calculated thermochemical properties for carboxylate ions are summarized in Table 1. Table 1 also includes literature-reported rate constants for other carboxylate ions. Typical time-dependent kinetic data for (SCN)2•formation from ClCH2COO that were obtained at 472-nm wavelength and room temperature are shown in Figure SI-2 of the SI. Least-square fits indicate clear linear correlations for the competition kinetics plots of CH2ClCOO, CHCl2COO, and Cl3CCOO, respectively (Figure SI-3 of the SI). The observed errors (i.e., 95% confidence intervals) in obtaining the secondorder reaction rate constants are within (10% and arise from the precision of the measurement (e.g., the electron beam stability) and of the chemical solution (e.g., purity, dilution). The Arrhenius plot of the logarithms of temperature-dependent rate constants versus the inverse of temperature also indicates a linear correlation, as shown in Figure SI-4 of the SI. The r2 values for all plots are greater than 0.900. The Arrhenius activation energies and the enthalpies of activation for a series of haloacetate ions range from 3.2 to 8.0 kcal/mol, and from 2.5 to 7.5 kcal/mol, respectively. These values are larger than the literature-reported values for other carboxylate ions (∼14 kcal/mol) because of the presence of halogenated functional groups with strong electron-withdrawing ability. The Arrhenius frequency factors are within the typical range (i.e., 10101012 M1s1), although perhalocarbons (i.e., Cl3CCOO and Br3CCOO) and ICH2COO are larger by 1 or 2 orders of magnitude because of the different reaction mechanisms involved (i.e., electron transfer).28 We obtained a mixture of negative and positive entropy of activation from the experiments (Table 1). Although a negative entropy change is typical in bimolecular reactions because the joining of two reactants to form an activated complex decreases the randomness of the solventsolute molecules (i.e., a loss of translational entropy occurs), because solvent molecules are released in forming the transition state, the entropy increases. In many cases this more than offsets the decrease caused by reactant association. It is commonly assumed that for the same reaction mechanism, the change in entropy is small. However, when ionized compounds cause tighter binding of nearby solvent molecules, and polar molecules result from the electrostatic contribution and loss of entropy, the entropy change becomes significant. The change in entropy of activation correlates linearly 6060
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
Environmental Science & Technology
ARTICLE
Figure 1. Isokinetic relation between the experimentally obtained enthalpy and entropy of activation.
with the change in enthalpy of activation (Figure 1). This is called the isokinetic effect,36 and this correlation turns out to be consistent with those obtained for neutral compounds. Details of the entropic contribution are investigated in the Theoretical Section. Theoretical Section. Exploring an Ab Initio Quantum Mechanical Approach and Solvation Model. There is a trade-off between accuracy in calculating thermochemical properties and computational cost. To seek a reasonable approach, we compared a limited number of methods and basis sets for the reaction of HO• with acetate ion in both the gaseous and aqueous phases (Table SI-1 of the SI). Due to space limitations, a full discussion is given in the SI. From this comparison, we decided to use the G4 theory with the SMD solvation model to calculate the aqueous phase free energy of activation. Optimized Structure of the Stationary, Prereactive Complex, and Transition States. Due to space limitations, full discussions on optimized structures are given in the SI. Tables SI-24 and Figures SI-6 and SI-7 of the SI summarize the aqueous-phase optimized stationary structures of HO•, H2O, and a series of ground state haloacetate ions as well as their prereactive complexes and transition state structures. Several gaseous phase optimized structures are provided for comparison. The SI also includes the z-matrices of all optimized structures. Correlation between LnkH and ΔGactaq,calc. We observe a linear correlation between ln kH and ΔGactaq,calc, as shown in Figure 2. The temperature that is used for the correlation is 298K (25 °C). The reaction rate constants were recalculated at 298K using experimentally obtained Ea and A. Figure 2 includes the literature-reported HO• reaction rate constants for formate, acetate, propionate, malonate, succinate and lactate as well as our experimentally obtained rate constants for a series of haloacetate ions (i.e., chloroacetate, difluoroacetate, dibromoacetate). The lowest ΔGactaq,calc was used for the correlation when more than one transition state and different conformers were found for the same compound. The transition state for dichloroacetate could not be located. The coefficients F and σ in eq 1 for the carboxylate ions are 0.728 and 23.4, respectively. The value of F is smaller than that obtained from the neutral compound (i.e., F = 0.418), whereas the value of σ is almost the same (i.e., σ = 21.3).15 However, with the exception of HCOO, the value of F is 0.541 that is very close
Figure 2. Plot of ln kH versus theoretically calculated aqueous phase free energies of activation.
to that for the neutral compound. This indicates that eq 1 is valid under the same H-atom abstraction reaction mechanism for a C—H bond regardless of whether the species is protonated or deprotonated. It is not clear if the literature-reported rate constant for HCOO is overestimated or the theoretically calculated free energy of activation is overcalculated. Further investigation will be conducted. In contrast, we found that F = 0.383 and σ = 23.2 for HO• addition to unsaturated alkenes from our previous study.16 HO• addition to a CdC bond is faster than H-atom abstraction from a C—H bond and close to the diffusion limit;52 therefore, the observed rate constant is larger (i.e., σ is larger) than that obtained for H-atom abstraction. Our theoretically calculated values of ΔGact aq,calc for various carboxylic ions are acceptable. For the 10 carboxylate ions that indicate H-atom abstraction mechanism from a C—H bond, the sample deviation (SD) obtained from eq 7 is 0.05. This SD is much smaller than those that are obtained for neutral compounds.16 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 u i act, i u 1 N ΔGact, aq, exp ðΔGaq, calc Þ t ð7Þ SD ¼ i N 1 i¼1 ΔGact, aq, exp
∑
It should be noted that following 5 compounds are not included in the analysis for the SD. Perhalocarbons (Cl3CCOO and Br3CCOO) and iodoacetate ion indicate different reaction mechanisms (i.e., electron-transfer) and transition states could not be located for CHOCOO and CHCl2COO. All 10 ΔGact aq,calc are within (2.0 kcal/mol as compared to the values ofΔGact aq,exp . The general error arising from the G4 gaseous phase calculations is 0.83 kcal/mol.50 Furthermore, the uncertainty remains when calculating the free energy of the transition state. For calculating standard free energy of solvation, the mean unsigned error on average for 112 ions is 4 kcal/mol.30 As a consequence, our results should be within a reasonable error range. Entropic Contribution to the Free Energy of Activation. As was observed from ΔSact aq,exp, the entropic contribution to the free energy of activation is significant for ionized compounds. 6061
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
Environmental Science & Technology
ARTICLE
Table 2. Calculated Entropic Portions That Contribute to Entropy of Activation for a Series of Reactions of HO• with Carboxylate Ions ΔVactaq,exp Å3 HCOO
ΔSactgas,calc cal/(mol K)
ΔSactsolv(cav),calc cal/(mol K)
ΔSactaq,calc cal/(mol K)
ΔSactsolv(order),calc cal/(mol K)
cal/(mol K)
2.38
23.57
8.61
14.96
4.26
10.7 ( 0.96a
4.03
29.27
9.42
19.85
7.15
12.7a
CH3CH2COO HOOCCH2COO
4.72 2.53
20.92 27.22
9.82 9.50
11.10 17.72
3.22 0.52
7.88 ( 0.48a 17.2 ( 2.15a
3.82
26.96
9.90
17.06
5.56
11.5 ( 0.96a
CH3COCOO
4.18
28.15
9.74
18.41
6.91
5.02 ( 0.48a
4.31
26.46
9.96
16.51
5.33
11.50
F2HC
3.72
20.29
9.63
10.66
27.56
16.9 ( 0.92
Br2HCCOO
5.43
18.36
10.74
7.62
4.11
3.51 ( 0.10
CH3COO
OOC(CH2)2COO
CH2ClCOO
CHCl2COO
a
ΔSactaq,exp
7.00 ( 0.15
Ervens et al., 200357.
Figure 3. Charge distributions of reactants, transition states and products for the gaseous and aqueous-phase reactions of HO• with acetate ion.
Reactions between ionized compounds have a higher charge density at the transition state that results in increased electrostriction and a decrease in volume and entropy. In this section, we will examine energies that contribute to the entropic change to determine which one is the dominant factor. In the next section we will examine the change in the charge distribution from reactants to transition state. Two major entropic contributions are (i) cavity formation and (ii) solvent ordering.53,54 These two factors originate from a change in solvent structure,30 and weak correlation is observed act between ΔSact aq,exp and changes in cavity volumes, ΔVaq,calc, for • reactions of HO with a series of carboxylate ions (data not shown). The standard cavitation entropy of solvation, ΔSsolv(cav), can be related to the standard cavitation free energy of solvation, ΔGsolv(cav), through a temperature derivative, as shown in eq 8: ! ∂ΔGsolvðcavÞ ð8Þ ΔSsolvðcavÞ ¼ ∂T P
ΔGsolv(cav) examines the effect of confining the solute in the accessible free volume of the solution and can be estimated using a methodology outlined by Pierotti.55,56 The detailed free volume theory is described in the SI. Ashcraft et al. (2007)53 showed that this approach can be used successfully to calculate the cavitation entropy. Table 2 summarizes the calculated gaseous phase entropy of activation, ΔSact gas,calc ; cavity formation entropy of solvation of activation, ΔSact solv(cav),calc ; calculated and experimental aqueous phase entropy of activation, ΔSact aq,calc and ΔSact aq,exp respectively; and calculated solvent ordering entropy of solvation of activation, ΔSact solv(order),calc . Each term is included in eq 9 and explained below: act act ΔSact solvðorderÞ, calc ¼ ΔSaq, exp ΔSaq, calc act act where ΔSact aq,calc = ΔSgas,calc + ΔSsolv(cav),calc
ð9Þ
The calculated cavitation entropy of solvation for ground state molecules is consistent with the values obtained by Ashcraft et al. (2007).53 Similar to Leung et al.54 and Ashcraft et al.,53 we observe that the entropy change is largely due to cavity formation. Because there is no solid scientific theory that indicates how to calculate solvent ordering entropy, we estimate it by subtracting the calculated aqueous-phase ΔSact aq,calc from the experimentalΔSact aq,exp, as shown in eq 9. For example, using the values of ΔSaq,exp for HCOO and CH3COO in the literature (30.8 cal mol1K1 and 37.1 cal1 mol1 K, respectively), formate and acetate ions have 0.38 cal mol1K1 and 3.49 cal mol1K1 of ΔSsolv(order),calc, respectively (please note that these are values of reactants at ground state). These values are within the range of the empirically obtained values (2∼5 cal mol1K1)53 and contribute little to the standard state entropy. The negative solvent-ordering value indicates that the polar carboxylate functional groups help to retain the hydrogen-bonding network of the water solvent as compared with an empty cavity. Furthermore, 1 1 ΔSact for reactions of HO• solv(cav),calc is from 8 to10 cal mol K with a series of carboxylate ions, whereas ΔSact solv(order),calc ranges from 4 to 7 cal mol1K1 for the analogous reactions. Although significant uncertainty results from the absence of experimental values at the transition state, the solvation process increases the entropy of activation for reactions of HO• with the series of carboxylate ions by approximately 1015 cal mol1K1 due to the interactions between solvent water molecules and carboxylate ions. Atomic Charge Distribution for the Reactions of HO• with Carboxylate Ions. The analysis of atomic charge distributions on each element enables one to understand the effects of different functional groups on the molecular reactivity in the progression reactants f transition state f products. The charges are obtained from a natural population analysis (NPA)58 at the level of MP2/Aug-cc-pVQZ//B3LYP/6-31G(2df,p) with the SMD 6062
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
Environmental Science & Technology
ARTICLE
Figure 4. Charge distributions of reactants, transition states and products for the aqueous-phase HO• reactions with haloacetate ion.
model. The following discusses the reaction of HO• with CH3COO in the gaseous and aqueous phases and then of HO• with a series of haloacetate ions. For the reaction of HO• with CH3COO (Figure 3), the analysis confirms that at the transition state the abstracted hydrogen of acetate becomes more positive and the oxygen of HO• becomes more negative. The negative charge on the oxygen of HO• indicates that this oxygen can be a hydrogen bond acceptor and provides an opportunity for the solvent water molecules to stabilize the transition state through its polarity and/or ability to participate in hydrogen bonding. In contrast, the hydrogen on the HO• (which is not involved in the reaction) bears a substantial portion of the positive charge of the reactant, transition state, and product. Although this hydrogen can also participate in hydrogen bonding, this interaction does not affect the relative energies because the charge on this hydrogen remains almost constant throughout the reaction. In the aqueous phase, the degree of polarizability at the transition state is less substantial, which implies a smaller barrier height and faster reactions than those that are in the gaseous phase. Accordingly, charge distribution at the transition state is condensed and results in high charge density. Because oxygen is more electronegative than carbon and hydrogen, in the transition state for hydrogen abstraction, the electron density is pulled toward the oxygen of the hydroxyl radical, giving it a partial negative charge, which places a partial positive charge on the alkyl portion of acetate ion of the transition state in the aqueous phase. The carboxylic functional group at the transition state in the aqueous phase becomes less negative due to the impact of the surrounding solvent water molecules, whereas little change in the charge distribution of the carboxylic functional group is observed in the gaseous phase. Figure 4 compares the charge distributions for the aqueous phase reactions of haloacetate ions with HO•. Halogenated atoms (i.e., F, Cl, and Br) significantly affect the charge distributions and hence the activation energies and reaction rates. When electronegative halogenated functional groups are placed beside carboxylic functional groups, the transition state is less polarized because the functional group competes for electron density; less transfer of negative charge to the oxygen of the HO• occurs, and hydrogen bonding interactions are expected to be weaker. Fluorine, which has the most negative charge of the halogens used, produces the least positive charge on the abstracted hydrogen, and the largest barrier height and smallest rate constant are obtained. Bromine affects the charge distribution in the process from reactant to transition state to product in the same manner as acetate. The abstracted hydrogen becomes slightly positive, and the oxygen of the HO• becomes more negative than that of the reactants containing chlorine and
fluorine. Nevertheless, the large rate constants for dibromoacetate suggest that the electron-transfer reaction between the bromine atom and HO• produces a 2σ/1σ* two-centerthreeelectron (2c3e) adduct containing two bonding σ and one antibonding σ* electrons.59
’ ASSOCIATED CONTENT
bS
Supporting Information. Additional explanation and discussion of experimental approaches and results, exploration of quantum mechanical methods, optimized structures and their z-matrices, and calculations of free volume theory are provided. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Phone: (404) 894-2242; fax: (404) 894-7896; e-mail: Daisuke.
[email protected].
’ ACKNOWLEDGMENT This work was supported by National Science Foundation Award 0854416. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the supporting organizations. The authors appreciate support from the Brook Byers Institute for Sustainable Systems, Hightower Chair, and the Georgia Research Alliance at the Georgia Institute of Technology. The authors also appreciate the Office of Information Technology at Georgia Tech for the high-performance and clustered computing resources. Support from University of Notre Dame Radiation Center and Department of Energy is appreciated. ’ REFERENCES (1) Westerhoff, P.; Yoon, Y.; Snyder, S.; Wert, E. Fate of endocrinedisruptor, pharmaceutical, and personal care product chemicals during simulated drinking water treatment processes. Environ. Sci. Technol. 2005, 39, 6649–6663. (2) Huber, M. M.; Canonica, S.; Park, G.-Y.; Von Gunten, U. Oxidation of pharmaceuticals during ozonation and advanced oxidation processes. Environ. Sci. Technol. 2003, 37, 1016–1024. (3) Rosenfeldt, E. J.; Linden, K. G. Degradation of endocrine disrupting chemicals bisphenol A, ethinyl estradiol, and estradiol during UV photolysis and advanced oxidation processes. Environ. Sci. Technol. 2004, 38, 5476–5483. (4) Glaze., W. H.; Kang, J.-W. Advaced oxidation processes. Test of a kinetic model for the oxidation of organic compounds with ozone and 6063
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
Environmental Science & Technology hydrogen peroxide in a semibatch reactor. Ind. Eng. Chem. Res. 1989, 28, 1580–1587. (5) Glaze, W. H.; Kang, J.-W.; Chapin, H. D. The chemistry of water treatment processes involving ozone, hydrogen peroxide and ultraviolet radiation. Ozone. Sci. Eng. 1987, 9, 335–352. (6) Buxton, V. B.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. Critical review of rate constants for reactions of hydrated electrons, hydrogen atoms and hydroxyl radicals (•OH/•O) in aqueous solution. J. Phys. Chem. Ref. Data 1988, 17 (2), 513–795. (7) von Sonntag, C.; Schuchmann, H.-P. In., Alfassi, Z. B. Peroxyl Radicals; John Wiley and Sons Ltd.: New York, 1997; p 173. (8) Whitman, K.; Lyons, S. Miller, R.; Nett, D.; Treas, P.; Zante, A.; Fessenden, R. W.; Thomas, M. D.; Wang, Y. In Proceedings of the ’95 Particle Accelerator Conference and International Conference on High Energy Accelerators, Dallas, Texas, May 15, 1995. (9) Stefan, M. I.; Mack, J.; Bolton, J. R. Degradation pathways during the treatment of methyl tert-butyl ether by the UV/H2O2 process. Environ. Sci. Technol. 2000, 34, 650–658. (10) Stefan, M. I.; Bolton, J. R. Reinvestigation of the acetone degradation mechanisms in dilute aqueous solution by the UV/H2O2 process. Environ. Sci. Technol. 1999, 33, 870–873. (11) Stefan, M. I.; Bolton, J. R. Mechanism of the degradation of 1, 4-Dioxane in dilute aqueous solution using the UV/hydrogen peroxide process. Environ. Sci. Technol. 1998, 32, 1588–1595. (12) Chemical Abstract Services (CAS). A division of the American Chemical Society. http://www.cas.org/ (accessed September 30, 2009). (13) Pfaendtner, J.; Broadbelt, L. J. Mechanistic modeling of lubricant degradation. 2. The autoxidation of decane and octane. Ind. Eng. Chem. Res. 2008, 47, 2897–2904. (14) Li, K.; Crittenden, J. C. Computerized pathway elucidation for hydroxyl radical-induced chain reaction mechanisms in aqueous phase advanced oxidation processes. Environ. Sci. Technol. 2009, 43 (8), 2831–2837. (15) Minakata, D.; Li, K.; Westerhoff, P.; Crittenden, J. Development of a group contribution method to predict aqueous phase hydroxyl radical (HO•) reaction rate constants. Environ. Sci. Technol. 2009, 43, 6220–6227. (16) Minakata, D.; Crittenden, J. Linear Free Energy Relationships between Aqueous phase Hydroxyl Radical Reaction Rate Constants and Free Energy of Activation. Environ. Sci. Technol. 2011, 45, 3479–3486. (17) Hindmarsh, A. C.; Gear, C. W. Ordinary differential equation system solver. UCID-30001 Rev. 3 Lawrence Livermore Laboratory, Livermore, Ca. 1974. (18) Crittenden, J. C.; Hu, S.; Hand, W. D.; Green, A. S. A kinetic model for H2O2/UV process in a completely mixed match reactor. Wat. Res. 1999, 33 (10), 2315–2328. (19) Li, K.; Hokanson, D. R.; Crittenden, J. C.; Trussell, R. R.; Minakata, D. Evaluating UV/H2O2 processes for methyl tert-butyl ether and tertiary butyl alcohol removal. Water Res. 2008, 42 (20), 5045–5053. (20) Li, K.; Stefan, M. I.; Crittenden, J. C. Trichloroethene degradation by UV/H2O2 advanced oxidation process: product study and kinetic modeling. Environ. Sci. Technol. 2007, 41, 1696–1703. (21) Li, K.; Stefan, M. I.; Crittenden, J. C. UV photolysis of trichloroethylene: Product study and kinetic modeling. Environ. Sci. Technol. 2004, 38, 6685–6693. (22) Bolton, J. R.; Carter, S. R. Homogeneous photodegradation of pollutants in contaminated water: An introduction. In Aquatic and Surface Photochemistry, Chapter 33; Helz, G. R., Zepp, R. G., Crosby, D. G., Eds.; CRC Press: Boca Raton, FL. (23) Richard, A. M.; Hunter, E. S., III Quantitative structure-activity relationships for the developmental toxicity of haloacetic acids in mammalian whole embryo culture. Teratology 1996, 53, 352–360. (24) Woo, Y.-T.; Lai, D.; McLain, J. L.; Manibusan, M. L.; Dellarco, V. Use of mechanism-based structure-activity relationships analysis in carcinogenic potential ranking for drinking water disinfection by-products. Environ. Health Perspect. 2002, 110, 75–87. (25) Eisenberg, J. N. S.; Mckone, T. E. Decision tree method for the classification of chemical pollutants: Incorporation of across-chemical
ARTICLE
variability and within-chemical uncertainty. Environ. Sci. Technol. 1998, 32, 3396–3404. (26) Lal, M.; Schoeneich, C.; Moenig, J.; Asmus, K.-D. Rate constants for the reaction of halogenated organic radicals. Int. J. Radiat. Biol. 1988, 54, 773–785. (27) Neta, P.; Simic, M.; Hayon, E. Pulse radiolysis of aliphatic acids in aqueous solutions. I. Simple monocarboxylic acids. J. Phys. Chem. 1969, 73 (12), 4207–4213. (28) Fliount, R.; Makogon, O.; Guldi, D. M.; Asmus, K.-D. Radicalmediated degradation mechanisms of tribromo- and other trishalogenated acetic acids in oxygen-free solutions as studied by radiation chemistry methods. J. Chem. Soc., Perkin Trans. 2 1997, 1535–1545. (29) Liu, J.; Kelly, C. P.; Goren, A. C.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Zhan, C.-G. Free energies of solvation with surface, volume, and local electrostatic effects and atomic surface tensions to represent the first solvation shell. J. Chem. Theory. Comput. 2010, 6, 1109–1117. (30) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J. Phys. Chem. B. 2009, 113, 6378–6396. (31) Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. Aqueous solvation free energies of ions and ion water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton. J. Phys. Chem. B. 2006, 110, 16066–16081. (32) Tanko, J. M.; Suleman, N. K. Solvent Effects in the Reactions of Neutral Free Radicals. In Energetics of Organic Free Radicals, SEARCH Series 4; Martinho Sim~oes, J. A., Greenburg, A., Liebman, J. F., Eds.; Blackie: Glasgow, 1996; pp 244293. (33) Mader, E. A.; Davidson, E. R.; Mayer, J. M. Large ground-state entropy changes for hydrogen atom transfer reactions of iron complexes. J. Am. Chem. Soc. 2007, 129, 5153–5166. (34) Eyring, H.; Gershinowitz, H.; Sun, C. E. The absolute rate of homogeneous atomic reactions. J. Chem. Phys. 1935, 3, 786–796. (35) Benson, S. W. The Foundations of Chemical Kinetics; Robert, E., Ed.; Krieger: Malabar, FL, 1982. (36) Brezonik, P. L. Chemical Kinetics and Process Dynamics in Aqueous Systems. Lewis Publishers: Boca Raton, FL, 2002. (37) Gaussian 09, Revision A.1, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, € Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. A. D.; Farkas, O.; Gaussian 09; Gaussian, Inc.: Wallingford CT, 2009 (38) Schlegel, H. B. Optimization of equilibrium geometries and transition structures. J. Comput. Chem. 1982, 3 (2), 214–218. (39) Li, X.; Frisch, M. J. Energy-represented DIIS within a hybrid geometry optimization method. J. Chem. Theory Comput. 2006, 2, 835–839. (40) Peng, C.; Schlegel, H. B. Combining Synchronous Transit and Quasi-Newton Methods for Finding Transition States. Isr. J. Chem. 1993, 33, 449–54. (41) Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, M. J. Using redundant internal coordinates to optimize equilibrium geometries and transition states. J. Comput. Chem. 1996, 17, 49–86. (42) Pfaendtner, J.; Broadbelt, L. J. Elucidation of structure-reactivity relationships in hindered phenols via quantum chemistry and transition state theory. Chem. Eng. Sci. 2007, 62, 5232–5239. 6064
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
Environmental Science & Technology
ARTICLE
(43) Wigner, E. Z. F. Physic. Chemie 1932, B19, 203. (44) Pascual-Ahuir, J. L.; Silla, E. GEPOL: An improved description of molecular surfaces. I. Building the spherical surface set. J. Comput. Chem. 1990, 11, 1047. (45) Cramer, J. C. Essentials of Computational Chemistry. Theories and Models, 2nd ed.; John Wiley & Sons, Ltd.: Chinchester, UK, 2004. (46) Pu, J.; Gao, J.; Truhlar, D. G. Multidimensional tunneling, recrossing, and the transmission coefficient for enzymatic reactions. Chem. Rev. 2006, 106, 3140–3169. (47) Liptak, M. D.; Shields, G. C. Accurate pKa calculations for carboxylic acids using complete basis set and gaussian-n models combined with CPCM continuum solvation methods. J. Am. Chem. Soc. 2001, 123, 7314–7319. (48) Okuno, Y. Theoretical investigation of the mechanism of the Baeyer-Villiger reaction in nonpolar solvents. Chem—Eur. J. 1997, 3, 212. (49) Ardura, D.; Lopez, R.; Sordo, T. L. Relative gibbs energies in solution through continuum models: Effect of the loss of translational degrees of freedom in bimolecular reactions on gibbs energy barriers. J. Phys. Chem. B. 2005, 109, 23618–23623. (50) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 theory. J. Chem. Phys. 2007, 126, 084108. (51) Liu, J.; Kelly, C. P.; Goren, A. C.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Zhan, C.-G. Free energies of solvation with surface, volume, and local electrostatic effects and atomic surface tensions to represent the first solvation shell. J. Chem. Theory. Comput. 2010, 6, 1109–1117. (52) Getoff, N. Radiation and photoinduced degradation of pollutants in water: A comparative study. Radiat. Phys. Chem. 1991, 37, 673–680. (53) Ashcraft, R. W.; Raman, S.; Green, W. H. Ab initio aqueous thermochemistry: Application to the oxidation of hydroxylamine in nitric acid solution. J. Phys. Chem. B. 2007, 111, 11968–11983. (54) Leung, B. O.; Reid, D. L.; Armstrong, D. A.; Rauk, A. Entropies in solution from entropies in the gas phase. J. Phys.Chem. A 2004, 108, 2720–2725. (55) Pierotti, R. A. The solubility of gases in liquids. J. Phys. Chem. 1963, 67, 1840–1845. (56) Hofinger, S.; Zerbetto, F. On the cavitation energy of water. Eur. J. Chem. 2003, 9, 566. (57) Ervens, B.; Gligorovski, S.; Herrmann, H. Temperature-dependent rate constants for hydroxyl radical reactions with organic compounds in aqueous solution. Phys. Chem. Chem. Phys. 2003, 5, 1811–1824. (58) Foester, J. P.; Weinhold, F. Natural hybrid orbitals. J. Am. Chem. Soc. 1980, 102, 7211–7218. (59) Asmus, K.-D.; Bonifacic, M. Sulfur-centered reactive intermediates as studied by radiation chemical and complementary techniques. In The Chemistry of Free Radicals S-Centered Radicals, Chapter 5; Alfassi, Z. B., Ed.; John Wiley & Sons: Chichester, U.K, 1999; pp 141191.
6065
dx.doi.org/10.1021/es200978f |Environ. Sci. Technol. 2011, 45, 6057–6065
