Mechanistic Insight into the Reactivity of Chlorine-Derived Radicals in

Article

Mechanistic Insight into the Reactivity of Chlorine-derived Radicals in the Aqueous-phase UV/chlorine Advanced Oxidation Process: Quantum Mechanical Calculations Daisuke Minakata, Divya Kamath, and Shaye Maetzold Environ. Sci. Technol., Just Accepted Manuscript • Publication Date (Web): 25 May 2017 Downloaded from http://pubs.acs.org on May 28, 2017

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Environmental Science & Technology

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Mechanistic Insight into the Reactivity of Chlorine-derived Radicals in the Aqueous-

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phase UV/chlorine Advanced Oxidation Process: Quantum Mechanical Calculations

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Prepared for Environmental Science and Technology

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Daisuke Minakata*1, Divya Kamath1, Shaye Maetzold1

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Michigan Technological University

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1400 Townsend Drive, Houghton, Michigan 49931

Department of Civil and Environmental Engineering

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*Corresponding author. Phone: +1-906-487-1830; fax: +1-906-487-2943; Email address:

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[email protected]

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ACS Paragon Plus Environment


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Abstract

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The combined ultraviolet (UV) and free chlorine (UV/chlorine) advanced oxidation

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process that produces highly reactive hydroxyl radicals (HO•) and chlorine radicals (Cl•)

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is an attractive alternative to UV alone or chlorination for disinfection because of the

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destruction of a wide variety of organic compounds. However, concerns about the

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potential formation of chlorinated transformation products require an understanding of

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the radical-induced elementary reaction mechanisms and their reaction rate constants.

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While many studies have revealed the reactivity of oxygenated radicals, the reaction

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mechanisms of chlorine-derived radicals have not been elucidated due to the data scarcity

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and discrepancies among experimental observations. We found a linear free energy

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relationship between the quantum mechanical (QM) calculations of the free energies of

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reaction and the literature-reported experimentally measured reaction rate constants, kexp,

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for 22 chlorine-derived inorganic radical reactions in the UV/chlorine process. This

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relationship highlights the discrepancy among literature-reported rate constants and aids

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in the determination of the rate constant using QM calculations. We also found linear

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correlations between the theoretically calculated free energies of activation and kexp for

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31 reactions of Cl• with organic compounds. The correlation suggests that H-abstraction

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and Cl-adduct formation are the major reaction mechanisms. This is the first

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comprehensive study on chlorine-derived radical reactions, and it provides mechanistic

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insight into the reaction mechanisms for the development of an elementary reaction-

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based kinetic model.

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Introduction

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Ultraviolet combined with free chlorine (UV/chlorine) that produces highly reactive

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hydroxyl radicals (HO•) and chlorine radicals (Cl•) at ambient temperature and

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atmospheric pressure is one of the attractive aqueous-phase advanced oxidation processes

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(AOPs).1-3 UV/chlorine can serve as an alternative AOP to UV with hydrogen peroxide

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because of the utilization of the existing chlorination process or as an alternative to the

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UV process alone for the disinfection of pathogens and the destruction of dissolved

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organic compounds by both HO• and Cl•.4 Previous studies indicated the different degree

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of contribution of initial reaction of Cl• with a target compound to the overall

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degradation.5-7 In addition, chlorine residue after the UV/chlorine AOP can be used as a

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secondary disinfectant, rendering this process suitable for the application of drinking

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water treatment as well as wastewater reclamation for direct potable reuse.

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In the aqueous-phase UV/chlorine AOP, photolysis of hypochlorous

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acid/hypochlorite ions (HOCl/OCl-) generates HO• and Cl• radicals,8,9 which react with

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target organic compound(s) as well as with HOCl/OCl-. These highly reactive HO• (2.73

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V vs. SHE)10 and Cl• (2.43 V) radicals transform organic compounds into various

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degradation byproducts via complicated radical-involved reactions. In addition, chloride

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ions (Cl-) generated by the reaction of Cl• with HOCl/OCl- further react with Cl• to

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produce dichlorine radicals (Cl2•-, 2.13 V) that may react with organic compound(s). The

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reactions of HO• and Cl• with HOCl/OCl- produce oxychlorine radicals (ClO•, 1.39 V)

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whose reactivity with organic compounds is not well understood.5,7,11 Consequently, the

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involvement of various chlorine species raises serious concerns about the potential

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formation of toxic degradation byproducts, such as chlorinated byproducts.12,13 Given

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that there are many organic compounds in commercial use and production,14 the

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development of a kinetic model that can predict the fate of degraded organic compounds

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is needed for the preliminary design and screening of a number of these compounds.

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This type of predictive kinetic model requires three components: (1) the identification of

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reaction pathways; (2) the prediction of reaction rate constants, and (3) the numerical

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solution of ordinary differential equations (ODEs) for each species. Once the ODEs are

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numerically solved, the time-consequent concentration profiles of each species can be

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predicted.

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Although HO•-induced initial degradation pathways of organic compounds have

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been studied over the past several decades15,16 and predicting the degradation byproducts

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for small molecular weight aliphatic compounds and alkenes has become feasible,17 the

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reaction mechanisms in the UV/chlorine AOP are not well understood. For example,

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literature-reported experimentally obtained reaction rate constants (kexp) for the reaction

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of HO• with HOCl vary from 104 to 109 M-1s-1.3,18,19 This rate constant significantly

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affects the calculations of the concentration profile of subsequent byproducts because

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HOCl is dominantly present near a neutral pH (i.e., the pKa of HOCl is 7.5).20 Among

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approximately 30 kexp studies on Cl•,21 for saturated aliphatic compounds, some claim that

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a single electron transfer (SET) is the major Cl• reaction, but others find that

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hydrogen(H)-atom abstraction from a carbon-hydrogen (C-H) bond is the major

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reaction.22-25 These inconsistencies cause difficulties in defining the reaction products

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(e.g., carbon-centered radical vs. alkoxyl radical) of each elementary reaction (e.g.,

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carbon-centered radical from H-abstraction vs. radical cation or Cl-adduct from SET).

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Furthermore, while HO• predominantly attacks the α–position of organic compounds,26 it

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is unclear whether chlorine-derived radicals selectively react with specific sites of organic

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compounds. This reactivity can affect the branching ratio of reaction pathways and the

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estimation of the byproducts.

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Ab initio quantum mechanical (QM) calculations are robust techniques to identify

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elementary reaction pathways, and they can be used to predict aqueous-phase reaction

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rate constants. Successful applications of these calculations include an identification of

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elementary reaction steps and determining rate constants for HO• reactions with

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phthalate27 and ibuprofen28, as well as those for the formation of N-nitrosodimethylamine

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during ozonation.29 These studies, in general, calculated the aqueous-phase enthalpies

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and free energies of reaction to identify the thermodynamically preferable reaction

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pathways (e.g., ozone30) and free energies of activation for reaction rate constants (e.g.,

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HO• 31-33). While the use of ab initio QM methods can be applied for H-abstraction by

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Cl•, the lack of applicable theory and experimental evidence limits the QM application to

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SET reactions. The Marcus theory34 was used to calculate the aqueous-phase free

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energies of reaction for SET reactions, but significantly higher values were reported

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compared with those for H-abstraction and HO• addition due to the uncertainty of the

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reorganization of water molecules.35

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In this study, we use ab initio QM calculations to identify the dominant reaction

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mechanisms for chlorine-derived radicals to ultimately develop an elementary reaction-

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based UV/chlorine kinetic model. Our hypothesis is that for chlorine-derived radical

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reactions, the theoretically calculated aqueous-phase free energies of reaction (i.e.,

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react ) are linearly correlated with kexp based on a linear free energy relationship ∆Gaq,calc

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(LFER),35 and the theoretically calculated aqueous-phase free energies of activation (i.e.,

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act ) are linearly correlated with kexp based on Eyring’s transition state theory ∆Gaq,calc

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(TST)36 under the same reaction mechanism. Once these correlations are developed, we

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can predict the reaction rate constants for reactions that have not been investigated

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experimentally; these results will be used to solve ODEs for predicting the formation of

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byproducts.

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Materials and Methods

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All of the ab initio molecular orbital and density functional theory (DFT)-based QM

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calculations were performed with the Gaussian 09 revision D.02 program37 using the

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Michigan Tech high performance cluster “Superior”. The electronic structures of the

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molecules and radicals in the ground and transition states were optimized at the level of

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B3LYP/6-31G(2df,p) implemented in Gaussian-4 theory (G4)38 in both the gaseous and

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aqueous phases. The aqueous-phase calculations were performed using an implicit

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polarizable continuum model [universal solvation model (SMD)].39 Previously, we

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verified the combination of G4 with the SMD model by successful application to other

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aqueous-phase radical-involved reactions.40 The Supporting Information provides the

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detailed calculations of the transition state search, the aqueous-phase free energies of

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activation and reaction, and the associated computational methods.

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Results and Discussion

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Reactivity of Chlorine-derived Radicals with Inorganic Radicals

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Table 1 summarizes each elementary reaction in the UV/chlorine AOP, the literature-

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react values at 25 °C and the chemical reaction reported kexp as well as our calculated ∆Gaq,calc

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rate constant (kchem) obtained from the relationship with the diffusion reaction rate

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constant (kD) from kexp (equation 1).

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kexp =

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react We find a LFER between lnkchem and ∆Gaq,calc (Figure 1). With the decrease in the

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react values below -20 kcal/mol, the kchem values became constant at approximately ∆Gaq,calc

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(1.0-2.0) × 1010 M-1s-1 because of the limitation of the diffusion contribution and the

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exothermic reactions caused by the highly hydrolyzed reaction products in the aqueous-

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phase. Our calculated kD values using Smoluchowski’s equation41 (see Supporting

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information) are approximately 1.1 × 1010 M-1s-1 and the upper kexp value is

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approximately 8.0 × 109 M-1s-1; therefore, the kchem value can be estimated as 2.9 × 1010

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M-1s-1, which is close to the observed kchem values in Figure 1. In general, the G4 method

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provides 0.83 kcal/mol of average absolute deviation from the experimentally obtained

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gaseous-phase energy values.38 The SMD model at the various levels of DFT methods

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with a 6-31G* basis set provides mean unsigned errors of 0.6-1.0 kcal/mol in solvation

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free energies for neutral compounds and 4 kcal/mol on average for ions.39 Based on the

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react estimated computational error, ±5.0 kcal/mol of ∆Gaq,calc , corresponding to ±2.8 of

k D kchem kD +kchem

(1)

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lnkchem, it is found that 64% of kexp is within this error from the LFER. Indeed, many

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radical-involved reactions such as addition, SET, and H-abstraction do not follow the

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thermodynamic law, and kinetics may overrun thermodynamics.30 However, our findings

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react indicate that ∆Gaq,calc can be used to predict the rate constants. The LFER can also be

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used to evaluate the series of kexp values systematically and provide critical feedback for

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future experimental studies. In the following section, we discuss each chlorine-derived

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inorganic radical reaction.

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(Table 1 goes here)

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(Figure 1 goes here)

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Reactions with Hypochlorous Acid/Hypochlorite Ions

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While Cl• reacts with both HOCl and OCl- rapidly (i.e., 3.0 × 109 M-1s-1 in reaction 1 and

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8.2 × 109 M-1s-1 in reaction 3)42, there is disagreement among the kexp values for the

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reaction of HO• with HOCl (8.5 × 104 M-1s-1 3, 1.1-1.4 × 108 M-1s-1 19, and 2.0 × 109 M-1s-

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1 18

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H bond of HOCl by Cl• and HO• as 14.7 kcal/mol and 11.8 kcal/mol, respectively. The

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act addition of 1~3 explicit water molecules did not significantly change the ∆Gaq,calc values.

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act The calculated ∆Gaq,calc value is apparently too large for the observed kexp of 108 ~ 109 M-

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1 -1

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act allows the estimation of the kexp value of 8.5 × 104 M-1s-1 to correspond with the ∆Gaq,calc

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act value. Second, the ∆Gaq,calc values for Cl-abstraction by Cl• and HO• are 3.2 kcal/mol

act in reaction 2). First, we calculated ∆Gaq,calc for the H-abstraction reaction from an O-

act s for Cl• because 109 M-1s-1 of kexp corresponds to ~2 kcal/mol of ∆Gaq,calc . This result

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and 8.4 kcal/mol, respectively. However, while the gaseous-phase Cl-abstraction with a

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product of Cl2 was reported53, the experimentally observed product, ClO•, in the aqueous-

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phase is different from Cl2, thus eliminating the possibility of Cl-abstraction. Third, we

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act obtained ∆Gaq,calc values of 4.6 kcal/mol and 7.2 kcal/mol for the formation of the Cl- or

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HO-adduct, respectively, between each radical and the oxygen atom of HOCl. However,

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react our theoretically calculated ∆Gaq,calc values are positive and the adduct formation

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react reactions are not thermodynamically favorable. Finally, the ∆Gaq,calc value for a SET

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between HOCl and Cl• was calculated for the products of ClO• and HCl, and this energy

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is found to be negative (i.e., -5.2 kcal/mol). Consequently, Cl• reacts with HOCl via a

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act , as shown in Figure SET. In this case, the kexp value adheres to the LFER with ∆Gaq,calc

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1. In contrast, HO• does not react with an oxygen or chlorine atom of HOCl via SET.15

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The investigations above lead to the conclusion that H-abstraction from the O-H bond of

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HOCl by HO• is more reasonable, as this mechanism is consistent with the observed

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product (i.e., ClO•). Furthermore, our estimation of kexp for HO• is supported by Curtin-

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Hammett principle54,55 describing that dominant species (i.e., HOCl) in equilibrium with

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OCl- at pH below pKa has lower reactivity with an identical reactant (i.e., HO•)

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compared to that for minor species (OCl-).

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react For the reaction with OCl-, the ∆Gaq,calc values for SET are -23.1 kcal/mol for the

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reaction with Cl• producing •OCl and Cl- and -5.2 kcal/mol for the HO• reaction

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producing •OCl and HO-; therefore, SET for these reactions is thermodynamically

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favorable. This reaction mechanism is verified by the LFER and is consistent with the

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experimental observation.42,43 9



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Reactions with Chlorine-Derived Radicals

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react Cl• reacts with Cl- to produce Cl2•- reversibly. The ∆Gaq,calc for reaction 5 is -13.1

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kcal/mol and adheres to the LFER. Since Cl2•- is a stable radical, the reverse reaction 7 is

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substantially slow (kexp ~105 M-1s-1). Cl2•- is an intermediate species as Cl2•- that

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subsequently reacts with other radicals and undergoes uni-molecular decay. Cl• also

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react reacts with Cl2•- very rapidly to produce molecular chlorine, Cl2, via SET with a ∆Gaq,calc

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value of -37.5 kcal/mol (reaction 8). Molecular chlorine Cl2 is also produced from the

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disproportionation reaction of Cl2•- (reaction 9). A subsequent Cl-Cl bond rupture at

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different sites forms the different products, such as Cl2 or Cl3-. Cl3- produces Cl2 and Cl-

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react via a slightly exothermic reaction with a value of -0.22 kcal/mol for ∆Gaq,calc (reaction

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11). Molecular chlorine also reacts with Cl- to produce stable Cl3- (reaction 6). Because

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the reactions 6 and 11 do not undergo radical-involved single electron transfer, we did

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not include these in the correlation analysis for LFER. Because of the nature of Cl2•-, the

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react reaction of Cl2•- with HO• produces stable HOCl (reaction 10) with a negative ∆Gaq,calc

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value (i.e., -34.5 kcal/mol), which is substantially different from the reaction of Cl• with

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HO•. Finally, we investigated the reactivity of ClO•. In our preliminary non-steady-state

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kinetic simulation of the UV/chlorine system that followed the changes in pH, a

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significant amount of •ClO was produced (10-4 ~10-5 mol/L under typical low-pressure

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UV lamps with 4~5 mgCl2/L in DI water at an approximately neutral pH initially).

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Limited information is available for the reactivity of •ClO with other species.5,7,11 The

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disproportionation reaction of ClO• was reported as (2.5~7.5) × 109 M-1s-1 (reaction

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22).42,43 We identified a thermodynamically stable pathway via an adduct of Cl-O…O-Cl

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react with -8.1 kcal/mol of ∆Gaq,calc , which adheres to the LFER. We propose that O2 and Cl•

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are the primary reaction products and postulate that this Cl• is rapidly hydrolyzed to

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produce •Cl(H2O), as shown experimentally.42 The majority of chlorine-derived radical

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reactions (reactions 5~11 and reaction 22) in the UV/chlorine AOP undergoes either

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radical combination or SET, and these reactions are found to adhere to the LFER in

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Figure 1.

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Formation of •OHCl- and •Cl(H2O)

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The formation of •OHCl- from the reaction of HO• with Cl- (reaction 12) has been studied

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experimentally46,55 and theoretically56-58 due to the intriguing nature of the reactions.

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While the majority of chlorine-derived reactions with other inorganic radials adheres to

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the LFER, the reactions involving •OHCl- do not apparently adhere to this relationship.

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Our attempt here is to identify the thermodynamic properties for reactions 12 by

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examining various solvated states of the •OHCl- species and to determine whether these

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reactions adhere to the LFER.

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The reaction of HO• with Cl- to produce a covalently bonded adduct, Cl- -•OH ,

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react was found to be endothermic with a ∆Gaq,calc value of 2.99 kcal/mol, which is

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inconsistent with the LFER. We added explicit water molecule(s) to hydrolyze Cl• and

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react found that while the ∆Gaq,calc value with one water molecule remained positive (i.e., 3.7

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react kcal/mol), the ∆Gaq,calc values became negative with two (i.e., -1.87 kcal/mol) and three

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explicit water molecules (i.e., -2.4 kcal/mol). The adduct with 2 or 3 explicit water

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molecules has a charge of -0.95 on Cl and 7% of the spin density distribution on Cl with

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the hemi-bonded structure, which is consistent with the ESR observation.46 With this

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react value, reaction 12 adheres to the LFER. Our observations with explicit water ∆Gaq,calc

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molecules are consistent with previous theoretical studies56-58 and highlight the

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importance of including explicit water molecules in calculating the thermodynamic

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properties of Cl- -•OH . For reaction 19, we observed the formation of a covalently

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bonded adduct •Cl(H2O) in the absence or presence of explicit water molecules.

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react values were positive Regardless of the addition of explicit water molecules, the ∆Gaq,calc

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but still adhered to the LFER because of the observed smaller kexp (i.e., ~105 M-1s-1). We

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propose that reaction 19 undergoes hydration where water molecules form new covalent

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bonds to •Cl.

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Reactivity of Chlorine-derived Radicals with Organic Compounds

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Chlorine Radicals

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act react We calculated the ∆Gaq,calc and ∆Gaq,calc values for each elementary reaction with 31

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organic compounds, including 9 alcohols, 5 aldehydes and ketones, 6 carboxylic acids

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and carboxylates, 6 esters and ethers, 2 haloalkanes, 2 alkenes and 1 aromatic compound

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(Table S1 of the Supporting Information).

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Overall, we find linear correlations for H-abstraction from a C-H bond and Cl-

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act act adduct formation between lnkexp and ∆Gaq,calc , respectively (i.e., lnkexp = -0.50 ∆Gaq,calc

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act +20.53 for H-abstraction from 23 organic compounds and lnkexp = -0.95 ∆Gaq,calc + 23.43

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for Cl-adduct formation from 14 alcohols and carboxylic compounds) (Figures 2 and 3).

251

The linear correlation results from Eyring’s TST based on quantum and statistical 12


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mechanics using partition functions to quantize energy states of reactants and activated

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intermediates.36 Note that the conventional TST requires an accuracy of ±0.4 kcal/mol of

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act to predict kexp within a difference of a factor of two from the experimental ∆Gaq,calc

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observations, which is analogous to the experimental accuracy of kinetic measurements.

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act Accordingly, the direct calculation of k based on ∆Gaq,calc values is not feasible because

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the estimated computational error resulting from the corresponding QM method exceeds

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the required accuracy. Based on the estimated computational error, ±5.0 kcal/mol of

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act , corresponding to ±2.4 of lnkchem, it was found that 96% of kexp is within this ∆Gaq,calc

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error from the linear correlation for H-abstraction. For Cl-adduct formation, based on the

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act ±5.0 kcal/mol of ∆Gaq,calc , corresponding to ±4.8 of lnkchem , it was found that 100% of

262

kexp is within the error from the linear correlation. Therefore, the linear correlations

263

developed here are valid within the estimated computational error and can be used to

264

predict k for compounds that have not been examined experimentally. Note that we did

265

react not observe the LFER based on our calculated ∆Gaq,calc for the reactions with organic

266

compounds, most likely because kinetics overrun thermodynamics for these reactions. In

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the following section, we discuss each Cl• reaction with organic compounds.

268

(Figures 2 and 3 go here)

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Alcohols

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A total of 9 compounds containing alcohol functional groups were investigated in this

271

study. Ninety nine percent of formaldehyde61, 55% of acetaldehyde62, and 0.1% of

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acetone are hydrolyzed to form geminal diols in the aqueous-phase; therefore, hydrated

13



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act forms of these compounds were included in the alcohol group. The calculated ∆Gaq,calc

274

values for H-abstraction from a C-H bond ranged from -4.5 kcal/mol to 5.3 kcal/mol.

275

act The experiment-based ∆Gaq,exp values calculated from the Arrhenius kinetic parameters

276

are 3.6±1.0 ~ 5.3±1.2 kcal/mol. Notably, both the theoretical calculation and the

277

act experimental values had the highest ∆Gaq,exp for methanol. The estimated k based on the

278

linear correlation for methanol was 6.0 × 107 M-1s-1, which was more than one order of

279

magnitude smaller than the value of kexp. The kexp value for H-abstraction from C-H bond

280

at β-position of ethanol also indicated the similar trend. Therefore, we did not include

281

these data points in the correlation. Except for methanol, we observe a linear correlation

282

act between kexp and ∆Gaq,calc obtained from the H-abstraction of all tested alcohols (Figure

283

2). Regardless of the addition of 1~3 explicit water molecule(s), no significant changes

284

act were observed in the ∆Gaq,calc values for methanol. This finding is probably because

285

methanol does not undergo H-abstraction by Cl• but by another reaction mechanism. For

286

H-abstraction from the oxygen-hydrogen (O-H) bond of alcohol functional groups, the

287

act values ranged from 5.4 kcal/mol to 12.0 kcal/mol, indicating the insignificance ∆Gaq,calc

288

react of this reaction. The calculated ∆Gaq,calc values for SET are positive and range from 23.6

289

kcal/mol to 27.1 kcal/mol for all the tested alcohols. Consequently, our theoretical

290

calculations indicate that SET by Cl• is not thermodynamically favorable.

291 292

Next, we investigated the formation of a Cl-adduct by the reaction of Cl• with the oxygen of alcohol functional groups. This reaction was studied because ab initio QM

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act calculations do not allow the calculation of ∆Gaq,calc for a specific site via SET, although

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act Gilbert (1988) proposed SET for these sites.22 The ∆Gaq,calc values range from 2.3

295

kcal/mol to 3.8 kcal/mol, indicating that the formation of the Cl-adduct competes with H-

296

atom abstraction reactions; accordingly, another linear correlation is found (Figure 3).

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The investigation here reveals that Cl• forms an adduct with the OH of alcohols and

298

subsequently SET is thought to occurs. Note that the data point for methanol is

299

consistent with a linear correlation, and Cl-adduct formation is the dominant mechanism

300

for methanol.

301

act To investigate the selectivity of Cl• for H-abstraction, we compared the ∆Gaq,calc

302

act values for longer chain alcohols. The ∆Gaq,calc values at the α- and β-positions of

303

ethanol are -2.4 kcal/mol and 4.8 kcal/mol, respectively. This observation agrees with

304

the experimentally obtained partial rate constants for ethanol (1.5 × 109 M-1s-1 at the α-

305

position and 7.5 × 108 M-1s-1 at the β-position).22 A similar trend was observed for 1-

306

propanol and 2-butanol (Table S2 of the Supporting Information). In general, Cl•

307

reactions have an earlier transition state with a lower occurrence of bond breaking and a

308

contribution from the resonance stabilization of H-abstraction at the α-position in the

309

transition state.22 This fact explains why the calculated bond length of carbon-hydrogen

310

is significantly shorter than that of the hydrogen-chlorine bond at the transition states.

311

Because of this phenomenon, Gilbert proposed the non-selective reactivity of Cl•;22

312

however, our calculations do not support this concept. Except for methanol, the

313

act values at the α-positions for the other 8 alcohols are much smaller (i.e., -5.3 ~ ∆Gaq,calc

15



314

2.0 kcal/mol). Our observation of the selective Cl• reactivity for H-abstraction can be

315

explained with the bond dissociation energies (BDE) of the C-H bonds in alcohols at

316

various positions25, although the BDE are measured in the gaseous-phase. For example,

317

the BDE of C-H at α- and β-positions in ethanol are 95.8 kcal/mol and 100.7 kcal/mol,

318

respectively.63 Similar trend can be seen for the BDE of 2-propanol (i.e., 91.7 kcal/mol

319

and 94.3 kcal/mol at α- and β-positions, respectively).

320

Aldehydes and Ketones

321

act The ∆Gaq,calc values for H-abstraction for a total of 5 aldehydes and ketones range from

322

0.17 kcal/mol to 7.1 kcal/mol, which are significantly larger values than those for

323

alcohols. These values are consistent with the kexp (i.e., 106~108 M-1s-1). In general, H-

324

abstraction involves a considerable charge separation between the negatively charged

325

chlorine atom and the positively charged hydrogen that is abstracted from a C-H bond in

326

act the transition state.22 As a result, a higher ∆Gaq is required for the reaction to occur.

327

Two reported kexp values for acetone have a large discrepancy (i.e., < 5.0 × 106 M-1s-1 23

328

and (7.8 ±0.7) × 107 M-1s-1 24). We investigated 0.1% of the hydrolyzed form of

329

act acetone,64 but we did not observe a significant difference in the ∆Gaq,calc values compared

330

with those for acetone. We find that a kexp of (7.8 ±0.7) × 107 M-1s-1 is consistent with the

331

linear correlation in Figure 2. It was found that the data point of chloroacetone

332

significantly decreased the linear correlation in Figure 2. It is not clear whether our

333

act or the kexp value caused the significant inconsistency with the correlation for ∆Gaq,calc

334

chloroacetone. Because of this, we did not include chloroacetone in the assessment of the

16


Page 16 of 38

Page 17 of 38


335

act linear correlation in Figure 2. An investigation of the ∆Gaq,calc values for

336

propionaldehyde (i.e., an aldehyde with a longer hydrocarbon branch) indicates that the

337

reactivity at the α-position (6.9 kcal/mol) is slightly higher than that at the β-position (7.1

338

kcal/mol).

339

Carboxylic Acids and Carboxylates

340

A total of six carboxylic compounds including dissociated forms of formate and acetate

341

were evaluated in this study. The dissociated forms of formate and acetate show higher

342

reactivity with Cl• than that of non-dissociated forms by approximately one order of

343

magnitude. Two inconsistent kexp values were reported for formic acid [(1.3±0.1) × 108

344

M-1s-1 23 and (2.8 ±0.3) × 109 M-1s-1 25] and acetic acid [[(3.2±0.2) × 107 M-1s-1 23 and

345

act (1.0±0.2) × 108 M-1s-1 25]. Our ∆Gaq,calc values for H-abstraction from a C-H bond of

346

formate and formic acid are -10.1 kcal/mol and 15 kcal/mol, respectively, and these

347

act values deviate greatly from the linear correlation in Figure 2. The ∆Gaq,calc values for the

348

same reaction for acetate and acetic acid are 0.94 kcal/mol and 5.3 kcal/mol, respectively,

349

act and both values agree with the linear correlation in Figure 2. The ∆Gaq,calc value for

350

act acetic acid is close to the ∆Gaq,exp of 6.7±2.4 kcal/mol.25 Consequently, the dominant

351

reaction mechanism for carboxylic acids/carboxylates, except for formic acid/formate, is

352

H-abstraction from a C-H bond; the same trend was also observed for propionic acid and

353

isobutyric acid.

17



354

To investigate the reaction mechanism for formate and formic acid, we calculated

355

act the ∆Gaq,calc for the Cl-adduct formation of formate and formic acid as 1.4 kcal/mol and 6

356

act kcal/mol, respectively, showing good agreement with the ∆Gaq,exp values (i.e., 3.8±0.48

357

kcal/mol for formate25 and 4.8±1.4 kcal/mol for formic acid25). Similarly, we obtained a

358

act value of 1.2 ~ 6.0 kcal/mol for the Cl-adduct formation for all other tested ∆Gaq,calc

359

carboxylic acids and carboxylates and found a linear correlation, as shown in Figure 3.

360

As was observed for the tested alcohols, Cl• reacts with carboxylic/carboxylate groups

361

via both H-abstraction and Cl-adduct formation. In particular, formate and formic acid

362

undergo Cl-adduct formation dominantly.

363

Esters and Ethers

364

Four of the kexp values for the tested esters show very low reactivity with Cl• (i.e., < 108

365

M-1s-1)24, and one kexp value for the tested diethyl ethers shows a much larger value of

366

(1.3±0.1) × 109 M-1s-1.25 This simple comparison implies that the overall reaction

367

mechanism with Cl• is H-abstraction from a C-H bond that is affected by the neighboring

368

act –COO- functional group. Our ∆Gaq,calc values range from -2.6 kcal/mol to 16.4

369

kcal/mol, and there is a linear correlation for these compounds under H-abstraction.

370

act Our ∆Gaq,calc values indicate that the H-abstraction from a C-H bond that is

371

bound to a –C(O)O functional group is preferable to H-abstraction from a C-H bond that

372

is bound to a –OC(O) functional group because of the stronger electron-withdrawing

373

effect from the –OC(O) functional group (e.g., a Taft constant of 2.00 for COOCH3 and

18


Page 18 of 38

Page 19 of 38


374

2.45 for OCOCH3).65 We observed the same effect from the ether functional group (-O-)

375

in diethylether and methyl-tert-butyl ether.

376

Halogenated alkanes

377

act The ∆Gaq,calc value for dichloromethane for H-abstraction from a C-H bond is 4.9

378

kcal/mol, which is consistent with the correlation in Figure 2. We were unable to find the

379

aqueous-phase transition state for trichloromethane in the absence and presence of 1~3

380

act explicit water molecules. The gaseous phase ∆Ggas,calc values (i.e., 4.8 kcal for

381

dichloromethane and 4.7 kcal/mol for trichloromethane) suggest a smaller value of

382

act for trichloromethane than that of dichloromethane if the solvation effect is ∆Gaq,calc

383

linear.

384

Alkenes and Aromatic Compounds

385

Two kexp values were reported as 1.9 × 108 M-1s-1 66 and 4.88 × 1010 M-1s-1 67 for

386

trichloroethylene and one kexp value of 2.8 × 108 M-1s-1 for perchloroethylene68. The

387

act values are 2.5 kcal/mol for Cl• addition to an unsaturated carbon (C) of ∆Gaq,calc

388

HClC=CCl2 and -0.25 kcal/mol for addition to HClC=CCl2. For perchloroethylene, we

389

act obtain a ∆Gaq,calc value of -0.49 kcal/mol. In the reaction of HO• with alkenes, the

390

addition occurs on an unsaturated carbon that has fewer functional groups because of the

391

stability of the generated germinal chlorohydrin carbon-centered radical; this finding is

392

act supported by our calculated ∆Gaq,calc (5.9 kcal/mol for HClC=CCl2 and 10.5 kcal/mol for

393

HClC=CCl2). However, our calculations indicate less selectivity for Cl• addition to the

19



394

act unsaturated carbons of alkenes. In addition, the calculated ∆Gaq,calc for Cl• addition is

395

much smaller than that for HO•. At this point, it is unclear what caused this result, as we

396

act have only two kexp values for alkenes. If the ∆Gaq,calc values are correct, then kexp should

397

be close to the diffusion limited rate constant, such as 4.88 × 1010 M-1s-1 67.

398

act The ∆Gaq,calc value for the addition of Cl• to an aromatic benzene ring is 8.9

399

react kcal/mol, yielding a chlorocyclohexadienyl radical as the product with a ∆Gaq,calc of -2.7

400

kcal/mol, which agrees with the experimental observation69. This Cl• addition to a

401

benzene ring is similar to that of HO• in which a hydroxycyclohexadienyl radical is

402

act formed as a product ( ∆Gaq,calc of 9.9 kcal/mol). While we were unable to locate the

403

transition state for H-abstraction from the benzene ring by Cl•, we obtained a value of

404

act 11.6 kcal/mol of ∆Gaq,calc for H-abstraction by HO•. Thus, we conclude that H-

405

abstraction from the benzene ring is a minor reaction and that addition to the benzene

406

ring is the major reaction mechanism. Although Martire et al. (2001)70 did not report the

407

kexp for an individual compound, their reported kexp, (1.8±0.3)×1010 M-1s-1, for

408

chlorobenzene, toluene, and benzoic acid and the reaction mechanisms are consistent

409

with our findings based on our QM calculations.

410

Reactivity of Cl2•- and ClO•

411

Because of the space limitation, a detailed discussion on the reactivity of Cl2•- and ClO•

412

with organic compounds is found in the Supporting Information.

20


Page 20 of 38

Page 21 of 38


413

Environmental Implications

414

The systematic evaluations of kexp with the LFER and TST-based correlations based on

415

ab initio QM calculations highlight several key gaps in the understanding of the reactivity

416

of chlorine-derived radicals. Previous experimental studies have shown discrepancies

417

among the kexp values for some Cl• and HO• radicals with inorganic species, particularly

418

act for the reaction of HO• with HOCl. Our investigations based on the ∆Gaq,calc and

419

react values revealed that H-abstraction is the major reaction mechanism, which ∆Gaq,calc

420

supports the kexp of 8.5 × 104 M-1s-1. This kexp value is critical in developing an

421

elementary reaction-based kinetic model because HOCl is the more dominant species at

422

an approximately neutral or below neutral pH, which is the typical condition in the

423

UV/chlorine AOP. In addition, the lower scavenging effect of HO• by HOCl indicates

424

that more HO• is used to destroy target organics and microorganisms in the UV/chlorine

425

AOP. We are currently evaluating this dynamic effect by developing our elementary

426

reaction-based kinetic model. The established LFER can also be used to evaluate the kexp

427

values in the literature and can provide mechanistic insight into various elementary

428

reaction mechanisms.

429

The systematic evaluations of the reactions of Cl• with a wide variety of organic

430

act react and ∆Gaq,calc values revealed the dominant reaction compounds based on the ∆Gaq,calc

431

mechanisms. Although a product study is necessary to confirm the reaction byproducts,

432

the identification of the major reaction mechanisms such as H-abstraction and Cl-adduct

433

formation for alcohol and carboxylic functional groups will help formulate an elementary

434

reaction-based kinetic model. The established correlation can be used to predict the

21



435

unknown reaction rate constants that have not been experimentally measured and to

436

screen a large number of potential organic contaminants for the applicability of the

437

UV/chlorine AOP. Finally, chlorine-derived radical species play critical roles in other

438

environmental processes, such as the formation of atmospheric water droplets, and

439

findings from this study can be used to advance the understanding of those environmental

440

processes.

441

Associated Content

442

Supporting information includes a table that summarizes the reactivity of Cl• with

443

organic compounds. The SI also includes detailed descriptions of the methods for the

444

theoretical calculations, the diffusion-limited reaction rate constants, the reactivity

445

of Cl• with aromatic compounds, and the reactivity of Cl2•- and ClO• with organic

446

compounds.

447

Acknowledgement

448

This work was partially supported by the National Science Foundation Award #:

449

CBET-1435926. Any opinions, findings, conclusions, or recommendations

450

expressed in this publication are those of the authors and do not necessarily reflect

451

the view of the supporting organization.

22


Page 22 of 38

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452

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Yamaguchi, M. Hemibonding of hydroxyl radical and halide anion in aqueous solution. J. Phys. Chem. A. 2011, 115, 14620-14628.

59.

Sevilla, M.D.; Summerfield, S.; Eliezer, I.; Rak, J.; Symons, M.C.R. Interaction

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of the chlorine atom with water: ESR and ab initio MO evidence for three-

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electron (σ2σ*1) bonding. J. Phys. Chem. A. 1997, 101, 2910-2915.

629 630

60.

Valiev, M.; D’Auria, R.; Tobias, D.J.; Garrett, B.C. Interactions of Cl- and OH radical in aqueous solution. J. Phys. Chem. A. Lett. 2009, 113, 8823-8825.

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edition. 2015, Cengage Learning. 62.

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Kurz, J.L. The hydration of acetaldehyde. I. Equilibrium thermodynamic parameters. JACS. 1967, 59 (14), 3524-3528.

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McMurry, J. Nucleophilic addition of H2O: Hydration in Organic Chemistry 9th

Lide, D.R.; Frederikse, H.P.R. in CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 2013-2014.

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Greenzaid, P.; Rappoport, Z.; Samuel, D. Limitations of ultra-violet spectroscopy

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for the study of the reversible hydration of carbonyl compounds. J. Chem. Soc.

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1967, 63, 2131-2139.

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Karelson, M. Molecular Descriptors in QSAR/QSPR; John Wiley & Sons, Inc.: New York, 2000.

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Li, K.; Stefan, M.I.; Crittenden, J.C. Trichloroethene degradation by UV/H2O2

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advanced oxidation process: Product study and kinetic modeling. Environ. Sci.

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Technol. 2007, 41, 1696-1703.

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study and kinetic modeling. 2004, 38, 6685-6693. 68.

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Li, K.; Stefan, M.I.; Crittenden, J.C. UV photolysis of trichloroethylene: Product

Martens, R.; von Sonntag, C. Photolysis (λ=254 nm) of tetrachloroethene in aqueous solutions. J. Photochem. Photobiol. A: Chemistry. 1995, 85, 1-9.

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Alegre, M.L.; Geronés, M.; Rosso, J.A.; Bertolotti, S.G.; Braun, A.M.; Mártire,

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D.O.; Gonzalez, M.C. Kinetic study of the reactions of chlorine atoms and Cl2•-

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radical anions in aqueous solutions 1. Reaction with benzene. J. Phys. Chem. A.

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2000, 104, 3117-3125.

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653

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Mártire, D.O.; Rosso, J.A.; Bertolotti, S.; Roux, G.C.L.; Braun, A.M.; Gonzalez,

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M.C. Kinetic study of the reactions of chlorine atoms and Cl2•- radical anions in

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aqueous solutions. II. Toluene, benzoic acid, and chlorobenzene. J. Phys. Chem.

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A. 2001, 105, 5385-5392.

657

32


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Page 33 of 38


658

Figure Captions

659

react Figure 1: Linear free energy relationship between lnkchem and ∆Gaq,calc for chlorine-

660 661 662 663 664 665 666

derived inorganic radical reactions. ◊ : reactions with HOCl/OCl-, : Cl• and Cl2•involving reactions, : •OHCl- involving reactions, and : OCl• reaction. The vertical bar results from the range of the reported kexp values in the literature. Note that data points 6 and 11 are not included in the LFER analysis due to the different reaction mechanism.

667

act Figure 2: Linear correlation between lnkexp and ∆Gaq,calc for H-abstraction by Cl• from a

668 669 670 671 672 673 674 675 676 677 678

C-H bond. The vertical bar results from the range of the reported kexp values in the literature. 2: ethanol (α-position); 3: 1-propanol; 4: 2-propanol; 5: 2-butanol; 6: tertbutanol (C-H bond); 6’ tert-butanol (O-H bond): 7: hydrated formaldehyde; 8: acetaldehyde; 9: hydrated acetaldehyde; 10: propionaldehyde; 11: acetone; 14: 2butanone; 17: acetate; 18: acetic acid; 19: propionic acid; 20: isobutyric acid; 21: methylformate; 22: ethylformate; 23: methylacetate; 24: ethylaceate; 25: diethyl ether; 26: methyl-tert-butyl ether, and 28: dichloromethane. Note that compounds are not included from 1: methanol; 12: hydrated acetone; 13: chloroacetone; 15: formate, and 16: formic acid due to either different mechanism or uncertainty.

679

act Figure 3: Linear correlation between lnkexp and ∆Gaq,calc for Cl-adduct formation of

680 681 682 683 684 685 686 687 688 689 690 691 692

alcohol and carboxylic compounds. The vertical bar results from the range of the reported kexp values in the literature. 1: methanol; 2: ethanol; 3: 1-propanol; 4: 2-propanol; 5: 2butanol; 6: tert-butanol; 7: hydrated formaldehyde; 9: hydrated acetaldehyde; 15: formate; 16: formic acid; 17: acetate; 18: acetic acid; 19: propion acid, and 20: isobutyric acid.

693

react literature and our calculated ∆Gaq,calc , kchem, and kD values.

Table Captions Table 1: Twenty-two elementary reactions in the UV/chlorine AOP with kexp values in the

694 695

33



Page 34 of 38

30 25

9

8

12 5

21

20

4 17

14

3

10

1 16 22

lnkchem

15

15

13 y = -0.53x + 17.25 R² = 0.78

10

19 7

11 6 18

20

5 0 -40 696 697

-20 0 ∆Greactaq,calc, kcal/mol

Figure 1

34


20

Page 35 of 38


25 4

3 26

17 20

5

6 8 18

25

20

2

7 14

lnkexp

6

19

24

11

9

22 21

13

15

28

10 23

y = -0.50x + 20.53 R² = 0.70

10

5

0 -10 698 699

-5

0

5 ∆Gactaq,calc, kcal/mol

Figure 2

35


10

15


25

17

4

5

1

20

15

2 19 6

20 3

7 9

lnkexp

Page 36 of 38

16 18

15

y = -0.95x + 23.43 R² = 0.70

10

5

0 0 700 701

2

4 6 ∆Gactaq,calc, kcal/mol

Figure 3

702

36


8

Page 37 of 38


703

Table 1

No.

Elementary reaction

kexp, M-1s-1

References

HOCl + Cl• → •OCl + HCl HOCl + Cl• → Cl2 + HO-

1

3×109

42

HOCl + Cl• → HOCl(Cl•) HOCl + HO• → •OCl + H2O 4

-5.9

3.2

-132.6

4.6

4.6

11.8

-20.8

8.4 7.2

kD , M-1s-1

4.2×109

1.1×1010

0

8.5×104 2.4×109

8.5×104 1.2×1010

3.3×1010 3.4×1010

1.1×1010 1.2×1010

HOCl + HO• → HO• + HOCl 8.46×10 - 2.0×10

3 4

HOCl + HO• → HOCl(HO•) OCl- + Cl• → •OCl + Cl8.2×109 OCl- + HO• → •OCl + HO8.8×109

42 43

5.7 -23.1 -5.2

5

Cl- + Cl• → Cl2•-

6.5-8.5 × 109

42,44

-13.1

1.6×1010

1.1×1010

6

Cl- + Cl2 → Cl3-

2.0 × 104

45

0.22

2.0 × 104

1.0×1010

7

Cl2•- → Cl• + Cl-

5.2 × 104 - 1.4 × 105 44,46

13.1

5.2 × 104 1.4 × 105

1.2×1010

8

(2.1 ± 0.05) × 109

47

-37.5

2.6 × 109

1.1×1010

(0.9-9.0) × 109

46,48,49

-24.4 (-24.2) 1.0 × 109

1.0×1010

10

Cl• + Cl2•- → Cl2 + ClCl2•- + Cl2•- → Cl2 + 2Cl- (or Cl3- + Cl-) Cl2•- + HO• → HOCl + Cl-

1 × 109

50

-34.5

1.1 × 109

1.2×1010

11

Cl3- → Cl2 + Cl-

1.1 × 105

45

-0.22

1.1 × 105

1.2×1010

12

HO• + Cl- → •OHCl-

(4.3 ± 0.4) × 109

50

2.99 (-2.4)* 6.8 × 109

1.2×1010

13

Cl• + H2O → •OHCl- + H+

(1.6 ± 0.2) × 105

46

1.6 × 105

1.2×1010

14

Cl• + OH- → •OHCl-

1.8 × 1010

42

-14.9

1.8 × 1010

1.1×1010

15

Cl2•- + OH- → •OHCl- + Cl-

4.5 × 107

51

-1.8

4.5 × 107

1.0×1010

16

•OHCl- → HO• + Cl-

(6.1 ± 0.8) × 109

46

-2.99

17

•OHCl- + H+ → Cl• + H2O

(2.6 ± 0.6) × 1010

46

18

•OHCl- + Cl- → Cl2•- + OH-

1.0 × 105

51

1.84

1.0 × 105

1.0×1010

19

Cl• + H2O → •Cl(H2O)

2.5 × 105

52

3.8

2.5 × 105

1.3×1010

20

Cl2•- + H2O → •Cl(H2O) + Cl- 1.3 × 103

52

16.9

1.3 × 103

1.2×1010

21

•Cl(H2O) + Cl- → Cl2•- + H2O 5 × 109

52

-16.9

9.9 × 109

1.0×1010

22

•OCl + •OCl + H2O → HClO + HClO2

42,43

-8.1

3.3 27.0 × 109

1.1×1010

2.5 - 7.5 × 109

3,18,19

14.7

kchem, M-1s-1

2

9

704

9

∆Gactaq,calc ∆Greactaq,calc kcal/mol kcal/mol

*value with 2 explicit water molecules

37


1.0×1010 1.0×1010


UV HOCl/OCl- HO Cl Cl2- ClO H-abstrac1on? Cl-adduct? Electron-transfer?


Page 38 of 38

Mechanistic Insight into the Reactivity of Chlorine-Derived Radicals in

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