Reactivities of hydrated electrons with organic compounds in aqueous-phase advanced reduction processes †

Advanced reduction processes (ARPs) that generate reactive electrons in homogeneous solution and heterogeneous electrochemical or catalytic processes are effective in degrading oxidized forms of organic and inorganic contaminants. However, the detailed mechanisms of compounds with multiple functional groups and the effect of those functional groups on the reactivities of these compounds toward electrons have not been elucidated. In this study, we use density functional theory to calculate the aqueous-phase one electron reduction potential E red ; aq ° of 251 conventional organic compounds containing a wide variety of functional groups. We investigate three possible elementary reaction mechanisms, namely, the associative, concerted and stepwise cleavage mechanisms, at all possible reactive sites and determine the linear free energy relationships (LFERs) between the experimentally measured rate constants of hydrated electrons (e aq − ) and the E red ; aq ° values. In addition, we use the 75 priority per- and polyfluoroalkyl substance (PFAS) subsets from the United States Environmental Protection Agency (U.S. EPA) to calculate the E red ; aq ° values of all possible elementary reactions of each PFAS to determine their dominant reaction mechanisms and reactive sites. LFERs of conventional organic compounds are used to predict the reactivities of e aq − with PFASs, which can be used as a screening tool to evaluate the electron-induced degradability of thousands of PFASs for both homogeneous and heterogeneous reduction processes. Finally, we develop a kinetic model to investigate the impact of an accurate rate constant prediction on the fate of an environmentally relevant organic compound induced by e aq − in a homogeneous aqueous-phase ARP. advanced reduction processes. A computational tool can be used to screen a number of contaminants to prioritize for the reduction processes.


Introduction
Free radical-based technologies are attractive and promising processes for destroying a wide variety of organic contaminants. Advanced oxidation processes (AOPs) that generate highly reactive oxygenated radical species (e.g., hydroxyl radicals) 1,2 and other reactive radicals (e.g., chlorine-, 3,4 bromine-5 and nitrogen-derived radicals 6,7 and carbonate radicals 8 ) at ambient temperature and atmospheric pressure have been proven to degrade reduced forms of organic contaminants in water at full-scale treatment plants. Advanced reduction processes (ARPs) that generate reactive radicals (e.g., superoxide anion radicals) and electrons in homogeneous solution 9,10 and heterogeneous electrochemical [11][12][13] or catalytic 14 processes are effective in degrading the oxidized forms of organic and inorganic contaminants. Homogeneous, electrochemical, and a combination of both ARPs have been successfully applied for the degradation of conventional organic contaminants such as alkyl halides and emerging groups of contaminants such as per-and polyfluorinated alkyl substances (PFASs). 15 While the reactivities of reactive radical species in AOPs have been actively studied and some predictive approaches have been reported in the literature, 16 few studies have holistically focused on the reactivities of electrons in aqueous-phase ARPs. The reactivities of aqueous-phase hydrated electrons, e aq − , with a wide variety of individual organic compounds have been experimentally measured, and the second-order rate constants, k exp , have been reported and compiled in the database 17 (see Fig. S1 in the ESI † for a box plot of k exp values). However, few studies have developed a predictive tool for the k exp values of e aq − due to a lack of mechanistic understanding of the reactivities with organic compounds. 18,19 In general, nucleophilic electrons react at the electron-deficient sites of organic compounds. The three major reaction mechanisms include (1) association with the π bond of a double bond; (2) concerted dissociative cleavage of a carbon halogen (C-X where X = F, Cl, Br or I) bond of haloalkanes or carbon-nitrogen (C-N) bond; and (3) stepwise cleavage of a C-X bond of haloalkanes and haloalkenes, a sulfur-sulfur (S-S) bond or a carbon-sulfur (C-S) bond of sulfides or disulfides. 20 Each reaction mechanism depends on the molecular structures and functional groups present in the same molecule. The overall reactivities with e aq − are reduced by electron-donating functional groups and increased by electron-withdrawing functional groups. However, the detailed mechanisms of multiple functional group compounds and the effect of these functional groups on the major reactivities have not been elucidated because of the difficulties in experimental investigations. The use of quantum mechanics-based methods such as ab initio calculations or density functional theory (DFT) can complement experimental observations of chemical reactivities and provide mechanistic insight into reaction mechanisms. Several DFT-based methods were used to investigate the thermodynamics and kinetics of electron-induced reactions with halogenated compounds such as polychlorinated ethylenes, 21,22 polybrominated electrophiles, 23 and PFAS. [24][25][26] The dissociation and reductive cleavage of a given molecule were investigated based on the optimized electronic structures, bond dissociation energies and reduction potentials of the corresponding bond. The k exp values represent the overall reactivities, and thus, the elementary reaction mechanisms of the overall reaction cannot be known. Calculating the oneelectron reduction potential (E red;aq°, V) in the aqueous phase of each component in a given molecule can provide quantitative information about all possible reactive sites and help determine the rate-determining reaction mechanism with electrons, which is more advantageous than investigating conventional qualitative molecular descriptors such as lowest unoccupied molecular orbitals.
In this study, we use DFT to calculate the E red;aq°v alues of conventional organic compounds with a wide variety of functional groups to determine the linear free energy relationships (LFERs) with the experimentally measured rate constants of e aq − . In addition, we use the 75 priority PFAS subset from the U.S. EPA 27 and calculate the E red;aq°v alues of all possible elementary reactions of each PFAS to determine its dominant reaction mechanism and reactive sites. The determined LFERs of conventional organic compounds are used to predict the reactivities of e aq − with PFASs, which can be used as a screening tool for thousands of PFASs for electron-induced degradability. Fig. 1 demonstrates the flowchart of methods used in this study from the determination of LFERs for conventional organic compounds to the prediction of k chem values for PFAS. While we demonstrate the prediction of k exp values for e aq − in the homogeneous reduction processes, the reactivities of electrons via direct electron transfer on a heterogeneous-electrode can be extrapolated from the e aq − reactivities and the LFERs are also useful for the heterogeneous processes.

Materials and methods
According to the previous experimental studies reported in the literature, three major reaction mechanisms of e aq − include: (1) associative; (2) concerted dissociative; and, (3) stepwise dissociative mechanisms. In the associative mechanism, e aq − reacts with the π bond that can 'hold' an extra electron to form an anionic radical species. 20 Compounds containing carbonyl functional groups are examples of compounds that undergo associative reactions: Both concerted and stepwise mechanisms involve bond cleavage. In the concerted mechanism, single-electron transfer to a parent compound and bond cleavage occur simultaneously, as shown in eqn (2). During the stepwise mechanism, the initial barrierless step of single-electron transfer results in the formation of an intermediate radical anion that has a longer lifetime than the bond vibration time (i.e., 10 −13 s). 28 The intermediate radical anion then undergoes bond cleavage, as shown in eqn (3). The nonexistence of a radical anion is a sufficient condition for the concerted mechanism to occur, but it is not a necessary condition. Thus, under the concerted mechanism, an intermediate radical anion may have a finite lifetime. 29 RX + e aq − → R˙+ X − In general, it is suggested that compounds containing a σ bond and/or a weak C-X bond are reduced via a concerted mechanism, and compounds containing a π bond (e.g., CS, SS, NO 2 , CN, CC), strong C-X bonds (e.g., C-F), and/or electron withdrawing groups (e.g., -F, -CN, NO 2 , -CO) are reduced via the stepwise mechanism. 23,30 However, caution should be taken for compounds with strong electron withdrawing groups and halogenated alkenes because a concerted mechanism could possibly occur due to an unstable intermediate radical anion or the requirement of reduced reaction barriers. 22,23 To determine which of reduction mechanisms in eqn (1)-(3) is the rate-determining step for a given molecule, we explored the LFER that relates the experimentally measured chemical reaction rate constant, k chem , and the E red;aq°v alues relative to the standard hydrogen electrode (SHE) for each mechanism through the relation described by eqn (4). We, then, determined the dominant rate-determining reaction mechanism by investigating the correlation of each LFER. The concept of a LFER may be developed as below. Assuming an elementary reaction proceeds by the same reaction mechanism, the log of the rate constant and the log of the equilibrium constant are linearly related. 31 The natural log of the equilibrium constants has a linear relationship with the free energy reaction, ΔG react aq , which relates to the standard state reduction potential in eqn (5). Combining these two concepts enables the development of the LFER. Upon the calculation of the ΔE red;aq°v alues, all possible e aq − attacking sites for each compound were included, and the largest E red;aq°v alue (i.e., the smallest free energy of formation) in a given molecule was used for the determination of the LFER. We determined the LFER for each reaction mechanism listed in eqn (1)-(3) to investigate the correlation with k chem values. The procedure to determine the k chem values and the critical evaluation of literature-reported k exp values are provided in Texts S1 in the ESI. † In the above equation, α and β are the coefficients that determine the slope representing the relationship between the reductive ability of the reaction site and the observed overall kinetics and the intercept representing the kinetics at the reference electrode, respectively. We argue that the LFER is a useful way to relate the kinetics (i.e., k chem values) with thermodynamic parameters (i.e., E red;aq°v alues) and the LFER helps elucidate the dominant reaction mechanism. Determining the aqueous-phase free energies of activation, a parameter that drives the kinetics, for hundreds of reactions involving e aq − by investigating the potential energy surfaces (PES) of reactants and products is not practical for systematic investigation. Thus, we conducted PES scan to determine the reaction mechanism for a few compounds that may undergo more than one reaction mechanism described above.
For the associative and concerted reaction mechanisms, the E red;aq°v alue was determined with eqn (5): where n is the number of electrons transferred, F is Faraday's constant, and E°(SHE) = 4.28 V. Per the thermochemical (Born-Haber) cycle, ΔG react aq , may be expressed as: ΔG react aq = ΔG react gas + ΔΔG react solv (6) where ΔG react gas is the difference in the standard state gaseous phase Gibbs free energy of reaction between reactants and products and ΔΔG react solv is the difference in the standard state Gibbs free energy of solvation between reactants and products. All energies values were simulated at 298 K in this study.
Regarding the stepwise investigation, we calculated E red;aq°w ith eqn (7), 26,32 which accounts for both the formation of the intermediate radical species and the resulting bond cleavage as an example of an RX bond. 26,32 where BDE is the bond dissociation energy of the cleaved bond, T is the absolute temperature in Kelvin, ΔS is the gaseous-phase entropy of the cleaved bond, ΔΔG solv is the difference in solvation energy between the parent compound and the two radical products in eqn (8), and E X˙=X −°is the reduction potential of the cleaved aqueous atom.
The BDE of the cleaved RX bond was calculated using the enthalpies (H) of the parent compound and the two radical products produced upon cleavage (eqn (9)).
To calculate the E red;aq°v alues for the determination of LFERs, single point energy calculations at the M06-2X functional 33 and the Aug-cc-pVTZ basis set for all the mechanisms based on the optimized structures determined at M06-2X/cc-pVDZ or Aug-cc-pVTZ, unless detailed method was specified. We used M06-2X/LANL2DZ for compounds that contained iodine because the Dunning's basis set does not cover iodinated compounds. For PFASs, we used M06-2X with a combination of cc-pVDZ or Aug-cc-pVTZ basis set. Table S1 in the ESI † summarizes the method and basis set used for the group of compounds. M06-2X is specifically designed for the accurate treatment of long-distance interaction and/or the stronger electron-acceptor properties of the R˙fragments resulting from the dissociation of a C-R bond, 34 which makes it suitable for this study that investigates nucleophilic reactivity. The M06-2X functional was successfully applied for the reductive dissociation of polybrominated compounds. 23 A continuum form of the universal solvation model (SMD) 35 was used in the aqueousphase calculations to account for the impact of an aqueous environment. It is noted that we did not aim to obtain the absolute E red;aq°v alues of each elementary reaction, as they are computationally prohibitive when obtaining highly accurate ΔG react aq values for a number of compounds. Thus, we used M06-2X to obtain reliable relative E red;aq°v alues so that we were able to relatively compare which reactive sites were dominant over other sites under the same reaction mechanism. The dominant reaction mechanism among the three major mechanisms was determined by the LFER with mechanistic insight into the reaction mechanisms, as the direct comparison of the E red;aq°v alues obtained from eqn (5) and (7) was not possible. The validation of the M06-2X method with various basis sets is provided in Table S2 in the ESI. † All DFT calculations were performed using Gaussian16 (ref. 36) with the Michigan Tech high-performance cluster 'Superior' and homemade LINUX workstations.

Results and discussion
Determination of linear free energy relationships Inconsistent experimental conditions (e.g., pH, temperature, and ionic strength) were reported to measure k exp values in a number of independent studies reported in the literature. Thus, the critical data evaluation of 268k exp values (Text S1, Fig. S1 and Table S3 in the ESI †) in the literature selected 251k exp values and calculated the chemical reaction rate constants by eliminating the diffusion contribution for the determination of LFERs (Text S1 in the ESI †). This critical data evaluation can potentially eliminate the uncertain k exp values that may indicate significantly larger k exp values that exceed the diffusion rate constant, k D , in eqn (S1) in the ESI. † It should be noted that the diffusion rate constant, k D , value used in eqn (S1) † has the limitations: (1) 31 Therefore, the extent of solvation effect may vary depending on the molecules. Thus, the k D values we calculated may not represent the real diffusion rate constants. Nevertheless, the Smoluchowski's treatment has been successfully applied for many radical reactions (e.g., hydroxyl radicals) and predicted the k D in consistent with the experimental values. 38 As a consequence, we decided to adapt this approach in our calculations. Fig. 2 displays LFERs between the k chem values and our theoretically calculated E red;aq°v alues for 251 organic compounds undergoing three major mechanisms: (a) associative, (b) concerted, and/or (c) stepwise. Table 1 summarizes all the data used to determine the LFERs. Tables S4 and S5 in the ESI † contains all the E red;aq°v alues for all possible reactive sites in a given molecule for the three reaction mechanisms. Regarding the association, we determined the LFER to be ln k chem = 4.43E red;aq°+ 31.76 (r 2 = 0.72, N = 66, where N is the number of compounds for the development of the LFER) (Fig. 2a). When the carbon of the CO functional group bonds with NH 2 or the OR functional group, the mesomeric effect of the -CO-NH 2or -CO-ORfunctional group occurs and decreases the double-bond character of the CO functional group, creating new electrophilic centers with lower reactivity. 37 While we determined one unified LFER for associative mechanism with both CO of ketones, aldehydes and carboxylate groups (blue dots in Fig. 1) and O of carboxylic acids, alcohols, esters, and amides (red dots in Fig. 1), the functional groups affect the associative mechanism with O in a different way from those with CO functional group (see the next subsection). Compounds 17, 33, 45, and 153, whose k chem values are close to or exceed the diffusion limit (k chem > 2.5 × 10 10 M −1 s −1 ), were not included in either LFER. Compound 39, methyl trifluoroacetate, appear to be slightly off the LFER of the associative mechanism or that of the stepwise mechanism. Our investigation on the PES and spin density distribution supports the associative mechanism (see the detailed discussion in the reaction mechanism section below). Thus, we included this compound in the LFER of the associative mechanism. For the associative mechanism with the CC of alkenes, the LFER was determined to be ln k chem = 7.82E red;aq°+ 41.25 (r 2 = 0.63, N = 13) (Fig. 2b). The reactions of the alkenes with k chem > 5.3 × 10 9 M −1 s −1 were close to or exceeded the diffusion limit; therefore, the k chem values did not change with an increase in the E red;aq°v alues. The sample deviation (SD) calculated with eqn (10) was 0.084 for the associative mechanism and 0.13 for the associative mechanism with the CC functional group. The SD values represent the statistical distribution of the experimental k chem values from the predicted values, k predicted , within the normal distribution. 38 For the concerted cleavage of the C-Cl bond of haloalkanes and halocarboxylate, we determined the LFERs to be ln k chem = 5.66E red;aq°+ 27.95 (r 2 = 0.73, N = 19) and ln k chem = 3.97E red;aq°+ 28.92 (r 2 = 0.99, N = 4), respectively (Fig. 2c). The SD values were 0.044 and 0.025, respectively. All the k chem values of the haloalkane and halocarboxylate compounds that contain C-Br and C-I bonds were close to or exceeded the diffusion limit; therefore, we did not determine their LFERs. The presence of carboxylate functional groups impacted the E red;aq°v alue of the cleavage of the C-Cl bond in the halocarboxylates; thus, a different LFER was determined for the group of chlorinated halocarboxylates. The four chlorinated carboxylates also appeared to adhere to the LFER for stepwise mechanism. According to experimental works, the group of these compounds undergo both concerted and stepwise mechanisms 21,22 and thus we keep these compounds in both LFERs. We also determined the LFER for the concerted cleavage of the C-N bond of alkyl ammonium (RNH 3 + ) as ln k chem = 4.92E red;aq°+ 24.67 (r 2 = 0.98, N = 7) ( Fig. 2c) with the exception of tetramethylammonium (no. 166) and tetraethylammonium (no. 167), which contain a different base structure of >N + -C. Additionally, we did not include compounds that contain oxygenated functional groups (no. 161, oxoethanaminium and no. 162, methoxyazanium) because of their dominant associative mechanism. The SD value was 0.051. For the stepwise mechanism, we determined the LFERs for compounds with (1) haloalkanes that contain CO functional groups (i.e., halocarboxylates, halooxygens and haloamides) or C-F bonds (fluorinated carboxylates), (2) haloalkenes, and (3) sulfides or disulfides for the stepwise mechanism to be the following: (1) ln k chem = 3.  (Fig. 2d). Because of the high strength of a C-F bond, the slope of the LFER for fluorinated carboxylates is significantly smaller than that of other haloalkanes. The SD values were 0.048 for haloalkanes, 0.26, for fluorinated carboxylates, 0.077 for haloalkenes, and 0.089 for disulfides. A detailed mechanistic discussion and prediction of PFAS are given below.

Impact of functional groups
The functional group(s) in the neighboring position of an e aq − attacking site substantially impact the reactivities with e aq − . In general, electron donating groups such as alkyl and amine functional groups in the neighboring position(s) decrease the nucleophilic reactivity of e aq − by increasing the electron density of the reactive site. For example, the negatively charged oxygen of the COO − functional group acts as an electron donor to the adjacent CO bond due to its lone pair of electrons and hence reduces the reactivity of e aq − in association with CO. In contrast, electron withdrawing functional groups such as ketones and carboxylic acids decrease the electron density of the reactive site and hence increase the reactivity of e aq − . Fig. 3 plots the total sum of the   neighboring functional groups resulting from inductive and mesomeric effects. The smaller slope (1.53) for the associative mechanism with O than that (1.69) for the associative mechanism with CO indicates the inhibition of reactivity resulting from the mesomeric effect. Hart et al. 37 examined the negative slope between log k exp and the Taft constants for groups of ketones with a limited number of data (N = 10) and concluded that the slowing effect due to the mesomeric effect was more extensive than expected from inductive electrondonating/withdrawing effects. They also acknowledged that both mesomeric and inductive effects could apply to carboxylic compounds (N = 3), and their data appeared to adhere to both correlations well. Notably, two compounds that we propose for the stepwise cleavage mechanism of the C-F bond of CF 3 COCH 3 (no. 98) and CH 3 COCH 2 F (no. 99) (see discussion on the reaction mechanism below) were included in the correlation with the Taft constant for the associative mechanism with CO by Hart. If these compounds and carboxylic compounds were removed from their correlation, a handful of compounds (N = 4) would remain in close proximity, and a negative correlation between the k chem values and the sum of Taft constants would not be observed. Most likely, our extensive analysis of data (N = 66) and the use of E red;aq°v alues revealed a better comprehensive picture of the impact of functional groups. Neighboring functional groups also affect the concerted cleavage mechanism of each C-Cl, C-NH 3 + , and S-S bond as well as the stepwise cleavage mechanism of each C-Cl and S-S bond. The slopes of the correlations for C-Cl bond cleavage for both concerted and stepwise mechanisms were found to be significantly steeper than those for C-N and C-S cleavages. The similar slopes of the correlations for C-Cl bond between concerted and stepwise mechanisms indicate that the impact of neighboring functional groups is similar despite of the formation of intermediate species in the stepwise mechanism. While the Taft constants for C-C bond cleavage were substantially different for various functional groups in the neighboring positions, the range of E red;aq°v alues was within approximately 1 V. These results indicated the higher sensitivity of the E red;aq°v alues associated with the properties of the electron-donating/withdrawing functional groups when compared with those examined for C-N and S-S bonds.

Reaction mechanisms
Associative mechanism. When the π-fragment of a CO functional group is present in ketone, aldehyde and carboxylate, the initial injection of an electron occupies lowenergy π*-orbitals via associative mechanism to form a carbon-centered radical. 150,151 However, it is unclear whether association with CO is maintained or the stepwise cleavage of a C-X bond occurs in the group of halooxygens. 21,22,152 Our investigation of the PES of methyl trifluoroacetate (no. 39) and the product of radical anion as a function of one of dihedral angles showed the merging point of these PESs at approximately −70 degree (Fig. S2 in the ESI †), indicating the possibility of stepwise dissociative mechanism. However, the spin density distributions of elongated C-F bond structures were located on the acetate carbonyl functional group with an increase in one of the C-F bonds, which confirmed the associative mechanism (Fig. S3 in the ESI †). Our investigation on the lowest unoccupied molecular orbital (LUMO) represents no antibonding orbitals with regard to the C-F bond (Fig. S4 in the ESI †), supporting the initial electron association with the CO functional group.
The Our E aq°v alues for the associative mechanism are approximately −1.6 V for all the compounds, whereas those for the concerted cleavage of C-NO 2 bond are approximately −2.2 V. This indicates the preference of the associative mechanism with e aq − and is supported by the spin density distribution on the NO 2 functional group (Fig. S7 in the ESI †). Due to the few datasets, we were not able to develop the LFER.

Concerted dissociative mechanism
Haloalkane and halocarboxylate. The concerted dissociative cleavage of a C-X (X = Cl, Br, and I) bond of haloalkanes is supported by the presence of σ* antibonding orbitals with respect to the C-X bond. Injection of an electron into such orbitals is accompanied by the barrierless dissociation of the C-X bond and the reductive cleavage follows the concerted dissociative mechanism. 21,22,153 Despite the fact that a carboxylate functional group was present in the given molecular structure of haloalkanes, we observed that the weak C-X (X = Br and I) bond of halocarboxylates underwent concerted reduction due to the inability to hold the e aq − . We investigated the spin density distribution in a given molecule to identify a possible attacking site by e aq − . The spin density distribution on four chlorinated carboxylates indicates the solvated electron was located on the carbon atom in the C-Cl group (Fig. S8 in the ESI †), suggesting that the C-Cl bond cleavage could occur upon the attack by the e aq − . It should be noted that we observed the significant elongation of a C-Cl bond upon the structure optimization for 2-chloropropanoate (3.77 Å of C-Cl) and trichloroacetate (3.58 Å of C-Cl). This bond elongation suggests that the C-Cl bonds may not cleave upon the attack by the solvated electron, and thus the stepwise reduction mechanism may occur. The e aq − was likely held in the σ* antibonding orbital of chlorine, forming an intermediate radical anion species. Because of the uncertainty of the aqueous-phase PES, we were not able to confirm the dominant mechanism on these two chlorinated carboxylates. The detailed investigation on the PES for this group of compounds are underway. The brominated and iodinated species appeared to undergo concerted reduction. In all radical anion structures, the C-X (X = Br or I) bond was elongated significantly and the e aq − was located on the carbon of the C-X group ( Fig. S9 and S10 in the ESI †). Because we did not observe any associative mechanism of e aq − with the CO functional group, the stepwise reduction mechanism seemed to be unlikely. The concerted mechanism is reasonable because the C-Br bond strength is also relatively weak (285 kJ mol −1 ) compared to C-Cl and C-F, which is consistent with experimental finding. 23 The C-N bond in general undergoes concerted dissociative cleavage. We determined two LFERs of ammonium compounds undergoing concerted and associative mechanisms and confirmed the concerted cleavage of a C-N bond of ammonium functional group for the rate determining step (Fig. S11 in the ESI †). The group of cyanide included 3k chem values of acetonitrile (no. 106), succinonitrile (no. 107), and cyanamide (no. 109). While the k chem value of acetonitrile was 10 7 -th order, the other two were 10 9 -th order. Our E aq°v alues for the concerted cleavage of C-CN bond for these compounds ranged from −3.33 V to −3.06 V, whereas those for the association were from −3.64 V to −3.33 V. These indicate the preference of concerted cleavage of C-CN bond to form cyanide ion (CN − ) and carbon-centered radicals. Our investigation on the spin density of cyanide compounds indicated the high spin density at the cyanide functional group (Fig. S12 in the ESI †). Due to the small number of compounds, we were not able to develop the LFER.
The group of thiol contained 12 compounds containing at least one -SH functional group. As discussed above, the C-S bond is generally the weak point of a molecule because of its bond weakness in comparison to the C-C and C-H bonds. In the thiol compounds, the e aq − likely attacks the C-S group and results in the immediate bond cleavage due to a lack of antibonding σ* orbitals on the -SH functional group to hold the extra electron. Or the e aq − associates with the CO bond and loosens the C-S bond to cleave in the stepwise mechanism. Among all compounds containing thiol functional group, we did not observe any clear LFERs for both mechanisms (Fig. S13 in the ESI †). However, for thiols that do not contain CO functional group, we observed the acceptable LFER for concerted mechanism due to the limited number of data. Therefore, this class of compounds is likely reduced by the concerted mechanism, generating R˙and HS − . 154 Stepwise mechanism Halocarboxylates, halooxygens, chlorinated amides and haloalkenes. We observed the consistent stepwise mechanisms for halocarboxylates (no. [49][50][51][52][53][54][55][56][57][58][59], halooxygens (no. [97][98][99][100][101][102][103][104][105], and chlorinated amides (no. 135 and no. 142) because of the presence of COO − , OH and CO functional groups, which are consistent with previous experimental observations. [20][21][22] When haloalkanes contain electronwithdrawing and π-acceptor functional groups or other π-fragments, the electrons may initially occupy low-energy π*orbitals and the reduction of these molecules may result in the transient formation of radical anions. 155  Electron-withdrawing functional groups adjacent to a CO functional group induce a shortening of the CO bond 156 (e.g., 1.30 Å of CF 3 COCH 3 (no. 98) and 1.31 Å of CH 3 COCH 2 F (no. 99) compared to 1.32 Å of CH 3 COCH 3 from our optimized structures), which leads to a lower electron density in the π orbitals, resulting in the higher reactivity toward e aq − . However, the k chem values of CF 3 COCH 3 and CH 3 -COCH 2 F do not appear to follow this trend and show substantially smaller rate constants (i.e., 10 7 -10 8 M −1 s −1 ) for associative mechanism. We propose that these two compounds undergo stepwise mechanism where e aq − associates with CO π bond and elongates the C-F bond, followed by the cleavage of the C-F bond. The E red;aq°v alues were not able to confirm the stepwise mechanism. Our investigation on the spin density distribution shown in Fig.  S17-S20 † for both compounds provide the evidence of electron association and elongation of the C-F bond, which support the stepwise mechanism. Furthermore, the LUMO of both compounds (Fig. S21 †) was the evidence of stepwise cleavage that holds the electron in one of the C-F bonds. Based on our investigation, we only propose stepwise mechanisms for these two compounds and further study is needed to confirm the reaction mechanism. Sulfides, disulfides, sulfoxide. A total of 8 compounds were investigated for the group of sulfides that contain a -C-S-Cfunctional group and disulfide that has a -C-S-S-Cfunctional group. We determined the LFER for the stepwise mechanism that cleave the C-S bond of sulfides and the S-S bond of disulfides. We did not observe any correlation for the concerted mechanism (Fig. S22a in the ESI †). Although some sulfides (no. 186, 187, 191, and 192) contain COO − functional group that implicates the initial association with e aq − , those functional groups are located far from the C-S and S-S sites and do not appear to impact the elongation of those bonds upon the injection of a first electron. Upon the attack by e aq − , the S-S or C-S bond initially elongates which results in a decrease in the energy of the antibonding σ* orbital that localizes over the elongated S-S or C-S bond. This antibonding orbital temporarily holds the e aq − for more than one vibration, creating a threeelectron bonded radical anion intermediate structure CSSC˙− or a C-centered radical. 157 After the formation of this radical anion, the S-S bond cleaves, resulting in the following products: RSȧ nd RS − via a stepwise mechanism. 158,159 The sulfoxide class (no. 173-175) has the characteristic of a central SO double bond. The presence of a π-bond which allows for electron localization, accessible antibonding π* orbitals, and two weak C-S bonds suggest that this class of compounds is reduced via the stepwise mechanism. The e aq − likely attacks the sulfur atom, resulting in the elongation of a C-S bond, as was observed in the sulfide and disulfide class. Simultaneously, the π-bond transforms into a σ bond by shifting two electrons to the oxygen atom, creating a negative charge on the oxygen.
Alkanes and amines. Compounds belonging to alkane and amines are generally difficult to reduce due to a lack of electron withdrawing functional groups in their chemical structures. We estimated E aq°v alues for the alkane class to be low with the values ranging from −5.27 V to −5.41 V. The k chem values are also significantly small in the range from 10 6 and 10 7 M −1 s −1 . For these reasons, we do not include any data in the groups of alkanes and amines in the analysis of LFERs.
Prediction of the reactivities with per-and polyfluoroalkyl substances (PFASs) We investigate the reactivities of e aq − with the 75 priority PFAS subset from the U.S. EPA. The 75 PFASs were grouped based on the functional groups. The E red;aq°v alues for (1) the associative mechanism with CO and influenced by π C¼O * orbitals, 160,161 (2) the associative mechanism with O, and (3) the stepwise C-F cleavage mechanism for all possible attacking sites in a given PFAS are summarized in Table 2. Fig. 4 displays the range of E red;aq°v alues for the stepwise cleavage of a C-F bond at different positions for the selected groups of PFASs investigated in this study. For this plot, we used M06-2X/cc-pVDZ for both structural optimization and frequency calculations and used the LFER determined from the same method to avoid significant computational time.
Notably, we verified that the trend of all energies from representative PFASs was consistent between M06-2X/cc-pVDZ and M06-2X/Aug-cc-pVTZ (Table S6 in the ESI †). The group of polyfluorocarboxylates (PFCAs) has 7 PFASs with E red;aq°v alues in the range from −4.1 V to −2.3 V for the associative mechanism with CO and in the range from −7.3 V to −6.0 V for the stepwise C-F cleavage mechanism. From the largest E red;aq°v alue in each reaction mechanism along with the LFER (ln k chem = 1.82E red;aq°+ 27.80 in Fig. S23 in the ESI †), the k chem values in neutral solution were predicted to range from 6.9 ×  162 Although this experimental study did not determine the mechanism for those measured rate constants, we believe they measured the rates of the associative mechanism. In contrast, the k exp values for C-F cleavage (10 6 -10 7 M −1 s −1 ) were previously reported 134 and used for the determination of our LFERs (compound no. 204-206), which confirm the significantly smaller k chem values of the stepwise cleavage mechanism of a C-F bond. The predicted k chem values in three reaction mechanisms for all 75 PFASs are shown in Fig. S24 in the ESI. † The k chem values that exceeded the diffusion limit (3 ×            with O, and 4k chem values are above the diffusion limit for the CC associative mechanism. We did not determine the LFERs for the functional groups of sulfonic acid (SO 3 − ), phosphinic acid (PO(OH) 2 ), sulfonamide (SO 2 NH), and sulfonyl (SO 2 ); thus, no rate constant predictions were conducted. The investigation of the E red;aq°v alues at all possible e aq − attacking sites for all possible e aq − reaction mechanisms highlights the significantly lower reactivity of e aq − for the stepwise cleavage mechanism of a C-F bond and higher reactivity of e aq − with functional groups in a given PFAS structure. The attachment of an e aq − to the group of PFCAs (N = 8) occurred near the α-carbon, and the resultant intermediate radical dianions were the most stable due to resonance stabilization by the π-system of carboxylate functional groups, which is consistent with previous predictions on PFOA 163 and perfluoropentanoic acid (PFPeA). 24 Attachment near the α-carbon was also observed for the group of perfluoroalkyl phosphinates (PFPiAs) due to the phosphonate functional group, perfluoroalkyl ether carboxylates (PFECA), perfluoroalkyl amides, polyfluoroalkyl aldehydes and acyl fluorides, and semifluorinated alkenes (SFAenes). In contrast, the group of perfluoroalkane sulfonates (PFSA) (N = 5) showed preferable attachment of an e aq − near the βor γ-carbon with the largest E red;aq°v alues due to the inability of π-stabilization due to the trigonal geometry of the sulfonate functional group. 24 A similar trend was observed for the groups of fluorotelomer alcohols (FTOH) and polyfluorinated alcohols, fluorotelomer acrylates (FTACs), perfluoroalkane sulfonamides (FASAs), perfluoroalkane sulfonyl chlorides (PASCs), and fluorotelomer carboxylates (FTCAs). The investigation of the E red;aq°v alues at all possible e aq − attacking sites for PFASs that contain a wide variety of functional groups highlights significant differences in regard to the most preferable reactive sites of e aq − . While the scope of the current study is on the initial reactivities of e aq − with a wide variety of organic compounds and PFASs, investigating the subsequent degradation pathways is underway. The cleavage of a C-F bond in a PFAS is the major goal for practical PFAS remediation using reductive technologies, and our LFERs and predicted k chem values for the stepwise cleavage mechanism of a C-F bond present significant challenges in cleaving a C-F bond from a kinetics point of view.

Impact of the accuracy of rate constant estimation to the fate
To assess the impact of the accuracy of rate constant estimation to the fate of a target organic compound, we develop an unsteady-state kinetic model for the homogeneous aqueous-phase UV/sulfite system to degrade a model compound (e.g., PFAS) with input parameters that are consistent with experimental observations in the literature 10 (see the details in Text S4 in the ESI †). It should be noted that the model was used to assess the impact of the initial rate constant prediction accuracy on the time-dependent fate  Fig. 5 represents the time-dependent concentration profile of a parent compound that has k chem = 1.0 × 10 6 M −1 s −1 with e aq − . The profiles were also predicted by changing the k chem values by a difference of a factor of 1.2, 2, and 5. Estimating the rate constant impacted the profile of the parent compound by 33% for k chem values with a factor of 1.2, 77% with a factor of 2, and 100% with a factor of 5.0 at 300 h. While our LFER for the C-F stepwise cleavage mechanism has the ability to predict the k chem values within the difference of a factor of 1.2, this prediction demonstrates the importance of an accurate rate constant of a target compound in estimating the decay of an environmentally relevant contaminant that requires significant amount of time (e.g., PFASs).

Conclusion
Reduction of oxidized forms of water contaminants using electrons in the aqueous-phase advanced reduction processes is a novel and attractive approach to destroying the contaminants. The mechanistic insight into the reactivities of solvated electrons with a wide variety of contaminants helps understand and predict the fate of contaminants of emerging concern, and can be extrapolated to the direct electron transfer mechanisms in the heterogeneous electrochemical processes. The determination of linear free energy relationships presented in this study elucidated which reaction mechanisms are the dominant rate-determining step for the reaction of solvated electrons with structurally diverse conventional organic compounds and the 75 priority PFAS subset that contains a wide variety of functional groups. The computational tools determined in this study can be used to predict the reaction rate constants with solvated electrons and screen a number of contaminants and prioritize for the application of advanced reduction processes.

Conflicts of interest
There are no conflicts to declare.

Acknowledgements
This work was supported by Central Chemicals Inc. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and