Mechanistic Insight into the Degradation of Nitrosamines via Aqueous-Phase UV Photolysis or a UV-Based Advanced Oxidation Process: Quantum Mechanical Calculations

Nitrosamines are a group of carcinogenic chemicals that are present in aquatic environments that result from byproducts of industrial processes and disinfection products. As indirect and direct potable reuse increase, the presence of trace nitrosamines presents challenges to water infrastructures that incorporate effluent from wastewater treatment. Ultraviolet (UV) photolysis or UV-based advanced oxidation processes that produce highly reactive hydroxyl radicals are promising technologies to remove nitrosamines from water. However, complex reaction mechanisms involving radicals limit our understandings of the elementary reaction pathways embedded in the overall reactions identified experimentally. In this study, we perform quantum mechanical calculations to identify the hydroxyl radical-induced initial elementary reactions with N-nitrosodimethylamine (NDMA), N-nitrosomethylethylamine, and N-nitrosomethylbutylamine. We also investigate the UV-induced NDMA degradation mechanisms. Our calculations reveal that the alkyl side chains of nitrosamine affect the reaction mechanism of hydroxyl radicals with each nitrosamine investigated in this study. Nitrosamines with one- or two-carbon alkyl chains caused the delocalization of the electron density, leading to slower subsequent degradation. Additionally, three major initial elementary reactions and the subsequent radical-involved reaction pathways are identified in the UV-induced NDMA degradation process. This study provides mechanistic insight into the elementary reaction pathways, and a future study will combine these results with the kinetic information to predict the time-dependent concentration profiles of nitrosamines and their transformation products.


Introduction
Nitrosamines, which contain N-NO functional groups, are a group of chemicals that pose mutagenicity, teratogenicity, and carcinogenicity [1]. Nitrosamines are the byproducts of various manufacturing, agricultural, and natural processes and have been found in natural aquatic environments and in the effluent of wastewater treatment processes [2]. As a type of nitrosamine, N-nitrosodimethyl amine (NDMA, (CH 3 ) 2 N-NO) is a low-molecular-weight, neutral, organic contaminant that has also been found to be present in aquatic environments. The California Department of Health Services has set notification levels of 10 ng/L for NDMA and other nitrosamines in drinking water [3].
Ultraviolet (UV) photolysis and UV-based advanced oxidation processes (AOPs) that produce highly reactive hydroxyl radicals (HO • ) are attractive and promising water treatment technologies, which can inactivate pathogens and destroy a wide variety of organic chemical contaminants [4,5].
at 254 nm of wavelength. We investigate NDMA, NMEA, and N-nitrosomethylbutylamine (NMBA), which have different alkyl side chains that are adjacent to the nitroso functional group (-N-NO), to elucidate the effect of the alkyl side chain on the overall reactivity with HO • . We also investigate UV-induced NDMA degradation using time-dependent (TD)-DFT to understand the molecular orbitals responsible for electron excitation and the nitrogen-containing radical reactions during the photolysis of NDMA. NDMA has three potential initial degradation mechanisms: (1) H atom abstraction from a C-H bond of the methyl group (pathway 1-1 in Figure 1), (2) HO • addition to amine nitrogen (pathway 1-2 in Figure 2), and (3) HO • addition to nitrosyl nitrogen (pathway 1-3 in Figure 3). Our QM calculations obtained ∆G act aq,calc values of 9.7 kcal/mol, 6.8 kcal/mol, and 9.6 kcal/mol for the respective pathways. H abstraction from a C-H bond forms a C-centered radical that reacts with the triplet state of molecular oxygen dissolved in water. Our previous studies indicate that the addition of molecular oxygen to a C-centered radical is a barrierless reaction with a ∆G act aq,calc of −20-30 kcal/mol, which enabled us to consistently predict the experimentally measured reaction rate constants [28]. The ∆G act aq,calc value obtained for the • CH 2 NNOCH 3 radical was 2.3 kcal/mol, which is significantly larger than those of typically observed reactions. This indicates that the N-NO functional group significantly affects molecular addition to the C-centered radical. The second-order reaction rate constant for the addition of molecular oxygen to a C-centered radical of NDMA was determined to be (5.3 ± 0.6) × 10 6 M −1 s −1 [9], which is three orders of magnitude smaller than the typically observed rate constants (~5 × 10 9 M −1 s −1 ) [29]. A more detailed discussion on the unique reactivity of molecular oxygen to C-centered radicals will be given in a later section. According to our calculations, the C-centered radical also undergoes electron transfer to produce CH 3 NNO=CH 2 (∆G act aq,calc of −2.0 kcal/mol), followed by the loss of NO • (∆G act aq,calc of −11.3 kcal/mol) to produce N-methylidenemethylamine (CH 2 =NHCH 3 ). This latter pathway involves several barrierless reactions, and is dominant over the pathway involving the addition of molecular oxygen. The formation of N-methylidenemethylamine was also postulated in a previous report [18,19]. (-N-NO), to elucidate the effect of the alkyl side chain on the overall reactivity with HO • . We also investigate UV-induced NDMA degradation using time-dependent (TD)-DFT to understand the molecular orbitals responsible for electron excitation and the nitrogen-containing radical reactions during the photolysis of NDMA.

HO • -Induced Degradation
2.1.1. N-Nitrosodimethylamine (NDMA) Degradation Pathways Induced by HO • NDMA has three potential initial degradation mechanisms: (1) H atom abstraction from a C-H bond of the methyl group (pathway 1-1 in Figure 1), (2) HO • addition to amine nitrogen (pathway 1-2 in Figure 2), and (3) HO • addition to nitrosyl nitrogen (pathway 1-3 in Figure 3). Our QM calculations obtained ΔG aq,calc act values of 9.7 kcal/mol, 6.8 kcal/mol, and 9.6 kcal/mol for the respective pathways. H abstraction from a C-H bond forms a C-centered radical that reacts with the triplet state of molecular oxygen dissolved in water. Our previous studies indicate that the addition of molecular oxygen to a C-centered radical is a barrierless reaction with a act aq,calc ΔG of −20−30 kcal/mol, which enabled us to consistently predict the experimentally measured reaction rate constants [28]. The act aq,calc ΔG value obtained for the • CH2NNOCH3 radical was 2.3 kcal/mol, which is significantly larger than those of typically observed reactions. This indicates that the N-NO functional group significantly affects molecular addition to the C-centered radical. The second-order reaction rate constant for the addition of molecular oxygen to a C-centered radical of NDMA was determined to be (5.3 ± 0.6) × 10 6 M −1 s −1 [9], which is three orders of magnitude smaller than the typically observed rate constants (~5 × 10 9 M −1 s −1 ) [29]. A more detailed discussion on the unique reactivity of molecular oxygen to C-centered radicals will be given in a later section. According to our calculations, the C-centered radical also undergoes electron transfer to produce CH3NNO=CH2 ( act aq,calc ΔG of −2.0 kcal/mol), followed by the loss of NO • ( act aq,calc ΔG of −11.3 kcal/mol) to produce N-methylidenemethylamine (CH2=NHCH3). This latter pathway involves several barrierless reactions, and is dominant over the pathway involving the addition of molecular oxygen. The formation of N-methylidenemethylamine was also postulated in a previous report [18,19]. The second pathway is HO • addition to the amine nitrogen, followed by the loss of an OH group.
Although initial HO • addition has a lower free energy of activation ( act aq,calc ΔG of 6.8 kcal/mol) than the H Figure 1. Free energy profile for pathway 1-1 of the HO • -induced reaction pathways for N-nitrosodimethylamine (NDMA) via H abstraction. TS denotes the transition state, and P denotes the product. The numbers (kcal/mol) are the free energy of activation for the TS and free energy of reaction for the P relative to the corresponding reactant. The second pathway is HO • addition to the amine nitrogen, followed by the loss of an OH group. Although initial HO • addition has a lower free energy of activation (∆G act aq,calc of 6.8 kcal/mol) than the H abstraction identified in pathway 1-1, the subsequent reaction has a larger activation barrier (∆G act aq,calc of 3.1 kcal/mol) to produce a N-centered radical (i.e., CH 3 • NCH 3 ). The N-centered radical undergoes either molecular oxygen addition or an H shift. The H shift has a significantly smaller ∆G act aq,calc of −1.9 kcal/mol than molecular oxygen addition to the N-centered radical (∆G act aq,calc of 9.8 kcal/mol). Thus, C-centered radical formation resulting from an H shift is the dominant pathway via TS8. The significantly large ∆G act aq,calc for the addition of molecular oxygen to a N-centered radical via TS7 can be verified by the experimentally obtained reaction rate constant for hydrazyl (k = 3.9 × 10 8 M −1 s −1 ) [30].        Pathway 1-3 involves initial HO • addition to the nitrosyl nitrogen with a ∆G act aq,calc of 9.6 kcal/mol. Although this reaction has an almost identical ∆G act aq,calc to that of pathway 1-1, the initial HO • addition reaction that produces an alkoxyl radical (i.e., CH 3 NNO • (OH)CH 3 ) is not thermodynamically favored (∆G react aq,calc of 6.4 kcal/mol). This alkoxyl radical undergoes two pathways to produce (1) a N-centered radical with a ∆G act aq,calc of 3.1 kcal/mol and (2) methyl diamine (CH 3 NHCH 3 ) with a ∆G act aq,calc of −8.0 kcal/mol. The above investigation confirms that H abstraction from a C-H bond of the methyl functional group of NDMA is the dominant initial reaction pathway as induced by HO • , which is consistent with the experimental investigation using the electron paramagnetic resonance (ESR) technique [9]. The experimentally determined second-order rate constant was (4.3 ± 0.12) × 10 8 M −1 s −1 , and this relatively slow H abstraction from a C-H bond by HO • results from the electron-withdrawing effect of the neighboring N-NO functional group and the abnormally stable C-centered radical [9]. In the following sub-sections, the reactivity of NDMA will be compared to two other nitrosamines that have longer alkyl side chains (i.e., -CH 2 CH 3 and -(CH 2 ) 2 CH 3 ) to investigate the unique reactivity of NDMA. It is still not clear why the pathway 2-2 had such a high barrier. All three pathways are thermodynamically favorable (∆G react aq,calc < 0). Each pathway produces a C-centered radical, i.e., CH 3 • CHNNOCH 3 in pathway 2-1, • CH 2 CH 2 NNOCH 3 in pathway 2-2, and CH 3 CH 2 NNO • CH 2 in pathway 2-3. The ∆G act aq,calc values for the addition of molecular oxygen to CH 3 • CHNNOCH 3 , • CH 2 CH 2 NNOCH 3 , and CH 3 CH 2 NNO • CH 2 are 3.8 kcal/mol, −13.9 kcal/mol, and −2.2 kcal/mol, respectively. As observed in pathway 1, the ∆G act aq,calc values of these three C-centered radicals are still larger than the typical values (−20 to −25 kcal/mol). This indicates that the functional group directly neighboring the N-NO functional group affects the slow reaction of molecular oxygen addition to • CH 2 CH 2 NNOCH 3 . Given that the other reaction pathways of the three C-centered radicals have either a larger ∆G act aq,calc than that for molecular oxygen addition or include thermodynamically unfavorable reactions (∆G react aq,calc > 0), the formation of peroxyl radicals resulting from the addition of molecular oxygen is the dominant reaction pathway in the subsequent NMEA degradation mechanism.
The above investigation confirms that H abstraction from a C-H bond of the methyl functional group of NDMA is the dominant initial reaction pathway as induced by HO • , which is consistent with the experimental investigation using the electron paramagnetic resonance (ESR) technique [9]. The experimentally determined second-order rate constant was (4.3 ± 0.12) × 10 8 M −1 s −1 , and this relatively slow H abstraction from a C-H bond by HO • results from the electron-withdrawing effect of the neighboring N-NO functional group and the abnormally stable C-centered radical [9]. In the following sub-sections, the reactivity of NDMA will be compared to two other nitrosamines that have longer alkyl side chains (i.e., -CH2CH3 and -(CH2)2CH3) to investigate the unique reactivity of NDMA.      [8]. The initial H abstraction reactions for all of the pathways are thermodynamically favorable.
Interestingly, we observed distinctive differences in the reactivity of molecular oxygen addition to different C-centered radicals for NMBA. The initial H abstraction from different C-H bonds in   [8]. The initial H abstraction reactions for all of the pathways are thermodynamically favorable.
Interestingly, we observed distinctive differences in the reactivity of molecular oxygen addition to different C-centered radicals for NMBA. The initial H abstraction from different C-H bonds in  [8]. The initial H abstraction reactions for all of the pathways are thermodynamically favorable.
Interestingly, we observed distinctive differences in the reactivity of molecular oxygen addition to different C-centered radicals for NMBA. The initial H abstraction from different C-H bonds in NMBA produced CH 3 NNO • CHCH 2 CH 3 by pathway 3-1, CH 3  and CH 3 NNO(CH 2 ) 2 • CH 2 (−23.9 kcal/mol) are very similar to those that were observed for typical molecular oxygen addition to C-centered radicals. Thus, the alkyl side chain affects the stability of the C-centered radicals and their subsequent reactivity. The significantly slower reaction of molecular oxygen addition to the C-centered radicals produced from NDMA and NMEA may be due to the delocalization of the radical spin density from the formed C-centered radicals onto the N-NO bond(s). This radical delocalization occurs only when a terminal • CH 2 is adjacent to N-NO or • CH 2 neighbors the N-NO functional group. When the alkyl chain contains three CH 2 functional groups, the • CH 2 three positions away from the N-NO functional group does not seem to contribute to the radical delocalization. Thus, the molecular oxygen adds to the C-centered radical without being affected by the delocalization. The different extent of radical delocalization can also explain the lower degradation efficiencies that were observed for NDMA and NEMA (approximately 80~85% degradation efficiency) as compared with nitrosodibutylamine (100% degradation efficiency) [8].
To investigate the effect of the location of the C-centered radical on the occurrence of radical delocalization, we calculated the ∆G act aq,calc values for radical transfer from a C-centered radical to a neighboring C-/N-centered radical. For example, CH 3 NNO • CHCH 2 CH 3 undergoes radical transfer from a carbon to the amine nitrogen to produce CH 3 • NNO=CHCH 2 CH 3 . This reaction has a ∆G act aq,calc of 0.41 kcal/mol, which indicates a low barrier for this radical delocalization (pathway 3-1). Similarly, • CH 2 NNO(CH 2 ) 2 CH 3 requires 3.7 kcal/mol to produce CH 2 = • NNO=CHCH 2 CH 3 (pathway 3-4). In contrast, CH 3 NNOCH 2 • CHCH 3 requires a ∆G act aq,calc of 38.6 kcal/mol to produce CH 3 NNO • CHCH 2 CH 3 (pathway 3-2). A similar significantly larger ∆G act aq,calc value of 40.0 kcal/mol was also observed for the radical transfer reaction from • CH 2 CH 2 NNOCH 3 to CH 3 • CHNNOCH 3 via pathway 2-2. Thus, there is a significant barrier for radical transfer from the functional group neighboring the N-NO functional group to the nearest CH 2 group. Therefore, a C-centered radical in • CH 2 CH 2 NNOCH 3 or CH 3 NNOCH 2 • CHCH 3 would rather undergo molecular oxygen addition than radical transfer to produce CH 3 • CHNNOCH 3 or CH 3 NNO • CHCH 2 CH 3 , respectively. CH3NNO(CH2)2 • CH2 (−23.9 kcal/mol) are very similar to those that were observed for typical molecular oxygen addition to C-centered radicals. Thus, the alkyl side chain affects the stability of the C-centered radicals and their subsequent reactivity. The significantly slower reaction of molecular oxygen addition to the C-centered radicals produced from NDMA and NMEA may be due to the delocalization of the radical spin density from the formed C-centered radicals onto the N-NO bond(s). This radical delocalization occurs only when a terminal • CH2 is adjacent to N-NO or • CH2 neighbors the N-NO functional group. When the alkyl chain contains three CH2 functional groups, the • CH2 three positions away from the N-NO functional group does not seem to contribute to the radical delocalization. Thus, the molecular oxygen adds to the C-centered radical without being affected by the delocalization. The different extent of radical delocalization can also explain the lower degradation efficiencies that were observed for NDMA and NEMA (approximately 80~85% degradation efficiency) as compared with nitrosodibutylamine (100% degradation efficiency) [8].
To investigate the effect of the location of the C-centered radical on the occurrence of radical was also observed for the radical transfer reaction from • CH2CH2NNOCH3 to CH3 • CHNNOCH3 via pathway 2-2. Thus, there is a significant barrier for radical transfer from the functional group neighboring the N-NO functional group to the nearest CH2 group. Therefore, a C-centered radical in • CH2CH2NNOCH3 or CH3NNOCH2 • CHCH3 would rather undergo molecular oxygen addition than radical transfer to produce CH3 • CHNNOCH3 or CH3NNO • CHCH2CH3, respectively.           The numbers (kcal/mol) are the free energy of activation for the TS and free energy of reaction for the P relative to the corresponding reactant.

NDMA Degradation Pathways Induced by UV Photolysis
NDMA absorbs photons at a wavelength of 228 nm with a molar absorptivity of 7380 M −1 cm −1 and quantum yield of 0.13 at pH 7 [7]. At a wavelength of 253.7 nm, where a typical low-pressure UV lamp emits photons, the molar absorptivity was reported to be 1650 M −1 s −1 , and the quantum yield was 0.24 at pH 7 [7]. Another smaller peak is observed at approximately 350 nm. Our TD-DFT calculation obtained one major and one minor peak at 212 nm and 341 nm, respectively. The molecular orbitals that were responsible for the π→π* and n→π transitions at 212 nm and 341 nm are shown in Figure 11. At 212 nm, the N-N bond comprises the highest occupied molecular orbital (HOMO), whereas the C-N bond comprises the HOMO at 341 nm. This analysis indicates that the N-N bond is susceptible breakage under photolysis with a low-pressure UV lamp. This finding is consistent with the experimental findings that were reported in the previous literature.

NDMA Degradation Pathways Induced by UV Photolysis
NDMA absorbs photons at a wavelength of 228 nm with a molar absorptivity of 7380 M −1 cm −1 and quantum yield of 0.13 at pH 7 [7]. At a wavelength of 253.7 nm, where a typical low-pressure UV lamp emits photons, the molar absorptivity was reported to be 1650 M −1 s −1 , and the quantum yield was 0.24 at pH 7 [7]. Another smaller peak is observed at approximately 350 nm. Our TD-DFT calculation obtained one major and one minor peak at 212 nm and 341 nm, respectively. The molecular orbitals that were responsible for the π→π* and n→π transitions at 212 nm and 341 nm are shown in Figure 11. At 212 nm, the N-N bond comprises the highest occupied molecular orbital (HOMO), whereas the C-N bond comprises the HOMO at 341 nm. This analysis indicates that the N-N bond is susceptible breakage under photolysis with a low-pressure UV lamp. This finding is consistent with the experimental findings that were reported in the previous literature.
The UV photolysis-induced NDMA degradation pathways were extensively studied [15,16]. According to their studies, NDMA undergoes three major degradation pathways induced by UV photolysis: (1)  The products of (CH3)2 • N(+)H and • NO in pathway 4-1 react in a solvent cage to produce N-methylidenemethylamine [(CH2=N(+)HCH3] and nitroxyl (HNO). Our calculation obtained a act aq,calc ΔG of 1.6 kcal/mol for this reaction. Then, N-methylidenemethylamine undergoes rapid hydrolysis to produce methylamine (CH3NH2 + ) and formaldehyde (HCHO). A total of 99% of the HCHO is hydrolyzed to form a germinal diol in the aqueous phase [30]; therefore, the hydrated form of HCHO (i.e., CH2(OH)2) exists in the aqueous phase. CH2(OH)2 reacts with HO • via H abstraction to produce • CH(OH)2 with a act aq,calc ΔG of 10.0 kcal/mol. As was examined in the HO • -induced pathways, this C-centered radical reacts with molecular oxygen to produce a peroxyl radical (i.e., • OOCH(OH)2) ( act aq,calc ΔG of −34.9 kcal/mol). The peroxyl radical undergoes uni/bimolecular decay to produce stable lower-molecular-weight products [31]. When • OOCH(OH)2 undergoes unimolecular decay (i.e., HO2 • elimination), formic acid (HCOOH) is produced ( act aq,calc ΔG of 31.6 kcal/mol), which has been experimentally observed [32]. The products of (CH 3 ) 2 • N(+)H and • NO in pathway 4-1 react in a solvent cage to produce N-methylidenemethylamine [(CH 2 =N(+)HCH 3 ] and nitroxyl (HNO). Our calculation obtained a ∆G act aq,calc of 1.6 kcal/mol for this reaction. Then, N-methylidenemethylamine undergoes rapid hydrolysis to produce methylamine (CH 3 NH 2 + ) and formaldehyde (HCHO). A total of 99% of the HCHO is hydrolyzed to form a germinal diol in the aqueous phase [30]; therefore, the hydrated form of HCHO (i.e., CH 2 (OH) 2 ) exists in the aqueous phase. CH 2 (OH) 2 reacts with HO • via H abstraction to produce • CH(OH) 2 with a ∆G act aq,calc of 10.0 kcal/mol. As was examined in the HO • -induced pathways, this C-centered radical reacts with molecular oxygen to produce a peroxyl radical (i.e., • OOCH(OH) 2 ) (∆G act aq,calc of −34.9 kcal/mol). The peroxyl radical undergoes uni/bimolecular decay to produce stable lower-molecular-weight products [31]. When • OOCH(OH) 2 undergoes unimolecular decay (i.e., HO 2 • elimination), formic acid (HCOOH) is produced (∆G act aq,calc of 31.6 kcal/mol), which has been experimentally observed [32].  kcal/mol to produce a nitrate ion (NO3 − ). This rearrangement was proposed as isomerization by Anbar and Taube (1954) [35]. ONOO − also reacts with HO2 • /O2 •− via single electron transfer to produce an • OONO radical. Our calculation indicates that this reaction is barrierless, with a  Figure 15). Although the disproportionation of NO2 • has the largest free energy barrier, the reaction product, N2O4, undergoes hydrolysis to produce NO3 − and NO2 − . One of the C-H bonds in the methyl group of the dimethylamine produced in pathway 4-2 undergoes H abstraction by HO • to produce a C-centered radical with a ∆G act aq,calc of 13.9 kcal/mol. Molecular oxygen adds to the C-centered radical to produce a peroxyl radical with a ∆G act aq,calc of −15.0 kcal/mol, and the peroxyl radical undergoes subsequent uni/bimolecular decay.    Figure 15). Although the disproportionation of NO2 • has the largest free energy barrier, the reaction product, N2O4, undergoes hydrolysis to produce NO3 − and NO2 − .

Environmental Implication and Future Study
Nitrosamines, and NDMA in particular, are extremely potent carcinogenic contaminants in water. The concentration at which NDMA shows potent carcinogenicity is extremely low (0.7 ng/L) [1]. Experimentally investigating the ng/L fate of many chemical contaminants during water treatment processes is time consuming and expensive. Our computational study highlights the usefulness of QM calculations to reveal the elementary reaction pathways that are embedded in the overall reaction pathways that are typically identified by analytical techniques. This technique becomes more useful when the contaminant concentrations are below the analytical detection limit.
Once the elementary reaction pathways are identified, the reaction rate constants should be determined or predicted to calculate the reaction rate of each molecule or species involved in each elementary reaction step. By combining the elementary reaction pathways and the reaction rate constants, one can predict the time-dependent concentration profiles of a target chemical contaminant and its transformation products. This elementary-reaction-based kinetic model could be used as an initial screening tool for many potentially toxic chemical contaminants to estimate the fate of degradation pathways. Our efforts towards the development of such elementary-reaction-based kinetic model are underway.

Materials and Methods
All of the QM calculations were performed with the Gaussian 09 revision D.02 program [36] using the Michigan Tech high-performance cluster "Superior" and homemade LINUX workstations. The M06-2X/cc-pVDZ [37] was used to optimize the electronic structures and calculate the frequencies in both the gas and aqueous phase for the HO • -induced reaction pathways with NDMA, NMEA, and NMBA. The UV-induced reaction pathways with NDMA was calculated with the Gaussian-4 theory (G4) [38]. The aqueous-phase structures and frequencies were obtained using an

Environmental Implication and Future Study
Nitrosamines, and NDMA in particular, are extremely potent carcinogenic contaminants in water. The concentration at which NDMA shows potent carcinogenicity is extremely low (0.7 ng/L) [1]. Experimentally investigating the ng/L fate of many chemical contaminants during water treatment processes is time consuming and expensive. Our computational study highlights the usefulness of QM calculations to reveal the elementary reaction pathways that are embedded in the overall reaction pathways that are typically identified by analytical techniques. This technique becomes more useful when the contaminant concentrations are below the analytical detection limit.
Once the elementary reaction pathways are identified, the reaction rate constants should be determined or predicted to calculate the reaction rate of each molecule or species involved in each elementary reaction step. By combining the elementary reaction pathways and the reaction rate constants, one can predict the time-dependent concentration profiles of a target chemical contaminant and its transformation products. This elementary-reaction-based kinetic model could be used as an initial screening tool for many potentially toxic chemical contaminants to estimate the fate of degradation pathways. Our efforts towards the development of such elementary-reaction-based kinetic model are underway.

Materials and Methods
All of the QM calculations were performed with the Gaussian 09 revision D.02 program [36] using the Michigan Tech high-performance cluster "Superior" and homemade LINUX workstations. The M06-2X/cc-pVDZ [37] was used to optimize the electronic structures and calculate the frequencies in both the gas and aqueous phase for the HO • -induced reaction pathways with NDMA, NMEA, and NMBA. The UV-induced reaction pathways with NDMA was calculated with the Gaussian-4 theory (G4) [38]. The aqueous-phase structures and frequencies were obtained using an

Environmental Implication and Future Study
Nitrosamines, and NDMA in particular, are extremely potent carcinogenic contaminants in water. The concentration at which NDMA shows potent carcinogenicity is extremely low (0.7 ng/L) [1]. Experimentally investigating the ng/L fate of many chemical contaminants during water treatment processes is time consuming and expensive. Our computational study highlights the usefulness of QM calculations to reveal the elementary reaction pathways that are embedded in the overall reaction pathways that are typically identified by analytical techniques. This technique becomes more useful when the contaminant concentrations are below the analytical detection limit.
Once the elementary reaction pathways are identified, the reaction rate constants should be determined or predicted to calculate the reaction rate of each molecule or species involved in each elementary reaction step. By combining the elementary reaction pathways and the reaction rate constants, one can predict the time-dependent concentration profiles of a target chemical contaminant and its transformation products. This elementary-reaction-based kinetic model could be used as an initial screening tool for many potentially toxic chemical contaminants to estimate the fate of degradation pathways. Our efforts towards the development of such elementary-reaction-based kinetic model are underway.

Materials and Methods
All of the QM calculations were performed with the Gaussian 09 revision D.02 program [36] using the Michigan Tech high-performance cluster "Superior" and homemade LINUX workstations. The M06-2X/cc-pVDZ [37] was used to optimize the electronic structures and calculate the frequencies in both the gas and aqueous phase for the HO • -induced reaction pathways with NDMA, NMEA, and NMBA. The UV-induced reaction pathways with NDMA was calculated with the Gaussian-4 theory (G4) [38]. The aqueous-phase structures and frequencies were obtained using an implicit polarizable continuum model [universal solvation model (SMD)] [39]. Previously, we verified the combination of M06-2X/cc-pVDZ or G4 with the SMD model by successfully applying it to other aqueous-phase radical-involved reactions [27,28]. Theoretically calculated absorption spectra were obtained from a TD-DFT analysis [40,41] of the optimized aqueous-phase structure of NDMA at the level of M06-2X/cc-pVDZ with the SMD solvation model. To investigate the contributions from molecular orbitals to the peak of the spectra, molecular orbitals were determined using a natural population analysis at the level of M06-2X/cc-pVQZ with the SMD solvation model. The detailed calculation procedures for the transition state search, the aqueous-phase free energies of activation and reaction, and the associated computational methods are found in previous reports [29].
Supplementary Materials: Supplementary materials are available on line.