Elementary reaction-based kinetic model for the fate of N-nitrosodimethylamine under UV oxidation

Abstract

UV photolysis is an effective process to remove nitrosamines from contaminated water resources. Nitrosamines represent a class of compounds with high potential for carcinogenicity and, therefore, there are serious concerns regarding their threat to human health and their environmental toxicity. Although the photochemical parameters of parent nitrosamines and their initial reaction pathways are well understood, the fate of nitrogen-containing species and reactive nitrogen species generated from nitrosamine degradation has not yet been elucidated. In this study, we develop an elementary reaction-based kinetic model for the photolysis of N-nitrosodimethylamine (NDMA) and the photochemical transformation products. We use density functional theory quantum mechanical calculations to calculate the aqueous-phase free energies of activation and reaction to investigate the kinetics and thermodynamics properties of the elementary reactions. We generate ordinary differential equations for all species involved in the identified reactions and solve them to obtain the time-dependent concentration profiles of NDMA and the degradation products at pH 3 and pH 7. The profiles are compared to experimental results in the literature to validate our elementary reaction-based kinetic model. This is the first study to develop an elementary reaction-based kinetic model for the photochemical reaction of NDMA and reactive nitrogen species. The findings of this study have a significant impact on the active research area of nitrosative stress and advanced oxidation processes that utilize nitrogen-containing compounds such as UV/nitrate and UV/chloramine advanced oxidation processes.

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Water impact

UV photolysis is employed in water treatment and reuse practices. Understandings of photolysis-induced radical-involved basic reaction mechanisms enables the predictions of contaminants' fate not only in engineered but also natural aquatic environmental systems.

Introduction

A group of nitrosamines present in water imposes high potential for carcinogenicity and is of serious concern about their threat to human health in potable waters and adverse ecotoxicological effects in environmental waters.¹ Although the potential formation of some disinfection byproducts (DBPs) such as iodinated trihalomethanes may occur, with an increase in the use of chloramine as a primary/secondary disinfectant to reduce the formation of trihalomethanes, haloacetic acids, and other halogenated disinfection DBPs, more N-nitrosamines than in the past have been detected in drinking water,² wastewater, and wastewater reclamation processes.³ The U.S. EPA calculated a screening level of 0.11 ng L⁻¹ for N-nitrosodimethylamine (NDMA), one of the most commonly detected and carcinogenic N-nitrosamines, for tap water based on a 10⁻⁶ lifetime excess cancer risk.⁴ In California, a 1.2-log NDMA removal is required for potable reuse of wastewater and the water reuse utilities must implement treatment processes that achieve the NDMA notification level of maximum of 10 ng L⁻¹ in the reclaimed water.⁵

N-Nitrosamines preferably undergo photolysis, which results in the degradation of the parent structure containing N–NO bond. While the parameters of the photochemical reactions of parent nitrosamine compounds are well understood⁶ such as the quantum yield, pH effect,^7,8 dissolved oxygen effect,⁹ and initial reaction pathways,⁷ the fate of nitrogen-containing species and reactive nitrogen species generated from the degradation of nitrosamine has not yet been elucidated. For example, each quantum yield of nitrogen species under the degradation of N-nitrosamines is not known. The reaction pathways and kinetics of peroxynitrite/peroxynitrous acid (ONOO⁻/ONOOH)¹⁰ with other degradation products of N-nitrosamines are not understood. Neither the kinetics of the reactions involving reactive nitrogen species nor the photochemical fate of nitrate/nitrite/peroxynitrite are fully understood.^11–14 Short-lived reactive nitrogen species are difficult to identify experimentally due to the lack of probe compounds and therefore it is not clear whether the experimentally reported rate constants represent the overall or elementary reaction steps. Consequently, challenges remain in identifying the elementary reaction pathways that are embedded in the overall photochemical degradation of N-nitrosamines. For these reasons, no mechanistic kinetic model of nitrosamines undergoing UV photolysis has been developed. Understanding the elementary reaction pathways and their kinetics enables the comprehensive prediction of the photochemical fate of nitrogen-containing compounds.

Density functional theory (DFT) quantum mechanical (QM) calculations provide complementary information about the kinetics and thermodynamics of elementary reactions to experimentally identified overall or elementary reaction steps.^16–22 QM calculations have been successfully used for the pathways of NDMA formation induced by ozonation.¹⁵ Thorough analysis of both thermodynamics and kinetics of each elementary reaction is important as experimentally determined rate constants do not always provide the reaction mechanisms. The thermodynamics (i.e., endergonic or exergonic) of elementary reactions can be determined by calculating the aqueous-phase free energies of reaction and the kinetics can be determined by calculating the aqueous-phase free energies of activation.^23,24 However, kinetics override thermodynamics for many radical reactions²⁵ and thus even though an elementary reaction is endergonic, the reaction may occur kinetically or there might be a backward reaction that may overtake a forward reaction. A kinetic model developed without the critical analysis of each elementary reaction or by blindly accepting literature-reported rate constants may fail to predict the fate of a target compound. For the aqueous-phase fate of nitrosamine where nitrogen-centered radicals are involved, challenges remain to identify the transition states or precursor complexes because of their possible shallow potential energy surfaces of singlet biradical reactions and the loose intermolecular bonds.^26–28

In this study, we investigate the photolysis of NDMA and the photochemical products with DFT QM calculations to identify the elementary reaction pathways. Although the rate constants of major reactions involving the fate of NDMA degradation are experimentally determined and reported, it is important to evaluate each elementary reaction based on our calculated thermodynamics and kinetic properties because each rate constant is generally obtained by independent studies under the different experimental conditions. Once we understand the elementary reaction mechanism of all possible reactions that are involved in the NDMA degradation, we generate ordinary differential equations (ODEs) for all species involved in the identified reactions and solve them to obtain the time-dependent concentration profiles of NDMA and the degradation products at different pH values. The numerical solution of ODEs is critical to understand the fate that is determined by both species concentrations and reaction rate constants of all the elementary reactions. The profiles are compared to those obtained experimentally in the literature to validate our elementary reaction-based kinetic model.

Materials and methods

All of the QM calculations were performed using the Michigan Tech high-performance cluster “Superior” and homemade LINUX workstations. All the DFT calculations were conducted with the Gaussian 16 revision A. 01. program.²⁹ Single point energy calculations using the unrestricted coupled-cluster theory³⁰ with single, double, and noniterative triplet excitations (UCCSD(T)) were conducted with the Molpro package.³¹ The unrestricted form of UM06-2X³²/Aug-cc-pVTZ level of theory was used to calculate the wavefunction for a given molecular and radical structures and calculate the frequencies in both the gas and aqueous phases because of the previous applications.^33,34 The augmented basis set was recommended to optimize the ionized molecular and radical structure by including the diffuse function.³⁵ To avoid false convergence due to small gradients on a flat potential energy surface, we used the ‘ultrafine’ integration grid in the self consistent field procedure and geometry optimization. The aqueous-phase structures and frequencies were obtained using an implicit polarizable continuum model [universal solvation model (SMD)].³⁶ To verify the impact by the multireference state (e.g., ground state oxygen molecule and the addition reaction and see the detailed analysis for Text S2 in the ESI†), we used hybrid single reference DFT, M05/Aug-cc-pVTZ,³⁵ as this method was previously used for the NDMA system in the literature.¹⁵ It was shown that unrestricted DFT (UDFT) performed well in comparison to multireference methods for deriving energies and geometries of singlet biradical.^37,38 For the radical–radical coupling reactions, we used a NoSymmetry keyword to prevent the reorientation of molecules and radicals and guess = mix for broken-symmetry approach. Spin contamination resulting from the use of UDFT was corrected for some transition states and the detailed method is given in Text S1 in the ESI.† We also performed the stability test for the optimized transition states routinely using a keyword ‘Stable’. To ensure the correct assignment to a local minima and a transition state, we analyzed the harmonic vibrational frequency. All transition states were verified by intrinsic reaction coordinate (IRC)^39,40 to ensure the connection among reactants, transition states and products in particular for the radical–radical coupling reactions. We paid special attention to the spin contamination in the systems studied. The detailed calculation procedures are found in Text S1 of the ESI.† Marcus theory^41,42 was used to calculate the activation energy for single electron transfer and the detailed procedure is provided in Text S3 and Fig. S1 in the ESI.† It is noted that we did not intend to obtain the absolute energy values of each reaction as this is computationally demanding and prohibitive in getting accuracy values in the aqueous phase; however, we aimed to obtain the relative energies accurate enough to evaluate the relative energies resulting from various structures under the same reaction mechanism.

Once the elementary reaction pathways and the corresponding reaction rate constants were identified, we numerically solved the ODEs using the Gear method⁴³ by modifying the original UV/H₂O₂ kinetic model⁴⁴ and compared them to the experimental results reported in the literature. Experimental studies were performed and reported by Lee et al. (2005).⁷ Text S4 in the ESI† summarizes the detailed experimental conditions. To evaluate the impact of each reaction rate constant on the simulated time-dependent concentration profiles, classical local sensitivity analysis was conducted. Text S5 in the ESI† provides the procedure, the results and a discussion of the sensitivity analysis.

Results and discussion

Overall results

Fig. 1 displays the time-dependent concentration profiles of NDMA, the major transformation products [i.e., methylamine (MA) and dimethylamine (DMA)] and the minor transformation products [i.e., formic acid (HCOOH), nitrite (NO₂⁻), and nitrate (NO₃⁻)] predicted at two pH values (pH 7 and pH 3) by our elementary reaction-based kinetic model and experimental studies in the literature.⁷ We chose pH 3 because the photochemical fate at pH 3 represents those in the acid solution (i.e., typical practices in direct potable reuse) as compared to those in the neutral solution. Table 1 includes the photochemical elementary reaction pathways identified in this study, the theoretically calculated free energies of activation, ΔG^act_aq,calc, kcal mol⁻¹, the free energies of reaction, ΔG^act_aq,calc, kcal mol⁻¹, activation energies, ΔE^act_aq,calc, kcal mol⁻¹, imaginary frequency of the transition states, the k values in the literature, and the known pK_a values of each species that undergoes dissociation. It is important to track the dissociation/nondissociation of species at different pH values because of the various pK_a values of different species and the different reactivities between dissociated and nondissociated species. The sample deviation (SD) was calculated as shown in eqn (1) to evaluate the discrepancy between the predicted profiles by our elementary reaction-based kinetic model and the experimental values in the literature.where N_i is the total number of data points for species i, and C_exp,j and C_calc,j are the experimental and calculated concentrations of species, i, respectively, for the j set of all times for which each data point is available. The SD value was calculated by weighting all data equally by dividing the difference between the experimental and calculated values by the experimental data, so that the outweighed data point(s) did not significantly affect the overall SD value for each species. The SD values were calculated as 0.27 for NDMA, 0.18 for DMA, 0.31 for MA, 0.23 for NO₂⁻, 0.10 for NO₃⁻, and 0.48 for HCOOH at pH 7. At pH 3, the SD value was 0.15 for NDMA, 0.16 for DMA, 0.33 for MA, 0.12 for NO₂⁻, 0.36 for NO₃⁻, and 0.23 for HCOOH. The SD values represent the statistical accuracy of predicted values as compared to the experimental observations. Although no kinetic model was previously developed and no comparison with other studies was possible, these SD values are reasonable from the results of our previously developed elementary reaction-based kinetic model for UV/H₂O₂ and UV/free chlorine AOPs.^23,24 It should be noted that the time-dependent concentration profiles of formaldehyde (HCHO) at both pH values were not included in Fig. 1 because HCHO is rapidly hydrolyzed to produce methylene glycol, CH(OH)₂. The CH(OH)₂ then partially undergoes a slow dimerization to dimethylene glycol, HO–CH₂OCH₂OH.⁴⁵ The pK_a value HCHO hydration was −3.36 and the hydration rate constants were reported as 10 M⁻¹ s⁻¹ at neutral pH and 5.37 × 10³ M⁻¹ s⁻¹ at acid pH.^46,47 This approach to HCHO and CH(OH)₂ chemistry was successfully validated in our previous study²³ and these rate constants were used in this work. The CH(OH)₂ further reacts with ONOOH/ONOO⁻ (see the details below).

Fig. 1 Experimental (exp)⁷ and predicted (calc) time-dependent concentration profiles of NDMA and the transformation products at pH 7 (above) and pH 3 (below).

Table 1 Photochemical elementary reaction pathways with theoretically calculated aqueous-phase free energies of activation and reactions, and reaction rate constants. All thermodynamic and kinetics parameters were theoretically calculated by this study. The quantum yields, reactions rate constants, and equilibrium constants that were obtained from previous studies in the literature, and otherwise, estimated by this study

Pathway no.	Mechanisms	Elementary reaction	Quantum yield of products	Molar absorptivity, M^−1 cm^−1	Reference for quantum yields
a Determined in this study, see text. b Obtained at the level of UM05/Aug-cc-pVTZ. c Obtained at the single point energy with UCCSD(T)/cc-pVTZ for the structure obtained at UM05/Aug-cc-pVTZ. d Estimated based on the ΔG^actaq,calc value and previously developed LFERs.^19,21
1	Photolysis	(CH3)2N–NO–H^+ → (CH3)2˙NH^+ + NO˙	0.02 (pH = 7) and 0.05 (pH = 3)^a	1650
2	Photolysis	(CH3)2N–NO–H^+ → (CH3)2NH2^+ + HNO2	0.20 (pH = 7) and 0.18 (pH = 3)^a
3	Photolysis	(CH3)2N–NO–H^+ → CH2=N^+HCH3 + NO˙ + O2˙^−	0.12 (pH = 7) and 0.27 (pH = 3)^a
4	Photolysis	NO3^− → [NO3^−]* → NO2˙ + O˙^−	0.037	15	48
5	Photolysis	NO3^− → [NO3^−]* → ONOO^−	0.102	15	48
6	Photolysis	NO2^− → [NO2^−]* → NO˙ + O˙^−	0.02	32	48
7	Photolysis	ONOO^− → [ONOO^−]* → NO˙ + O2˙^−	0.1	555	49

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Pathway no.	Mechanisms	Elementary reaction	ΔG^actaq,calc, kcal mol^−1	ΔG^reactaq,calc, kcal mol^−1	ΔE^actaq,calc, kcal mol^−1	Imaginary frequency	k, M^−1 s^−1 unless noted	Reference for rate constants
8	Radical coupling	(CH3)2˙NH^+ + ˙NO → CH3N(+)H=CH2 + HNO	9.9	−12.0	−3.8	−743.5	7.2 × 10^8	7, 9
9	Dimerization	2HNO → HN(OH)–N=O	9.5	−33.4	−3.2	−1773.3	8.0 × 10^6 s^−1	50
10	Cleavage of N–O bond	HN(OH)–N=O → N2O + H2O	53.3	−60.0	57.0	−1874.9
11	Hydrolysis	CH3N(+)H=CH2 + H2O → CH3NH3^+ + HCHO	34.0	5.2	22.6	−1585.7	1.0 × 10^3 s^−1
12	1,2-H shift	(CH3)2˙N → ˙CH2NHCH3	31.6 (2 explicit water molecules)	2.6	12.9	−303.6	1.0 × 10^6 s^−1
13	O2 addition	˙CH2NHCH3 + O2 → ˙OOCH2NHCH3	−13.3 (−7.0^b and −6.9^c)	−25.3 (−19.2^b and −22.0^c)	−24.6 (−18.5^b and −18.3^c)	−118.3 (−85.2^b)	4.5 × 10^9
14	Radical coupling	NO˙ + O2˙^− → ONOO^−	6.8	−9.2	−2.9	−278.9	4.2 × 10^9	52
15	Radical coupling	NO˙ + HO2˙ → ONOOH	5.3 (1 explicit water molecule)	−9.6 (trans) −11.6 (cis)	−16.4	−194.1	3.2 × 10^9	52
16	Radical coupling	NO˙ + HO˙ → HNO2	5.5	−37.1	−0.8	−156.7	1.0 × 10^10	52
17	Radical coupling	NO2˙ + HO˙ → ONOOH	−13.4	−45.7	−23.4	−674.8	4.5 × 10^9	53
18	Radical coupling	NO2˙ + O˙^− → ONOO^−	−4.9	−61.3	−13.1	−760.8	3 × 10^9	54
19	Radical coupling	NO˙ + NO2˙ → N2O3	8.0	−2.7	−2.7	−165.2	1.1 × 10^9	55
20	Radical coupling	NO2˙ + NO2˙ → N2O4	5.0	−5.1	−2.1	−26.9	4.5 × 10^8	56
21	Radical coupling	NO˙ + NO˙ + (O2) → 2NO2˙	26.3^c	−9.2^c	5.0^c	−257.7^c	1.0 × 10^9	57
22	Isomerization	ONOO^− → NO3^−	48.5	−50.9	49.7	−1446	8.0 × 10^−6 s^−1	54
23	Isomerization	ONOOH → NO3^− + H^+	38.9 (2 explicit water molecules)	−88.9	29.3	−506.4	0.65 s^−1	58, 59
24	Radical coupling	HO2˙ + NO2˙ → OONOOH	−25.5	−46.8	−37.8	−170.3	1.8 × 10^9	60, 61
25	Radical coupling	O2˙^− + NO2˙ → OONOO^−	−28.2	−47.8	−38.2	−92.5	4.5 × 10^9	60, 61
26	Single electron transfer	NO2^− + HO˙ → NO2˙ + OH^−	3.5	−2.7	—	—	6.0 × 10^9	53
27	Adduct formation	HCHO˙ + ONOO^− ↔ H2C(ONOO^−)O	8.4 (trans) and 11.9 (cis) (forward)3.8 (trans) and 7.3 (cis) (backward)	4.6 (trans) and 8.3 (cis) (forward)−4.6 (trans) and −8.3 (cis) (backward)	−3.3	−186.9	—
28	Hydrolysis	HCHO + H2O → CH2(OH)2	31.5	−1.2	8.6	−812.8	10 s^−1 (neutral)5.4 × 10^3 s^−1 (acidic)	46, 47
29	H abstraction	CH2(OH)2 + HO˙ → ˙CH(OH)2 + H2O	8.8	−24.9	3.2	−881.4	7.4 × 10^7
30	H abstraction	CH2(OH)2 + ONOO^− → ˙CH(OH)2 + ˙NO2 + OH^−	40.1	−11.4	33.3	−1089.7	2.5 × 10^4
31	H abstraction	CH2(OH)2 + ONOOH → ˙CH(OH)2 + ˙NO2 + H2O	53.4	−14.5	46.1	−996.9	1.0 × 10^4
32	O2 addition	˙CH(OH)2 + O2 → ˙OOCH(OH)2	−9.7 (−8.3^b and −5.1^c)	−32.9 (−28.3^b and −30.7^c)	−21.8 (−19.7^b and −17.2^c)	−231.9 (−77.8^b)	4.8 × 10^9
33	Unimolecular decay	˙OOCH(OH)2 → HO2˙ + HCOOH	9.2	−9.1	11.9	−969.2	8.7 × 10^3 s^−1	23
34	H-Abstraction	HCOOH + HO˙ → ˙COOH + H2O	10.5	−18.1	4.9	−1103.1	4.5 × 10^7	23
35	H-Abstraction	HCOO^− + HO˙ → ˙COO^− + H2O	5.2	−31.0	−1.4	−790.6	2.4 × 10^9	23
36	Single electron transfer	˙COO^− + O2 → ˙O2^− + CO2	2.3	−33.1	—	—	2.4 × 10^9	62

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	Species	Equilibrium reaction	pKa	Reference
37	NDMA	(CH3)2NNO–H^+ ↔ (CH3)2NNO + H^+	8.5	6
38	Aminium radical	(CH3)2˙NH^+ ↔ (CH3)2˙N + H^+	6.5	63
39	Dimethylamine	(CH3)2NH2^+ ↔ (CH3)2NH + H^+	10.77	64
40	Methylamine	CH3NH3^+ ↔ CH3NH2^+ + H^+	10.64	64
41	Peroxynitrous	ONOOH ↔ ONOO^− + H^+	6.6	65
42	Peroxynitric acid	O2NOOH ↔ O2NOO^− + H^+	5.85	52
43	Hydroperoxyl radical	HO2˙ ↔ O2˙^− + H^+	4.8	66
44	Nitrate	HNO3 ↔ NO3^− + H^+	−1.38	64
45	Nitrite	HNO2 ↔ NO2^− + H^+	3.2	64
46	Hydroxyl radical	HO˙ ↔ O˙^− + H^+	11.9	67
47	Hydrogen peroxide	H2O2 ↔ HO2^− + H^+	11.6	64

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Photolysis pathways and quantum yields of NDMA

We performed TD-DFT calculations at the level of M06-2X/Aug-cc-pVTZ with the SMD solvation model to reveal highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for the corresponding transition. We confirmed the n → π* transition at 347 nm and the π → π* transition at 202 nm, whose absorbance peaks are consistent with experimental observations at 332 nm and 228 nm.^3,8 The detailed TD-DFT method and results about MO are given in Text S6 and Fig. S3 in the ESI.†

The photolysis of NDMA by the 253.7 nm radiation emitted from a low-pressure UV lamp results in products via three major pathways: (1) homolytic cleavage of the N–NO bond of NDMA to produce aminium radicals [(CH₃)₂N˙H⁺] and nitric oxide (NO˙) (pathway 1 in Table 1); (2) heterolytic cleavage of the N–NO bond to produce dimethylamine [(CH₃)₂NH₂⁺] and nitrous acid (HNO₂) (pathway 2); and (3) photooxidation in the presence of dissolved oxygen to produce N-methylidenmethylamine (CH₂=N⁺HCH₃), NO˙, and superoxide anion (O₂˙⁻) radicals (pathway 3). For the elementary reaction-based kinetic model, we included the photolysis of NDMA degradation products such as nitrate (pathways 4 and 5),⁴⁸ nitrite (pathway 6), and peroxynitrite ion (pathway 7),⁴⁹ although these pathways may not be the major ones for the productions of ONOO⁻, NO˙, HO˙ and O₂˙⁻. These photolysis reactions are well known and are reported in the literature, and we use these reactions for our kinetic model (Table 1). We determined the partial quantum yields of each photochemical reaction at pH 7 and 3 by fitting with the time-dependent concentration profiles of each species obtained by the experiments (see the detailed procedure in the following sections). The overall quantum yield for NDMA degradation is well known to be 0.31 at pH 2–8.⁹ We determined a quantum yield of 0.02 for pathway 1, 0.20 for pathway 2, and 0.12 for pathway 3 at pH 7. At pH 3, a partial quantum yield of 0.05 for pathway 1, 0.18 for pathway 2, and 0.27 for pathway 3 was determined. These partial quantum yields are consistent with the experimental observation and reaction mechanism for the following reasons. First, the formation of DMA result from both pathways 1 and 2, where the pathway 1 has smaller partial quantum yields than pathway 2 by 10 times at pH 7 and 3.6 times at pH 3. The significantly smaller quantum yield of pathway 1 is consistent with the experimental observation.⁹ Second, similar partial quantum yields of pathway 2 determined at both pH values in this study (i.e., 0.2 at pH 7 and 0.18 at pH 3) are consistent with the experimental observation of similar amounts of NO₂⁻ produced at both pH values,⁹ although the highest yield was observed at pH 4. The highest yield at pH 4 was proved by the fact that the formation of HNO₂/NO₂⁻ result from the acid-catalyzed mechanisms of pathway 2 alone.⁷ The sum of the partial quantum yields should be equal to that of the overall pathway if each species in the specific pathway does not participate in the other photochemical reactions.⁶⁸ While the sum of the quantum yields at pH 7 was determined to be 0.34 which is consistent with the experimental value, the overall calculated quantum yield of 0.50 at pH 3 was significantly larger than the experimental value (0.31). In particular, the quantum yield of 0.27 determined for pathway 3 at pH 3 is significantly larger than 0.12 at pH 7 for photolysis pathway 3. Two major possibilities could explain this discrepancy: (1) the non-cage reaction of pathway 3 and (2) the way of determining the partial quantum yield. Unlike pathways 1 and 2, pathway 3 does not occur in cage but is catalyzed by dissolved oxygen. Thus, the products of pathway 3 do not necessarily result from the direct photolysis of NDMA. However, the dependency of non-cage reaction on the solution pH is not clear as the dissolved oxygen concentrations at both pH values do not differ significantly and the concentration profiles of NDMA and other products were obtained in O₂-saturated solution experimentally.⁹ The other possible reason is that we determined the partial quantum yield based on the available experimentally determined time-dependent concentration decays of NDMA, DMA, MA, nitrate and nitrite but with no experimental information on the concentrations of species involved in pathway 3 (i.e., N-methylidenmethylamine, NO˙ and O₂˙⁻). The experimental data showed a more significant decrease in the nitrate formation yield at pH 7 under N₂-saturated condition (i.e., non-oxygenated solution) than at pH 3.⁷ This indicates that the production of NO˙ and O₂˙⁻ from the pathway 3 is key for the formation of nitrate through reactions 14 and 19. Thus, the nitrate concentration profile dominantly determined the partial quantum yield at pH 7 but did not necessarily determine the quantum yield for the formation of NO˙ and O₂˙⁻. Because of this reason, we may have obtained significantly larger partial quantum yield (i.e., 0.27). At pH 3, the nitrate formation was not significantly affected by different experimental conditions (i.e., O₂- and N₂-saturated solutions).⁷ Our determined partial quantum yield (i.e., 0.12) at pH 3 is consistent with the experimental value of 0.144⁹ determined from the formation yield of O₂˙⁻ at pH 7, indicating that the formation of O₂˙⁻ from pathway 3 is pH-independent. The concentration profile of methylamine is affected by the formation of N-methylidenmethylamine that is produced by both pathway 3 and radical reaction of pathway 8. Given that our predicted time-dependent concentration profile of MA is consistent with experimental observations at both pH values (Fig. 1), the partial quantum yield of 0.12 for the formation of N-methylidenmethylamine at pH 3 should also represent that at pH 7. It should be noted that we determined the partial quantum yields using the concentration profiles for ∼15 minutes but experimental data are also available at pH 7 for up to 300 minutes for higher NDMA initial concentration.⁷ While there is an approach to theoretically calculate the quantum yield for the elementary reaction pathways,⁶⁹ uncertainty remains and it could be applied for only small molecular size compounds. More mechanistic investigation on each photolysis pathway is needed.

Radical-involved reactions

The aminium radical [(CH₃)₂˙NH⁺] and the NO˙ produced in pathway 1 react in a solvent cage to produce N-methylidenmethylamine. The pK_a of aminium radicals is 6.5,⁶⁴ and approximately 75% of the total concentration is present in a nonprotonated form at pH 7; the protonated form is dominant at pH 3. The protonated aminium radical reacts with NO˙ undergoing a radical–radical coupling at 9.9 kcal mol⁻¹ of the ΔG^act_aq,calc value and producing methylidenmethylamine and HNO (reaction 8). The HNO produced in reaction 8 undergoes dimerization and arrangement to produce the final product of N₂O and H₂O (k = (8 ± 3) × 10⁶ M⁻¹ s⁻¹).⁵⁰ The overall reaction contains two elementary reaction steps: (1) the formation of HN(OH)–N=O via dimerization of HNO at the ΔG^act_aq,calc value of 9.5 kcal mol⁻¹ (reaction 9) and (2) arrangement by cleaving the N–O bond of HN(OH) to produce N₂O and H₂O at the ΔG^act_aq,calc value of 53.3 kcal mol⁻¹ (reaction 10). Methylidenmethylamine undergoes hydrolysis to produce MA and HCHO (reaction 11) and the first order rate constant, 10³ s⁻¹, is used based on the similar hydrolysis reaction with previously determined ΔG^act_aq,calc value.^46,47 Nonprotonated aminium radicals have an unpaired electron adjacent to an electron lone pair, and conjugative delocalization transfers the unpaired electron of the N-centered radical to the carbon,^70,71 which produces a carbon-centered radical, ˙CH₂NHCH₃ (reaction 12). Unlike the addition of molecular oxygen to a carbon-centered radical, this delocalization of the radical spin density causes an N-centered radical to undergo abnormally slow reactions for molecular oxygen addition (i.e., 5.3 × 10⁶ M⁻¹ s⁻¹)⁷¹ and results in no competition with the unimolecular H-shift from an alkoxyl radical to a C-centered radical (∼1.0 × 10⁶ s⁻¹).⁵¹ Since no experimentally measured first-order reaction rate has been reported for this H-shift reaction, we used 1.0 × 10⁶ s⁻¹, as estimated based on the similar H-shift from the C-centered radical and the similar ΔG^act_aq,calc value.⁵¹ Our calculations obtained 31.6 kcal mol⁻¹ of ΔG^act_aq,calc for the H-shift of the N-centered radical with two-explicit water molecules and the ΔG^react_aq,calc value indicates the slight endergonic reaction. Text S8 in the ESI† includes the detailed procedure to calculate the thermodynamic parameters in the presence of explicit water molecules. The carbon-centered radical further reacts with dissolved oxygen to produce the peroxyl radical (CH₃NHCH₂OO˙) (reaction 13). The ΔG^act_aq,calc value is −13.3 kcal mol⁻¹, which was used to estimate the rate constant using the previously developed LFER.¹⁹ We have investigated the impact of multireference state and spin flip of this addition reaction in Text S2 in the SI. The peroxyl radicals undergo uni-/bimolecular decay to produce various intermediates, including CH₃NHCHO, CH₃NHCH₂O˙, CH₃NHCH₂OH, and CH₃N⁺H=CH₂via the Bennett reaction mechanism^72,73 and other bimolecular reactions that produce the alkoxyl radical⁷⁴ and the alcohol via the Russell mechanism.⁷⁵ Lee et al. reported the production of CH₃NHCHO from NDMA photolysis at approximately neutral pH values (pH 5.5–8) in a deoxygenated environment and proposed the reaction of ˙NO with ˙CH₂NHCH₃.⁷ This finding indirectly supports the pathway of peroxyl radical bimolecular decay for the formation of CH₃NHCHO in an oxygenated environment. The other reaction pathway induced by NO˙ will be discussed for pathway 3.

DMA and nitrous acid (HNO₂) are produced by the homolytic pathway 2 of NDMA photolysis. DMA, whose pK_a is 10.77, is present as protonated DMA [i.e., (CH₃)₂NH₂⁺] at both pH 7 and pH 3. There is no other pathway to produce DMA in NDMA degradation, and thus, DMA formation was solely used to determine the partial quantum yield of pathway 2 (i.e., 0.20 at pH 7 and 0.18 at pH 3). HNO₂, whose pK_a is 3.2, is present as nitrite as the dominant form at pH 7, but both HNO₂ and nitrite are present at pH 3. The photochemical fate of nitrite is discussed in the section below. Although the nitrogen of DMA reacts with HO˙ via single electron transfer to produce a two-electron three-centered (2e–3c) adduct, and H-atom abstraction from a C–H bond of methyl functional groups occurs to produce a carbon-centered radical,⁷⁶ the apparent low concentration of HO˙ in UV photolysis (10^{–13–−14} M at pH 7 and 10^{–13–−12} M at pH 3) makes this reaction insignificant. Consequently, the formation of DMA was dominant and became saturated as NDMA decay slowed at the later reaction time (Fig. 1).

N-Methylidenmethylamine, NO˙ and O₂˙⁻ are produced by photooxidation pathway 3 of NDMA photolysis. NO˙ reacts with HO₂˙/O₂˙⁻ (pK_a = 4.8)⁶⁷ in the solvent cage to produce ONOOH/ONOO⁻ (pK_a = 6.6)⁶⁶ in reactions 14 and 15 (Table 1). The ΔG^act_aq,calc values for the reaction with O₂˙⁻ is 6.8 kcal mol⁻¹ and this is an exergonic reaction at the ΔG^react_aq,calc value of −9.2 kcal mol⁻¹. We obtained 5.3 kcal mol⁻¹ of ΔG^react_aq,calc value in the presence of one explicit water as the water molecule stabilizes the reactants in reaction 15 and confirmed the products of ONOOH at −9.6 kcal mol⁻¹ for the trans and −11.6 kcal mol⁻¹ for the cis form, respectively. NO˙ also reacts with HO˙ to produce HNO₂ with 5.5 kcal mol⁻¹ of the ΔG^act_aq,calc value (reaction 16). ONOOH and dissociated form, ONOO⁻, are also produced by the reaction of HO˙/O˙⁻ with NO₂˙ (reactions 17 and 18),^54,55 which is the product of nitrate photolysis. The negative ΔG^act_aq,calc values of reactions 17 and 18 (and reactions 26 and 27) imply the possible formation of precursor-complexes; however, we were not able to optimize the loosely bound structures of any precur-complexes. The single Slater determinant formalism used in DFT may have caused issues in calculating the potential energy surface for interactions of two multicenter free radicals, although the gaseous phase NO₂–NO₂ isomers were determined with several post ab initio and DFT methods including a mutireference method.²⁶ The use of a multireference method for aqueous-phase reactions is beyond the scope of this study but we are now investigating the cause of possible errors. Because of the uncertainties of these negative values, we did not include these datapoints in the analysis of a linear free energy relationship shown below. NO˙ reacts with NO₂˙ to produce a short-lived intermediate, N₂O₃ (reaction 19) at the ΔG^act_aq,calc value of 8.0 kcal mol⁻¹. Similar reactions occur for the disproportionation reaction of NO₂˙ (reaction 20), which produces N₂O₄ and the ultimate products of NO₂⁻ and NO₃⁻.⁵⁰ Our theoretical calculation indicates that the disproportionation of NO₂˙ requires 5.0 kcal mol⁻¹ of ΔG^act_aq,calc. While our transition state clearly showed the nitrogen–nitrogen radical coupling and confirmed by the IRC analysis, small imaginary frequency and unexpectedly small free energy of activation for the reported rate constant (k = 4.5 × 10⁸ M⁻¹ s⁻¹) raises concern about our value. We were not able to locate the transition state with other methods and no studies in both gaseous and aqueous phases reported the transition state structures. The disproportionation of NO˙ in the presence of molecular oxygen (reaction 21) requires 26.3 kcal mol⁻¹ of ΔG^act_aq,calc. ONOO⁻ or ONOOH undergoes an isomerization reaction to produce NO₃⁻. Our calculation indicates 48.5 kcal mol⁻¹ or 38.9 kcal mol⁻¹ of ΔG^act_aq,calc (reactions 22 and 23). While ONOO⁻ is very stable, as verified by the experimental k value of 8.0 × 10⁻⁶ s⁻¹,⁵⁴ ONOOH undergoes much faster decay (i.e., k = 0.65 s⁻¹).^59,60 The cis-form of ONOOH undergoes O–O bond cleavage as a result of orbital interactions between the two separating parts of the ONO⋯HO radical pair to produce an activated species, HOONO˙.^59,60 This activated species eventually produces HNO₃.

NO₂˙ reacts with O₂˙⁻ /HO₂˙ to produce peroxynitric acid/peroxynitrate (OONOOH/OONOO⁻), which are stronger acids than ONOOH/ONOO⁻.⁴⁸ The pK_a of peroxynitric acid is 5.8,⁵² and OONOOH is dominant at weakly acidic and neutral pH values. The formation of OONOOH and OONOO⁻ requires −25.5 kcal mol⁻¹ and −28.2 kcal mol⁻¹ of ΔG^act_aq,calc (reactions 24 and 25).

Pathway from HCHO to HCOOH

At 254 nm, HCHO does not have a noticeable absorbance (Fig. S4 of the ESI†). Thus, the direct photolysis pathway from HCHO to HCOOH is not feasible. HCHO and the hydrolyzed form of CH₂(OH)₂ may undergo HO˙ reactions and produce HCOOH as the ultimate product.²³ Merényi et al. calculated a yield of 30–40% for HO˙ + NO₂˙ from the HCOOH decay.⁷⁷ However, the experiment was performed with a pulse radiolysis system and utilized a high concentration of nitrite (i.e., 0.06–6.5 mM NO₂⁻) to generate ONOOH. In the NDMA photolysis, HO˙ that is produced by multiple radical pathways reaches considerably lower concentrations, such that, in our kinetic model HO˙ does not contribute significantly to the formation of HCOOH from HCHO/CH₂(OH)₂. One possible reaction pathway is the oxidation of HCHO or CH₂(OH)₂ by ONOO⁻/ONOOH. The ONOO⁻/ONOOH abstracts a H-atom from a C–H bond of CH₂(OH)₂ to produce carbon-centered radicals.⁹ The ΔG^act_aq,calc values for these reactions are 40–54 kcal mol⁻¹ (reactions 30 and 31). Due to the unavailable kinetic data about these reactions, we estimated the k values (2.5 × 10⁴ M⁻¹ s⁻¹ for reaction 30 and 1.0 × 10⁴ M⁻¹ s⁻¹ for reaction 31) for both reactions based on our ΔG^act_aq,calc values and the previously developed LFER²¹ for H-atom abstraction by HO˙. The orders of estimated rate constants are consistent with the experimental k value observed for similar compounds with ONOO⁻/ONOOH.⁷⁸ It should be noted that previous LFER was develop based on the G1–G4 methods²¹ and our ΔG^act_aq,calc values were calculated with M06-2X/Aug-cc-pVTZ and thus a few energy differences resulting from two different methods are present. The concentrations of ONOO⁻/ONOOH are approximately 10⁻⁸ M and are significantly higher than those of other radical species. Thus, even though smaller rate constant of about 10⁴ M⁻¹ s⁻¹, the reaction products (i.e., carbon centered radicals and subsequent HCOOH) are significant (see the discussion below).

ONOO⁻ also attacks the carbonyl group of HCHO nucleophilically (reaction 27), producing an intermediate, H₂C(ONOO⁻)O, in cages.^78,79 The intermediate undergoes three possible reactions: (1) in-cage isomerization to produce HCHO and NO₃⁻; (2) electron transfer to produce HCOO⁻, NO₂⁻, and H⁺; and (3) cleavage of the O–N bond to produce NO₂˙ and alkoxyl radicals.^79,80 However, this reaction is an endergonic reaction, indicating a faster backward reaction. Thus, we believe the reaction 27 does not significantly contribute to the formation of products that are involved in the subsequent reactions. The calculated relative probability is that at the point of 10 minutes reaction time, 78% and 22% of ONOO⁻ reacts with CH₂(OH)₂ and HCHO, respectively, at pH 7. At pH 3 for the same reaction time, 91% and 19% of ONOO⁻ reacts with CH₂(OH)₂ and HCHO, respectively. HCOO⁻/HCOOH is the end product of NDMA oxidation and is mineralized into CO₂ (reactions 34–36). Fig. S5 of the ESI† summarizes all the reaction pathways of the NDMA initial transformation induced by photolysis.

Photochemical fate of reactive nitrogen species

Reactive nitrogen species are the initial intermediate products of the photolysis of nitrate, nitrite and ONOO⁻/ONOOH, and therefore, these photochemical reactions are included in our kinetic model. Photolysis of nitrate at 254 nm (15 M⁻¹ cm⁻¹ of molar absorptivity, ε, at 254 nm) follows two pathways: (1) the production of NO₂˙ and O˙⁻ with 0.037 quantum yield and (2) the production of ONOO⁻ with a quantum yield of 0.102.⁴⁸ O˙⁻ is the conjugate base of HO˙ (pK_a = 11.9),⁶⁸ and the photolysis of nitrate is the major source of HO˙. The photolysis of nitrite (ε = 32 M⁻¹ cm⁻¹) produces NO˙ and O˙⁻ with a quantum yield of 0.02.⁴⁸ Nitrite also reacts with HO˙ via single electron transfer to form NO₂˙. The calculated ΔG^act_aq,calc using the Marcus theory^41,42 (see Text S3 in the ESI† for a detailed procedure) is 3.5 kcal mol⁻¹ (reaction 26). Finally, ONOO⁻ has a significantly larger molar absorptivity (i.e., ε = 555 M⁻¹ cm⁻¹) than those of nitrate and nitrite, and the photolysis reaction produced NO˙ and O₂˙⁻ with a quantum yield of 0.1.⁴⁹ All photochemical pathways of nitrate, nitrite, and ONOO⁻/ONOOH identified in this study and compiled based on past experimental studies are summarized in Fig. S6 of the ESI.† The eventual products of these photochemical pathways are nitrate and nitrite.

Linear free energy relationship for reactive nitrogen species

Although the number of datasets is small (N = 5), we have developed a linear free energy relationship between the ΔG^act_aq,calc values and lnk. The detailed development and evaluation is provided in Text S9 and Fig. S7 of the ESI.†

Conclusions

This study highlights the elementary reaction pathways and kinetics of reactive nitrogen species and oxygenated radicals that are produced in the photolysis of NDMA in the aqueous phase. In particular, the photochemical reactions of nitrogen-centered radicals, peroxynitrous acid/peroxynitrite, and peroxynitric acid/peroxynitrite are studied, and the aqueous-phase free energies of activation and reaction are determined to advance our understanding of the fate of nitrosamine compounds in the water treatment process. The photochemical reactions of these reactive nitrogen species in oxygenated environments occur in natural aquatic systems for nitrogen-containing anthropogenic compounds (e.g., pesticides and herbicides) and atmospheric water droplets in clouds for nitrate, nitrite, and nitric oxide. Similar reactions also occur in human cells, where the toxic substances peroxynitrous acid/peroxynitrite play important roles because of the potential damage to cells, which may cause the formation of cancer cells. Our study also provides mechanistic insight into reaction mechanisms in emerging AOPs that utilize the combination of UV with chloramine in water reclamation processes. Given that many toxic chemicals contain nitrogen species, it is important to develop a fundamental kinetic model that can be used to predict the fate of nitrogen-containing species in various environmental processes. Finally, the elementary reaction-based kinetic model developed in this study contains general water quality and photolysis operational parameters. Thus, the validated model can be used to simulate the photochemical decay of nitrosamines in real water with possible addition of other water quality parameters such as alkalinity, co-presented ions, and dissolved organic matter.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was partially supported by the National Science Foundation Award: CHE-1808052. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the supporting organization. E.C. appreciates the scholarship from AWWA through the 2018 Carollo/Bryant L. Bench Scholarship and Michigan Space Grant Consortium fellowship. Finally, the authors appreciate the support from the Michigan Tech HPC cluster ‘Superior’.

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Footnote

† Electronic supplementary information (ESI) available: Additional information for the aqueous-phase computational calculations, molecular oxidation addition, Marcus theory, experimental apparatus and procedures, sensitivity analysis, toxicity calculations, TD-DFT analysis, thermodynamic properties in the presence of explicit water molecules, absorbance of HCHO, and experimentally proposed NDMA and reactive nitrogen species photochemical degradation pathways, linear free energy relationships and xyz-matrix of all transition states is given in the electronic ESI. See DOI: 10.1039/d1ew00262g

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