Gas-Phase Mechanisms of the Reactions of Reduced Organic

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Gas-Phase Mechanisms of the Reactions of Reduced Organic Nitrogen Compounds with OH Radicals Nadine Borduas, Jonathan P.D. Abbatt, Jennifer Grace Murphy, Sui So, and Gabriel da Silva Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b03797 • Publication Date (Web): 03 Oct 2016 Downloaded from http://pubs.acs.org on October 7, 2016

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Environmental Science & Technology

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Gas-Phase Mechanisms of the Reactions of Reduced

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Organic Nitrogen Compounds with OH Radicals

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Nadine Borduas1*, Jonathan P. D. Abbatt1, Jennifer G. Murphy1, Sui So2, Gabriel da Silva2

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1

Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6

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2

Chemical and Biomolecular Engineering, University of Melbourne, Victoria 3010, Australia

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ABSTRACT: Research on the fate of reduced organic nitrogen compounds in the atmosphere

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has gained momentum since the identification of their crucial role in particle nucleation and the

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scale up of carbon capture and storage technology which employs amine-based solvents.

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Reduced organic nitrogen compounds have strikingly different lifetimes against OH radicals,

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from hours for amines to days for amides to years for isocyanates, highlighting unique functional

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group reactivity. In this work, we use ab initio methods to investigate the gas-phase mechanisms

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governing the reactions of amines, amides, isocyanates and carbamates with OH radicals. We

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determine that N−H abstraction is only a viable mechanistic pathway for amines and we identify

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a reactive pathway in amides, the formyl C−H abstraction, not currently considered in structure-

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activity relationship (SAR) models. We then use our acquired mechanistic knowledge and

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tabulated literature experimental rate coefficients to calculate SAR factors for reduced organic

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nitrogen compounds. These proposed SAR factors are an improvement over existing SAR

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models because they predict the experimental rate coefficients of amines, amides, isocyanates,

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isothiocyanates, carbamates and thiocarbamates with OH radicals within a factor of two, but

ACS Paragon Plus Environment

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more importantly because they are based on a sound fundamental mechanistic understanding of

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their reactivity.

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TOC GRAPHIC

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INTRODUCTION

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Reduced organic nitrogen compounds, characterized by a C−N bond, are important for the study

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of air quality and climate.1-3 Prominent examples of reduced organic nitrogen compounds in the

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atmosphere include amines, amides, isocyanates, carbamates, cyanates and their sulfated

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homologues, thiocarbamates and isothiocyanates. The C−N bond, where the N atom is in its -3

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oxidation state, cannot typically be formed in the atmosphere. Thus, reduced organic nitrogen

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compounds are emitted as such, and their fate in the atmosphere is govern by oxidation reactions,

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particle formation and deposition.

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These molecules have a wide range of biogenic and anthropogenic sources to the atmosphere and

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have been identified and quantified in ambient air.4 Mixing ratios of reduced organic nitrogen

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compounds vary from below pptv up to ppmv levels depending on the molecule, location, time

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of day and meteorology. Amines are the most commonly measured organic nitrogen molecules

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in the atmosphere. For example, gas phase trimethylamine concentrations were reported up to 40

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pptv in rural areas and up to 6 pptv up in urban areas, suggesting an agricultural source.5-7 The


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significant role of amines in aerosol formation and growth, as well as their recent large scale use

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as solvents in carbon capture and storage (CCS) technologies, has validated focused attention on

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understanding their fate in the environment.1,8-11 Indeed, at a CCS plant in Norway, peaks of up

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to 10 ppbv of monoethanolamine (MEA), 300 ppbv of pyrazine and 800 ppbv of nitromethane

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were reported at the top of a stripper column.12 It is known that the current benchmark solvent

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for CCS, MEA, has a short atmospheric lifetime of approximately 2 h, governed by its reactivity

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towards the OH radical.13-15 Other sources of reduced organic nitrogen molecules to the

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atmosphere include direct emissions from industrial solvents, biomass burning, cigarettes, and

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animal husbandry as well as oxidative chemistry of amines.1,4,8,16,17 Indeed, the gas-phase

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oxidation of amines produces amides as well as isocyanates.13,15,18,19

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The major atmospheric sinks for reduced organic nitrogen compounds are recognized as being

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oxidation by OH radicals, and to a lesser extent by NO3 radicals and ozone. Because most

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amines, amides and isocyanates do not absorb photons of wavelengths in the actinic window,

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photolysis is not generally competitive.20,21 Loss to aerosol particles is another important sink for

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some species. For example, amines may act as bases and help nucleate particles and/or contribute

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to particle growth, which can impact climate directly by scattering light and indirectly by acting

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as cloud condensation nuclei.20 Reduced organic nitrogen compounds are also thought to be

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responsible for some of the colouring in brown carbon aerosols, again impacting climate through

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their light-absorbing properties.22 Some reduced organic nitrogen compounds are also toxic. In

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particular, methyl isocyanate and isocyanic acid may pose serious health effects if inhaled in

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mixing ratios above 1 ppbv.23-25 In addition, nitrosamines and nitramines, oxidation products of

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aminyl radicals reacting with NOx in urban areas for example, are carcinogens.21 Generally,

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reduced organic nitrogen compounds are not important radiative forcing agents due to their small


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gas-phase concentrations. However, the highest global warming potential of any compound

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detected in the atmosphere is currently perfluorotributylamine.26

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When organic nitrogen is quantified in both the gas and particle phases, the majority is typically

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found in the particle phase and often in the water soluble fraction of particles.1,10 For example,

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the concentration of aliphatic amines contributing to dissolved organic nitrogen in rainwater was

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estimated to be < 1-14 nmol N m -3.3 Wet and dry deposition of organic nitrogen compounds are

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estimated to be ~ 25% of the atmospheric global nitrogen deposition flux.2

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A number of laboratory experiments, theoretical calculations and field studies have aimed to

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better understand the fate of reduced organic nitrogen compounds and were recently reviewed in

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the context of their use and/or production in CCS plants.4,8,20,21 Their chemical mechanisms have

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been largely developed by experimental product studies, and more recently are being supported

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by computational chemistry studies on amines,27-32 as well as recent studies on amide oxidation

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mechanisms.17,33,34 In this study, we evaluate through computational chemistry, the mechanisms

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involved in the gas-phase oxidation of reduced organic nitrogen compounds with OH radicals to

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better understand their overall atmospheric fate. We then compare their mechanisms to highlight

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the impact adjacent functionalities have on the nitrogen atom. Particular attention is given to

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amines, amides and isocyanates, common functionalities found in the gas and particle phases.

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Their lifetimes are also strikingly different, ranging from hours to years depending on the

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functional group.8,21 We opted to study the simplest molecule of each class, i.e. methylamine,

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formamide and isocyanic acid for relevance and calculation simplicity. We find that when

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exposed to OH radicals, oxidation generally occurs on the adjacent C atom of N-containing

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functionalities. In other words, amines are oxidized to amides and amides are oxidized to

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isocyanates. We also evaluate a model carbamate molecule, N-methyl methylcarbamate since


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structure-activity relationship (SAR) analyses for many reduced organic nitrogen compounds

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originate from the evaluation of carbamate rate coefficients with OH radicals.35 Our mechanistic

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approach is comprehensive as we consider all possible reaction sites on each functionality

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including C−H and N−H abstractions, OH additions to carbonyl and OH additions to N atoms,

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and subsequently identify probable reaction pathways. We then use this insight alongside a

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compiled database of experimental rate coefficients to build SAR factors that rely on a

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fundamental understanding of the reactivity of N-containing molecules.

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COMPUTATIONAL METHODS

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Computational ab initio methods were employed using the Gaussian 09 code.36 Structures of the

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reactants were first optimized using the M06-2X density functional, with the 6-31G(2df,p) basis

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set, and subsequently evaluated using the G3X-K composite theoretical method which combines

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a series of Hartree-Fock, Møller-Plesset perturbation (MP4/6-31G(2df,p) and MP4/6-31+G(d))

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and coupled cluster theory calculations (CCSD/6-31G(d)).37,38 A sample input file for the

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execution of the G3X-K method in Gaussion 09 as well as optimized geometries are presented in

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the Supplementary Information. G3X-K theory is used in this study because it was specifically

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designed for thermochemical kinetics and reproduces barrier heights in the DBH24/08 database

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with an average accuracy of 0.6 kcal mol-1.38 In addition, we did not use diffuse functions (+) in

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the basis set throughout our calculations, simply to optimize computation time as the energies are

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similar with and without their incorporation (see Table S1). The energies reported are for 0 K

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and were calculated from the sum of the electronic and the zero point energies. The accuracy of

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the energies stated is expected to be within 1 kcal mol-1.38 Bond dissociation energies (BDE) are

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the difference between ground state energies of the products and the reactants of the bond

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dissociated reaction.


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Throughout this work, we describe transition state energy, used interchangeably with barrier

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height energy, as the energy difference between the transition state and the sum of the reactants’

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energies. Although many systems exhibit weak pre-complex formation between the reduced

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organic nitrogen compound and the OH radical, these pre-complexes do not necessarily lie along

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the reaction coordinate and/or may not be collisionally stabilized. Thus, we assume that their

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energies do not dominate the overall flux through the transition state.39 While we approach the

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mechanistic analysis by assuming that the reactivity will largely scale with the height of the

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transition state, we recognize that entropic factors and tunneling may also play a role,

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particularly for cases with transition states that are submerged relative to the reactant energy. In

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addition, we estimate that a 1 kcal mol-1 difference in activation energy translates to

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approximately a factor of 5 difference in rate coefficients using the Arrhenius equation for room

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temperature rate coefficients that are on the order of 10-12 cm3 molec-1 s-1. Nonetheless, we

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emphasize here that the theoretical calculations serve solely to identify reactive pathways and not

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to calculate rate coefficients.

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CALCULATION RESULTS

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1. Bond dissociation energy (BDE)

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From the energy diagrams of methylamine, formamide, N,N-dimethylformamide, N,N-

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dimethylacetamide, N,N-dimethylpropanamide, N-methylpropanamide, isocyanic acid and N-

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methyl methylcarbamate with OH radicals presented in this section (Schemes 1-4 and S1-S4), we

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calculate bond dissociation energies (BDE) of C−H and N−H bonds in reduced organic nitrogen

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compounds (Table 1). In general, our values compare well with previously reported

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literature.40,41 We are aware of only one experimentally determined C−H bond BDE for the


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reduced organic nitrogen compounds we investigated (methylamine). However, computed BDEs

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exist and all compare well with our calculated BDEs for C−H bonds.40,42-44 For carbamates for

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example, the methylamine C−H bond and the methoxy C−H bond were computed at 96 kcal mol-

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1

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the experimental BDE value for the N−H bond in formamide is 100.8 kcal mol-1, whereas we

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calculate a value of 114.6 kcal mol-1.41 Yet, three previous ab initio studies have calculated

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similar BDEs at 114.5 kcal mol-1, 113.6 kcal mol-1 and 113.2 kcal mol-1.42,43,45 Moreover, the

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BDE of the N−H bond in amines (like methylamine) is expected to be lower than in amides (like

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formamide) due to the delocalisation of the nitrogen’s lone pair in the amide functionality as

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predicted by molecular orbital theory.

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Table 1: Calculated and experimental bond dissociation energies for reduced organic nitrogen

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compounds

and 100 kcal mol-1 respectively by Berry et al. and are comparable to our values.44 In addition,

Organic nitrogen

Formyl C−H bond (kcal mol-1)

alkyl C−H bond (kcal mol-1)

N−H bond (kcal mol-1)

Calculated

Calculated

Experimental

Calculated

Experimental

methylamine

NA

91.9

92.746,47

98.8

10042,48,49

formamide

93.3a

114.6

100.841

N,N-dimethylformamide

93.7

N,N-dimethylacetamide

NA

N,N-dimethylpropanamide

NA

N-methylpropanamide

NA

NA 92.5a

?

90.6a 97.9b 90.6a 93.6b 93.3a 95.1b

? ? ? ? ? ?

NA NA NA 105.5

~98.741


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Isocyanic acid

141 142 143 144 145

NA

NA

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109.8

109.750

NA 93.2a ? N-methyl 106.8 ~10551 c methylcarbamate NA 98.5 ? a b c C−H bond on the N-alkyl side; C−H bond on the amide side C−H bond on the methoxy side; ref 49 is for N-methyl ethylcarbamate51 NA = not applicable; ? = yet to be measured/reported

2. Methylamine + OH

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Scheme 1 shows the three possible mechanisms for the OH radical to react with methylamine,

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the simplest of amines, in the gas phase. Both the C−H and the N−H abstraction mechanisms are

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competitive for this alkylamine, with barriers to reaction close to the entrance level energies of

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the reactants and within 1 kcal mol-1 of each other. Both reactions are exothermic, as expected

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due to the formation of water as a by-product. The third mechanism investigated is OH addition

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to the N atom with a concerted C−N bond cleavage, which is highly endothermic with a clearly

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inaccessible transition state energy.

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Methylamine’s gas phase reaction was experimentally investigated by Atkinson et al., by Carl et

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al. and by Onel et al.27,52,53 These authors find a room temperature rate coefficient of around 2 ×

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10-11 cm3 molec-1 s-1 (lifetime of ~ 7 h); this fast rate coefficient is consistent with a low transition

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state energy. Onel et al. also investigated this reaction by ab initio methods and found transition

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states for both H-abstraction mechanisms slightly below the entrance level energies of the

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reactants.27 Our results are consistent, albeit slightly higher in energy, a difference in part

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attributable to the different model chemistries employed and our own theoretical method

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uncertainty of 1 kcal mol-1.


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Scheme 1. Theoretical energy diagram for methylamine + OH. Energies are 0 K enthalpies in

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kcal mol−1, at the G3X-K level of theory.

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3. Amides + OH

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Amides are known to be products of amine oxidation but our understanding of their fate in the

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atmosphere is limited.8,15,21,54 Their functionality differs from amines in that amides have a

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carbonyl moiety adjacent to the nitrogen. The nitrogen’s lone pair is largely delocalized in the

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carbonyl’s -system, as evidenced by higher BDEs for the N−H bond compared to amines

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(Table 1). This effect translates to poor nucleophilicity and thus poor reactivity with electrophilic

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OH radicals, and explains amides’ longer atmospheric lifetimes.17,54 Scheme 2 depicts the energy

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diagram of formamide’s four possible mechanisms of reaction with OH radicals. The lowest


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energy transition state is the formyl C−H abstraction, 6 kcal mol-1 lower than the next lowest

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transition state energy. Thus, this pathway governs the majority of formamide’s reactivity,

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analogous with the formyl C−H bond in aldehydes.55,56 This mechanism is also quite exothermic

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compared to the N−H abstraction pathway. In contrast to amines, amides have the potential to

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react with OH radicals by addition to the carbonyl moiety. We find that this pathway is 9.9 kcal

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mol-1 above the entrance level energy of the reactants but is exothermic and so is a viable yet an

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unlikely mechanism. As with amines, the OH addition to the nitrogen in amides is high in energy

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and endothermic.

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In previous studies, the room temperature rate coefficient of formamide and OH radicals was

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measured to be 4.4 × 10-12 cm3 molec-1 s-1 and was supported by ab initio calculations, yet solely

182

focused on the H-abstraction mechanisms.17,34 The formyl C−H abstraction produces a C-

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centered formyl radical which can go on to react with O2 and form isocyanic acid.17

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Interestingly, the formyl C−H abstraction is also competitive for N-alkylated amides (see

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Scheme S1). To complement the previous ab initio work on the reactivity of amides with OH

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radicals, we also investigated the mechanistic pathways of N,N-dimethylacetamide, N,N-

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dimethylpropanamide and N-methylpropanamide in Schemes S2, S3 and S4 respectively. Similar

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mechanistic observations can be made when comparing all these amides: an easy C−H

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abstraction from methylated amides and an unlikely N−H bond abstraction from amides (in

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contract to amines).


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Scheme 2. Theoretical energy diagram for formamide + OH. Energies are 0 K enthalpies in kcal

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mol−1, at the G3X-K level of theory.

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4. Isocyanic acid + OH

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Isocyanates differ from the amide functionality by being hybridized sp2 at the nitrogen and sp at

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the adjacent carbon. In isocyanic acid, the nitrogen’s lone pair is perpendicular to the -system

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and is therefore not delocalised.57 Isocyanic acid’s OH-reaction energy diagram is presented in

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Scheme 3. Three mechanisms are plausible: N−H abstraction and OH additions to the carbonyl

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or to the nitrogen. All three mechanisms are high in energy and so isocyanic acid’s rate


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coefficient is expected to be very slow at room temperature (Scheme 3). Indeed, the experimental

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rate coefficient for the reaction of isocyanic acid with OH radicals was measured only at high

202

temperatures and if extrapolated to room temperature is approximately 10-15 cm3 molec-1 s-1,

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translating to a lifetime of decades.24,58 The OH-addition to the carbonyl (barrier height of + 9.1

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kcal mol-1) and the N−H abstraction (barrier height of + 19.4 kcal mol-1) pathways are

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exothermic compared to the OH-addition to the nitrogen which we have now shown is

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consistently endothermic in amines, amides and isocyanates. No pre-complex could be isolated

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in our ab initio calculations between isocyanic acid and OH, consistent with all the mechanisms

208

having transition state energies significantly above that of the reactants. Thus, we do not expect

209

gas phase OH radicals to be a sink for isocyanic acid. Rather, it will likely partition to the

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aqueous phase and undergo further reactions including hydrolysis.59


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Scheme 3. Theoretical energy diagram for isocyanic acid + OH. Energies are 0 K enthalpies in

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kcal mol−1, at the G3X-K level of theory.

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5. N-Methyl methylcarbamate + OH

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We opted to use N-methyl methylcarbamate as our carbamate substrate rather than the simpler

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methylcarbamate as the latter does not yet have a reported rate coefficient with OH radicals in

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the literature. Scheme 4 shows the theoretical energy diagram of the five mechanistic pathways

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relevant to the reaction of N-methyl methylcarbamate with OH radicals. The difference between

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carbamates and amides is the presence of an oxygen atom next to the amide functionality. This

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extra oxygen atom provides additional electron density into the carbonyl, decreases the degree of


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lone pair delocalization at the nitrogen and enhances the reactivity of the molecule towards the

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electrophilic OH radicals. This claim is supported by the smaller bond dissociation energy (BDE)

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for the N−H bond in N-methyl methylcarbamate (106.8 kcal mol−1) than in formamide (+ 114.6

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kcal mol−1) for example (Table 1). Nonetheless, the C−H abstraction mechanisms are expected to

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dominate the reactivity of carbamates since the two C−H abstraction transition state energies for

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N-methyl methylcarbamate are below the energies of the reactants. Both OH addition

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mechanisms, i.e. to the carbonyl or to the nitrogen, require high energy to proceed and are

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endothermic.

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We note here that N-methyl methylcarbamate’s experimental rate coefficient (4.3 × 10-12 cm3

230

molec-1 s-1) is slower than that of methylamine (2 × 10-11 cm3 molec-1 s-1) despite the former

231

having calculated lower transition state energies (see Table 2).27,35 Transition state energies are

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relative to the entrance level energy of the reactants and are therefore not directly comparable

233

between molecules. On the other hand, BDEs are absolute values and we see then that the C−H

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bond in methylamine has a lower BDE than N-methyl methylcarbamate (see Table 1), consistent

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with a faster rate coefficient.


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Scheme 4. Theoretical energy diagram for N-methyl methylcarbamate + OH. Energies are 0 K

238

enthalpies in kcal mol−1, at the G3X-K level of theory.

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MECHANISTIC DISCUSSION

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We gain insight into the mechanisms governing the reactivity of the four subclasses of reduced

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organic nitrogen compounds investigated, namely amines (Scheme 1), amides (Scheme 2, S1,

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S2, S3 and S4), isocyanates (Scheme 3) and carbamates (Scheme 4), by comparing their

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calculated transition state energies (Table 2). We note here that we use the calculated transition

244

state energy solely to inform us on likely mechanisms and reactive sites.


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Table 2: Tabulated transition state values from Schemes 1-4 and S1-S4 (with a 1 kcal mol-1

246

accuracy)

Transition state energies (kcal mol-1)

Organic nitrogen + OH

248

N−H abstraction

OH addition to carbonyl

OH addition to nitrogen

Formyl C−H

Nmethylated C−H

methylamine

NA

+ 1.2

+ 0.2

NA

+ 37.4

formamide

+ 0.2

NA

+ 6.3

+ 9.9

+ 41.7

- 0.9

- 1.2

NA

-

-

NA

- 2.4

NA

-

-

NA

- 2.4

NA

-

-

N-methylpropanamide

NA

- 2.2

+ 2.1

-

-

Isocyanic acid

NA

NA

+ 19.4

+ 9.1

+ 32.7

- 1.6 / - 0.1

+ 2.5

+ 14.1

+ 43.6

N,Ndimethylformamide N,Ndimethylacetamide N,Ndimethylpropanamide

247

C−H abstraction

N-methyl NA methylcarbamate NA = not applicable, - = not computed 1. C−H abstraction

249

The C−H abstraction mechanism dominates the reactivity of reduced organic nitrogen

250

compounds when present. This observation is expected as the C−H bond is less polarized than

251

heteroatom X−H bonds, making it more prone to break homolytically and react with the

252

electrophilic OH radical. C−H bonds in organic nitrogen compounds have consistently lower

253

bond dissociation energies than N−H bonds as seen in Table 1. The preference of OH radicals to


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254

react with C−H bonds over N−H bonds leads to the oxidation of carbon while the nitrogen

255

remains in the -3 oxidation state throughout oxidative conversion from amines to amides to

256

isocyanates. Building upon this logic, we do not expect oxidation of reduced organic nitrogen

257

compounds to substantially contribute to the production of nitrogen oxides in ambient air. In

258

other words, the N atom in reduced organic nitrogen molecules does not end up as the N atom in

259

nitrogen oxide molecules.

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2. N−H abstraction

261

The N−H abstraction mechanism which leads to aminyl radicals after the initial OH attack is

262

solely competitive for amines. The increasing trend observed for transition state energies of the

263

N−H abstraction mechanism is as follows: amine < carbamate < amide < isocyanate (see Table

264

2). Indeed, the N−H abstraction in methylamine is the only calculated barrier height which is

265

close to the entrance level energy of the reactants (at + 0.2 kcal mol-1), indicating a rapid and

266

favorable reaction. Importantly, aminyl radicals may go on to react with nitrogen oxides to form

267

nitramines and nitrosamines, which are known carcinogens.60-66 It is noteworthy that amides,

268

isocyanates and carbamates are not expected to form nitramines and nitrosamines directly from

269

OH radicals abstracting N−H bonds, based on the high energy barrier that yields their

270

corresponding aminyl radical. Nonetheless, as Bunkan et al. explicitly discuss, further reactions

271

of amide C-centered radicals may eventually lead to fragmentation and formation of aminyl

272

radicals from amides, yielding nitramines.33

273

3. OH addition to carbonyls

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The addition of OH radicals to unsaturated bonds is a common mechanistic pathway for alkenes

275

and alkynes. For completeness, we also explored this mechanism for carbonyls, as they exist in


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276

reduced organic nitrogen compounds. Although this mechanism is exothermic in formamide and

277

isocyanic acid, it is slightly endothermic for N-methyl methylcarbamate (Schemes 2, 3 and 4).

278

Nonetheless, it possesses a high energy barrier to reaction and is not expected to be competitive

279

with C−H or N−H abstraction pathways. In the case of isocyanic acid, this mechanism dominates

280

its reactivity, but this mechanism is still sufficiently slow at ambient temperatures to be

281

negligible in the context of isocyanic acid’s atmospheric fate.

282

4. OH addition to nitrogen

283

The OH addition to the N atom pathway was also investigated for methylamine, formamide,

284

isocyanic acid and N-methyl methylcarbamate’s reactions with OH radicals. This mechanism

285

was proposed to occur for sulfides and was originally thought to extend to amines.67 We show in

286

Schemes 1 to 4 that this mechanism is consistently high in energy and endothermic for all classes

287

of N-containing compounds studied. This observation remains true even for electron rich amines

288

like trimethylamine, where we calculate at the G3X-K level an activation energy of + 42.3

289

kcal/mol. Therefore, OH additions to N may lead to weak complexes,68 but will not lead to a

290

productive reaction pathway and would simply dissociate.

291

SAR MODELLING DISCUSSION

292

We now use our mechanistic insight to develop structure-activity relationship (SAR) group rate

293

constants and substituent factors to predict the atmospheric fate of reduced organic nitrogen

294

compounds. Our study is constructed on a fundamental mechanistic understanding of reactivity

295

with OH radicals to improve the existing empirical SAR model. We would like to emphasize at

296

this point that we do not calculate rate coefficients with our computed potential energy surfaces.

297

Rather, we use these energy diagrams to identify reactive and non-reactive pathways to lead us in


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298

our development of the SAR factors described in this part of the study. We center our discussion

299

on aliphatic reduced organic nitrogen while appreciating that related aromatic compounds are

300

also of environmental importance.

301

1. Description of SAR models

302

Structure-activity relationships (SAR) models were developed as a predictive tool for estimating

303

the room temperature rate coefficients and hence the atmospheric lifetime of organic compounds

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against the OH radical and later against other atmospheric oxidants.56,68-71 The SAR model’s

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general approach consists of predicting an overall rate coefficient by summing the individual rate

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constants of every reactive site on a molecule of interest. Relevant mechanisms for volatile

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organic compound reactions with OH radicals include H-abstraction, addition to unsaturated

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carbon-carbon bonds and addition to heteroatoms.68 The SAR method includes two types of

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factors relevant to our reduced organic nitrogen analysis. First, there are the SAR group rate

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constants for H-abstractions from any atom (C, N, O, etc.), denoted by a k value with a subscript

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denoting the site (or functional group such as k-NH-, k-OH) of abstraction. There are three types of

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SAR group rate constants specifically for C−H abstractions, one for each reaction occurring at a

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primary (kprim), secondary (ksec) or tertiary (ktert) carbon center. Second, this C−H abstraction

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SAR group rate constant (kprim, ksec, or ktert) is then multiplied by a substituent factor denoted as

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F(X) to obtain an overall rate constant specific to the functional group’s reactivity. Sample

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equations for C−H abstractions are given below and are based on Atkinson et al.68

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𝑘𝑜𝑣𝑒𝑟𝑎𝑙𝑙 (𝐶𝐻3 − 𝑋) = 𝑘𝑝𝑟𝑖𝑚 𝐹(𝑋)

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𝑘𝑜𝑣𝑒𝑟𝑎𝑙𝑙 (𝑌 − 𝐶𝐻2 − 𝑋) = 𝑘𝑠𝑒𝑐 𝐹(𝑋)𝐹(𝑌)


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Page 20 of 37

𝑘𝑜𝑣𝑒𝑟𝑎𝑙𝑙 ( 𝑌𝑍>𝐶𝐻 − 𝑋) = 𝑘𝑡𝑒𝑟𝑡 𝐹(𝑋)𝐹(𝑌)𝐹(𝑍)

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There currently exist published empirical SAR group rate constants and substituent factors for

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amines, carbamates or thiocarbamates functionalities, derived from limited experimental rate

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coefficients.8,35,68,69,72 There are no SAR group rate constants specifically for amides,

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isocyanates or isothiocyanates. Guided by our ab initio results, we examine the mechanisms

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governing reduced organic nitrogen molecules’ reactivity in order to build upon past SAR

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analyses. We tabulate existing experimental rate coefficients for reduced organic nitrogen

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molecules with OH radicals and formulate SAR model equations defining koverall for each

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compound (see Table S1 and model equations in the Supplementary Information). We use only

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experimental rate coefficients in our statistical analysis and omit theoretically calculated rate

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coefficients although the latter are becoming more reliable (but still few exist for N-containing

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compounds).71,73 We then solve this overdetermined linear system of equations using a built-in

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function in the program IGOR Pro (see Supplementary Information). Revised SAR factors are

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proposed to better capture the differences in reactivity based on substituents on the N atom and

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to disambiguate the existing factors for N-containing molecules (Figure 1 and Table 3). The SAR

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factors are reported with two significant figures and without uncertainties as they represent

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solutions to the overdetermined linear equations, remaining consistent with the SAR

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literature.68,69,74

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338 339

Figure 1: The SAR group rate constants represent reactivity at the highlighted H atom in

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yellow and the SAR substituent factors represent reactivity imparted by the functionality

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highlighted in blue to the H atom in bold. R1 and R2 can be either H or any alkyl group.

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Table 3: The proposed SAR group rate constants kX-H and substituent factors F(X) for

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aliphatic reduced organic nitrogen compounds Functional group Methyla

Group rate constant (cm3 molec-1 s-1) k-CH3 = 0.136 × 10-12 k-CH2- = 0.934 × 10-12 k-CH< = 1.94 × 10-12

Substituent factor (unitless) F(-CH3) = 1.00 F(-CH2) = 1.23 F(-CH

Gas-Phase Mechanisms of the Reactions of Reduced Organic

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