Pressure Dependence of Butyl Nitrate Formation in the Reaction ofButylperoxy Radicals with Nitrogen OxideN. I. Butkovskaya,†,⊥ A. Kukui,‡ G. Le Bras,*,† M.-T. Rayez,§ and J.-C. Rayez§

†Institut de Combustion, Aerothermique, Reactivite et Environnement (ICARE), CNRS-INSIS, 1C Avenue de la RechercheScientifique, 45071 Orleans cedex 2, France‡Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (LPC2E), CNRS-INSU, 3A Avenue de la RechercheScientifique, 45071 Orleans cedex 2, France§Institut des Sciences Moleculaires, CNRS/UMR5255, Universite Bordeaux 1, 351 Cours de la Libération, 33405 Talence cedex,France

ABSTRACT: The yield of 1- and 2-butyl nitrates in the gas-phase reactions of NO with n-C4H9O2 and sec-C4H9O2, obtained from the reaction of F atoms with n-butane in the presence ofO2, was determined over the pressure range of 100−600 Torr at 298 K using a high-pressureturbulent flow reactor coupled with a chemical ionization quadrupole mass spectrometer. Theyield of butyl nitrates was found to increase linearly with pressure from about 3% at 100 Torr toabout 8% at 600 Torr. The results obtained are compared with the available data concerning nitrate formation from NO reactionwith other small alkylperoxy radicals. These results are also discussed through the topology of the lowest potential energy surfacemainly obtained from DFT(B3LYP/aug-cc-pVDZ) calculations of the RO2 + NO reaction paths. The formation of alkyl nitrates,due essentially to collision processes, is analyzed through a model that points out the pertinent physical parameters of thissystem.

1. INTRODUCTION

This study completes the series of studies on alkyl nitrateformation in RO2 + NO reactions

+ → +

→ −

RO NO RO NO (a)

RO NO (b)2 2

2

where R = CnH2n+1 is the alkyl radical with n ≤ 4. The aim of theseries was to provide data on the formation of small alkylperoxyradicals, for whom branching fractions of channel b were veryuncertain and pressure and temperature effects on these ratioswere unknown. The interest in such data is explained mainly bythe importance of the above reaction in atmospheric chemistry,where channel b, acting as free radical chain termination and asource of NOx reservoir, affects production rates of ozone onlocal and global scales.1,2 The above reaction following thephotochemical oxidation of organic compounds is a major sourceof alkyl nitrates in the atmosphere,3 while for methyl and ethylnitrates, emission from oceans is also important.4 The mixingratio of alkyl nitrates with n ≤ 5 presents a significant fraction ofall alkyl nitrate atmospheric contents.1 Another aspect is that thenitrate formation channel in the ROO + NO system presents achallenge for theoretical chemistry.5,6 Previous ab initio andsemiempirical calculations [e.g., refs 7−9] have established thatthe reaction proceeds through the formation of the ROONOintermediate complexes, which can isomerize to RO−NO2. Asearch for the stationary points on the reaction potential energysurface (PES), including the transition state for isomerization toRO−NO2 for small R radicals, remains an intriguing part of thesestudies.

In previous chamber studies of Atkinson et al.,10,11 it wasrevealed that at room temperature and atmospheric pressure, theyield of alkyl nitrates in the reactions of alkylperoxy radicals withNO increases from ∼4% for propyl nitrate (n = 3) to ∼30% forheavier alkyl nitrates with n≥ 8. In particular, the value of α = kb/(ka + kb) = (7.7± 0.9)%was determined for the total butyl nitrateyield from the OH-initiated oxidation of n-butane in air.10 Thealkyl nitrate yield increases with pressure, as was first shown bythe Atkinson’s group for C5−C7 nitrates.

12−14 On the basis ofthese data, a general expression for the estimation of thebranching ratios β = kb/ka for the nitrate-forming channels in thereactions of alkylperoxy radicals with NO, β = Y(n,P,T), wasderived by Carter and Atkinson.15

The pressure and temperature dependences observed inlaboratory experiments were, in general, qualitatively confirmedby RRKM-like calculations of the isomerization/dissociationbranching ratio of ROONO based on the semiempirical PES. Inparticular, positive pressure dependence can be explained bycollisional deactivation of the excited RO−NO2. However, thereare still many discrepancies both within the theoreticalpredictions and between theory and experiment5−.9

In this context, a turbulent flow reactor (TFR) coupled with achemical ionization mass spectrometer (CIMS) was used atCNRS-ICARE to study the formation of RO−NO2 from the RO2

+ NO reactions with R = CH3,16 C2H5,

17 and i-C3H7.18 Increase

Special Issue: Mario Molina Festschrift

Received: September 17, 2014Revised: November 7, 2014

Article

pubs.acs.org/JPCA

© XXXX American Chemical Society A dx.doi.org/10.1021/jp509427x | J. Phys. Chem. A XXXX, XXX, XXX−XXX

of β = kb/ka with pressure for C1−C3 nitrates was confirmed inthese experiments. The present article presents the determi-nation of the pressure dependence for butyl nitrate formation inthe C4H9O2 + NO reaction

+ → +C H O NO C H O NO4 9 2 4 9 2 (1a)

+ →C H O NO C H ONO4 9 2 4 9 2 (1b)

The branching ratio, β = k1b/k1a, was determined as theconcentration ratio of the final products from channels 1b and 1a,as described in the Experimental Methods section. Themethodology of this study is similar to that used to investigatethe pressure dependence of isopropyl nitrate formation.18

However, the determination of the branching ratio in the butanesystem was strongly complicated by additional unimolecularisomerization/decomposition pathways for the intermediatebutoxy radicals, C4H9O. The reaction products were detectedusing negative ion chemical ionization (NICI). The branchingratio for reaction 1 was determined over the 100−600 Torrpressure range at room temperature. The data obtained arecompared with the formation yields for other small alkyl nitratesand analyzed using DFT(B3LYP/aug-cc-pVDZ) theoreticalcalculations presented in the Theoretical Examination section.

2. EXPERIMENTAL METHODSChemical Reactor. Chemical reactions took place in the

TFR coupled with a chemical ionization quadrupole massspectrometer (Figure 1). The reactor was operated at roomtemperature (298 ± 2 K) and a pressure from P = 100 to 600Torr (Reynolds number Re ≈ 4000 at 100 Torr and Re ≈ 12000at 600 Torr).

Fast reaction of F atoms with butane

+ ‐ → ‐ +

→ ‐ +

n n

sec

F C H C H HF (2b)

C H HF (2b)

4 10 4 9

4 9

with k2 = 7.3 × 10−11 cm3 molecule−1 s−1 at 298 K19 andbranching ratio k2a/k2b = 57:4320−22 was used to initiate thechemical transformations in the presence of O2 and NO. F atomswere generated by a microwave discharge in CF4 (AlphaGazN45) in a quartz tube connected to the moveable injector. Thecarrier gas He (AlphaGaz 2) in the discharge tube was purified by

passing through a trap with molecular sieves immersed intoliquid nitrogen. The initial concentration of F atoms was about 2× 1012 molecules cm−3. The distance from the injector tip to theorifice of the inlet cone of the ion−molecule reactor (IMR) was36 cm, which corresponded to residence times in the TFR from18 ms at 100 Torr to 35 ms at 600 Torr. Butane (n-C4H10,AlphaGaz N45) and oxygen (AlphaGaz 2) were introduced intothe reactor upstream of the tip of the movable injector throughCELERITY flow controllers. Nitrogen monoxide (AlphaGazN20) was added to the main nitrogen flow through a special linepassing successively through an ethanol−liquid-N2-cooled trapand an (Fe)IISO4 filter to reduce penetration of NO2 into thereactor. Typical concentrations of the reactants were [C4H10] ≈5× 1014 and [O2]≈ 1.2× 1016, while [NO] was varied in the (2−10) × 1015 molecules cm−3 range.Two isomers of butyl radicals formed in reactions 2a and 2b

add oxygen, producing peroxy radicals

‐ + → ‐n nC H O C H O4 9 2 4 9 2 (n3)

‐ + → ‐sec secC H O C H O4 9 2 4 9 2 (s3)

with kn3 = 7.5 × 10−12 and ks3 = 1.7 × 10−11 cm3 molecule−1 s−123

(rate constants are given in the text at 298 K unless specified).Addition of NO producing stable 1- and 2-C4H9NOmolecules ismore than 2 orders of magnitude slower than that of O2 and wasnot important. Formation of n-C4H9O2 and sec-C4H9O2 peroxyradicals gives rise to two parallel sequences of reactions

‐ + → ‐ +

→ ‐

n nC H O NO C H O NO (n1a)

1 C H ONO (n1b)

4 9 2 4 9 2

4 9 2

‐ + → ‐n nC H O NO C H ONO4 9 2 4 9 2 (n4)

‐ + → +n C H O O C H CHO HO4 9 2 3 7 2 (n5)

‐ + → ‐

→ +

n nC H O NO C H ONO (n6a)

C H CHO HNO (n6b)

4 9 4 9

3 7

‐ + → +n C H O M HOC H M4 9 4 8 (n7)

and

‐ + → ‐ +

→ ‐

sec secC H O NO C H O NO (s1a)

2 C H ONO (s1b)

4 9 2 4 9 2

4 9 2

‐ + → ‐sec secC H O NO C H ONO4 9 2 4 9 2 (s4)

‐ + → +sec C H O O CH CH C(O)CH HO4 9 2 3 2 3 2 (s5)

‐ + → ‐

→ +

sec secC H O NO C H ONO (s6a)

CH CH C(O)CH HNO (s6b)

4 9 4 9

3 2 3

‐ + → +sec C H O M C H CH CHO4 9 2 5 3 (s7)

In all the experiments, reaction 1 was completed within less than0.1 ms, giving stable products NO2 (channel 1a) and 1- and 2-butyl nitrates (channel 1b). Butoxy radicals produced in channel1a transform to nitrites, n- and sec-C4H9ONO, butyraldehyde(BA), C3H7CHO, and methyl−ethyl ketone (MEK),CH3CH2C(O)CH3, through their reactions with NO (channels

Figure 1. Experimental setup: 1 , ion source; 2, ion−molecule reactor(IMR); 3, temperature controller; 4, turbulizer; 5, injector; 6, resistance;7, cooling bath; 8, discharge tube; 9, microwave discharge; 10, samplingcones; 11, temperature sensor; 12, FeII(SO4) filter; 13, liquid nitrogen/ethanol cold bath; 14, NO cylinder.

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n6b and s6b, respectively). The contribution from the butoxyreactions with oxygen, reactions n5 and s5, was negligiblebecause their rate constants, kn5 = 9.5 × 10−15 cm3 molecule−1

s−124−26 and ks5 = 7.6 × 10−15 cm3 molecule−1 s−1,24,27,28 aremore than 3 orders of magnitude lower than that with NO, kn6 ≈ks6 = 3.2× 10−11 cm3molecule−1 s−1.23,28,29 Under the conditionsof our experiments, reactions 4, 5, and 6 are in their high-pressurelimit region. The secondary reactions 4 of n- and sec-C4H9Obutoxy radicals with NO2 also produce butyl nitrates with k4 = 3.6× 10−11 cm3 molecule−1 s−1,29 which can interfere with themeasurements of nitrates from reaction 1. NO2 was present inthe reactor as a trace impurity in NO and a product from reaction1a. Typically, the NO2 background in the presence of NO wasless than 1× 1012 molecules cm−3, so that the total concentrationwas on the order of (2−3) × 1012 molecules cm−3. Otherimportant processes were unimolecular reactions of the butoxyradicals, isomerization for n-butoxy (reaction n7)26,30,31 anddecomposition for sec-butoxy (reaction s7).28,30 Under theconditions of our study, both reactions are in the falloff regionand both compete with NO reactions. Competing reactions 5, 6,and 7 served as butoxy radical scavengers with respect toreactions 4, making the contribution from reactions 4 to thenitrate concentration less than 1%, as was shown by computersimulation of the chemical system under study.To determine the yields of the stable products, ks7(P) was

calculated using a conventional Troe’s expression with low- andhigh-pressure limit rate coefficients obtained by Falgayrac et al.from the falloff analysis of their LFP-LIF experimental resultsbetween 8 and 608 Torr.28 The calculated ks7 was scaled to give avalue of ks7(760) = (2.13± 0.11)× 104 s−1 (error of 1 σ), which isthe average of the six coefficients tabulated in the review byAtkinson et al.23 Under the conditions of our experiments, thefraction of the decomposed sec-butoxy radicals was less than 10%.The rate coefficient for isomerization of n-C4H9O is

sufficiently higher, kn7(760) = 1.8 × 105 s−1, as obtained byaveraging the results from the recent PLP-CRDS study ofSprague et al.31 and the studies referenced herein. It is necessaryto note that the kn7 values were determined from the relative kn7/kn5 measurements, assuming kn5 = 9.5× 10−15 cm3molecule−1 s−1

for the reference reaction with oxygen recommended byAtkinson,24 which seems to be more reliable than the morerecent recommendation of 1.4 × 10−14 cm3 molecule−1 s−1,23 asthe latter is based on the results of Morabito and Heicklen26

extracted from the relative kn5/kn6 measurements using an earlygeneric kn6 value of 4.4 × 10−11 cm3 molecule−1 s−1, while newresults give kn6 = 3.2× 10−11 cm3 molecule−1 s−1.28 The influenceof the additional complicating factor, prompt isomerization ofthe chemically activated n-butoxy radicals, was analyzed bySprague et al.31 They found that the fraction of n-butoxy thatpromptly isomerized was 0.04 ± 0.02. In their study, n-butoxywas generated by photolysis of butyl nitrite when the n-C4H9Oand NO fragments contained 40 kcal mol−1 of available energy.As well, production of “hot” n-butoxy was supposed to take placein the RO2 + NO reaction.30 The energy available for theproducts of reaction n1a is about 16 kcal mol−1 (vide infra), andthe effect of prompt isomerization in this case is not expected tobe more important. In the absence of experimental data for thepressure dependence of kn7, isomerization parameters werecomputed by us using the falloff curve from the ab initio-RRKMstudy of Somnitz and Zellner with inclusion of tunnelling.32

Their study showed that, though kn7(760) is close to its high-pressure limit, it is still in the falloff region with kn7(760) = 1.4 ×105 s−1 and kn7(760)/kn7∞ = 0.89, in good agreement with the

results of the DFT-RRKM theoretical study of Mereau et al.,33

which gave kn7(760) = 1.6 × 105 s−1 and kn7(760)/ kn7∞ = 0.88.The curve was fitted over the 100−760 Torr range using a simpleLindemann’s approximation and scaled to give kn7∞ = 2.0 × 105

s−1. Reaction n7 competes with reaction with NO consuming upto 50% of n-butoxy radicals.Because the detection method used registrated total nitrate

species (vide infra), attention must be paid to the possiblecontribution from the hydroxy nitrates that could be formed dueto transformations of the isomerization product, HOC4H8radical, in the presence of O2 and NO. Possible reactions ofthis radical were investigated by Morabito and Heicklen26 andHeiss and Sahetchian.34 By GC/MS detection of the finalproducts, it was found that this δ-hydroxy butyl radical reactswith oxygen either through O2 addition or producing BA viahydrogen abstraction and rearrangement of the biradical formed

+ →

→ +

HOC H O HOC H O (n8a)

HO C H CHO (n8b)

4 8 2 4 8 2

2 3 7

Morabito and Heicklen also proposed that reaction 8 competeswith some fast HOC4H8 reactions (involving internal rearrange-ment or bond cleavage) leading to lower (C1−C2) aldehydes.Heiss and Sahetchian showed that the HOC4H8O2 adduct canundergo further isomerization, producing peroxideHOOC3H7CHO, as was identified by GC/MS at 487 K.34

However, the high activation energy (17.6 kcal mol−1 byevaluation) makes this second isomerization unimportant atroom temperature. In the recent PLP-CRDS work with directobservation of HOC4H8 and HOC4H8O2 radicals in real time,

31

Sprague et al. found that within 40 μs after photolysis of n-butylnitrite, the only significant products were the primaryisomerization products, HOC4H8 in the absence of O2 andHOC4H8O2 with O2. This rules out the possibility of anyHOC4H8 reactions competing with reaction with oxygen(reaction n8) because the characteristic reaction times forreaction 8 are expected to be on the order of 10 μs. Also, it wasshown that all HOC4H8 were totally converted to HOC4H8OOperoxy, some part of which having an internal hydrogen bond.This allows one to neglect reaction n8b and to expect somehindrance of the HOC4H8OO reaction with NO compared tothe title reaction due to hydrogen bonding

+ → +

→

HOC H O NO HOC H O NO (n9a)

HOC H ONO (n9b)

4 8 2 4 8 2

4 8 2

Estimations by computer simulation, assuming kn8a = kn3, kn9 =kn1, and similar branching for reactions n9 and n1, shows that thepossible contribution from reaction n9b to the nitrateconcentration is about 12%. Taking into account possible effectsof the internal hydrogen bonding in theHOC4H8OO radical, thisestimation can be considered as an upper limit. The simulationalso showed that the contribution from ethyl nitrate due totransformations of C2H5 produced in the decompositionreaction s7 was less than 0.5%.Characteristic times for reactions 6 and 7 were on the order of

10−5 s, ensuring complete conversion of the butoxy radicals tothe final stable products. Therefore, the branching ratio fornitrate formation, β = k1b/k1a, could be obtained by relating themeasured nitrate concentration to the sum of the BA and MEKconcentrations, taking into account the branching ratios of

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reactions 1 and 6 and the loss of the butoxy radicals in reactions 7.The disproportionation−combination ratios for reactions n6 ands6 were obtained by the MS technique, giving the BA and MEKyields γn = kn6b/(kn6a + kn6b) = 0.29 ± 0.0535 and γs = ks6b/(ks6a +ks6b) = 0.21 ± 0.02.36 Thus, the effective branching ratio can bedetermined as

β = = ΔΔ

=·ΔΔ

kk

y[nitrate][butoxy]

[nitrate][prod]

1b

1a (E1)

where Δ[nitrate] is the sum of of n- and sec-butyl nitrateconcentrations, Δ[prod] is the sum of concentrations ofproduced BA and MEK, and y = y(P,[NO]) is the yield factorindicating what fraction of butoxy radicals was converted into BAand MEK. The latter was calculated as follows

φ γ η φγη= + = +y y yn s n n n s s s (E2)

where φn and φs are the yields of n-butyl and sec-butyl radicals inreaction 2; ηn = kn6[NO]/(kn6[NO] + kn7), and ηs = ks6[NO]/(ks6[NO] + ks7). As the φ and γ yields do not depend on pressureand NO concentration, one can write yn = 0.165ηn and ys =0.089ηs.Butyraldehyde, MEK (both Fluka, 99.9%), and isobutyl nitrate

(Sigma-Alrdrich, 99.8%) used for calibration purposes wereintroduced into the reactor as preprepared ∼4% mixtures in He.Their concentrations were calculated from the rate of thepressure drop in a calibrated volume. NO2 was calibrated usingcommercial mixture (AlphaGaz, 0.5% in N2), whose flow ratewas regulated by a Tylan controller.Detection System. Gas mixture from the TFR was sampled

through a Teflon cone into the IMR. The pressure of the Arcarrier gas in the IMR was about 1 Torr. The primary Ar+ ionsand electrons were generated in the ion source with a heatedfilament. The ions formed in the IMR entered the ion-opticalzone through the 180 μmorifice in the nickel skimmer biased at apotential of several volts and presenting a first focusing element.After passing a quadrupole mass analyzer (EXTREL), the ionswere registered using a Channeltron multiplier and a MTS-100preamplifier. The signals were measured in ion counting mode incounts per second (cps) with averaging over the dwell time of 2 s.It was shown that alkyl nitrates and organic compounds such

as aldehydes and ketones can be detected both in positive modeusing the proton-transfer reaction (PTR)37 and in negative modeusing CH4−NICI

38 and NF3−NICI39 methods. Both methods

were employed in our previous studies.16−18 In the present study,testing of the PTR method showed that the main peaks in thespectra of BA andMEKwere “regular”C4H8OH

+ andC4H8OH+·

(H2O) peaks (masses 73 and 91), while the spectrum of isobutylnitrate consisted of one intense C4H9

+ peak (mass 57) with aminor C4H9O

+ peak (mass 73). Similarity of the PTR spectra forn- and isobutyl nitrates was shown earlier.37 Unfortunately, thepeak at mass 57 was also observed in the mass spectrum of n-butane. Though it is generally considered that alkanes cannot bedetected by PTR, occurrence of the reaction

+ ‐ → + ++ +nH O C H C H H O H3 4 10 4 9 2 2 (1i)

with k1i ≈ 3 × 10−12 cm3 molecule−1 s−1 was reported.40 Thisreaction is relatively slow, but high n-butane concentrations usedin our experiments made the PTR method inapplicable fordetection of low butyl nitrate concentrations resulting fromreaction 1b.An ionization scheme using primary F− ions (NF3−NICI) was

used in this study for detection of stable products. In this scheme,

NF3 was flowed into the IMR downstream of the ion source togenerate F− ions through the dissociative electron attachmentreaction. It was found that both F−-NICI spectra of C3H7CHOand C2H5C(O)CH3 consisted practically of a single peak at m/e71, corresponding to the M−H

− ion

+ → +− −F C H O C H O HF4 8 4 7 (2i)

These spectra confirm the previous results of Tiernan et al.39

using NF3−NICI to detect organic compounds. The major peaksin the F−-NICI mass spectrum of isobutyl nitrate acquired in thepresent study are m/e 46, 62, and 71 with relative intensities78:20:2, independent of pressure. Commercially availableisobutyl nitrate was chosen for calibration as similar spectra areexpected for the three isomers of butyl nitrate (n-, sec-, andisobutyl nitrates) having a hydrogen atom in the β-positon withrespect to the bridge oxygen atom of the NO3 group attacked bythe F− ion. The following ion−molecule reactions can accountfor the ions observed (R = C4H9)

+ → + +− −F RONO NO BA or MEK HF2 2 (3ia)

+ → +− −F RONO NO RF2 3 (3ib)

+ → + +− −F RONO C H CO HF HNO2 3 7 2 (3ic)

The thermochemistry of analogous reactions for isopropylnitrate was analyzed in our previous study.18 Monitoring nitratesusing NO2

− ions was not possible because of the interferencewith the NO2

− ion formed in the reaction of the F− ion with n-and sec-C4H9ONO from reactions n6a and s6a

+ → +− −F RONO NO RF2 (4i)

Thus, only observation of the mass 62 peak could be used fordetection of butyl nitrates from reaction 1b. It is worth notingthat the NF3−NICI method has a very low sensitivity to NO2because the charge-transfer reaction with the F− ion

+ → +− −F NO NO F2 2 (5i)

is slow (k5i ≤ 6 × 10−12 cm3 molecule −1 s−141), while reactionslike 4i proceed through a single channel with k ≈ 3 × 10−9 cm3

molecule−1 s−1 for all nitrites containing β-hydrogens.42 Hence,the intensity of the peak at m/e 46 from the reaction system canbe ascribed to the nitrites formed in reactions n6a and s6a with asmall contribution from the nitrates, which could be easily takeninto account. Relating the nitrate signal at m/e 62 to that ofnitrites at m/e 46 gives an additional way to obtain pressuredependence. Moreover, in our study of ethyl nitrate formationusing NF3−NICI17, it was found that the sensitivity to ethylnitrate atm/e 62 was approximately the same as the sensitivity toethyl nitrite atm/e 46, implying similar rates for reactions 3ib and4i in the case of R = C2H5.The background NO2 concentration was determined using

charge transfer from the SF6− ion

+ → +− −SF NO NO SF6 2 2 6 (6i)

In this case, SF6 was introduced instead of NF3 into the IMR,where the agent SF6

− ions were generated by electronattachment. During calibration, the signal intensities were linearup to 1 × 1013 molecules cm−3 of NO2, isoC4H9ONO2,C2H5COCH3, and C3H7CHO.

3. EXPERIMENTAL RESULTSBranching Ratio Measurements. The branching ratio of

reaction 1 was determined between P = 100 and 600 Torr at T =

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298 ± 2 K using the F−-NICI detection method to measureconcentrations of the nitrate, BA, and MEK. The branching ratiodefined in eq E1 was calculated using the following equation

β =·ΔΔ

=· ΔΔ

y y I SI S

[nitrate][prod]

( / )

( / )62 62

nit

71corr

71eff

(E3)

whereΔI62 andΔI71 are the discharge on−off signal intensities atm/e 62 and m/e 71; S62

nit and S71eff are the apparatus sensitivity to

isobutyl nitrate at m/e 62 and the effective sensitivity to BA andMEK atm/e 71, respectively. The total signal intensity atm/e 71,ΔI71, was corrected for the contribution from the nitratedetermined from its calibration plot: ΔI71corr = ΔI71• − ΔI62(S62nit/S71nit). The S62

nit in cps units/molecules cm−3 was determined atdifferent pressures from the intensity (cps) versus concentration(molecules cm−3) calibration plots for isobutyl nitrate. Asmentioned above, similar sensitivities are expected for the n-, sec-,and isobutyl nitrates as the F− ion attacks the NO3 group, and allthree isomers have β-hydrogens providing similar ion−moleculereactions. The effective sensitivity S71

eff in the same units wascalculated as a superposition of individual sensitivities, S71

eff=(ynS71

BA + ysS71MEK)/(yn + ys), determined from the calibration plots

for BA and MEK. The yield factors yn and ys were defined above.Combining this expression with eqs E2 and E3, the desiredbranching ratio can be written as β = (ΔI62/ΔI71corr)[(ynS71BA +ysS71

MEK)/S62nit]. This expression is valid within an accuracy of the

coefficient (1 − βn) for the first term and (1 − βs) for the secondterm, where βn and βs are the individual branching ratios βn =kn1b/kn1a and βs = ks1b/ks1a. Assuming equal ratios, this coefficientchanges from 0.985 for 100 Torr to 0.96 for 600 Torrr. Becauseneither y factors nor sensitivities of BA and MEK differessentially, this estimation shows the degree of overestimationof β values obtained at any β partitioning. The results arepresented in Table 1.The plot of the branching ratio as a function of pressure, which

is shown in Figure 2, was least-squares fitted with a lineardependence resulting in the equation

β = ± × · + ±−P P( )(%) (1.13 0.10) 10 (Torr) (1.19 0.35)2

(E4)

where the error limits are the standard deviations of the fitting.Extrapolation to zero pressure gives a nonzero intercept of about

1%, and extrapolation to atmospheric pressure gives β(760) =(9.8 ± 1.1)%, where the uncertainty corresponds to the standarddeviation of the linear fitting.The uncertainty in β consists mainly of the uncertainties in

kinetic data used to determine the yield factors for BA andMEK.The branching ratio of reaction 2 was taken as the average of thefour k2a/k2b values measured using gas chromatography andgiving k2a/k2b = 1.32 ± 0.03.20−22 The uncertainties in the γcoefficients for the branching ratio of reactions n6 and s6 areabout 15 and 10%, respectively, so that the yield factors are yn =(0.165 ± 0.023)ηn and ys = (0.089 ± 0.009)ηs. The estimatedaccuracy of ηn and ηs is about 8%, giving the total uncertainty ofabout 20%. The uncertainties in β indicated in Table 1 alsoinclude experimental errors in nitrate, BA, and MEK calibration(∼5%). Additional errors in the determination of the branchingratio are connected with the possible contribution from thesecondary reaction n8b producing δ-hydroxy-1-butyl nitrate.

Table 1. Determination of the Branching Ratio β = k1b/k1a for the C4H9O2 + NO Reaction at 298 Ka

P (Torr) [C4H10] 1014 [NO] 1015 [O2] 10

16 Δ[nitrate]b 1010 Δ[prod]c 1011 kn7 105 (s−1) ks7 10

4 (s−1) yn (%) ys (%) β (%)

100 4.5 4.7 1.2 7.92 4.28 1.03 0.94 7.80 7.77 2.88 ± 0.57″ 5.8 ″ 8.26 4.81 8.54 7.87 2.82 ± 0.56

200 4.8 1.1 1.2 8.25 1.93 1.37 1.31 2.45 5.80 3.55 ± 0.71″ 2.0 ″ 6.42 2.30 4.19 6.87 3.09 ± 0.61″ 3.9 ″ 5.64 2.80 6.18 7.91 2.84 ± 0.57″ 4.9 ″ 5.60 2.77 6.95 8.08 3.04 ± 0.61

300 6.0 6.1 1.5 4.61 1.82 1.54 1.55 7.16 7.64 3.76 ± 0.755.9 6.0 1.5 5.18 1.51 7.13 7.63 5.06 ± 1.01″ 7.6 ″ 4.77 1.61 7.92 7.76 4.68 ± 0.94

400 6.3 5.1 1.6 3.41 0.904 1.64 1.74 6.25 7.54 5.20 ± 1.04″ 6.8 ″ 3.04 0.814 7.24 7.73 5.59 ± 1.12″ 8.5 ″ 2.70 0.720 8.01 7.86 5.96 ± 1.19

600 6.8 6.7 1.7 5.21 0.915 1.76 1.97 6.80 7.56 8.18 ± 1.63″ 9.0 ″ 6.28 1.22 7.98 7.73 8.11 ± 1.62″ 11.2 ″ 6.30 1.28 8.73 7.83 8.12 ± 1.62

aConcentrations are in units of molecules cm−3. bΔ[nitrate] is the sum of 1- and 2-butyl nitrate concentrations. cΔ[prod] is the sum of BA and MEKconcentrations. Uncertainties (1σ) were estimated accounting for uncertainties in the kinetic parameters and precision of the measurements (videinfra).

Figure 2. Pressure dependence of the branching ratio kb/ka for the sumof 1- and 2-butyl nitrate formation in the n-C4H10/F/O2/NO reactionsystem at 298 ± 2 K. The open triangle shows the result of Atkinson etal.10 for the C4H10/OH/O2/NO reaction system. The solid line is thelinear fit. The dashed line represents the calculation using the empiricalequation with the parametrization from ref 2, assuming equal branchingratios for primary and secondary nitrates.

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The upper limit for this contribution is about 12% as estimatedby computer simulation (vide supra).Figure 3 shows the pressure dependence of the branching

ratios calculated by relating the nitrate signal to the signal of

nitrites n-C4H9ONO and sec-C4H9ONO from reactions n6a ands6a, respectively

β = = ΔΔ

=Δ

Δk yk

[nitrate][butoxy]

[nitrate][nitrite]

ONO 1b

1a

ONO

(E5)

where yONO = φn(1 − γn)ηn + φs(1 − γs)ηs is the yield factor fornitrites. In the Detection System section, it was shown that thesignal at m/e 46 can be attributed to nitrites, so that βONO =yONO(ΔI62/ΔI46corr), where ΔI46corr = ΔI46 − ΔI62(S62nit/S46nit), whereS62nit and S46

nit are the apparatus sensitivities to butyl nitrate at m/e62 and m/e 46, respectively. The points presented in Figure 3correspond to the maximal NO concentration for each pressure.The obtained values appeared to be very close to the averagebranching ratios obtained by normalization using BA and MEKstable products. It means that the apparatus sensitivity to butylnitrites, S46

ONO, is approximately equal to the sensitivity to butylnitrates S62

nit, similarly to ethyl nitrite and ethyl nitrate. Althoughbeing in agreement with calibrated data, the normalization bynitrites was carried out only to check a general shape of thepressure dependence and was not taken into account in thefurther discussion.Comparison with Previous Studies. In the chamber study

of Atkinson et al.10 using gas chromatography with flameionization detection (GC-FID), the value of α = kb/(ka + kb) =(7.7 ± 0.9)% (β = kb/ka = 8.3%) was determined for the totalbutyl nitrate yield from the OH-initiated oxidation of n-butane inair at T = 299 K and 735 Torr of pressure. The total yieldconsisted of the mixture of 1- and 2-butyl nitrates withconcentration ratio [1-C4H9ONO2]/ [2-C4H9ONO2] = 0.07 ±0.21. The individual nitrate isomer yields for n-C4H9O2 + NOand sec-C4H9O2 + NO reactions derived from the data of thatstudy were given in ref 11 as ≤4 and (9.0 ± 0.9)%, respectively.Extrapolation of our results to 735 Torr gives β(735) = (9.5 ±1.1)%. However, having so significant of a difference for theyields from n- and sec-isomers, our results cannot be compareddirectly because they correspond to different ratios of isomerconcentrations; OH reaction with n-butane gives 17% of n-butyland 83% of sec-butyl radicals,10 while F reaction gives 57% and43%, respectively. When the above individual yields, correspond-

ing to βn = 0.44βs in accord with the recommendation,2 arecombined in proportion of our case, one obtains the total yield of0.062 or β = 6.6%, which is substantially lower than our resultβ(735) = 9.5%. One can see that simple assumption of equalbranching (βn = βs = 8.3%) gives better agreement. Moreover, anaccurate solution of the system of two equations that satisfiesboth studies gives βn even higher than βs/βn = 10.5% and βs =7.3%, or βn ≈ 1.3βsec. This contradicts the conclusion that n-alkylperoxy radicals are approximately twice less efficient inproducing nitrates than 2-alkylperoxy radicals.10−13 It is not thefirst time when such contradiction was observed. Much lessdifference for nitrate formation yields was obtained by Cassanelliet al.43 from n-pentyl and 2-pentyl radicals generated byphotolysis of iodopentane precursors in an air−NO mixture, βn= 8.7% and βsec = 12%.The approximate relationships βpri ≈ 0.4βsec, based on the

measurements of propyl and butyl nitrate isomers from propaneand n-butane reactions with OH performed in the early study,10

and βter ≈ 0.3βsec for tertiary nitrates based on observations ofisomers from the OH reactions with branched C5−C6

alkylperoxy radicals11,13 were proposed by Carter and Atkinsonas general ones.2,15 Apparently, the former was confirmed by themeasurement of the C5 alkyl nitrate yield from neopentane, βpri =5.4%,11 that could be compared to the 2- and 3-pentylnitrateyields from n-pentane10,12 or 2-methyl-3-butyl nitrate yield from2-methylbutane,11 βsec ≈ 12−14%. The above scaling wasproposed as a part of the empirical falloff equation, Y = Y(n,P,T),constructed for prediction of alkyl nitrate yields from theatmospheric reactions of secondary alkylperoxy radicals.2,15 For n= 4 (butylperoxy) and P = 735 Torr, this function gives βsec =9.0%, which rather well agrees with our results. With allowancefor a specific curvature, the full falloff curve assuming βn = βsagrees with our results as presented in Figure 2. It seems that byconsidering formation of nitrates, it is necessary to distinguishbetween linear (βn) and branched primary peroxy radicals.It is also interesting to compare the results obtained for butyl

nitrate with the data available for other C1−C5 systems (Figure 4and Table 2). Figure 4 shows that for C3 propyl nitrate

Figure 3. Comparison of the branching ratios obtained by relating thenitrate signal to the signal at m/e 46 (◇) (not calibrated nitrites) andm/e 71 (■) (calibrated BA and MEK products).

Figure 4. Comparison of the branching ratios kb/ka of alkyl nitrateformation in RO2 + NO reactions for small alkylperoxy radicals: ▽, ref14; ■, this work; ●, ref 18; ▲, ref 17; ◆, ref 16; atmospheric pressuredata for propyl nitrate (○) and butyl nitrate (□) are from ref 10, andthose for n-pentyl (Δ) nitrate are from ref 43. The open circle at 100Torr is the branching ratio for isopropyl nitrate from ref 44.

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extrapolation of our data to 740 Torr gives β = 3.9%, practicallycoinciding with the result of Atkinson et al.,10 β = 3.7% (totalnitrate yield of 3.6%). Similarly to n- and sec-butyl nitrates, theseclose values correspond to very different ratios of the initial n- toisopropyl radical concentrations, 5:95 in our experiments(initiation by H + propene reaction) and 31:69 in the chamberstudy (initiation by OH + n-propane reaction). It is clear thatnearly equal total nitrate yields can be obtained only if individualyields are close values. Proceeding as in the case of n-butane, onefinds that the results of both studies are consistent with βn = 3.4%and βs = 3.9% or βn ≈ 0.9βsec.Considering the application of the empirical falloff expression

with the most recent parametrization2 to the formation of smallC1−C5 alkyl nitrates, we found that the 298 K atmosphericpressure values can be fitted applying the scaling coefficient of∼0.8 for secondary and ∼1.2 for primary alkyl radicals. Table 2contains the experimental branching ratios for P = 740 Torr data,which are compared with the calculation using the above-mentioned coefficients. Such approximation gives satisfactory

agreement between all of the data, though the result of Cassanelliet al.43 for 2-pentyl nitrate appears to be substantially lower thanthis estimation. Taking into account rather large experimentalerrors in the determination of the nitrate yields in all of theexperiments, it can be concluded that (1) the empirical functionsomewhat overestimates β = kb/ka for C1−C5 secondary alkylradicals and (2) the branching ratios of the reactions of primaryand secondary alkylperoxy radicals are not very different. Theseresults are now analyzed in the Theoretical Examination section.

4. THEORETICAL EXAMINATION

In order to discuss the Experimental Results, and specifically therelation of the branching ratio β = kb/ka with the structure of theRO2, the mechanism of the RO2 + NO reactions was analyzed onthe basis of quantum chemical calculations of the PES for C1−C5systems.The PESs of the RO2 +NO reactions have been explored using

a DFT approach with the B3LYP functional and the aug-cc-pVDZ basis set45 As explained in ref 46 (and references therein),the biradical character of the transition states has been taken intoaccount properly by mixing HOMO and LUMO orbitals.Minima and transition states were fully optimized andcharacterized by harmonic vibrational frequency analysis.The zero-point vibrational corrected energies (ZPVEs) of the

relevant points on the PESs of different C1−C5 reactants arepresented in Table 3. It can be observed that the general trend ofenergy variation along the reaction paths is similar regardless ofthe system studied. Figure 5 depicts the corresponding energydiagram where the energies correspond to the n-C4H9O2 + NOreaction. As was found earlier (e.g., refs 7−9), the reactionproceeds first by the barrierless formation of two ROONOintermediate complexes, denoted ROONOcisperp and ROO-NOtransperp. These notations mean that the RO bond is almostperpendicular to the OONO plane, the four-atom OONOpresenting either a cis or a trans configuration with respect to themid ON bond.The two ROONO conformers are connected to the fragments

RO + NO2 via two transition states TS1cis and TS1trans (ROO···NO structure). As can be seen in Figure 5 and Table 3, onlyTS1cis is below the energy of the entrance valley RO2 + NO.Then, at room temperature, TS1trans is expected to play a minorrole in the evolution of the reactive process, and it was neglectedin this work.After having crossed the TS1cis barrier, the activated RO···

ONO systems come out into an almost flat valley of the PES

Table 2. Comparison of the Measured Branching Ratios atRoom Temperature and 740 Torr for Nitrate Formation inRO2 + NO Reactions with Calculated Ones Using the ScaledEmpirical Function (β = kb/ka = Y) from Reference 2

alkyl (Y) R βexp ref βcalca scaling

C1(0.0098)

methyl 0.0105 ± 0.0013 16 0.012 1.07b

C2 (0.023) ethyl 0.032 ± 0.004 17 0.028 1.39b

C3 (0.049) 0.05 n-propyl +0.95 isopropyl

0.039 ± 0.002 18 0.040 0.80

0.31 n-propyl +0.69 isopropyl

0.037 ± 0.005 10 0.045 0.76

C4 (0.089) 0.57 n-butyl + 0.43sec-butyl

0.095 ± 0.011 thiswork

0.091 1.07

0.17 n-butyl + 0.83sec-butyl

0.077 ± 0.010 10 0.078 0.87

C5 (0.144) n-pentyl 0.087 ± 0.021 43 0.172 0.60b

2-pentyl 0.120 ± 0.022 43 0.120 0.83b

0.08 n-pentyl +0.92 (2+3)-pentyl

0.106 ± 0.008 14 0.117 0.74

0.08 n-pentyl +0.92 (2+3)-pentyl

0.122 ± 0.017 10 0.117 0.85

aCalculation using βn = 1.2Y for linear alkyls and βs = 0.8Y forsecondary alkyls. bScaling factors βexp/Y for “pure” cases devoid ofalkyl isomers.

Table 3. Energies of Stationary Points (in kcal/mol) on the PES for RO2 + NO Reactionsa

R ΔE0 ROONO cisperp ΔE0 ROONO transperp ΔE0 rxn RONO2 ΔE0 cis# RO···ONO ΔE0 trans

# RO···ONO ΔE0 rxn RO + NO2

Primary CarbonCH3 −19.15 −17.92 −49.69 −10.30 4.20 −15.20C2H5 −19.08 −17.84 −48.23 −9.31 5.20 −15.31n-C3H7 −19.13 −17.87 −48.41 −9.60 4.80 −15.66n-C4H9 −19.13 −17.88 −48.43 −9.66 4.66 −15.58i-C4H9 −18.36 −17.11 −47.83 −8.85 5.82 −15.64n-C5H11 −19.11 −17.85 −48.93 −9.63 4.67 −15.58Secondary Carboni-C3H7 −18.39 −17.02 −47.30 −8.88 5.54 −12.83sec-C4H9 −23.63 −16.91 −44.84 −9.70 4.78 −14.22Tertiary Carbontert-C4H9 −17.87 −16.49 −44.00 −8.27 6.10 −12.45

aData related to n- and sec-butyl nitrates are displayed in bold characters.

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(zone notedW in Figure 5; also see ref 46), leading mainly to thedissociation into RO + NO2. This almost flat region (energeti-cally slightly below the products RO + NO2) favors a roamingmotion of RO and ONO parts. In some cases, when the relativeorientation of the RO and ONO fragments is favorable to theformation of activated RO···NO2 structures, RONO2 moleculescan then be formed via collisional stabilization. These resultsagree with the trajectory study of Chen et al.47 for R = H. As amatter of fact, their calculations show that once HO···ONObegins to dissociate, a few trajectories undergo a rotation of OH,causing the incipient fragments to return and form an HO−NO2structure. Therefore, to explain the nitrate formation (describedthrough the β = kb/ka ratio), we have been looking for a simplequalitative collisional model that can be used for a large family ofRO···NO2 structures.The β = kb/ka ratio depends essentially on the relative

efficiency of the collisional deactivation of the excited RO···ONOleading to the RONO2 formation. This β ratio is expected todepend upon several parameters, (i) the frequency z of thecollisions per pressure unit, (ii) the total pressure P, (iii) thefraction Ω of a solid angle corresponding to a favorableorientation of RO with respect to NO2 for the creation of abonding between these two entities (the oxygen atom of ROshould be oriented toward the nitrogen atom of NO2), and (iv) aCeff term that we call the “efficiency coefficient”, which isexpected to be mainly a function of two factors, (a) theprobability P(E,ΔE) to remove a given amount ΔE of energyfrom excited RO···NO2 during the collision event at the energy Eand (b) the density of states ρ(E) at this energy level E. The termz mainly depends, at a given temperature, on the ratio d2/√μ,where d is the “diameter” of the nitrate molecule and μ thereduced mass of the nitrate/air system. Then, because z is aslightly increasing function of the molecular mass of RONO2, thecollision frequency, z × P, increases with P and becomes largerfor larger ROONO molecules, in agreement with experimentalobservations. For the fraction Ω, we estimate that its value is inthe range of 10−20%, independent of the R structure. Then, theefficiency of the nitrate formation should bemainly influenced bythe R structure via the efficiency coefficient Ceff, a function ofP(E,ΔE) and ρ(E). For P(E,ΔE), we assume that it does not varysignificantly for different molecules within the family of

analogous molecular systems considered here. Then, theinformation concerning the discrimination between all of thecompounds is now focused on the density of states ρ(E).The energy domain corresponding to the dissociation of a

nitrate into RO + NO2 is between 35 and 50 kcal mol−1 (roughly

12000−17000 cm−1). Figure 6 gives the variation of the density

of states calculated using the Beyer−Swinehart (BS) method48for a set of linear aliphatic nitrates from HO−NO2 to C5H11O−NO2 with the energy E over this range. Figure 7 shows, for thesame domain, the variation of the density of states ρ(E) of thefour possible butyl nitrate isomers.

Because ρ(E) is always an increasing function of the number ofcarbon atoms, we may expect higher efficiency of the alkyl nitrateformation for larger peroxy radicals RO2. For the isomers ofC4H9O−NO2 the density of states of n-nitrate (linear) is largerthan that of the branched one for any value of energy. Similarbehavior is also observed for propyl and pentyl nitrates. This canbe explained by the fact that a branched system involves larger

Figure 5. General correlation diagram for RO2 + NO reactions. Energyvalues displayed are ZPVE corrected energies in kcal/mol for the n-C4H9O2 + NO reaction. The point noted W does not correspond to aprecise minimum but indicates a rather flat region of the PES connected(i) to TS1cis, (ii) to the fragments RO + NO2, and (iii) to RO−NO2(see text). The energy associated with this W region is slightly below theRO + NO2 one.

Figure 6. BS density of states of C0−C5 linear aliphatic nitrates versusenergy.

Figure 7. BS density of states for the four isomers of butyl nitrate. Thefour schemes associated with the curves represent the aliphatic radicalpart R of each nitrate. The dot represents the electron bounded to theO−NO2 radical.

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internal interactions than a linear one. Such internal effectsincrease the curvatures of the PES, leading to larger gaps betweenthe energy levels and, consequently, to a smaller number of statesin branched systems.All of these conclusions are in qualitative agreement with

experimental findings; β increases as long as the pressure P andthe size of the RO2 radical increase. Even if the density of states isexpected to play an important role, the comparison betweenexperimental β values corresponding to linear and branched alkylradicals is totally convincing. Then, it is difficult so far to givedefinite conclusions for several reasons; (i) for a given family ofalkyl radicals R (linear and branched), experimentally available βvalues are close together with relatively large uncertainties, (ii)the data on which these comparisons can be done are rathersparse, and (iii) our model presented here focuses only on theparameter density of states, but the role of other parameters (sofar not fully investigated) can be nonnegligible.

5. CONCLUSIONSThe summary yield of 1- and 2-butyl nitrates in the gas-phasereactions of NO with n-C4H9O2 and sec-C4H9O2 obtained fromthe reaction of F atoms with n-butane was found to increaselinearly with pressure from about 3 to about 8% over the pressurerange of 100−600 Torr at 298 K. The results agree with the onlyavailable data from the study with OH radical initiation,10

assuming approximately equal rates of nitrate formation for bothisomers. The yield of primary and secondary butyl nitrate wasestimated to be 10.5 and 7.3%, respectively.The experimental findings are in general agreement with

performed DFT(B3LYP/aug-cc-pVDZ) calculations and theproposed mechanism. The calculations confirm experimentalresults about the higher efficiency of the nitrate formation forlarger nitrates and positive pressure dependence of the nitrateyield. The calculations also predict a lower density of energystates for the ramified than for linear excited ROONO structures,leading to the nitrate formation via their collisional stabilization.On the basis of this result, it is predicted that the efficiency of thenitrate formation for the branched RO2 should be lower than thatfor linear RO2 radicals.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: georges.lebras@cnrs-orleans.fr.Present Address⊥N.I.B.: Institute of Chemical Physics of the Russian Academy ofSciences, Moscow, Russian Federation.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work has been supported by the French Ministry ofResearch through the ANR program (ONCEM Project No.ANR-12-BS06-0017-01).

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The Journal of Physical Chemistry A Article

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The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp509427x | J. Phys. Chem. A XXXX, XXX, XXX−XXXJ