Branching Ratios and Vibrational Distributions in Water-Forming

Article pubs.acs.org/JPCA

Branching Ratios and Vibrational Distributions in Water-Forming Reactions of OH and OD Radicals with Methylamines N. I. Butkovskaya*,† and D. W. Setser‡ †

Semenov Institute of Chemical Physics, Russian Academy of Sciences, 119991 Moscow, Russian Federation Department of Chemistry, Kansas State University, Manhattan, Kansas 66506, United States

‡

S Supporting Information *

ABSTRACT: Reactions of OH and OD radicals with (CH3)3N, (CH3)2NH, and CH3NH2 were studied by Fourier transform infrared emission spectroscopy (FTIR) of the water product molecules from a fast-flow reactor at 298 K. The rate constants (4.4 ± 0.5) × 10−11, (5.2 ± 0.8) × 10−11, and (2.0 ± 0.4) × 10−11 cm3 molecule−1 s−1 were determined for OD + (CH3)3N, (CH3)2NH, and CH3NH2, respectively, by comparing the HOD emission intensities to the HOD intensity from the OD reaction with H2S. Abstraction from the nitrogen site competes with abstraction from the methyl group, as obtained from an analysis of the HOD and D2O emission intensities from the OD reactions with the deuterated reactants, (CD3)2NH and CD3NH2. After adjustment for the hydrogen−deuterium kinetic isotope effect, the product branching fractions of the hydrogen abstraction from the nitrogen for di- and monomethylamine were found to be 0.34 ± 0.04 and 0.26 ± 0.05, respectively. Vibrational distributions of the H2O, HOD, and D2O molecules are typical for direct hydrogen atom abstraction from polar molecules, even though activation energies are negative because of the formation of pre-transition-state complexes. Comparison is made to the reactions of hydroxyl radicals with ammonia and with other compounds with primary C−H bonds to discuss specific features of disposal of energy to water product.

1. INTRODUCTION Computer simulation of infrared chemiluminescent spectra from a fast-flow reactor have provided vibrational distributions for H2O and HOD products from the reactions of OH and OD radicals with a number of inorganic hydrides, alkanes, and oxygen- and sulfur-containing organic molecules.1 The vibrational energy and the distribution of this energy between the stretching and bending modes of water depend upon the reagent, and these vibrational distributions of H2O and HOD serve to illustrate the reaction dynamics.1 Comparison of the relative emission intensities from different reactions allows measurements of relative reaction rate coefficients, and comparison of relative emission intensities from HOD and D2O products from OD reactions with a deuterium labeled reagent gives product branching ratios.1−3 These methods were used in the present work to study the reactions of OH and OD radicals with trimethylamine (TMA), dimethylamine (DMA), and monomethylamine (MMA). Amines are important species in atmospheric chemistry due to their role in the formation of aerosols and particles4,5 and their use in carbon capture and storage.6 Wet and dry removal of amines competes with OH radical reactions, and rate coefficients and products from these processes are needed to predict the composition of the atmosphere. Atkinson and co-workers,7,8 using a vacuum ultraviolet flash photolysis resonance fluorescence technique, found that the room temperature rate constants were large, 6.1 × 10−11, 6.5 × 10−11, and 2.2 × 10−11 cm3 molecule−1 s−1 for TMA, DMA, and © XXXX American Chemical Society

MMA, respectively, and the temperature dependence of these reactions in the 298−426 K range corresponded to negative Arrhenius activation energies of about −0.5 kcal mol−1. Later, Carl and Crowly9 measured the rate constants at 295 K by laser photolysis resonance fluorescence technique and confirmed the values for MMA and DMA, but the rate constant for TMA was two times smaller, 3.6 × 10−11 cm3 molecule−1 s−1. Two measurements were reported for TMA in 2012: Onel and coworkers10 using similar methods as Carl and Crowley found 3.2 × 10−11 cm3 molecule−1 s−1, but Nielsen et al.11 obtained 5.4 × 10−11 cm3 molecule−1 s−1 in experiments at the EUPHORE chamber. The most recent experiments from Onel et al.12 gave 5.8 × 10−11 cm3 molecule−1 s−1. Additional experiments with a different technique may help to resolve this discrepancy. The OH reactions with amines are presumed to proceed by H atom abstraction either from carbon or from nitrogen, with a possible role of hydrogen-bonded complexes.12−15 The branching fraction for abstraction from nitrogen has been reported as 0.416,17 and 0.2417 for DMA and MMA, respectively, even though the bond dissociation energies for the C−H bonds are lower than those for the N−H bonds in both DMA and MMA. The goal of the present work was to obtain the nascent vibrational distributions of H2O and HOD, to determine the Received: June 24, 2016 Revised: August 9, 2016

A

DOI: 10.1021/acs.jpca.6b06411 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 1. HOD and H2O spectra from the reactions of OH and OD radicals with amines. (a) [TMA] = 4.7 × 1012, [NO2] = 6.3 × 1013 molecules cm−3; arrows indicate the centers of the ν3, 2ν3-ν3, and 3ν3-2ν3 bands of HOD and ν3, 2ν3-ν3/ν1ν3-ν1, and mixed 3ν3-2ν3/2ν3ν1-ν3ν1/2ν1ν3-2ν1 bands of H2O in the 3200−4000 cm−1 range, and the centers of the ν1, 2ν1-ν1, 3ν1-2ν1, and 4ν1-3ν1 bands of HOD in the 2400−2900 cm−1 range. (b) [DMA] = 5 × 1012, [NO2] = 6.8 × 1013 molecules cm−3. (c) [MMA] = 4.3 × 1012, [NO2] = 7.6 × 1013 molecules cm−3. All spectra were corrected for the response function. Intensities of the HOD spectra in the 2400−2900 cm−1 range are enlarged by a factor of 2.

infrared chemiluminescence spectra from the vibrationally excited H2O, HDO, and D2O molecules generated by the reactions of OH and OD radicals with a reagent in a fast-flow chemical reactor were recorded by a Fourier transform infrared spectrometer (BIORAD FTS-60). The spectral resolution was 2 cm−1. The spectrometer chamber and the tube connecting the observation window (NaCl) with the spectrometer collecting lens (CaF2) were continuously flushed with dry air to remove water vapor that would absorb the chemiluminescent radiation. The wavelength response of the liquid N2 cooled InSb detector was calibrated with a standard blackbody source. The carrier gas in the 40 mm (inside diameter) Pyrex-glass flow reactor was Ar; the operating pressure was between 0.5 and 1.0 Torr. The OH or OD radicals were produced 30 cm upstream of the observation window via the H(D) + NO2 reaction, and the H(D) atoms were generated by a microwave discharge of H2(D2)/Ar mixture. The degree of the dissociation of H2(D2) was measured as 50 ± 5%. Standard conditions were [OH] ≈ 2 × 1013 molecules cm−3 with excess NO2 (1−2 × 1014 molecules cm−3). The amine reagents diluted by Ar were introduced into the reactor 3.5 cm upstream from the observation window. For measurements of the reaction rates of CH3NH2, (CH3)2NH, and (CH3)3N relative to H2S, the emission intensity was measured as the reagent concentrations were changed over the range 1 × 1012 to 2 × 1013 molecules cm−3. These data also were used to define the amine

product branching ratios for the CH3NH2 and (CH3)2NH reactions, and to verify the rate constants of water-forming channels. To estimate the branching ratios, the relative HOD and D2O intensities were recorded from OD reacting with CD3NH2 and (CD3)2NH. The vibrational distributions were compared to the previously published data for NH3, HBr, and other molecules with primary C−H bonds, such as C2H6, neoC5H12, and CH3OCH3,1 in order to establish specific features of energy disposal to water molecules formed by H atom abstraction from the N−H or C−H sites that have radical stabilization energies and pre- and postreaction hydrogenbonded complexes. All three amines react rapidly with OH, and the secondary reactions could have a role as an atmospheric source of NOx.11,12,16 Taking into account the atmospheric importance of these reactions, we examined the spectra at reaction times long enough for secondary reactions of fragment radicals with NO2 to take place. No additional products were observed in the case of CH3NH2 and (CH3)2NH. However, (CH3)3N showed formation of HNO, as identified from the IR emission spectrum18 in the 2000−3000 cm−1 range.

2. EXPERIMENTAL METHODS The experimental methods and the procedure for analysis of the H2O, HOD, and D2O emission spectra have been discussed in preceding papers (see ref 1 and references therein). The B


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The Journal of Physical Chemistry A Table 1. BDEs and Mean Available Energies for OH Reactions with Amines (in kcal mol−1)a D298(R−H)exp

molecule (CH3)2NCH2−H CH3NHCH2−H (CH3)2N−H NH2CH2−H CH3NH−H

83.8, 82.7 , 89.0, 91 86.927 90.4c,33 93.9,27 85.3c,28 92.624 98.4c,33 101.235

NH2−H

105c,33 107.6 ± 0.137

27

c 28

24

D0(R−H)exp 30

D0(R−H)calc 24

93.631 98.8 ± 0.636 101.431

91.0, 90.9,24 93.212 91.4,24 98.5,12

12

91.5 91.512 91.5,12 94.614 99.814

An uncertainty of ±2 was assigned to all the experimental BDE values according to McMillen and Golden. zero temperature. cCorrected for ΔfH0298 of benzyl29 (see Supporting Information). a

D0(R−H)b

Ea

⟨Eav⟩

89.6 89.6 91.3 92.6 99.4

−0.5 −0.5 0 −0.5 1

32.5 32.0 29.2 28.3 22.0

106.2

1.415

15.6

34 b

Selected values after conversion to

CD3NH2 and (CD3)2NH, where H2O augments the red side of the HOD spectrum, P1,2(v1,2) distributions are determined neglecting the emission from the states with v3 > 0, which seems a reasonable assumption, since the energy is preferentially released to the forming O−D bond. In order to extract relative concentrations from comparison of the intensities of the emission spectra, the dependence of the emission probabilities on the vibrational distributions must be considered. Thus, the band-sum intensities for emission, S′v, are needed for the Δv3 = −1 transitions of H2O, HOD, and D2O. The band strength coefficients, αν3, for (ν3ν1,2) bands of HOD were calculated as [ν(v3)/ν(1)]3·v3·S′v(ν3,HOD), where ν(v3) is the center of the (00v3)-(00v3-1) band, which gives α1 = 1.0, α2 = 1.75, α3 = 2.28. Since the populations in the v1 and v3 levels are coupled for H2O and D2O, the Δν1 = −1 transitions are included in the simulation model. Combining the 298 K Boltzmann weights of the vibrational states forming a given equilibrated ν1,3ν2 band and band strengths relative to S′v(ν3), the band strength coefficients, αν1,3 = S′v(ν1,3)/S′v(ν3), were calculated:1 α1 = 0.44, α2 = 0.77, α3 = 0.93 for H2O and α1 = 0.45, α2 = 0.82, α3 = 1.11, α4 = 1.27 for D2O. For a given vibrational distribution, the emission strength from a certain reaction at unit water concentration is equal to I(H2O or D2O) = β·S′v(ν3,H2O or D2O) = ∑αi·P1,3(i)·S′v(ν3,H2O or D2O) and I(HOD) = β·S′v(ν3,HOD) = ∑αi·P3(i)·S′v(ν3,HOD). Finally, the band sum intensity ratio for H2O, HOD, and D2O, S′v(ν3,H2O):S′v(ν3,HOD):S′v(ν3,D2O) = 0.76:1.0:0.22, must be taken into account.1 To estimate the population of the P1,3(0) and P3(0) states, theoretic-information analysis19 of the H2O and HOD vibrational distributions was used as described in ref 1. Experimental distributions, P(v), are compared with the prior distribution, P0(v), for a given average available energy, ⟨Eav⟩. The surprisal is defined as I(v) = −ln[P(v)/P0(v)] and surprisal plots show I(v) vs f v = Ev/⟨Eav⟩. Vibrational surprisal plots are usually linear for H atom abstraction reactions,20−23 ( f v) = λv0 + λv f v; the slope, λv, is a global measure of the deviation from the statistical prediction, and the intercept provides estimation for the Pv(v = 0) population. One advantage from observation of HOD is that modeling the 2400−2900 cm−1 spectrum provides an experimental estimation of populations of v3 = 0 states, which can be used to test the estimates from surprisal analysis. The average available energy was obtained as ⟨Eav⟩ = -ΔHo0 + Ea + ET, where -ΔHo0 is the reaction enthalpy and ET = 4RT, assuming that the thermal energy consists of rotational and translational components. In the case of amines, low-frequency vibrations such as CH3 torsions and rocking can contribute to the thermal energy. These contributions for TMA, DMA, and MMA were estimated to be 1.7, 1.0, and 0.4 kcal mol−1, respectively, from the ΔHo298 − ΔHo0 values calculated by

concentration below which the H2O and HOD vibrational distributions were free from vibrational relaxation. Spectra that were suitable for analysis without vibrational relaxation were acquired at 0.5 Torr of Ar and typical reaction time τ ≈ 0.25 ms with concentrations of the amines 5−6 × 1012 molecules cm−3. The secondary reactions of the primary product radicals with NO2 were examined at τ ≈ 0.5 ms and a range of NO2 concentrations. Commercial tank grade Ar passed through three molecularsieve traps cooled by acetone/dry ice mixture and liquid N2 to reduce H2O and CO2 impurities. The reagents were purified by freeze−pump−thaw procedure before loading into gas storage reservoirs as 17% mixtures with Ar. Monomethyl-d3-amine was prepared by reacting CD3NH3·HCl (purchased from C/D/N Isotopes Inc.; 99.9% D) with CH3OCH2CH2O−Na+ in CH3OCH2CH2OH solvent; its purity was checked by analytical mass spectrometry. Dimethyl-d6-amine (purchased from MSD Isotopes; 99.6% D) was used without purification.

3. METHODS OF SPECTRA ANALYSIS Typical water spectra from the OH and OD reactions with three amines are presented in Figure 1. The spectra in the 3200−4000 cm−1 range consist mainly of Δν3 = −1 transitions of HOD and Δν3 = −1 and Δν1 = −1 transitions of H2O and D2O. Under our experimental conditions, the resonant ν1 and ν3 levels of H2O (and D2O) and the ν1 and 2ν2 levels of HOD are coupled by collisions with Ar. Thus, H2O, D2O, and HOD are represented by two rather than three quantum numbers. The experimental spectra were modeled as a superposition of the emission from the vibrational v1,3v2 states of H2O (D2O) from the OH + HR (OD + DR) reactions, and v3v1,2 states of HOD from the OD + HR and OH + DR reactions; the rotational distributions were always taken as 298 K Boltzmann for the simulations. Construction of the hot and combination bands was described in ref 1 and references therein. Leastsquares fitting of the experimental spectrum gives vibrational distributions. Summation over the bending (bending + O−D stretch in the case of HOD) states gives the so-called stretching populations P1,3(v1,3) of H2O and D2O, and P3(v3) of HOD. Summation over the v1,3 levels gives the overall bending distribution of H2O and D2O. The weak emission in the 2400−2900 cm−1 range shown in Figure 1 consists of Δν1 = −1 transitions of HOD with a very minor contribution of Δν2 = −2 transitions. Model spectra consist of a superposition of ν3ν1,2 bands, where emission of the bands with v3 = 0 provides an experimental measurement for P3(0) of HOD. For simplicity, P1,2(v1,2) is denoted as P1,2(v2), where v2 is the maximum bending number in a set of resonant states; for example, P1,2(4) is a sum population of the (040), (120), and (200) states. In the case of the OH reactions with C


Article

The Journal of Physical Chemistry A Wayner et al.,24 and were added to ⟨Eav⟩ of Table 1. The reaction enthalpy −ΔHo0 = D0(HO−H) − D0(R−H) was obtained from the bond dissociation energies (BDEs) of amines and D0(HO−H) = 118.08 ± 0.03 kcal mol−1.25 Since the prior distributions are very sensitive to ⟨Eav⟩, the bond dissociation energies for TMA, DMA, and MMA were reviewed (see Supporting Information). A summary of the bond dissociation energies is given in Table 1. For OD reactions, zero-point energy considerations led to 0.3 kcal mol−1 larger ⟨Eav⟩. For OH reactions with deuterated reactants, corrections for isotopic effect lowered −ΔHo0 = D0(HO−D) − D0(R−D) by 0.8 kcal mol−1. The activation energies, Ea, were taken as zero, except for the abstraction from the NH2 group of CH3NH2, which was taken as 1 kcal mol−1 14,26 by analogy to the OH + NH3 reaction and with recognition of the smaller rate constant for OH + MMA relative to OH + DMA.

P3(1−3) = 65.0:34.3:0.7 were obtained from simulation of the Δν3 = −1 and Δν1 = −1 emission in the 3200−3900 cm−1 range. These distributions have a noticeable population in the second stretching levels, v1,3 and v3 = 2, while the population of the third level is less definite. The available energy of 32.5 kcal mol−1 allows excitation of v1,3 and v3 with 3 quanta; Ev(03)/ ⟨Eav⟩ = 0.94 (H2O) and 0.93 (HOD). The uncertainty associated with the least-squares fitting method has been discussed before.38 The populations of the P1,3(0) and P3(0) states were determined from surprisal plots, which were calculated using two models for the prior: the three-body prior (model 1) and also a model that includes three rotational degrees of freedom of the radical product (model 2) (Figure 3). Linear surprisal plots give λv13 = −1.3 ± 0.3 for H2O and λv3 = −4.0 ± 0.3 for HOD (model 1) and λv13 = −4.1 ± 0.4 for H2O and λv3 = −6.4 ± 0.3 for HOD (model 2), where the error limits correspond to 1 kcal mol−1 uncertainty in ⟨Eav⟩. The uncertain populations of the third level were excluded from the linear surprisal fits. The corresponding renormalized full stretching distributions are P1,3(0−3) = 40.4:41.5:17.6:0.5 and P3(0−3) = 40.0:39.0:20.6:0.4 (model 1) and P1,3(0−3) = 32.5:46.9:20.0:0.5 and P3(0−3) = 33.3:43.3:22.9:0.5 (model 2). The overall distributions given in Table 2 (and all other tables) are based upon model 2 surprisal plots. The mean vibrational energy is ⟨f v⟩ = 0.41 for both H2O and HOD. The vibrational energy is distributed between the bending mode and the newly formed O−H mode as ⟨f v2⟩ = ⟨Ev2⟩/⟨Ev⟩ = 0.30 (model 2) and 0.38 (model 1) in H2O and ⟨f v3⟩ = ⟨Ev3⟩/⟨Ev⟩ = 0.70 (model 2) and 0.60 (model 1) in HOD. The P3(0) population was also obtained from modeling the HOD spectra in the 2400−2900 cm−1 range (Figure 2c). Simulation showed bending population up to v2 = 7. For the states with v3 = 0 the following distributions were obtained: P1,2(2−7) = 11.3:6.7:4.9:2.1:2.8:0.35 (normalization corresponds to that of P3 with neglected P3(0)). The population of the 020/100, 030/110, 040/120/200, and 050/130/210 states could be reliably determined, whereas the higher states with maximum v2 = 6 and 7 close to the thermochemical limit were excluded from the surprisal analysis. P3(0) was estimated as 36.5 ± 3.0 and 33.8 ± 2.8 for models 1 and 2, respectively; the error limit corresponds to the standard deviation of linear regression, plus 1 kcal mol−1 uncertainty in ⟨Eav⟩, plus ∼4% uncertainty due to the noise in the baseline of the spectrum. Populations of the “dark” 000 and 010 states were estimated from the surprisal plot shown in Figure 3c, giving the full distribution in v3 = 0 P1,2(0−7) = 31.8:18.3:19.7:11.7:8.6:3.7:4.9:1.2 (model 1) and P1,2(0−7) = 26.9:17.8:22.1:13.1:9.7:4.1:5.5:0.7 (model 2). From Table 2 we see that the P1,2(v3=0) distribution in model 2 only slightly deviates from the statistical distribution (λv12 = −0.42 ± 0.11), whereas model 1 gives a nonphysical distribution with λv12 = 2.41 ± 0.23. For this reason the bending distribution in P1,3(0) of H2O was assumed to be equivalent to the statistical distribution, which is probably a lower limit to the bending energy. Since better agreement was obtained between the experimentally based P3(0) and the extrapolated value from model 2 prior than for model 1 prior for HOD, we prefer model 2 for analysis of the remaining distributions. The spectrum in Figure 4 was recorded for a longer reaction time and higher [NO2] in search for secondary reactions. The HNO ν1 fundamental band19 was observed in the 2400−2800

4. RESULTS 4.1. Trimethylamine. The H2O and HOD emission spectra from reactions 1 and 1D together with the simulated spectra are shown in Figure 2. OH + (CH3)3 N → H 2O + (CH3)2 NCH 2

OD + (CH3)3 N → HOD + (CH3)2 NCH 2

(1) (1D)

Figure 2. Computer simulation of the HOD and H2O spectra from the reactions of OH and OD radicals with trimethylamine. Fitted spectra are shown in red color.

The vibrational distributions from several experiments with variable TMA concentrations showed that vibrational relaxation of the stretch levels does occur for [(CH3)3N] ≥ 7 × 1012 molecules cm−3, with transfer from v1,3 = 2 to v1,3 = 1 or v3 = 2 to v3 = 1 being noticeable. This relaxation does not seem to change the bending excitation in levels 1 and 2. The distributions presented in Table 2 were assigned from the spectra recorded for TMA concentrations less than 7 × 1012 molecules cm−3. The populations P1,3(1−3) = 69.6:29.6:0.8 and D


Article

The Journal of Physical Chemistry A Table 2. H2O and HOD Vibrational Distributions from the Reactions of OH and OD with (CH3)3Na H2O v2 = v1,3 d

0 1 2 3

0

1

2

3

4

5

≥6

15.1 17.4 13.0 0.52

8.9 13.9 4.7

4.8 11.8 2.3

2.3 2.8

0.97 1.04

0.30

0.06

P1,3b

P1,3c

P01,3

69.6 29.6 0.8

32.5 46.9 20.0 0.52

64.8 29.8 5.35 0.124

P3b

P3c

P03

HOD v1,2 = v3 e

0 0d 1 2 3

0 9.1 10.0 23.6 18.4 0.45

1 6.0 6.3 8.7 4.0

2 7.5 7.7 5.0 0.47

3 4.4 4.2 3.3

4

5

3.3 3.2 2.4

1.4 1.30 0.47

≥6

e

1.7 0.67 65.0 34.3 0.7

33.8 33.3 43.3 22.9 0.45

82.1 16.1 1.73 0.037

a v1,3 = v1 + v3; v1,2 = max(v2) in a series of equilibrated (v1/2v2) levels; P03 and P01,3 are the statistical distributions. bP1,3(0) and P3(0) are not included. cP1,3(0) and P3(0) from linear surprisal plot using model 2. dPopulation of bending states is assumed to be analogous to the statistical distribution. eFrom simulation of the spectra in the 2400−2900 cm−1 range.

Figure 4. Raw H2O and HNO spectra from the reactions of OH with trimethylamine in the presence of NO2. [TMA] = 1.2 × 1013, [NO2] = 3.6 × 1014 molecules cm−3, τ = 0.5 ms. The inset presents the calculated (100)−(000) fundamental band of HNO; arrows indicate the centers of the ν1 and hot 2ν1−ν1 bands.

4.2. Dimethylamine, (CH3)2NH, and (CD3)2NH. The reaction with DMA can proceed by H atom abstraction either from the methyl group or from the nitrogen atom. Previous measurements gave a branching fraction of 0.3716 and 0.4117 for abstraction from nitrogen even though the reaction path degeneracy is 6:1 in favor of the H atoms in the methyl group. OH + (CH3)2 NH → → OD + (CH3)2 NH → →

Figure 3. Surprisal plots for H2O (a) and HOD (b, c) from OH and OD reactions with (CH3)3N.

(3a) (3b) (3Da) (3Db)

Spectra were acquired over a range of dimethylamine concentrations. The vibrational relaxation rates are similar to those discussed above for trimethylamine. The spectra for simulation were measured with [(CH3)2NH] between 5 and 7 × 1012 molecules cm−3 (Figure 1b). Simulation gave the stretching distributions, P1,3(1−3) = 71.0:28.8:0.3 and P3(1−3) = 72.1:27.2:0.7, which extend to the thermochemical limit of reactions 3b and 3Db (see Table 3). A rough estimate of P3(0)

cm−1 range, and it can be assigned to the secondary reaction with NO2: NO2 + (CH3)2 NCH 2 → HNO + other products

H 2O + (CH3)2 N H 2O + CH3NHCH 2 HOD + (CH3)2 N HOD + CH3NHCH 2

(2)

A possible reaction mechanism is discussed in the Supporting Information. E


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The Journal of Physical Chemistry A Table 3. H2O and HOD Vibrational Distribution from the Reactions of OH and OD with (CH3)2NH and CH3NH2a H2O v2 = v1,3

0

1

2

3

0d 1 2 3

15.1 18.8 13.2 0.2

8.6 15.2 4.7

4.5 11.3 1.9

2.1 3.4

0d 1 2

19.6 21.4 7.7

9.8 18.6 4.3

4.3 8.6 0.4

1.6 3.2

4 (CH3)2NH 0.79

CH3NH2 0.4

5

≥6

0.22

0.03

P1,3b

P1,3c

P01,3f

71.0 28.8 0.3

31.4 48.7 19.7 0.2

72.1 25.4 2.46 0.0013

80.7 19.3

35.8 51.8 12.4

79.7 19.5 0.84

P3b

P3c

P03f

72.1 27.2 0.7

48.3e 42.0 41.8 15.8 0.4

86.1 13.0 0.81 0.0014

84.7 15.3

49.6 42.6 7.7

90.7 9.08 0.213

0.07

HOD v1,2= v3

0

1

2

3

0e 0 1 2 3

12.1 13.4 21.0 12.6 0.4

8.6 8.3 10.5 2.5

12.6 9.7 5.3 0.6

5.9 5.1 2.7

NH(CH3)2 6.1 3.6 1.5

0 1 2

19.4 24.1 4.8

10.8 8.2 1.9

11.1 4.3 1.0

4.8 3.1

CH3NH2 2.7 2 0.9

4

5

≥6

2.0 1.4 0.8

1.0 0.6

0.7

0.2

a

v1,3 = v1 + v3; v1,2 = max(v2) in a series of equilibrated (v1/2v2) levels. bP1,3(0) and P3(0) are not included. cP1,3(0) and P3(0) from linear surprisal plot using model 2. dPopulation of bending states is assumed to be analogous to the statistical distribution. eFrom simulation of the spectra in the 2400−2900 cm−1 range. fP30 and P1,30 are the statistical distributions built as a linear composition of two channels.

was done by simulation of the Δν1 = −1 emission of HOD with ⟨Eav⟩ = 32.3 kcal mol−1 of channel b, as described above for TMA, and P3(0) = 0.50 was obtained. The assignment to P3(0) and P1,3(0) will be considered after the product branching ratio is determined from the experiments with (CD3)2NH. To distinguish between channels a and b, reactions with deuterated dimethylamine were examined: OH + (CD3)2 NH → → OD + (CD3)2 NH → →

H 2O + (CD3)2 N HOD + CD3NHCD2 HOD + (CD3)2 N D2 O + CD3NHCD2

(3′a) (3′b) (3′Da) (3′Db)

Reactions 3′ and 3′D give different water isotopes, and the spectra are shown in Figure 5b. The D2O and HOD emissions from reaction 3′D are fully resolved, and they were used to estimate the branching ratio in this reaction, because the H2O emission from reaction 3′a in the 3200−3900 cm−1 range has contributions from the HOD emission from reaction 3′b. The available energy allows excitation of 4 stretching quanta for D2O in reaction 3′Db and 2 OH stretchings for HOD in reaction 3′Da. Simulation of the D2O and HOD spectra gave distributions P1,3(1−4) = 49.1:38.1:12.6:0.14 and P3(1:2) = 77:23. Surprisal plots with ⟨Eav⟩ = 31.5 kcal mol−1 for D2O are presented in Figure S1a. The slopes are λ1,3 = −1.4 ± 0.2 (model 1) and λ1,3 = −4.4 ± 0.2 (model 2), and the P1,3(0) populations obtained from the intercepts give P1,3(0−4) = 26.6:36.0:28.0:9.2:0.24 (model 1) and P 1,3 (0−4) = 21.4:38.6:30.0:9.8:0.26 (model 2). For reaction 3′Da with ⟨Eav⟩ = 29.5 kcal mol−1 only two excited stretching states are allowed for HOD. The slopes of the two-point surprisal plots

Figure 5. HOD and D2O spectra from the reactions of OH (a) and OD (b) radicals with (CD3)2NH. (a) [DMA-d6] = 5.3 × 1012, [NO2] = 8.5 × 1013 molecules cm−3; (b) [DMA-d6] = 8.1 × 1012, [NO2] = 4.4 × 1013 molecules cm−3. Arrows in the 2400−2900 cm−1 range indicate the centers of the hot bands of HOD, and the centers of the ν3, 2ν3ν3/ν1ν3-ν1, and mixed 3ν3-2ν3/2ν3ν1-ν3ν1/2ν1ν3-2ν1 and 4ν3-3ν3/ 3ν3ν1-2ν3ν1/2ν32ν1-ν32ν1/3ν1ν3-3ν1 bands of D2O.

were λ3 = −2.8 ± 0.3 and λ3 = −5.7 ± 0.4 from models 1 and 2, respectively; the uncertainty corresponds to the 1 kcal mol−1 uncertainty in ⟨Eav⟩. The full distributions are P3(0−2) = 52.9:36.2:10.8 (model 1) and P3(0−2) = 43.8:43.3:12.9 (model 2). The overall distributions are presented in Tables 4a and 4b; energy disposal parameters are ⟨f v⟩ = 0.46; ⟨Ev2⟩/⟨Ev⟩ = 0.32 F


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Table 4. (a) D2O Vibrational Distributions from the Reactions of OD with (CD3)2NH and CD3NH2a and (b) HOD Vibrational Distributions from the Reactions of OH and OD with (CD3)2NH and CD3NH2e (a) D2O Vibrational Distributions D2O v2 = v1,3

0

1

2

0d 1 2 3 4

8.1 13.1 11.3 5.8 0.26

5.4 8.2 6.4 2.5

3.5 6.3 6.0 1.6

0d 1 2 3

9.1 18.2 12.4 3.3

5.8 12.4 6.4 2.2

3.5 8.9 4.7

3

4

≥6

5

OD + (CD3)2NH (Reaction 3′Db) 2.1 1.2 0.6 4.5 2.8 2.2 4.2 2.1

1.9 3.5 2.9

OD + CD3NH2 (Reaction 4′Db) 1.0 0.41 2.6 0.73

0.38 1.6

P1,3b

P1,3c

P01,3

49.1 38.1 12.6 0.14

21.4 38.6 30.0 9.8 0.26

55.8 33.3 9.85 1.04 0.0023

59.2 33.8 6.9

21.9 46.3 26.4 5.5

62.3 31.0 6.46 0.26

P3f

P3g

P03

77 23

43.8 43.3 12.9

87.9 11.6 0.491

99.2 0.8

51.4 48.2 0.4

94.1 5.85 0.0034

0.17

(b) HOD Vibrational Distributions H−OD v1,2 = v3

0

1

2

0h 1 2 P1,2

15.1 25.3 10.1 50.5

9.0 7.8 2.3 19.1

10.1 5.3 0.5 15.9

0h 1 2 P1,2

24.3 34.9 0.4 59.6

12.1 9.4

10.5 3.8

21.5

14.3

v3

0

1

2

0i 1h 2h P1,2

7.8j 6.5 0.6 14.9

8.4j 3.1 0.1 11.6

23.8 2.4 26.2

0i 1h P1,2

9.1j 6.1 15.2

9.7j 2.4 12.1

34.7 1.4 36.1

3

4

≥6

5

OD + (CD3)2NH (Reaction 3′Da) 5.0 3.2 1.1 3.3 1.5 8.3 4.7 1.1 OD + CD3NH2 (Reaction 4′Da) 3.4 1.1 0.05

3.4

1.1 HO−D

0.3

0.3

0.05

v1,2 = 3

4

OH + (CD3)2NH (Reaction 3′b) 12.4 18.8 0.7 0.1 13.1 18.9 OH + CD3NH2 (Reaction 4′b) 10.8 12.8 0.2 11.0 12.8

5

6

7

P3 = P03

7.4

5.7

2.1

86.4 12.8 0.7

7.4

5.7

2.1

8.3

4.2

8.3

4.2

89.6 10.1

a

v1,3 = v1 + v3; P01,3 are the statistical distributions. bP1,3(0) is not included. cP1,3(0) from linear surprisal plot using model 2. dPopulation of bending states is assumed to be analogous to the statistical distribution. ev1,2 = max(v2) in a series of equilibrated (v1/2v2) levels; P03 is the statistical distributions. fP3(0) is not included gP3(0) from linear surprisal plot using model 2. hPopulation of bending states is assumed to be analogous to the statistical distribution. iFrom simulation of the spectra in the 2400−2900 cm−1 range. jP1,2(0) and (1) from linear surprisal plot using model 2.

distributions given above for model 2, and the ratio of the ν3 band-sum intensities of HOD to D2O is 4.55. We obtain a branching ratio for reaction 3′D of 1.13 ± 0.09, and k3′Da/ (k3′Da+ k3′Db) = 0.53 ± 0.04. To evaluate the branching ratio for reaction 3 we must take into account the primary kinetic isotope effect of the CD3 group. It changes from about 5 for the abstraction of primary hydrogen in neopentane39 or propane,40 to 2.6 for secondary hydrogen in propane,40 and to 2.2 for tertiary hydrogen in isobutane.41 The latter was chosen to represent the abstraction from the methyl group in (CH3)2NH, because the Arrhenius activation energy of −0.35 kcal mol−1 and rate constant per H atom of 2 × 10−12 cm3 molecule−1 s−1

for D2O from reaction 3′Db and ⟨f v⟩ = 0.38; ⟨Ev3⟩/⟨Ev⟩ = 0.65 for HOD from reaction 3′Da. The branching ratio of reaction 3′D can be determined as k 3 ′ Da /k 3 ′ Db = [HOD]/[D2 O] = IHOD·βD2O·S′v (ν3 , D2 O) /[ID2O·βHOD ·S′v (ν3 , HOD)]

where IHOD and ID2O are the emission intensities of HOD and D2O. The average ratio obtained from two experiments was IHOD/ID2O = 6.4 ± 0.2; the emission efficiency coefficients are βD2O = 0.53 ± 0.02 and βHOD = 0.66 ± 0.04 for the G


Article

The Journal of Physical Chemistry A are similar. Assuming a secondary isotope effect to be negligible, we obtain k3a/(k3a+ k3b) = 0.34 ± 0.04 (the uncertainty includes a 10% uncertainty in the primary kinetic isotope effect). Model 1 gives a slightly higher value of k3a/ (k3a+ k3b) = 0.36 (βD2O = 0.48 and βHOD = 0.55). Both values agree rather well with the branching fraction obtained in previous studies. To obtain more information, the HOD spectra in the 2400− 2900 cm−1 range from reaction 3′b were analyzed, assuming that the emission from the states with v3 > 0 made no significant contribution. The average of fitting two spectra gave P1,2(2−7) = 33.9:17.6:26.8:10.5:8.1:3.1; the v2 = 7 level corresponds to the energy of 26.8 kcal mol−1. As in the case of the OD + TMA reaction, the populations of the 000 and 010 states were determined with the help of the surprisal plots (Figure S2a) with λv1,2 = −0.89 (model 1) and λv1,2 = −4.3 (model 2), from which the full distributions in v3 = 0 P1,2(0−7) = 17.5:13.8:23.3:12.1:18.4:7.2:5.6:2.1 (model 1) and P1,2(0−7) = 9.0:9.7:27.6:14.3:21.8:8.6:6.6:2.5 (model 2) were obtained. Assuming statistical distributions for levels with v3 > 0, the overall distribution in Table 4b was obtained. The energy disposal parameters are ⟨f v⟩ = 0.41 and ⟨Ev1,2⟩/⟨Ev⟩ = 0.88 (model 2). The latter means that only about 10% of vibrational energy is in O−H stretch, indicating its “spectator” role. Returning to reaction 3, we calculated the overall prior distributions as a linear combination of the two channels with ⟨Eav⟩ = 29.2 and 32.0 kcal mol−1 with a weighting of 0.34 and 0.66, respectively (Table 3). Surprisal plots (model 2) gave λv1,3 = −4.4 and λ3 = −5.6; extrapolation led to P1,3(0−3) = (31.4 ± 5):48.7:19.7:0.2 and P3(0−3) = (42.0 ± 3):41.8:15.8:0.4. The extrapolations excluded the P v(3) points close to the thermochemical limit. Modeling the HOD spectrum in the 2400−2900 cm−1 range using a combined P01,2 prior gave λv12 = −0.9 and P3(0) = 48.3 ± 4, in reasonable accord with the result from the surprisal analysis. The energy disposal parameters are ⟨f v⟩ = 0.42; ⟨Ev2⟩/⟨Ev⟩ = 0.29 for H2O and ⟨f v⟩ = 0.40; ⟨Ev3⟩/ ⟨Ev⟩ = 0.64 for HOD. 4.3. Monomethylamine, CH3NH2, and CD3NH2. The reaction with monomethylamine also proceeds via two pathways: OH + CH3NH 2 → → OD + CH3NH 2 → →

H 2O + CH3NH H 2O + CH 2NH 2 HOD + CH3NH HOD + CH 2NH 2

OH + CD3NH 2 → → OD + CD3NH 2 → →

H 2O + CD3NH HOD + CD2 NH 2 HOD + CD3NH D2 O + CD2 NH 2

(4′a) (4′b) (4′Da) (4′Db)

Just as for reaction 3′, the H2O and HOD emissions in the 3200−3900 cm−1 region from reaction 4′ overlap. To separate channels a and b, we, therefore, used the HOD and D2O spectra from reaction 4′D, which are presented in Figure 6b.

Figure 6. HOD and D2O spectra from the reactions of OH (a) and OD (b) radicals with (CD3)NH2. (a) [MMA-d3] = 8.1 × 1012, [NO2] = 1.2 × 1014 molecules cm−3; (b) [MMA-d3] = 8.8 × 1012, [NO2] = 1.0 × 1014 molecules cm−3.

The HOD spectrum from reaction 4′Da is nearly a pure ν3 = 1 emission band, although a small contribution from v2 = 1 and 2 bending states was needed in the fitting. The presence of v3 = 2 excitation, which requires 20.7 kcal mol−1, is questionable, though the least-squares fitting gave a small population of about 1%. This population, if any, is too uncertain to be used in the analysis and was ignored. The P3(0) was determined by assuming that the λ3 surprisal parameter for reaction 4′Da is similar to that for reaction 3′Da (λv3 = −5.7) and OD + NH3 (λv3 = −5.6).1 The HOD prior distribution for ⟨Eav⟩ = 22.2 kcal mol−1 is P03(0−2) = 94.1:5.9:0.0034 (model 2). If the surprisal parameter λv3 for reaction 4′Da is the same as for reaction 3′Da, λv3 = −5.7, the P3(0−2) distribution is 51.4:48.2:0.4. The D2O stretching distribution from reaction 4′Db is P1,3(1−3) = 59.2:33.8:6.9. For ⟨Eav⟩ = 27.8 kcal mol−1 the surprisal plot gives λv3 = −4.8 (model 2) leading to the full distribution P1,3(0−3) = 21.9:46.3:26.4:5.5 (Figure S1b). The overall distributions presented in Table 4 give ⟨f v⟩ = 0.35; ⟨Ev3⟩/ ⟨Ev⟩ = 0.67 for HOD from reaction 4′Da and ⟨f v⟩ = 0.45; ⟨Ev2⟩/⟨Ev⟩ = 0.28 for D2O from reaction 4′Db. The branching ratio k4′Da/k4′Db was calculated as in the case of reaction 3′D. The average ratio of HOD to D2O emission intensities obtained from three experiments was IHOD/ID2O = 3.9 ± 0.3, and the emission efficiency coefficients are βD2O = 0.44 and βHOD = 0.49 (model 2), leading to [HOD]/[D2O] = 0.77 ± 0.13, which gives a branching fraction k4′Da/(k4′Da + k4′Db) = 0.43 ± 0.07. Assuming as for (CD3)2NH a primary isotope effect of 2.2, and neglecting a secondary isotope effect, we obtain k4a/(k4a + k4b) = 0.26 ± 0.05 for reaction 4.

(4a) (4b) (4Da) (4Db)

Two previous measurements of the branching for this reaction gave k4a/(k4a+ k4b) = 0.2417 and 0.25.42 The spectra from these reactions are presented in Figure 1c. The overall stretching distributions are P1,3(1:2)= 80.7:19.3 and P3(1:2)= 84.7:15.3 from fitting two spectra below [CH3NH2] = 6 × 1012 molecules cm−3. The lack of emission from ν3 and ν1,3 = 3 is quite definite, as shown by comparing spectra from CH3NH2 to (CH3)2NH or (CH3)3N, indicating that D(H−CH2NH2) must be higher than for (CH3)2NH or (CH3)3N. The HOD emission in the 2400−2900 cm−1 range was too weak to be useful. In order to determine the product branching ratio, experiments with CD3NH2 reactions were carried out: H


Article

The Journal of Physical Chemistry A Simulation of the 2400−2900 cm−1 spectrum of the HOD from reaction 4′b (Figure 6a) followed by the surprisal analysis gave λv1,2 = −1.1 (model 1) and λv1,2 = −4.7 (model 2), and the full distributions P1,2(0−7) = 19.1:14.9:32.4:10:12:7.8:3.9 (model 1) and P1,2(0−7) = 10.1:10.9:38.7:12.0:14.3:9.3:4.6 (model 2). The overall distributions (model 2) presented in Table 4b give ⟨f v⟩ = 0.40; ⟨Ev1,2⟩/⟨Ev⟩ = 0.90 for HOD. The branching ratio of 0.26 to 0.74 obtained above was used to assign P1,3(0) and P3(0) for the OH(OD) reaction with CH3NH2.Prior distributions were calculated using Eav= 22.2 and 28.6 kcal mol−1 with a weighting of 0.26 and 0.74, respectively. The surprisal plots (model 2) with slopes of λ1,3 = −4.4 and λ3 = −5.3 gave intercepts that permitted P1,3(0) and P3(0) to be assigned (see Table 3). The final vibrational distributions P1,3(0−2) = 35.8:51.8:12.4 and P3(0−2) = 49.6:42.6:7.7 give ⟨f v⟩ = 0.43; ⟨Ev2⟩/⟨Ev⟩ = 0.30 for H2O and ⟨f v⟩ = 0.39; ⟨Ev3⟩/⟨Ev⟩ = 0.60 for HOD. These distributions are dominated by abstraction from the CH3 group, and the results resemble the energy disposal for TMA (see Table 7). 4.4. Rate Constant Measurements. The rate constants of the OD + amine reactions were measured by comparison with the OD + H2S reaction. The relative rate constants can be determined as kamine/kH2S = γamine·βH2S/γH2S·βamine, where γamine and γH2S are the slopes of I(HOD) vs [HR] plots of the amine and reference reaction, and β-factors were defined above. Figure 7 shows the dependence of the integrated emission intensities of the HOD product in the 3200−4000 cm−1 range on the reagent concentration for three amines and H2S.

intensity from the same number of HOD molecules in the v3 = 1 vibrational state, was found to be β(H2S) = 1.24 ± 0.07. Analogous calculations for TMA, DMA, and MMA gave β(TMA) = 0.84, β(DMA) = 0.69, and β(MMA) = 0.56 with an estimated uncertainty of 10%. The ratios of the rate constants were calculated as k1D/kH2S = 9.3 ± 1.1, k3D/kH2S = 11.0 ± 1.6, and k4D/kH2S = 4.3 ± 0.8. Neglecting the secondary kinetic isotope effect and taking kH2S = 4.7 × 10−12 cm3 molecule−1 s−1,16 we obtain for reactions 1, 3, and 4: k1 = (4.4 ± 0.5) × 10−11, k3 = (5.2 ± 0.8) × 10−11, and k4 = (2.0 ± 0.4) × 10−11 cm3 molecule−1 s−1, where the uncertainty consists mainly in the assignment of P3(0). Comparison with existing experimental values is made in Table 5. Table 5. Rate Constants for the OH Reactions with Amines reaction OH + (CH3)3N

OH + (CH3)2NH

OH + CH3NH2

OH + NH3 OH + H2S a

k (298 K) × 1011 cm3 molecule−1 s−1 ± ± ± ± ± ±

0.6 0.2 0.1 0.5 0.5 0.5

3.86a 6.5 ± 6.5 ± 6.3 ± 5.2 ±

0.7 0.6 0.6 0.8

5.69a 2.2 ± 1.7 ± 2.0 ± 2.0 ±

0.2 0.1 0.1 0.4

6.1 3.6 3.2 5.1 5.8 4.4

3.28a 2.98a 0.016 ± 0.002 0.47 ± 0.02

ref 8 9 10 11 12 this work 12 8 9 12 this work 12 7 9 12 this work 12 14 15 15

kN/k

ref

0.37 ± 0.05 0.41 ± 0.07

16 17

0.34 ± 0.04

this work

0.24 ± 0.08 0.25 ± 0.04

17 42

0.26 ± 0.05

this work

TST calculation.

5. DISCUSSION 5.1. Rate Constants. Previous measurements of the rate constants for the OH + amine reactions were based upon monitoring the time dependence of the OH radical concentration for various amine concentrations,7−10,12 or monitoring amine concentration relative to a reference compound in the presence of OH.11 Our measurements are based upon comparing the rate of formation of HOD for OD reacting with a range of amine concentrations to that from H2S. The good agreement of our rate constants with those of previous studies ensures that H atom abstraction is the sole reaction channel for hydroxyl radicals with amines at room temperature and 1 Torr pressure. In addition to possible uncertainty of the rate constant for H2S, our method has uncertainty associated with the need to assign a population to v3 = 0 of HOD and, for comparison to the reactions of OH radicals, neglect of the secondary kinetic isotope effect. Nevertheless, our measurements are in close agreement with previous reports as shown in Table 5. The role for the P3(0) assignment can be demonstrated for OD + (CH3)2NH

Figure 7. Dependence of the HOD integrated emission intensity on the reactant concentration.

The dependence is linear for the concentration range 3.5 × 1013 molecules cm−3 for H2S, 1.5 × 1013 molecules cm−3 for CH3NH2, and 7 × 1012 molecules cm−3 for (CH3)2NH and (CH3)3N. The decrease in intensity for the amines is due to relaxation to dark states of HOD. The ratios of the slopes of the linear parts of (CH3)3N, (CH3)2NH, and CH3NH2 plots to that of H2S are 6.3 ± 0.1, 6.1 ± 0.1, and 1.93 ± 0.02, respectively; the uncertainty corresponds to the least-squares deviation of the slopes. The HOD vibrational distribution obtained from the OD + H2S reaction P3(0−3) is 14.6:34.3:48.8:2.3, which agrees with the earlier study.38 The corresponding emission efficiency, which is the ratio of the observed intensity from H2S to the I


Article

The Journal of Physical Chemistry A Table 6. Energy Disposal for Specific Channels of OH and OD Reactions with Amines (in kcal mol−1)a

a

⟨f v⟩ = ⟨Ev⟩/⟨Eav⟩, ⟨f vn⟩ = ⟨Evn⟩/⟨Ev⟩. bAssumed to be equal to that for (CD3)2NH.

Table 7. Energy Disposal for OH and OD Reactions with Amines and Some Example Compounds (in kcal mol−1)a

a

reactant

⟨Eav⟩

⟨Ev⟩ H2O/HOD

⟨f v⟩ H2O/HOD

⟨f v1,3⟩

⟨f v2⟩

⟨f v3⟩

⟨Ev2⟩/⟨Ev3⟩

ref

N(CH3)3 (CH3)2NH CH3NH2 NH3 C2H6 neo-C5H12 CH3OCH3 CH3SCH3 CH2O HBr

32.5 31.1 26.5 15.6 23.1 22.4 27.6 28.9 33.2 33.6

13.3/13.5 13.1/12.3 11.4/10.3 8.7/8.8 11.7/10.8 11.3/10.2 12.4/13.1 14.3/15.2 18.0/18.3 20.8/20.3

0.41/0.42 0.42/0.40 0.43/0.39 0.54/0.55 0.51/0.47 0.50/0.46 0.45/0.47 0.50/0.52 0.56/0.54 0.62/0.60

0.70 0.71 0.70 0.82 0.83 0.84 0.72 0.70 0.67 0.69

0.30 0.29 0.30 0.18 0.17 0.16 0.28 0.30 0.33 0.31

0.70 0.64 0.60 0.77 0.81 0.80 0.69 0.64 0.64 0.62

0.43 0.45 0.50 0.23 0.21 0.20 0.41 0.47 0.52 0.50

this work this work this work 1 1 1 1 1, 38 1 1, 48

⟨f v⟩ = ⟨Ev⟩/⟨Eav⟩, ⟨f vn⟩ = ⟨Evn⟩/⟨Ev⟩.

reaction. The kDMA = (5.2 ± 0.8) × 10−11 cm3 molecule−1 s−1 in Table 5 was obtained using P3(0) = 0.42 from surprisal analysis. If P3(0) = 0.48 from fitting the spectra in the 2400−2900 cm−1 range is used, the rate constant would be (5.7 ± 0.9) × 10−11 cm3 molecule−1 s−1, which agrees slightly better with the other rate constants in Table 5. Although the TMA reaction is the simplest of the three amines, since abstraction from the methyl group is the only pathway, the reported rate constants seem to fall into two groups: two near 3.4 × 10−11 cm3 molecule−1 s−1 and three near 5.6 × 10−11 cm3 molecule−1 s−1. Our value of (4.4 ± 0.5) × 10−11 cm3 molecule−1 s−1 lies between the two groups and does not favor either group. The product branching fractions for reactions 3′D and 4′D should be reliable to within the limits of the estimates for P3(0) of HOD. It is worth noting that our data on branching ratios were obtained by direct observation of the products from different channels, whereas previous studies involved considerations based on secondary chemical reactions. Certainly, H atom abstraction from the nitrogen atom sites is competitive at room temperature. As Onel et al.12 state, the competition depends on the small relative energy difference between the transition-state barriers. It is instructive to examine the rate constants (in cm3 molecule−1 s−1 units) after adjustment for reaction path degeneracy. The rate constants per H−C bond are 0.49 × 10−11 (TMA), 0.57 × 10−11 (DMA), and 0.49 × 10−11 (MMA) using our total rate constants. The rate constants per H−N bond are 1.8 × 10−11 (DMA) and 0.26 × 10−11 (MMA). These rate constants are consistent with the relative energies of the transition states calculated by Onel et al.,12 i.e., the energy of

the transition state for H−N abstraction is below that for H−C abstraction for DMA, but the two energies are nearly equal for MMA. The 7-fold smaller rate constant for H−N abstraction from MMA suggests that its threshold energy is higher than for DMA which corresponds to our choice of 1 kcal mol−1 for Ea of reaction 4a and with Tian et al.14 in contrast to Onel et al.,12 who found a negative barrier. 5.2. Vibrational Distributions and Energy Disposal. The emission spectra from H2O, D2O, and HOD provide information about how the potential energy of the reactions is released to the vibrations of H2O, D2O, and HOD and identify the fractions of energy in the stretch and bend modes.1 The results from the reactions of OH with methylamines are a part of a large data set that describes the energy disposal for H atom abstraction by OH radicals. Two special aspects for amines are hydrogen bonding interactions that result in complex formation with OH in the entrance channel, which is responsible for the negative activation energies, and complex formation in the exit channel, which provides an attractive interaction between H2O and the N atom of the radical. The dynamics associated with H atom abstraction by OH radicals belong to the class of reactions typified by the reactions of halogen and oxygen atoms, which involves the rapid transfer of the light (L) atom from one heavy atom (H′) to another heavy atom (H) (H′−L−H). The transfer of the light atom (the hydrogen atom) occurs with virtually no movement of the two heavy atoms. Such direct transfer reactions have characteristic features including the release of a large fraction of the available energy to vibrational energy of the new bond. The rapid transfer occurs without a J


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According to the calculated TS geometries,12 the relative elongations of the breaking and forming bonds in DMA and MMA reactions are similar for abstraction from C and N atoms, which suggests similar energy disposal patterns from channels a and b. And, in general, the surprisal parameters λv1,3 ≈ −4.5 and λv3 ≈ −6 are typical for direct abstraction mechanism for both C−H and N−H channels (Table 6). However, some small difference in the abstraction from C and N atoms in DMA vs TMA can be noted. For example, the surprisal parameter for H abstraction by OD from the methyl group in TMA (−λ3 = 6.4) is higher than that from N atom in DMA (−λ3 = 5.7). As well, the total vibrational energy of HOD is higher for TMA (⟨f v⟩ = 0.42) than for (CD3)2NH (⟨f v⟩ = 0.38). For CD3NH2 ⟨f v⟩ = 0.35 is even lower, though P3(0) was estimated assuming equal λ-parameters. It is interesting to compare these results with the hydrogen atom abstraction by F atoms with the same reagent. Two channels of F atom reaction were studied using the CH3ND2 isotopic reaction.32 The ⟨f v⟩ (corrected for the new bond energies in CH3ND2) is 0.37 for DF and 0.44 for HF. Note that the relation between these values is similar to those for the channels a and b of (CD3)2NH (0.38 vs 0.46) and CD3NH2 (0.35 vs 0.45) (Table 6). Table 6 also shows rather close fractions of reaction energy released as H2O and D2O vibrational energy for abstraction from C atom of TMA, (CD3)2NH, and CD3NH2 (⟨f v⟩ = 0.41, 0.46, and 0.45, respectively), with similar partitioning between the stretching and bending modes. The result for the abstraction from the methyl group by F atom (⟨f v⟩ = 0.44) falls in this range. Although no real difference exists in C−H abstraction from TMA, DMA, and MMA, abstraction from the N−H site seems to favor a smaller ⟨f v⟩, which leads to the possibility that the attractive interactions in the exit channel are more important for abstraction from the N−H site than from the C−H site. Comparison with the H abstraction by F atoms helps to learn more about the energy released to the bending mode and the second stretching mode in water-forming reactions. The fraction of the total energy released as vibrational energy of H2O (HOD) from H atom abstraction by OH (OD) from the amines is similar to that of HF from F atom reacting with MMA. However, the vibrational energy of H2O (HOD) is divided between bending and stretching modes, indicating that excitation of the bending mode is due mainly to the redistribution of energy from the stretching mode. Inspection of Table 7 shows that for reactions with ⟨Eav⟩ = 30 ± 5 kcal/ mol the ratio of bend-to-stretch energies is 0.45 ± 0.05 with HBr and CH2O having the highest ratio. The bend-to-stretch ratios for the H−C abstraction reactions with the amines also fall into this range. Based upon quasi-classical calculations for the OH (OD) + HBr reaction,45−47 two mechanisms for excitation of the bending mode have been suggested. The first is the coupling of the bend and stretch modes as the H2O (HOD) traverses the exit channel of the potential and senses weak forces with the radical fragment. The second mechanism is direct release of potential energy to the bend mode during the transfer of the H atom to the OH radical. Since the transition-state structure associated with C−H−O(H) tends to be collinear and the H−O−H angle tends to be close to the equilibrium angle of H2O, direct bending mode excitation can be limited. In fact, two quasi-classical calculations for the OH + HBr underestimated the bend-to-stretch ratio, ⟨Ev2⟩/⟨Ev3⟩ (0.2345 and 0.3046 vs the experimental value of 0.50) even though the calculated ⟨f v⟩ reproduced the experimental result. The most recent quasi-classical trajectory calculation47 with a

significant change in the structure of the polyatomic fragment. Subsequent relaxation of the radical to its equilibrium structure on a slower time scale, well after the H−L product is formed, can release internal energy to H′, if the equilibrium structure of the radical differs from that of the parent molecule. Thus, another special aspect is that abstraction of H atoms from the methyl groups of amines is expected to involve a substantial radical stabilization energy. The reactions of OH radicals extend the H′−L−H class of dynamics to triatomic H2O products, and the most intriguing question is the role of the bending mode in energy disposal. The experimental vibrational distributions serve as a test for theoretical models of the reactions which employ quasi-classical trajectory calculations on computed potential surfaces. Although such calculations have not been done for amines, extensive calculations have been done for stationary points on the potential surfaces. We will first consider transition states, the pre- and post-transition-state complexes, and the radical stabilization energy for the amines, before examining recently published theoretical models for the OH + NH343,44 and HBr45−47 reactions for additional insight. A summary of the energy disposal for reactions with amines is given in Table 6, and a comparison with some reference reactions is provided in Table 7. The transition states (TS) for OH reactions with amines have been examined with electronic structure calculations by three groups. In the earliest study of Galano and AlvarezIdaboy,13 the BHansHLYP-6-311++ G (2d,2p)/CCSD(T) level of theory was used to identify the TS for the MMA and DMA for both the C atom and N atom sites. Tian et al.14 studied the OH + MMA reaction paths at the CCSD(T)/6311++G(2d,2p)//CCSD/6-31G(d) level of theory, including prereaction and postreaction complexes. In the most recent work of Onel et al.,12 the OH + TMA, DMA, and MMA reactions were examined at a high MP2/aug-cc-pVTZ level with improved single-point energies of stationary points obtained in CCSD(T*)-F12a calculations. This study identified pre- and postreaction complexes for all three reactions. A common result of all three studies is that the transition states for the H abstraction from both C and N atoms are reactantlike, i.e., they are characterized by a small elongation of the breaking C−H′ or N−H′ bond, with a larger distance between the departing H′ and O atom. The most early TS was found for the TMA reaction:12 R(C−H′) = 1.16 Å and R(H′−O) = 1.51 Å, which corresponds to 6.4% and 55% elongation of the breaking and forming bonds with respect to the equilibrium distances. The analogous elongations were 8.1% and 42% (Cabstraction) and 5.6% and 47% (N-abstraction) in DMA, and 6.6% and 45% (C-abstraction) and 6.6% and 42% (Nabstraction) in MMA. Another common feature of the transition states is that the three atoms involved in the abstraction process (C−H′−O or N−H′−O) are nearly collinear, and the H′−O−H angle in the forming water molecule only slightly differs from the equilibrium angle. Such configurations of the transition states do not promote excitation of the bending mode. The P3(v) population of HOD formed by abstraction of an H atom directly reflects the release of potential energy into the new OH bond, and the P3(v) distribution from TMA (see Table 2) shows an inversion with the maximum population in v3 = 1 (43%) as is expected from the preceding discussion and comparison to numerous other examples. The question of the bending mode excitation requires more analysis. K


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The Journal of Physical Chemistry A high level ab initio potential surface seems to give slightly better agreement with ⟨Ev2⟩/⟨Ev3⟩ = 0.36 (this value was obtained from diagram 5B of ref 47). De Oliveira-Fihlo et al.47 suggested the possible role of the bending force constants at the transition-state configuration in controlling bending excitation. In summary, the bending mode excitation for both C−H and N−H abstraction from amines is likely to be a combination of direct energy release during the H atom transfer, as well as stretch−bend coupling in traversing the exit channel. Comparison with the results from the HBr, CH 2 O, CH3SCH3, and CH3OCH3 reactions does not identify any special effects from the attractive interactions associated with H-bonding forces in the exit channel of the amines. The reactions with the hydrocarbons form a second category with ⟨Eav⟩ = 24 ± 2 kcal mol−1 and ⟨Ev2⟩/⟨Ev3⟩ = 0.21 ± 0.02, and several examples for abstraction from secondary H−C have ratios of 0.25 ± 0.02.1 The stretch distributions for hydrocarbon reactions are definitely more inverted with less bending excitation than for the category previously discussed. The OH + NH3 case with a ratio of 0.23 also can be placed in this group. These examples suggest that the coupling mechanism may depend on the total energy in the H2O (HOD) molecules. De Oliveira-Filho et al.47 also studied OH + DBr reaction, which showed an inverted population in OD stretching mode in accord with our experimental results.48 The calculated fraction of available energy in total HOD vibrations was ⟨f v⟩ = 0.66 compared to the experimental value of 0.57. The ⟨f v⟩ in amine reactions with D atom abstraction by OH from (CD3)2NH and CD3NH2 is noticeably less, ≈0.40 for both reactions, in line with the general pattern (Table 6). The mean vibrational energy is practically the same for TMA, DMA, and MMA (⟨f v⟩ ≈ 0.4), which is lower than that for many other compounds, including NH3 and hydrocarbons (⟨f v⟩ = 0.5−0.6). Only reactions with alkanes are free from attractive interactions in the exit channel. A dynamical study of EspinosaGarcia et al.43 on the energy disposal in the OH and OD + NH3 reactions on high level analytical PES gave ⟨f v⟩ that agreed well with our results. Reaction with ammonia is characterized by a low rotational excitation of both H2O and NH2 radical;44 however, this can hardly explain lower ⟨f v⟩ of amines compared to the reaction with NH3, as rotational energy mainly comes from reduction of the translational energy after H2O is already formed. The lower ⟨f v⟩ values than in reactions with NH3, CH3OCH3, CH3SCH3, CH2O, and HBr, for which high level ab initio calculations show formation of postreaction complexes similar to that of amines,47,49−51 can be evidence for retention of energy by the amine radical. It was already noted that, if the geometry at the TS differs from the equilibrium geometry of the radical, the “stabilization” energy, i.e., the energy released during relaxation to the equilibrium geometry, is not available to the water product. The vibrational distributions themselves do not provide any evidence for a role of the stabilization energy, since the bending states in each v3 (v1,3) level of HOD and H2O are populated up to the limit defined by the average available energy (Tables 2−4). On the other hand, the energy difference between the bending states of H2O and HOD is large, about 4 kcal mol−1, and only slightly less for D2O (3 kcal mol−1), and only really large stabilization energies would be revealed by the absence of expected levels. The average reaction event may not utilize the full available energy, even though a few events do access the total energy. According to Wayner et al.,24 all amine radicals should rearrange to the anticoplanar configuration of semioccupied and lone pair orbitals. Besides,

the interatomic distances change from the amine molecule to product radical during the C abstraction: for example, R(N−C) shortens from 1.45 to 1.38 (5.0%) in TMA, from 1.46 to 1.38 (5.4%) in DMA, and from 1.47 to 1.39 (5.9%) in MMA. Accurate ab initio calculations of the relative energies of a radical fragment in the TS and a free radical (as it was done by Whitney et al.23 for C2H5 in F + C2H6 reaction, predicting a relaxation energy of 4.2 kcal mol−1) are needed to identify the radical relaxation energies of methylamines.

6. CONCLUSIONS The vibrational distributions for isotopic water products from OH and OD reactions with (CH3)3N, (CH3)2NH, and CH3NH2 were obtained by computer simulation of the observed infrared spectra. The mean vibrational energy and the fraction of energy in the newly formed bond are typical for direct abstraction of hydrogen from either carbon or nitrogen atom. Lower mean vibrational energy relative to those from abstraction of primary H atoms from alkanes, CH3OCH3, or CH3SCH3 can be explained by a radical stabilization effect. The bending mode excitation for both C−H and N−H abstraction from amines is likely to be a combination of direct energy release during the H atom transfer, as well as stretch−bend coupling in traversing the exit channel. Similarity of the mean vibrational energies of water molecules formed in the reactions of methylamine with OH and F atoms supports the conclusion that bending excitation is mainly a result of energy transfer from the intrinsically excited local OH stretch. Experiments with deuterated methylamines clearly demonstrated the energy release into a newly formed bond and a “spectator” role of the initial hydroxyl bond. For example, the fraction of the total available energy in the O−H (ν3) vibration of the HOD produced in the OD + (CH3)3N and OH + (CD3)2NH reactions is equal to 29% and 4.9%, respectively. Comparison with other compounds suggests that the coupling mechanism may depend on the total energy in the H2O (HOD) molecules. The vibrational distribution of H2O, D2O, and HOD can serve to test theoretical models for the dynamics associated with the reactions of hydroxyl radicals with methylamines. The C−H and N−H channels were separated by using the deuterated (CD3)2NH and CD3NH2 reagents, and the product branching fractions of the hydrogen abstraction from the nitrogen of 0.53 ± 0.04 and 0.43 ± 0.07, respectively, were obtained. After adjustment for the hydrogen−deuterium kinetic isotope effect, the branching fractions of the N−H channel were found to be 0.34 ± 0.04 for OH + (CH3)2NH reaction and 0.26 ± 0.05 for OH + CH3NH2 reaction. The rate constants (4.4 ± 0.5) × 10−11, (5.2 ± 0.8) × 10−11, and (2.0 ± 0.4) × 10−11 cm3 molecule−1 s−1 determined for OD + (CH3)3N, (CH3)2NH, and CH3NH2, respectively, are in agreement with previous reports for the OH reactions with methylamines. The formation of HNO was detected among the products of the secondary NO2 + (CH3)2NCH2 reaction in TMA chemical system.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b06411. Review of BDEs, surprisal plots, discussion of secondary reactions with NO2, and comparison of experimental and fitted spectra (PDF) L


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +7 495 939 7316. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS N.B. is grateful for the support through Grant No. 16-05-00432 of the Russian Foundation for Basic Research. REFERENCES

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Branching Ratios and Vibrational Distributions in Water-Forming

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