N Reactional System

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A: Kinetics, Dynamics, Photochemistry, and Excited States 3

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Thermochemical and Kinetcs of the CHOH + (S)N Reactional System Rhayla Mendes Ferreira, Orlando Roberto-Neto, Francisco Bolivar Correto Machado, and Rene Felipe Keidel Spada J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03070 • Publication Date (Web): 25 Jun 2018 Downloaded from http://pubs.acs.org on June 26, 2018

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The Journal of Physical Chemistry

Thermochemical and Kinetcs of the CH3OH + (4S)N Reactional System Rhayla Mendes Ferreira,† Orlando Roberto-Neto,‡ Francisco B. C. Machado,¶ and Rene F. K. Spada∗,§ †Departamente de Física, Universidade Federal do Espírito Santo, Vítória, 29.075-910, Espírito Santo, Brazil ‡Divisão de Aerotermodinâmica e Hipersônica, Instituto de Estudos Avançados, São José dos Campos, 12.228-001 São Paulo, Brazil ¶Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12.228-900 São Paulo, Brazil §Departamento de Física, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12.228-900 São Paulo, Brazil E-mail: [email protected]

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The reaction of methanol (CH3 OH) with atomic nitrogen was studied considering three elementary reactions, the hydrogen abstractions from the hydroxyl or methyl groups (R1 and R3 , respectively) and the C – O bond break (R2). Thermochemical properties were obtained using ab initio methods and density functional theory approximations with aug-cc-pVXZ (X=T and Q) basis sets. The minimum energy path was built with a dual-level methodology using the BB1K functional as the low-level and the CCSD(T) as the high-level. This surface was used to calculate the thermal rate constants in the frame of variational transitional state theory considering the tunneling effects. Our results indicate the dehydrogenation of the methyl group (R3) as the dominant path with kR3 = 7.5 × 10−27 cm3 · molecule−1 · s−1 at 300 K. The thermal rate constants were fitted to a modified Arrhenius equation for use in mechanism studies of the methanol decomposition.

Introduction In the last decades there is a demand in substitute fossil for renewable fuels. In order to predict the possible pollutants created from these fuels, it is necessary a detailed knowledge of the physical-chemical process of the involved molecules in the atmosphere and reactors. 1 Christensen et al. 1 developed a mechanism for small hydrocarbons combustion consisting of 98 species and 1098 reactions. Among the possible pollutants released by petroleum based fuels, there are nitrogen oxides (NOx) that starts a mechanism to produce nitric acid (HNO3 ), which contributes to the atmosphere acidification 2 and formation of acid rain. 3 However, as was pointed out in the review by Sarathy et al, 4 there is a lack of results in the literature about the formation of NOx by alcohols combustion. Considering the possible renewable fuels, methanol (CH3 OH) is the simplest hydrocarbon. In comparison to fossil fuels, it releases a low-level of pollutants. 4 In the available 2


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mechanism, 1 82 reactions involving methanol, formaldehyde and subsets of these molecules were recently updated, but the mechanism does not contain elementary reactions involving CH3 OH with atomic or molecular nitrogen, the predominant specie in the atmosphere. Atomic nitrogen may be formed in the atmosphere during lightning thunderstorms through of the dissociation of the N2 molecule. It was observed by Railsback 5 that the pH of rain water decreases due to lightning. This suggests that atomic nitrogen may be present in the atmosphere, playing an important role in the rain acidification. In this context, we propose three elementary reactions for the CH3 OH + ( 4S)N reactional system, described in R1, R2 and R3.

SP

1 CH3 OH + N −−→ CH3 O + NH

SP

2 CH3 OH + N −−→ CH3 + NOH

SP

3 CH3 OH + N −−→ CH2 OH + NH

(R1) (R2) (R3)

Reaction paths R1 and R3 proceed via hydrogen abstractions from the hydroxyl and methyl groups from methanol, respectively. These elementary reactions produce important radicals for the combustion mechanism, like CH3 O and CH2 OH, that may suffer another subsequent dehydrogenation to form formaldehyde (H2 CO). The reaction R2 leads to the C – O bond break, forming NOH, that may be converted to nitrogen monoxide. In order to provide reliable results for use in the CH3 OH combustion mechanism, the thermochemical calculations were performed using high correlated ab initio methodologies and the rate constants were obtained by means of variational transition state theory considering tunneling contributions.

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Methodology The thermochemical properties of the CH3 OH + N reaction were calculated optimizing the geometry of stationary points (reactants, products and saddle point (SP)), which were recognized by frequencies analysis. From the harmonic frequencies, the zero-point energy (ZP E) were obtained. These calculations were carried out using the second order Møller-Plesset perturbation theory (MP2) 6,7 and the density functionals: BB1K, 8 M06-2X, 9,10 M05-2X, 11 B3LYP. 12,13 For these methods the triple zeta basis set from Dunning with diffuse functions was employed (aug-cc-pVTZ). 14 Considering the stationary geometries obtained with the BB1K and MP2 methods, singlepoint calculations were performed with coupled cluster theory considering single, double and connected triple excitations (CCSD(T)) 15 using the aug-cc-pVXZ (X=T,Q) 14 basis sets, which are denoted as aVXZ along this paper. To check the reliability of the CCSD(T) results, the T1 diagnostic was calculated for each geometry. Next, the results were extrapolated to the complete basis set (CBS) limit with the procedure by Halkier et al.,

ECBS =

[E(n) × n3 − E(n − 1) × (n − 1)3 ] [(n3 − (n − 1)3 ]

(1)

where n is equal 4 for the aVQZ basis set. The thermochemical properties calculated were the electronic reaction energy (∆E, electronic energy difference of the products and reactants), the enthalpy of the reaction at 0 K (∆H0◦ , ∆E +∆ZP E), classical barrier height (V ‡ , difference of the electronic energy between SP and reactants) and adiabatic barrier (∆VaG,‡ , V ‡ + ∆‡ ZP E). The connection of reactants, SPs and products were verified by means of the intrinsic reaction coordinate (IRC) 16 calculations. The thermal rate constants were calculated by transition state theory (TST) 17,18 and variational transitional state theory in the frame of improved canonical variational theory (ICVT). 19,20 The minimum energy path (Vmep ) required for this calculations was obtained

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employing the algorithm proposed by Page and McIver. 21 Considering the geometries along the Vmep , the harmonic frequencies and ZP Es were calculated to obtain the adiabatic energy path (VaG ). Next, to improve the reaction path in order to get a higher accuracy of the calculated rate constants, the electronic energy of the stationary points were corrected with the CCSD(T)/CBS single-point calculation results. This approach is well-known in the literature as variational transition state theory with interpolated single-point energies (VTST-ISPE). 22 Moreover, the tunneling effects were included with the Small Curvature Tunneling (SCT) method. 23 Finally, the rate constants for each elementary reaction obtained by the ICVT method were used to fit a modified Arrhenius equation. 24 All the electronic structure calculations were performed with the Gaussian 09 package 25 and the chemical kinetics calculations were carried out with the Polyrate 2008 26 and the Gaussrate 2009 27 codes. The last one interfaces the Gaussian and Polyrate packages.

Results and Discussion The bond lenghts of the R1, R2 and R3 stationary points structures optimized with MP2 and BB1K using the aVTZ basis set are shown in Figure 1 together with selected experimental data. The complete optimized geometries can be found in the Support material where the cartesian coordinates are provided. The equilibrium geometries obtained with the BB1K and MP2 methods can be compared with the experimental data. First considering the CH3 OH molecule, the larger difference is in the C – O bond length, equals to 0.025 Å to the distance obtained with the BB1K functional. For the NH and CH3 molecules, the differences between the experimental and calculated bond lengths are on the third decimal. Therefore, the obtained geometries are in good agreement with the available experimental data. Analyzing the SPs structures and considering the BB1K/aVTZ values, for SP2 the C – O bond stretches 0.5 Å if compared to

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0.956 (0.951) [0.961] 1.096 (1.082) [1.086]

R2

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+

1.427 (1.402) [1.424]

R3 R1

SP2

SP1 (1.925) [1.852]

1.079 (1.073) [1.075]

+

(0.963) [0.972]

SP3

(1.114) [1.110]

(1.650) [1.604]

(1.405) [1.426]

(1.377) [1.371]

(1.353) [1.377] (1.303) [1.325]

(1.201) [1.196]

+

1.036 (1.031) [1.031]

(0.952) [0.962] (1.348) [1.366]

+

Figure 1: Representation of elementary reactions R1, R2 and R3 with selected bond lengths (Å). Experimental values for CH3 OH 28 , CH3 29 and NH 30 are presented in the first line. The BB1K/aVTZ results are between parenthesis and the MP2/aVTZ values are between brackets. the methanol geometry, while the N – O bond length changes 0.3 Å from SP2 to the NOH molecule. Similar changes are present in R1 and R3. Considering SP1 and SP3 structures, the C – H bond stretches by at least 0.4 Å (comparing methanol and SP1 geometries), while the N – H bond length decreases by 1.7 Å (considering the SP3 and NH geometries). According to Hammond’s postulate, 31 on the reaction coordinate, the SPs should be closer to the products than to the reactants and it is expected an endothermic reaction. The calculated harmonic frequencies are listed in Table 1. All the SPs have only one imaginary frequency, characterizing first-order saddle points. The accuracy of this mode plays an important role in chemical kinetics calculations, since it is related to the curvature of the reactional path around the SP and consequently to the tunneling effects. 32 The difference of the imaginary frequency for the BB1K and MP2 methodologies are at least 400 cm−1 (SP3 ). In previous works, it was observed that the BB1K functional produces vibrational harmonic

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frequencies close to the ones obtained by the CCSD(T) method. 33,34 Table 1: Harmonic vibrational frequencies (cm−1 ) for the reatctants, saddlepoints and products calculated using BB1K (first line) and MP2 (second line) methods with aug-cc-pVTZ basis set. Molecule CH3 OH CH3 NOH CH3 O NH CH2 OH SP1 SP2 SP3

3972 3860 3359 3364 3797 3715 3107 3130 3366 3395 3966 3857 3130 3138 3895 3756 3960 3844

3185 3183 3359 3364 1293 1246 3062 3089

3119 3125 3173 3174 1182 1144 2986 3004

3342 3343 3097 3108 3335 3319 3245 3238

3199 3193 3031 3025 3318 3302 3124 3109

Harmonic Frequencies 3064 1537 1526 1505 1392 1199 1131 1084 310 3054 1536 1526 1492 1372 1184 1189 1057 290 1428 1428 516 1439 1439 488

1538 1397 1396 1164 1539 1433 1415 1126

981 989

740 809

1515 1509 1537 1535 3162 3143 1510 1503

563 623 1171 1167 1022 1101 1157 1156

426 433 1148 1115 713 787 1075 1094

1381 1368 1441 1454 1460 1474 1395 1378

1266 1213 1434 1436 1450 1466 1245 1243

1073 1067 1299 1169 1157 1204 1190 1184

1031 1017 658 725 1055 1067

793 721 421 513 553 580

677 669 245 279 484 478

147 149 233 257 311 303

131 134 107 121 142 138

945i 1823i 1141i 1666i 1658i 2066i

The IRC calculation was performed for each reaction path, starting at the saddle point and following the direction of the imaginary mode. This calculation confirmed the connection of the saddle point to the reactants and products of the reaction paths R1, R2 and R3. The classical and adiabatic barrier heights usually are the main factor in the accuracy of the rate constants. In this context, four DFT functionals (BB1K, M06-2X, M05-2X and B3LYP) and the MP2 method were tested. Also, single-point CCSD(T) calculations were performed considering the MP2 and BB1K optimized geometries, and all the thermochemical results are listed in Table 2. Moreover, to check the reliability of the CCSD(T) results, the T1 diagnostic was calculated for each geometry optimized with the BB1K functional. The larger value was found for the SP2 structure (0.036). According to Rienstra-Kiracofe, 35 if the T1 diagnostic value is lower than 0.044, the system is well described by a single-reference methodology. The T1 diagnostic values for all structures are found in the supplemental information. Thus, it is expected that the CCSD(T) method provides results with errors lower than the chemical accuracy 7



(1 kcal/mol) for the thermochemical properties. Table 2: Thermochemical properties (kcal/mol) for the R1, R2 and R3 reaction paths. The CCSD(T) results with the aVTZ and aVQZ basis sets are found in the supplemental information. Method BB1K/aVTZ M06-2X/aVTZ M05-2X/aVTZ B3LYP/aVTZ MP2/aVTZ CCSD(T)/CBS1 CCSD(T)/CBS2 Method BB1K/aVTZ M06-2X/aVTZ M05-2X/aVTZ B3LYP/aVTZ MP2/aVTZ CCSD(T)/CBS1 CCSD(T)/CBS2 Method BB1K/aVTZ M06-2X/aVTZ M05-2X/aVTZ B3LYP/aVTZ MP2/aVTZ CCSD(T)/CBS1 CCSD(T)/CBS2 1

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R1 ∆E ∆H0◦ 26.6 22.0 28.2 23.8 27.7 23.7 19.8 15.1 38.7 34.6 30.1 25.4 30.1 26.0 R2 ∆E ∆H0◦ 25.0 20.0 24.2 19.1 23.8 18.9 15.8 11.0 32.0 27.2 25.4 20.4 25.3 20.4 R3 ∆E ∆H0◦ 20.1 15.9 19.5 15.2 18.9 14.7 12.7 8.6 24.6 20.7 19.9 15.7 19.9 15.9

V ‡ ∆VaG,‡ 29.2 24.9 28.4 24.7 29.3 25.0 19.3 15.7 42.4 38.2 32.4 28.1 32.2 28.0 V ‡ ∆VaG,‡ 61.8 59.2 58.2 55.6 57.7 55.3 48.1 45.7 74.2 72.3 59.2 56.6 60.5 58.6 V ‡ ∆VaG,‡ 24.9 21.2 22.8 19.0 23.6 19.9 16.8 13.4 31.2 27.7 26.1 22.4 26.2 22.7

Single point calculations performed considering the BB1K/aVTZ optimized geometry. Single point calculations performed considering the MP2/aVTZ optimized geometry.

All calculations provide endothermic reactions for all paths with ∆H0◦ equal to 25.4−26.0 (R1), 20.4 (R2) and 15.7−15.9 (R3) kcal/mol (CCSD(T)/CBS), in agreement with Hammond’s postulate, 31 as discussed before. There is an excellent agreement between both CCSD(T)/CBS results obtained with the MP2 and BB1K optimized geometries for the adiabatic barrier height (∆VaG,‡ ). In ascending order, the obtained results are 22.4−22.7 (R3), 28.0−28.1 (R1) and 56.6−58.6 (R2) kcal/mol. This values indicates that R3 is the dominant path for the chemical kinetics. The adiabatic energy profile of the three reaction paths is presented in Figure 2. In an earlier work, 36 we discussed the chemical kinetic results sensitivity to the coupling of the high- and low-level methodologies, concluding that the thermochemical values should 8


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SP2 (56.6) 50

40

Energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


SP1 (28.1)

30

SP3 (22.4)

20

CH3O + NH (25.4) CH3+NOH (20.4) CH2OH + NOH (15.7)

10

0

CH3OH + N

Figure 2: Adiabatic energy profile for R1 to R3 reaction paths calculated with CCSD(T)/CBS//BB1K/aVTZ. be as close as possible between these methods to avoid excessive distortion in the reactional path and, consequently producing excessive amount of tunneling. In this context, comparing these results to the DFTs and MP2 ones, the B3LYP underestimates the barrier height and the MP2 overestimate it, as usual. The root-mean-square deviation for the BB1K, M052X and M06-2X functionals are 2.5, 2.4 and 2.8 kcal/mol, respectively. However, since it is expected that R3 to be the dominant reaction path and the BB1K functional results are the closest ones among the density functionals, it will be used for the chemical kinetic calculations. The reactional paths were built using the VTST-ISPE methodology. The BB1K/aVTZ method was employed to calculate the minimum energy path (Vmep ). Next, the CCSD(T)/ CBS//BB1K/aVTZ single-point values were used to improve the classical barrier (V ‡ ) and the energy of the reaction (∆E). The ZP Es required to obtain the adiabatic barrier (∆VaG,‡ ), enthalpy of the reaction at 0 K (∆H0◦ ) and build the adiabatic energy path (VaG ) were calculated with the BB1K functional. The Vmep and VaG for R1 to R3 are shown in Figure 3. All reactional paths show smooth variation, indicating that the methodology is adequate. The results for the thermal rate constants calculated with TST and ICVT methods, and considering tunneling effects for the last with the SCT approximation, are listed in Table 3. It is important to point that the three hydrogens from the methyl group of methanol

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90 80 70 Energy [kcal/mol]

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R1 Vmep R1 VaG R1 Vmep

60

R1 VaG R3 Vmep

50

R3 VaG

40 30 20 10 0 −2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

s [(amu)1/2 Å)]

Figure 3: Vmep and VaG for R1-R3 calculated using a dual-level methodology employing BB1K/aVTZ as the low-level and CCSD(T)/CBS//BB1K/aVTZ as the high-level. were considered equivalent. As a consequence, the symmetry number for the rate constant calculation for R3 is equal 3, while for R1 and R2 it is equal 1. Moreover, the rotation of the OH, CH3 (in the CH3 OH and SPs) and CH2 (in the CH2 OH) groups were treated with the hindered-internal-rotor approximation. Considering the frequencies order in Table 1, this rotation is the 12th vibrational mode in methanol, 14th in SP1 and SP2 , 12th in SP3 and 9th in CH2 OH. The whole set of results for the rate constants and the equilibrium constants are found in the supplemental information. The variational effect is given by the ratio of the rate constants calculated with the ICVT and TST methodologies, that is, a smaller ratio means a larger variational effect. This ratios are is equal to 0.65 (R1), 0.97 (R2) and 0.96 (R3) at 300 K. A larger variational effect for R1 is expected due to its smaller imaginary (945i) frequency that implies in a flatter surface around the SP. Moreover, this effect becomes negligible for R1 above 1000 K and is negligible for R2 and R3 above 400 K. The tunneling contributions for the rate constants can be obtained from the ratio of the ICVT/SCT and ICVT results. At 300 K, these contributions are equal to 1.82, 5.75 and 11.9 for R1, R2 and R3, respectively. A larger tunneling for R3 is also expected, since it presents a larger imaginary frequency (1658i), resulting in a narrower curve around SP3 and consequently a larger tunneling.

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Table 3: Thermal rate constants (cm3 · molecule−1 · s−1 ) for the R1, R2 and R3 reaction paths. T (K) 250 300 400 700 1000 2000

TST 1.2×10−36 1.7×10−32 3.0×10−27 2.4×10−20 1.8×10−17 8.0×10−14

T (K) 250 300 400 700 1000 2000

TST 1.5×10−61 3.4×10−53 1.1×10−42 6.1×10−29 2.7×10−23 1.6×10−16

T (K) 250 300 400 700 1000 2000

TST 3.1×10−31 6.5×10−28 1.0×10−23 4.0×10−18 9.6×10−16 1.1×10−12

R1 ICVT 6.7×10−37 1.1×10−32 2.4×10−27 2.3×10−20 1.8×10−17 8.0×10−14 R2 ICVT 1.5×10−61 3.3×10−53 1.1×10−42 6.0×10−29 2.6×10−23 1.6×10−16 R3 ICVT 3.0×10−31 6.3×10−28 1.0×10−23 3.9×10−18 9.5×10−16 1.1×10−12

ICVT/SCT 1.5×10−36 2.0×10−32 3.3×10−27 2.5×10−20 1.9×10−17 8.1×10−14 ICVT/SCT 4.4×10−60 1.9×10−52 2.4×10−42 7.5×10−29 2.9×10−23 1.6×10−16 ICVT/SCT 9.2×10−30 7.5×10−27 4.3×10−23 6.6×10−18 1.2×10−15 1.1×10−12

Considering the ICVT/SCT rate constants as our best results, these values were taken to fit a modified Arrhenius equation in the range of 250 − 2000 K. The results are in Table 4. −Ea

Table 4: Parameters for the modified Arrhenius equation (k(T ) = A × T b × e RT ). Units for k and Ea are cm3 · molecule−1 · s−1 and kcal/mol, respectively, and R = 1.98 × 10−3 kcal · mol−1 · K −1 A R1 5.00 × 10−18 R2 1.18 × 10−23 R3 9.80 × 10−22

b Ea 2.17 27.06 3.94 52.51 3.37 18.39

The results for the rate constants, the branching ratio at 300 K is given by 0.00:0.00:1.00 for R1:R2:R3. At 2000 K, R3 is still the most important path, being the branching ratio equals to 0.07:0.00:0.93. Therefore, the hydrogen abstraction from the methyl group (R3) is the most important reaction path among the ones studied for the CH3 OH + ( 4S)N reactional system. 11



A comparisson can be carried out considering the present total rate constants and the results for the CH3 OH + O and CH3 OH + H reactions, 37,38 At 300 K the, the rate constants are equal to 7.5 × 10−27 , 1.4 × 10−14 and 6.6 × 10−16 cm3 · molecule−1 · s−1 for the reactions with N, O and H. At 2000 K, the difference decreases and the thermal rate constant values are equal to 1.2 × 10−12 (N), 4.1 × 10−11 (O) and 4.8 × 10−11 (H). Therefore, in environments where atomic oxygen and hydrogen are also present, the reaction of methanol and atomic nitrogen must has a minor effect, specially at low temperatures. At 2000 K, the nitrogen must be at least 34 times more abundant than the other species for this reaction to consume as much methanol as the one with atomic oxygen.

Conclusion The thermochemical properties were calculated for three elementary reactions considering the CH3 OH + ( 4S)N reaction with four DFT functionals, MP2 and CCSD(T) methods. The hydrogen abstraction from the methyl group (R3) presents the lowest adiabatic barrier height (22.4 kcal/mol) followed by the hydrogen abstraction from the hydroxyl group (R1, 28.1 kcal/mol), and the C – O bond break (R2, 56.6 kcal/mol). The thermal rate constants were calculated with a variational transition state theory, in the frame of ICVT considering tunneling corrections with the SCT approximation. At 300 K, kR3 = 7.5×10−27 and is higher than kR1 by 5 orders of magnitude. The R3 path keeps its importance at high temperatures, e.g. at 2000 K it corresponds to 93% of the methanol consumption among the elementary reactions studied. Also, a comparison of the thermal rate constants was carried out with the values obtained for the CH3 OH + O and CH3 OH + H reactions. The thermal rate constants for the title reaction are lower than the reactions with atomic oxygen and hydrogen by at least 11 orders of magnitude at 300 K and one order of magnitude at 2000 K. Therefore, the title reaction has a minor effect to the methanol consumption in environments where atomic hydrogen and

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oxygen are present. Moreover, the rate constants were fitted to a modified Arrhenius equation. We believe our results present high accuracy and can be added to mechanisms involving methanol decomposition in atmospheric environment and combustion reactors.

Supporting Information Available This work includes Supporting Information containing Cartesian coordinates (in Å) and the T1 diagnostic values for all stationary points, thermochemical results obtained with CCSD(T)/AVXZ (X=T, Q) methodology, considering the optimized geometries with the BB1K/AVTZ and MP2/AVTZ approachs and the equilibrium constants for the R1, R2 and R3 reaction paths.

Acknowledgement We acknowledge the support by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under Grant Nos. 2017/07707-3, and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grants Nos. 307052/2016-8, 404337/2016-3, 480119/20120, 304789/2016-0. We also acknowledge the fellowship support from Universidade Federal do Espírito Santo (UFES).

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