Article pubs.acs.org/JPCA

Hydrogen Abstraction from the Hydrazine Molecule by an Oxygen Atom Rene F. K. Spada,†,‡,# Luiz F. A. Ferraõ ,† Roberta J. Rocha,† Koshun Iha,† José A. F. F. Rocco,† Orlando Roberto-Neto,§ Hans Lischka,*,∥,⊥ and Francisco B. C. Machado*,†,# †

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 § Divisão de Aerotermodinâmica e Hipersônica, Instituto de Estudos Avançados, São José dos Campos, 12.228-001 São Paulo, Brazil ∥ Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States ⊥ Institute for Theoretical Chemistry, University of Vienna, A-1090 Vienna, Austria ‡

S Supporting Information *

ABSTRACT: Thermochemical and kinetics properties of the hydrogen abstraction from the hydrazine molecule (N2H4) by an oxygen atom were computed using high-level ab initio methods and the M062X DFT functional with aug-cc-pVXZ (X = T, Q) and maug-cc-pVTZ basis sets, respectively. The properties along the reaction path were obtained using the dual-level methodology to build the minimum energy path with the potential energy surface obtained with the M062X method and thermochemical properties corrected with the CCSD(T)/CBS//M06-2X/maug-cc-pVTZ results. The thermal rate constants were calculated in the framework of variational transitionstate theory. Wells on both sides of the reaction (reactants and products) were found and considered in the chemical kinetics calculations. Additionally, the product yields were investigated by means of a study of the triplet and singlet surfaces of the N2H4 + O → N2H2 + H2O reaction.

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expression k = (7.35 ± 2.16) × 10−13 exp[(640 ± 60)T−1] cm3 molecule−1 s−1, whereas Gehring et al.12,13 found a positive dependence with the temperature, k = 1.4 × 10−10 exp[(−604 ± 60)T−1] cm3 molecule−1 s−1. There is also a main difference in the setup of the experiments. Gehring et al.12,13 measured the hydrazine consumption in an atmosphere of oxygen and reported N2H2 and H2O as the main product, whereas Vaghjiani17,18 measured the oxygen depletion in an atmosphere of N2H4 in excess. As far as we know, there is only one theoretical study for the set of the three N2H4 + O reaction paths,19 which are the dehydrogenation reaction path, the N−N bond breaking and the hydrogen elimination. In that work, Troya and O’Neill employed the B3LYP and the BHandHLYP density functionals and the second-order Møller−Plesset theory (MP2) with the 631G* and aug-cc-pVDZ basis set to optimize the geometries of the reactants, products, and saddle point, followed by singlepoint calculations using the coupled cluster theory with single,

INTRODUCTION The reaction of hydrazine (N2H4) with isolated atoms and radicals plays an important role in combustion and decomposition processes. In particular, several spacecrafts use fuels based on hydrazine and its derivatives as propellant.1,2 Due to the importance of hydrazine, our group has previously investigated theoretically its properties and some elementary dehydrogenation reactions involved in the hydrazine decomposition.3−9 Reactions of the atomic oxygen (O(3P)) with hydrazine have received special attention,10−19 mainly because the unburned monopropellant (N2H4) used in the spacecraft vehicles, as well as in satellites, is ejected into the low atmosphere where ground-state atomic oxygen is abundant. Therefore, the studies of the chemical transformation processes that occur in the low Earth orbit, above 180 km with temperature around 880 K, are very important.17,18 Some experimental measurements of the thermochemical properties were reported by Foner and Hudson,10,11 and the total rate constants have been reported close to room temperature.12−15,17,18 For the temperature ranges 243−463 K12,13 and 243−423 K17,18 the Arrhenius equation was applied; however, the determined Arrhenius parameters differ significantly between different measurements. Vaghjiani17,18 measured a negative temperature dependence, which leads to the © XXXX American Chemical Society

Special Issue: 25th Austin Symposium on Molecular Structure and Dynamics Received: August 1, 2014 Revised: September 5, 2014

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employed. In the improved canonical variational theory (ICVT) models,25,26 the calculation of the free energy along the whole reaction path is required and, to avoid excessive computational effort, it is usual to employ the dual-level methodology.27 This approach involves the use of two levels of calculation, a low level to calculate the reaction path and zero point energy (ZPE) contributions, and a high level to calculate the classical barrier height and the reaction energy. The reaction paths were obtained by the dual-level methodology, using M06-2X/maug-cc-pVTZ method as the low level and the CCSD(T)/CBS results as the high level. For the hydrogen abstraction from N2H4, the rate constants were obtained for the range from 250 to 3000 K using TST and ICVT, with small curvature tunneling (SCT)28 approximations. The rate constants were used to obtain the parameters for the modified Arrhenius equation.

double, and quasiperturbative treatment of the connected triple excitations, and extrapolating the results for the complete basis set limit (CCSD(T)/CBS) to obtain improved values of the barrier heights and reaction energies. They also evaluated several reaction-dynamics properties, such as cross sections and product-energy distributions using quasiclassical trajectory calculations at the BHandBLYP/6-31G* level. They considered the hydrogen abstraction reaction paths as the most important one. However, Troya and O’Neill19 reported the results of the hydrogen abstraction for only one reaction path. Because the hydrazine molecule possesses C2 symmetry, there are two different hydrogen atoms to be abstracted, inner and outer with respect to the C2 axis, which will be referred to as Hin and Hout, respectively (Figure 1). In the present study, we have characterized both hydrogen abstraction reaction paths. In this process we have found a reactant well (RW), as well as a product well (PW), which were considered in the chemical kinetic calculations. Also, we have explored some possible reaction paths that should lead to N2H2 + H2O as the main product of the N2H4 + O reaction, as suggested by previous experimental works.10−13 For that, we search for a saddle point for the two simultaneous hydrogen abstraction reaction paths, and also the consecutive dehydrogenation reaction from the N2H3 + OH in a singlet surface, and other paths involving the triplet and singlet surfaces including a possibility of intersystem crossings. To study the abstraction of the Hin and Hout atoms, two triplet reaction paths are proposed, described in reactions Rin and Rout, SPin

N2H4 + O ⎯→ ⎯ N2H3 + OH SPout

N2H4 + O ⎯⎯⎯→ N2H3 + OH

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METHODOLOGY To obtain the properties of the stationary points for reaction paths Rin, Rout, R1, and R2, the reactants, products, reactant wells (RW), product wells (PW), and saddle points (SP) were optimized using the M06-2X20,21 functional with the maug-ccpVTZ basis set,22 which will be abbreviated as maTZ along the text. The equilibrium geometries were also identified by vibrational analysis. The energetic properties calculated were the classical barrier height (V‡, electronic energy difference between the reactants and the saddle point), the adiabatic ‡ barrier height (ΔVG,‡ a , defined as V + ΔZPE), the electronic energy of the reaction (ΔE), the enthalpy of the reaction at 0 K (ΔH = ΔE + ΔZPE), and the electronic energy and enthalpy at 0 K to the RW (ΔERW and ΔHRW) and PW (ΔEPW and ΔHPW). To improve the results for the reaction properties ΔE, ΔERW, ΔEPW, and V‡, single-point frozen-core CCSD(T) calculations were performed with the aug-cc-pVXZ (X = T, Q) basis sets,29 abbreviated as aXZ, using the geometries obtained in the M062X calculations, and the results were extrapolated to the CBS limit using the procedure proposed by Halkier et al., eq 1,30

(Rin) (Rout)

where SPin and SPout, respectively, represent the two differents saddle points which connects the reactants with the products. The study of the hydrogen abstractions of the N2H3 radical by OH, which leads to N2H2 as a product, was studied by the R1 and R2 reaction paths. SP1

N2H3···OH → N2H 2 + H 2O SP2

N2H3 + OH ⎯→ ⎯ cis‐N2H 2 + H 2O

ECBS =

(R1)

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

(1)

where n is equal 4 for the aug-cc-pVQZ (aQZ) basis set. To verify the capability of the CCSD(T) method to describe the reaction properties, the T1 diagnostic31 was calculated in the geometries obtained with the M06-2X functional. This diagnostic takes into account the single excitations on the CCSD method to estimate the multireference character of the system, and according to Lee and Taylor,31 a value higher than 0.02 indicates a certain MR character, but Rienstra-Kiracofe et al.32 have argued that systems with T1 diagnostic values lower than 0.044 may be characterized with single reference wave function methods. Intrinsic reaction coordinate (IRC)33 calculations were carried out with the M06-2X method to verify the connections of the transition states with reactants and products. The singlet potential curve from SPin to PW of the Rin reaction path was also calculated using the structures of the triplet IRC. To test the singlet stability for this calculations and for the R2 reaction path, we performed the restricted and unrestricted calculations. To obtain the minimum energy path (Vmep) for both reaction paths the algorithm proposed by Page and McIver34 was employed. Next, the frequencies and ZPE contributions were calculated along the reaction path, using the same level of

(R2)

The reactant of reaction R1 is the PW (N2H3···OH) from the Rin and Rout reaction paths on the triplet surface whereas the reactants for reaction R2 are the uncoupled N2H3 and OH radicals, which couples on the singlet surface. In this study we use the M06-2X20,21 density functional with the maug-cc-pVTZ22 basis set to characterize the stationary states of all reaction paths. To compute more accurate values of the barrier heights and reaction energies, we employed the coupled cluster theory, in particular the coupled cluster with the single and double excitations and a quasiperturbative treatment of the connected triple excitations, denoted as CCSD(T),23 including their extrapolation to a complete basis set (CBS) limit using the M06-2X optimized geometries. In the rate constants calculation, the transition-state theory (TST)24 assumes a transition state located at the saddle point, in this sense, accurate values for the stationary points are the main factor to determine the rate constants. However, it is wellknown that the transition state is located at the free energy maximum along the reaction path. To locate better transition states, the variational transition-state theory (VTST) may be B

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Figure 1. Reaction paths for the N2H4 + O with some selected bond lengths (Å) calculated with the M06-2X/maTZ methodology.

Table 1. Harmonic Frequencies (cm−1) for the Stationary Points Involved in the Rin and Rout Reaction Paths Calculated with the M06-2X.maTZ Methodology frequencies N2H4 N2H3 OH SPin SPout RW PW

3610 828 3676 3752 3613 781 3644 724 3622 815 3669 485

3605 453 3525

3503

3498

1689

1675

1333

1306

1142

3447

1659

1488

1286

1144

708

520

3550 561 3567 366 3605 452 3535 470

3436 306 3532 281 3515 192 3499 241

2558 127 2561 102 3509 178 3495 113

1672 460i 1674 497i 1678 113 1667 71

1588

1394

1199

1110

849

1606

1396

1219

1149

886

1668

1329

1296

1149

954

1477

1319

1147

699

592

theory, to obtain the adiabatic energy curve (VGa ). To obtain more accurate rate constants, the electronic properties of the reaction paths were corrected with the CCSD(T)/CBS//M062X/maTZ results, this procedure is known as dual-level methodology, in particular variational transition-state theory with interpolated single-point energies (VTST-ISPE).27 Using this methodology to build the energy surfaces for the reaction paths Rin and Rout, the rate constants were calculated employing the TST and ICVT approaches, and the nonclassical effects were considered within the SCT correction. The results obtained with the ICVT/SCT methodology were used to calculate the three parameters Arrhenius equation, given by k(T ) = AT be−Ea / RT

974

and the results for the harmonic frequencies for each equilibrium geometry are presented in Table 1. The whole set of geometric parameters are available in the Supporting Information. To estimate the multiconfigurational character of these molecules, the T1 diagnostic was calculated and the results are presented in the Supporting Information. All the values are lower than 0.044, the limit proposed by RienstraKiracofe et al.32 According to Hammond’s postulate,38 if the SP is similar to the reactant, the reaction presents a low barrier and is of high exoergicity. The equilibrium geometries presented in Figure 1 show that the lengths of the N−H bonds are equal to 1.069 (SPin) and 1.061 (SPout), similar to the reactants, which are equal to 1.013 and 1.010 for Hin and Hout, respectively. The O− H bond length is about 1.53 Å, 1.57 times longer than the OH product bond length. This is not the case for the reaction of the hydrogen abstraction from hydrazine by a nitrogen atom,8 where the SP’s N−H bond length is about 1.28 Å, and therefore the SP’s are not similar to the reactants. So, for the reaction N2H4 + O, a lower barrier is expected and more energy is expected to be released. The frequency analysis in Table 1 shows that both SP’s present only one imaginary frequency and correspond to the hydrogen abstraction vibrational mode, confirmed by the IRC calculation. This calculation also confirmed that both SPin and SPout lead to the same reactant well (RW) and product well (PW), structures with lower energies than the reactants and products, respectively.

(2) b

where A is a pre-exponential constant, T is the pre-exponential temperature dependent factor, Ea is the activation energy, and R is the ideal gas constant. All the electronic structure calculations were performed using the Gaussian 0935 package and the chemical kinetics properties were obtained with the Polyrate 2008 program.36 The Vmep and VGa curves were obtained with the Gaussrate 2009 package,37 which interfaces the Polyrate and Gaussian programs.

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RESULTS AND DISCUSSION Rin and Rout Reaction Paths. The thermochemistry properties were obtained optimizing the geometries for the stationary points using the M06-2X approximation to the DFT together with the maTZ basis set. A representation of these structures with selected bond lengths are presented in Figure 1, C

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using the M06-2X/maTZ as the low level and the CCSD(T)/ CBS//M06-2X/maTZ as the high level. The Vmep and VGa for Rin and Rout are presented in Figure 3.

Generally, the classical and adiabatic barrier heights are the main factor to obtain reliable rate constants, and in this sense we performed single-point calculations with the CCSD(T) methodology and extrapolated the results to the CBS limit. The results for the thermochemical properties are presented in Table 2, and the energy profile for this reactions calculated with the CCSD(T)/CBS//M06-2X/maTZ is presented in Figure 2. Table 2. Thermochemical Properties (kcal/mol) for the Rin and Rout Reaction Pathsa method

ΔE

ΔH

ΔERW

ΔHRW

ΔEPW

ΔHPW

M06-2X/maTZ CCSD(T)/aTZb CCSD(T)/aQZb CCSD(T)/CBSb

−17.7 −16.0 −16.9 −17.6

−21.2 −19.4 −20.3 −21.0

−4.5 −2.4 −2.4 −2.3

−3.9 −1.7 −1.7 −1.7

−25.7 −23.0 −24.0 −24.7 Rout

−27.3 −24.6 −25.6 −26.3

Rin ‡

method

V

M06-2X/maTZ CCSD(T)/aTZb CCSD(T)/aQZb CCSD(T)/CBSb

−1.5 2.4 2.1 1.9

ΔVG,‡ a

V‡

ΔVG,‡ a

−2.7 1.2 0.9 0.7

0.7 4.6 4.4 4.2

−0.6 3.3 3.1 2.9

Figure 3. Vmep and VGa for the Rin and Rout reaction paths calculated with the M06-2X/maTZ methodology and corrected with ΔE and V‡ obtained with the CCSD(T)/CBS//M06-2X/maTZ.

The rate constants were calculated using the TST and ICVT approaches, and for the latter, the SCT correction for nonclassical effects was employed. The results are presented in Tables 3 and 4. The ratio of TST and ICVT rate constants

a

All energies are relative to the reactants N2H4 + O. bAll the CCSD(T) calculation were performed considering the M06-2X/maTZ optimized geometry.

Table 3. Rate Constants (cm3 molecule−1 s−1) for the Rin Reaction Path temp (K) 250 300 400 500 600 700 800 900 1000 1500 2000 2500 3000

Figure 2. Adiabatic energy profile for the N2H4 + O reaction calculated with the CCSD(T)/CBS//M06-2X/maTZ methodology.

The results for ΔE and ΔH obtained with the M06-2X/ maTZ approach are equal to −17.7 and −21.2 kcal/mol, respectively, whereas CCSD(T)/CBS//M06-2X/maTZ predicts the values of −17.6 kcal/mol for ΔE and −21.0 kcal for ΔH. For the stabilization energies of RW and PW, the M06-2X predicts higher values than the CCSD(T) methodology. For the classical barrier heights, the values obtained with the M062X functional is negative for Rin (−1.5 kcal/mol) and positive for Rout (0.7 kcal/mol), whereas the values obtained with CCSD(T)/CBS are both positive, 1.9 and 4.2 kcal/mol for Rin and Rout, respectively. In this sense, the results presented in Table 2 are in good agreement with Hammond’s postulate.38 Troya and O’Neill19 reported an adiabatic barrier height of 1.24 kcal/mol and ΔH equals to −20.8 kcal/mol, which are in good agreement with our results (0.7 and 2.9 for ΔVG,‡ and −21.0 a kcal/mol for ΔH) . However, they only studied one reaction path for the hydrogen abstraction and did not consider the reactant and product wells (RW and PW). To build the electronic and adiabatic energy surfaces, Vmep and VGa , respectively, the dual-level methodology was employed,

TST 2.54 3.37 5.22 7.33 9.70 1.23 1.52 1.84 2.18 4.28 6.98 1.02 1.39

× × × × × × × × × × × × ×

10−12 10−12 10−12 10−12 10−12 10−11 10−11 10−11 10−11 10−11 10−11 10−10 10−10

ICVT 9.13 1.44 2.76 4.40 6.30 8.46 1.08 1.35 1.63 3.36 5.57 8.18 1.11

× × × × × × × × × × × × ×

10−13 10−12 10−12 10−12 10−12 10−12 10−11 10−11 10−11 10−11 10−11 10−11 10−10

ICVT/SCT 1.39 1.93 3.25 4.89 6.79 8.93 1.13 1.39 1.67 3.40 5.61 8.22 1.12

× × × × × × × × × × × × ×

10−12 10−12 10−12 10−12 10−12 10−12 10−11 10−11 10−11 10−11 10−11 10−11 10−10

Table 4. Rate Constants (cm3 molecule−1 s−1) for the Rout Reaction Path temp (K) 250 300 400 500 600 700 800 900 1000 1500 2000 2500 3000 D

TST 4.35 1.26 5.24 1.34 2.66 4.52 6.93 9.92 1.35 3.97 7.91 1.30 1.92

× × × × × × × × × × × × ×

10−14 10−13 10−13 10−12 10−12 10−12 10−12 10−12 10−11 10−11 10−11 10−10 10−10

ICVT 2.22 7.50 3.75 1.06 2.18 3.86 6.10 8.90 1.23 3.73 7.52 1.25 1.84

× × × × × × × × × × × × ×

10−14 10−14 10−13 10−12 10−12 10−12 10−12 10−12 10−11 10−11 10−11 10−10 10−10

ICVT/SCT 4.58 1.22 4.90 1.26 2.45 4.21 6.51 9.37 1.28 3.80 7.60 1.25 1.85

× × × × × × × × × × × × ×

10−14 10−13 10−13 10−12 10−12 10−12 10−12 10−12 10−11 10−11 10−11 10−10 10−10

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this abstraction, which are represented in R1 and R2 (Figure 4). The R1 reaction path occurs on the triplet surface. It starts with the PW from the Rin and Rout reaction paths as reactant to abstract another hydrogen to form N2H2(3B) with C2 symmetry (the C2v 3B1 structure is 13.2 kcal/mol higher) plus water in the 1 A1 state through the saddle point SP1. The R2 reaction path continues on the singlet surface having the dissociated N2H3 and OH radicals as the reactants. It leads to the final products cis-N2H2(1A1) state with C2v symmetry plus 1A1 water through the formation of a reactant well (RW2) and followed by the saddle point SP2. Also, we explored the possibility of an intersystem crossing at an earlier stage of the reaction along the reaction path from SPin to PW of the Rin reaction path to lead to a stable structure of the PW on the singlet surface. For that, we have constructed a singlet potential curve in that region (Figure 6). The stationary geometries with selected bond lengths are presented in Figure 4, the thermochemistry results are presented in Table 6 and the energy profile is presented in Figure 5. The whole set of geometries, harmonic frequencies, and results for the T1 diagnostic are presented in the Supporting Information. All the values for the T1 diagnostic are in the interval from 0.010 (H2O) to 0.032 (N2H2(3B)), lower than the limit 0.044 suggested by Rienstra-Kiracofe et al.32 The CCSD(T)/CBS//M06-2X/aTZ results (best estimate) in Table 6 and Figure 5 show that the R1 reaction path presents values of ΔE and ΔH equal to −22.3 and −25.1 kcal/mol, respectively, but it leads to the triplet N2H2 conformer as product, which has C2 symmetry. It presents a classical barrier height of 11.2 kcal/mol and an adiabatic barrier of 8.4 kcal/mol. In the R2 reaction path, the energy difference of the PW and the dissociated products N2H3 + OH is 5.3 kcal/mol, lower than ΔVG,‡ for R1, the classical and adiabatic barrier for R2 are a negative, presenting values of −21.5 and −18.3 kcal/mol, respectively. There is a formation of a complex (RW2) between the reactants and the SP2, with a stabilization energy of −20.3 kcal/mol with respect to the N2H3 + OH reactants. The adiabatic barrier from RW2 to SP2 is equal 2.0 kcal/mol and leads to the most stable products cis-N2H2 and H2O(1A1) with an exothermic ΔE equal to −68.2 and ΔH equal to −67.2. Thus, this reaction is significantly more exothermic than R1. Because the adiabatic barrier for SP2 is negative (−18.3 kcal/ mol), the rate constant for the R2 reaction path may be much larger than the ones for Rin and Rout. Foner and Hudson10,11 reported the ΔH of the reaction N2H4 + O → N2H2 + H2O equals −90 kcal/mol. Considering the same reactants, our present CCSD(T)/CBS calculations provide ΔH values for the products of the R1 reaction path equals to −51.4 kcal/mol, whereas for the products of R2 is −88.2 kcal/mol. These results suggest that Foner and Hudson10,11 measured the products on the singlet surface. As stated above, we also investigated the possibility of a direct intersystem crossing starting from the saddle point SPin of Rin reaction path on the triplet surface to PW on the singlet surface. For that, we performed unrestricted DFT/M06-2X/ maTZ singlet calculations using the triplet geometries along the reaction path between SP1 and PW. The results are presented in Figure 6. The optimized PW singlet structure becomes 1.5 kcal/mol lower than the PW of the triplet system. As the singlet excited state of the oxygen is 45.4 kcal/mol higher than the ground-state oxygen (O(3P)),39 the starting point of our singlet scan at SPin (Figure 6) presents a higher energy than for the

shows that the variational effects are important for both reaction paths, because the rate constant calculated at 300 K with the TST approach is higher by a factor of 2.3 for Rin and 1.68 for Rout than the calculated one using ICVT. Analyzing the nonclassical effects for Rin, the tunneling raises the rate constant especially at low temperatures and dominates the nonclassical reflection in the whole range of temperatures, because the rate constants calculated considering these effects are higher than the ones calculated with the ICVT approach. However, these effects become negligible above 800 K. For Rout the tunneling also plays an important role at low temperatures, but it becomes negligible at 1000 K. Considering the ICVT/SCT results, the rate constants for Rin are higher than for Rout up to 1500 K, which was expected because the barrier heights for the former reaction path are lower. However, above this temperature, the rate constants for Rout become higher. Note that after including both variational (ICVT) and tunneling effects (SCT), due to compensation factors, the ICVT/SCT rate constants are in good agreement with the TST results, mainly for the Rout path. A comparison of our computed reaction constants (2.05 × 10−12 for kin + kout at 300 K) with the experimental ones obtained by Gehring et al.12,13 (18.7 × 10−12 cm3 molecule−1 s−1 at 300 K), Shane and Brennen14 (3.0 ± 1.5 × 10−12 cm3 molecule−1 s−1 at 295 K), Lang15 (9.9 ± 0.12 × 10−12 cm3 molecule−1 s−1 at 296 K), and Vaghjiani17,18 (6.1 × 10−12 cm3 molecule−1 s−1 at 298 K) show that our result is consistent with the experimental results14,17,18 but closer to the ones reported by Shane and Brennen.14 Based also on the other experimental results, the value obtained by Gehring et al.12,13 seems to be too large. The ICVT/SCT results were used to find the three parameters of the Arrhenius equation, eq 2, in the temperature range 250−3000 K. The results for Rin and Rout are listed in Table 5. Vaghjiani17,18 observed a negative dependence of the Table 5. Parameters for Arrhenius Equation k(T) = ATbe−Ea/RT for the Rin and Rout Reaction Pathsa reaction path Rin Rout

A −16

1.26 × 10 1.15 × 10−16

b

Ea

1.71 1.83

0.08 2.05

a The units for k and Ea are cm3 molecule−1 s−1 and kcal/mol, respectively.

temperature with the rate constant in the temperature range 243−423 K. We could not observe this effect in the Rin and Rout elementary reactions. In this sense, the negative temperature dependence may be caused by an effect that was not considered in the present calculations. Product Yields. In this section we explore some reaction paths that should lead to N2H2 + H2O as the main product of the N2H4 + O reaction, as suggested by experimental works.10−13 First, we tried to find a saddle point that leads to the removal of two hydrogen atoms by oxygen simultaneously using the M06-2X/maTZ methodology, without success. Potential energy surface calculations were performed; however, they showed that the preferable reaction path is Rin, or they occur with a conformer of hydrazine as reactant, but still abstracting only one hydrogen atom. Therefore, we studied the consecutive hydrogen abstraction of the N2H3 molecule by the OH radical as an alternative to the simultaneous abstraction of two hydrogen atoms. Two reaction paths were proposed for E

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Figure 4. Reaction paths for the N2H3 + OH with some selected lengths (Å) calculated with the M06-2X/maTZ methodology.

Table 6. Thermochemical Properties (kcal/mol) for the R1 and R2 Reaction Pathsa R1 method

V‡

ΔVG,‡ a

ΔE

ΔH

M062X/maTZ CCSD(T)/aTZb CCSD(T)/aQZb CCSD(T)/CBSb

10.6 11.1 11.1 11.2

7.9 8.3 8.4 8.4

−21.1 −21.0 −21.7 −22.3

−24.0 −23.9 −24.6 −25.1

R2 method

ΔE

ΔH

ΔERW2

ΔHRW2

V‡

ΔVG,‡ a

M062X/maTZ CCSD(T)/aTZb CCSD(T)/aQZb CCSD(T)/CBSb

−63.9 −66.3 −67.4 −68.2

−63.0 −65.4 −66.5 −67.2

−23.6 −24.8 −25.6 −26.2

−17.7 −18.9 −19.7 −20.3

−14.4 −20.0 −20.9 −21.5

−11.2 −16.9 −17.7 −18.3

The energies are relative to N2H3···OH (PW) and N2H3 + OH, respectively. bAll the CCSD(T) calculation were performed considering the M062X/maTZ optimized geometry.

a

Figure 6. Singlet and triplet potential curves calculated considering the geometries of the Rin reaction path. The energies between 3.5 and 4.0 Å are for the PW. All energies are relative to the N2H4 + O reactants and were calculated with the M06-2X/maTZ methodology. Figure 5. Adiabatic energy profile for R1 and R2 reaction paths calculated with the CCSD(T)/CBS//M06-2X/maTZ methodology.

geometry reveals that the singlet state is 1.4 kcal/mol lower than the triplet one. Therefore, an intersystem crossing can occur, leading by an intermolecular reorganization of the singlet coupled N2H3···OH (PW) to the minimum RW2 and consequently via SP2 to cis-N2H2 + H2O.

triplet state. Both singlet and triplet potential curves presented in Figure 6 show a close approach with the singlet slightly higher, but a singlet single-point calculation at the triplet PW F

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It is our hope that the results reported in this work encourage further development for the hydrazine decomposition mechanism at the atmosphere.

It is of great interest to determine whether the character of the singlet state is open shell or closed shell. For that purpose, unrestricted open shell and restriced closed shell calculations were performed along the reaction paths SPin to PW described above (see also Figure 3) and for the singlet path R2 (Figure 4). Moreover, a stability analysis of the restricted wave function was performed as described in the section on Methodology. For the SPin to PW path the singlet open shell potential curve (Figure 6) is significantly more stable than the closed shell one. At the SPin structure, the difference between the two curves is 19.2 kcal/mol and at the PW structure it is 45.9 kcal/mol. However, for the singlet R2 reaction path the reactant well has a N −O bond distance equal to 1.5 Å (RW2, Figure 4) and presents a closed shell character. The reactant (N2H3 + OH) is a two radical system with an open shell electronic structure. To determine where between this singlet open shell structure and the closed shell RW2 minimum the change in the character of the electronic wave function occurred, a potential energy curve was constructed varying the N−O distance from 3.0 to1.5 Å to connect the dissociated reactants with the region of RW2. The stability analysis40 showed that this transition occurred at a N−O distance of ∼1.8 Å. The stability analysis further showed that in continuation from RW2 also the saddle point (SP2) possessed closed shell character, with a N−O distance already elongated to 2.0 Å. The possibility of an intersystem crossing can make the reaction path on the singlet surface even more efficient. In this context, it is possible that Gehring et al.12,13 and Foner and Hudson10,11 could not measure a significant presence of the N2H3 and OH products because the reaction of these radicals occurs much faster than the reaction involving hydrazine and oxygen. Therefore, the N2H4 + O → N2H3 + OH reaction, which occurs through Rin and Rout reaction paths, is the slowest and dominating the reaction.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates (in Å) and the T1 diagnostic values for all stationary geometries and also harmonic frequencies for the SP1, N2H2(3B), RW2, SP2, cis-N2H2, and H2O systems. This material is available free of charge via the Internet at http:// pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Authors

*F. B. C. Machado. E-mail: [email protected]. *H. Lischka. E-mail: [email protected]. Present Address #

Department of Chemistry and Biochemistry, Texas Tech University Lubbock, TX 79409−1061, USA Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the research and fellowship support ́ of the Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq) under Process No. 304914/2013-4 and Fundaçaõ de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under Process No. 2011/11303-9, 2013/02972-0. This work was supported in part by the Robert A. Welch Foundation under Grant No. D-0005.

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REFERENCES

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CONCLUSION In this work, the thermochemical and kinetics properties for two reaction paths (Rin and Rout) in the triplet state that lead to a hydrogen abstraction from the hydrazine molecule were reported. Our results show that the barrier heights for the Rin reaction path are lower than Rout and consequently, the rate constant for the former reaction path is higher for temperatures lower than 1000 K. However, above this temperature the rate constants are higher for Rout. The calculated rate constants are in quite good agreement with the more recent experimental measurements,14,15,17,18 closer to the ones reported by Shane and Brennen14 and Vaghjian.17,18 The product yields of N2H2 + H2O reported by Gehring et al.12,13 and Foner and Hudson10,11 were studied by considering a second hydrogen abstraction from the N2H3 radical. By comparison of the computed and measured10,11 reaction enthalpies we concluded that the final N2H2 + H2O reaction products referred to the singlet surface. To investigate the regions of intersystem crossing from triplet to singlet, both potential curves were computed along the reaction path from the saddle point (SPin) to the product well (PW) of the N2H4 + O reaction, concluding that an intersystem crossing can occur in that region. The change in the character of the electronic wave functions from an open shell singlet to a closed shell character was investigated as well providing the regions in the potential curve where these changes occurred. G

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