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Kinetics of Thermal Unimolecular Decomposition of Acetic Anhydride - An Integrated Deterministic and Stochastic Model Tam V.-T. Mai, Minh van Duong, Hieu Thanh Nguyen, Kuang C. Lin, and Lam K Huynh J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b00015 • Publication Date (Web): 06 Apr 2017 Downloaded from http://pubs.acs.org on April 7, 2017

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The Journal of Physical Chemistry

Kinetics of Thermal Unimolecular Decomposition of Acetic Anhydride An Integrated Deterministic and Stochastic Model

Tam V.-T. Mai,1 Minh v. Duong,1 Hieu T. Nguyen,1 Kuang C. Lin2 and Lam K. Huynh3,* 1

Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam.

2

Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan.

3

International University, Vietnam National University - HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam.

* Corresponding authors. Email address: [email protected] | [email protected] (LKH) Tel: (84-8) 2211.4046 (Ext. 3233) Fax: (84-8) 3724.4271

ACS Paragon Plus Environment


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Abstract An integrated deterministic and stochastic model, within the master equation/Rice–Ramsperger– Kassel–Marcus (ME/RRKM) framework, was first used to characterize temperature- and pressuredependent behaviors of thermal decomposition of acetic anhydride in a wide range of conditions (i.e., 300–1500 K & 0.001–100 atm). Particularly, using potential energy surface and molecular properties obtained from high-level electronic structure calculations at CCSD(T)/CBS, macroscopic thermodynamic properties and rate coefficients of the title reaction were derived with corrections for hindered internal rotation and tunneling treatments. Being in excellent agreement with the scattered experimental data, the results from deterministic and stochastic frameworks confirmed and complemented each other to reveal the main decomposition pathway proceeds via a 6-membered-ring transition state with the 0-K barrier of 35.2 kcal⋅mol-1. This observation was further understood and confirmed by the sensitivity analysis on the time-resolved species profiles and the derived rate coefficients with respect to the ab initio barriers. Such an agreement suggests the integrated model can be confidently used for a wide range of conditions as a powerful post-facto and predictive tool in detailed chemical kinetic modeling and simulation for the title reaction and thus can be extended to complex chemical reactions.

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1. Introduction Anhydride acetic, (CH3CO)2O (referred to as AH), can be considered as an acetylating reagent1,2 that thermally decomposes to give ketene and acetic acid, (CH3CO)2O → CH2CO + CH3COOH (Rxn. 1)3-7. This reaction has truly received considerable interest for the purpose to produce ketene (CH2CO)5, an important intermediate in the combustion of hydrocarbon fuels. Despite its importance, only a few kinetic investigations concerning the title reaction have been studied both experimentally3-5 and theoretically5. Using a flow reactor, Szwark and Murawski3 measured a rate constant of k(T) = 1.00×1012×exp(-34500 cal⋅mol-1/RT) s-1 within the temperature range of 553 – 646 K and the total pressure range of 6 – 13 torr. By analyzing the reaction products, they found the decomposition took place in the unimolecular process to yield equal molarity of ketene and acetic acid with no other products observed. Blake and Speis4 conducted this reaction in a static and flow apparatus at the temperature of 470 – 643 K and over a wide pressure range of 7 – 232 torr, leading to the rate constant k(T) = 1.48×1011×exp(-32194 cal⋅mol-1/RT) s-1. They also found that the only products were ketene and acetic acid. More recently, Akao et al.5 reported a rate constant expression as k(T) = 6.31×1011×exp(-32983 cal⋅mol-1/RT) s-1 by using the shock tube method to evaluate the Arrhenius parameters of this composition at higher temperature of 750 – 980 K and pressure range of 19 – 80 torr. They also performed ab initio molecular orbital calculations by identifying the conceivable transition states (TSs) and discussed the reaction mechanism. To our best knowledge, there is no detailed computational study on the mechanism and kinetics of the title reaction even though a 6membered-ring transition state has been suggested for this reaction by analogy with ester elimination8.



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The master equation (ME) has been shown to be a powerful framework for modelling kinetic behaviors of a complex gas-phase chemical system for a wide range of conditions (e.g., temperature and pressure). The solutions of the ME equation, i.e., the species profiles as well as the rate coefficients, can be obtained by either deterministic9,10 or stochastic11,12 approaches. In principles, it is challenging for a deterministic model to provide reliable results if there is no clear separation between the two time scales, namely internal energy relaxation eigenvalues (IEREs) and chemically significant eigenvalues (CSEs) (e.g., the time-scale difference is less than one order of magnitude which normally occurs at high temperature and low pressure). Alternatively, a stochastic model can reveal the real physics/chemistry only with a statistically–sufficient number of trials, which normally requires much computational time and effort to correctly describe minor events or channels/species. Therefore, the use of both approaches will help to complement each other, and thus gain more confidence on the calculated numbers for a wide range of different conditions, even at the extreme cases as mentioned above. In such a case, they certainly will help to gain more confidence in the calculated data as well as to shed more light to the nature of complicated processes. In this study, we explored the mechanism of the title reaction by carrying out accurate ab initio calculations whose results are then used to characterize its pressure and temperaturedependent behaviors in a wide range of conditions using the combined deterministic and stochastic statistical rate model. It is expected to provide an integrated picture to bridge the gap between fundamental chemistry and reaction engineering for this significant issue in atmospheric chemistry and combustion.

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2. Computational Details Structures of reactants, products and TSs of the title reaction were optimized using B3LYP level of theory13,14 and 6-311G(2d,d,p) basis set denoted as CBSB7. The calculated B3LYP/CBSB7 vibrational frequencies with the scaling factor of 0.9915 were used to calculate the zero-point energy (ZPE) corrections. Electronic energies were calculated with the B3LYP geometries by using the coupled cluster theory with single and double excitations16-18 and perturbative estimate of triple excitations [CCSD(T)]19.

Extrapolation for the calculated

electronic energies was further performed to complete basis set (CBS) using cc-pVDZ and ccpVTZ20,21 basis sets suggested by Truhlar22. The total single point energy is a sum of the HartreeFock (HF) energy, EHF and the correlation energy, Ecorr: E∞tot = E∞HF + E∞corr. The HF energy is assumed to approach its CBS limit by power laws: ExHF = E∞HF + AX-α and Excorr = E∞corr + BX-β, where X = 2, 3 for D, T extrapolation with the Dunning’s correlation consistent polarized valance cc-pVXZ basis sets20,21, and A, B, α and β are constants (α = 3.4 and β = 2.4 for CCSD and CCSD(T) calculations)22. The reported root-mean-square (RMS) deviation of the CCSD(T)/CBS procedure was from 1.3 to 2.4 kcal/mol for the total energies of the considered test cases22. The energetic profiles extrapolated from CCSD(T)/CBS calculations, were then compared with other accurate composite methods such CBS-QB315, CBS-APNO23, G324 and G425 levels of theory. The CCSD(T)/CBS energies, accompanied with the B3LYP/CBSB7 geometries and frequencies information, were used to carry out kinetic analysis. All these electronic structure calculations were calculated using the GAUSSIAN 09 package26. Thermodynamic and kinetic analyses, using both deterministic and stochastic models, were carried out using the Multi-Species Multi-Channels (MSMC) code27. The hindered internal rotation (HIR) correction28 and tunneling effect29 were taken into account. For the HIR treatment, 5



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the hindrance potentials, V(θ) , as a function of torsional angle, θ, along the single bonds (i.e., C−C and C−O, cf. supplementary Figure S1) were explicitly obtained at the B3LYP/6-31G(d) level via relaxed surface scans with the step size of 10o for the dihedral angles corresponding to the rotations. The HIR parameters were determined with the use of MSMC-GUI30. The calculated m‡ σ external rate constants included the reaction path degeneracy, L = × ‡ (where m‡ and m are the m σ external #

‡ number of optical isomers of transition states and reactant, and σ exter nal and σ external are the external

rotation symmetry numbers of the transition state and reactant, respectively). Note that the internal symmetry number σ internal (e.g., σ internal = 3 for the rotation of the methyl CH3 group along the C-C bond) was explicitly included in the HIR treatment. The energy-transfer process was computed on the basis of the exponential-down model with Edown = 500 cm-1 for Ar as the bath gas31. The Lennard-Jones (L-J) parameters Ar32 while

ε / kB = 93.3 K and σ = 3.542 Å were used for

ε / kB = 454.0 K and σ = 5.413 Å were taken from the data of C4H7O333 to represent

C4H6O3. The density/sum of states were directly counted using the Beyer-Swinehart algorithm34 (for HO modes) in combination/convolution with the modified Stein-Rabinovitch algorithm35 (for external/hindered rotational modes) with the energy step of 1 cm-1. The maximum energy level was determined by the convergence tolerance ε = 1.0×10-6 in the sum of the partition function, which is temperature dependent. For the title system, maximum energy level at T = 1500 K is roughly 40,000 cm-1. For kinetic calculations, the energy grain size of 200 cm-1 was used.

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3. Results and Discussion Potential Energy Surface Acetic anhydride has two non-planar minima, labeled AH[sp,sp] and AH[sp,ac], related to each other by large amplitude motions36 via the transition state TS1 of the rotation of the (O=C−O-C) dihedral angle (cf. Figures 1 & 2). The tittle molecule AH can decompose via two 4membered-ring transition states (TS2 and TS4 from AH[sp,sp] and AH[sp,ac], respectively) and a 6-membered-ring transition state (TS3 from AH[sp,ac]). Figure 2 presented the optimized geometries of the reactants, products and transition states of the title reaction at the B3LYP/CBSB7 level of theory and compared with literature data. The calculated bond lengths and angles are consistent with those of the literature data with maximum errors of ~ 0.1 Å and ~ 1o in bonds and angles, respectively. In particular, the geometries of the TS2, TS3 and TS4 obtained at the B3LYP/CBSB7 level in this study are very similar to the HF/3-21G values reported by Akao et al.5, indicating that the geometries are not sensitive to the calculation methods. The corresponding harmonic vibrational frequencies provided in the Supplementary Table S1 are slightly higher than those available in the literature. (e.g., the average differences are 88 and 49 cm-1 for CH3COOH and CH2CO, respectively).

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Figure 1. Possible pathways for the unimolecular decomposition of (CH3CO)2O to form CH3COOH and CH2CO. (TS1 is in the conformational process between AH[sp,sp] and AH[sp,ac]; TS2 and TS4 are TSs for the pyrolysis via the 4-membered ring from AH[sp,sp] and AH[sp,ac] conformers, respectively; TS3 occurs in the unimolecular decomposition via the 6membered ring from AH[sp,ac] conformer). Details of the species and transition states involved were presented in Figure 2.

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Figure 2. Optimized geometries (distances in Å and angles in degrees) of reactants (AH[sp,sp] and AH[sp,ac]), products (CH3COOH and CH2CO) and transition states (TS1, TS2, TS3 and TS4) at B3LYP/CBSB7 level of theory. The numbers in the parentheses are the reference values from the work of a Atkinson et al.6; b Hellwege et al.37; c Kuchitsu38; d Akao et al.5.

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Figure 3 presents the energy obtained from single-point energy CCSD(T)/CBS calculations at the optimized B3LYP/CBSB7 geometries (denoted as CCSD(T)/CBS//B3LYP/CBSB7) as extrapolated benchmark values39. The structure of TS3 is similar to those of the elimination of ethyl esters to form carboxylic acids and ethylene40-43; that is, a hydrogen atom in the terminal methyl group migrates to the oxygen atom of carboxyl group [-C(=O)-] to produce acetic acid and ketene. As a result, the pathway through the 6-membered-ring TS is expected to be more favourable than the higher barrier channels via the 4-membered-ring TS2 and TS4. Besides this reaction path, we found three dissociation channels where C-C, C-O and C-H bonds of AH can be broken via barrierless reactions with very high endothermicity (e.g., 89.1, 90.7, and 97.6 kcal/mol above the reactant energy, respectively, cf. Figure S5). Therefore, their contribution to the total rate of decomposition of AH can reasonably be neglected, at least for the kinetic purpose. The energies computed at CCSD(T)/CBS//B3LYP/CBSB7 match very well with those of the other methods except for the calculated data of Akao et al.5 who employed a very small basis set, namely 3-21G (cf. Table 1). Our analysis herein suggests the CCSD(T)/CBS energetic profiles accompanied with the geometry and frequency information from B3LYP/CBSB7 can be considered as the most accurate data available for detailed kinetic analysis. In order to examine the validity of the single-reference electron-correlation CCSD(T) method, T1 diagnostics for the species involved were calculated and presented in the supplementary Table S5.

The T1

diagnostic values of less than 0.02 and 0.04 for closed shell and open-shell species, respectively, suggest the nondynamic correlation energy is small44-48; thus, there is no need to consider highorder methods for the title systems.

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Figure 3. ZPE-included potential energy surface of the unimolecular decomposition reaction, (CH3CO)2O → CH3COOH + CH2CO at the CCSD(T)/CBS//B3LYP/CBSB7 level of theory. Values in the parentheses are the reference numbers from the work of Akao et al.5. All numbers are in kcal⋅mol-1. Table 1. Relative energies (in kcal⋅mol-1) of the species involved and the corresponding transition states at different levels of theory at 0 K. The zero-point energy (ZPE) correction was included. AH AH TS1 [sp,sp] [sp,ac] CCSD(T)/CBS[a],[b] 0.0 0.2 0.3 CBS-QB3[a] 0.0 0.3 0.3 CBS-APNO[a] 0.0 0.1 0.8 [a] G3 0.0 0.0 0.3 G4[a] 0.0 0.4 0.3 MP4(SDTQ)//HF[c] 0.0 0.4 [a] This work; [b] CCSD(T)/CBS//B3LYP/CBSB7; [c] The MP4(SDTQ)/3-21G//HF/3-21G. Method

TS2

TS3

TS4

Products

59.0 35.2 58.9 22.6 59.1 36.6 58.8 23.5 34.5 23.6 34.9 23.0 36.3 58.3 22.8 61.3 37.4 60.3 work of Akao et al.5, calculated at

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Because

the

energy

is

~0.2

kcal·mol-1

higher

than

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that

of

AH[sp,sp]

at

CCSD(T)/CBS//B3LYP/CBSB7 level (the experimental value36 is ~ 0.1 kcal⋅mol-1), AH[sp,ac] was included in the hindered internal rotation treatment along the CH3COO−COCH3 axis for AH[sp,sp] (cf. Figure 4). The similar treatment was also used for TS4 in which TS2 was included in the HIR treatment (cf. Supplementary Figure S1). Therefore, the unimolecular decomposition of AH[sp,sp] can proceed via either the 6-membered-ring TS (TS3) or the 4membered-ring one (TS4) with the corresponding HIR treatments, where all possible conformers were implicitly included, as described above.

AH[sp,ac] AH[sp,sp]

AH[sp,sp]

Figure 4. Hindrance potentials for AH[sp,sp] at B3LYP/6-31G(d) level of theory with the step size of 10 degrees. AH[sp,ac] is located at the dihedral angle of 120o or 180o due to the rotation of the C-O bonds.

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The calculated thermodynamic properties including heat of formation (∆Hf298) and entropy (S298) for the species involved were compared to the literature data (cf. Table 2) in an attempt to evaluate the reliability of our computed numbers. In general, the calculated values are consistent with the literature data (e.g., when compared to the ATcT data, the differences are less than 0.5 kcal⋅mol-1 and 2.0 cal⋅mol-1⋅K-1 for ∆Hf298 and S298, respectively). Therefore, more confidence has been gained in our calculated data which were derived from a solid framework as presented previously.

Table 2. Comparison of calculated thermodynamic properties of species explicitly considered in the kinetic analysis with literature data (NIST= Webbook NIST, webbook.nist.gov, ATcT = Active Thermochemical Tables49,50,[a], GA = Group Additivity51). Unit: △Hf

298 K

in kcal.mol-1,

S298 K in cal.mol−1·K−1 (1 kcal = 4.184 kJ). Method ∆Hf298 K S298 K Ab initio[b] -139.4 91.5 NIST N/A 93.252 AH[sp,sp] GA -137.1 93.2 [b] Ab initio -103.3 87.0 TS3 Ab initio[b] -80.7 95.9 TS4 Ab initio[b] -103.9 68.3 ATcT[a] -103.3 67.7 CH3COOH 53 NIST -103.5 ± 0.6 67.654 GA -103.4 67.5 -11.4 57.8 Ab initio[b] [a] ATcT -11.6 60.1 CH2CO NIST -11.4 ± 0.455 N/A GA N/A N/A [a] Values collected from Burcat’s online database, http://garfield.chem.elte.hu/Burcat/burcat.html (access date: May 2016); [b] This work at CBS-QB3 level. △Hf was calculated by atomization method. Species

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Kinetic Analysis The pressure- and temperature-dependent analyses were carried out using the potential energy surface and molecular properties calculated at the CCSD(T)/CBS//B3LYP/CBSB7. In particular, both deterministic and stochastic simulations were independently performed within the ME/RRKM framework to predict the species profiles as well as macroscopic rate coefficients for engineering purposes. Representatively, Figure 5 shows the normalized time-resolved profiles for acetic anhydride and the products (CH3COOH and CH2CO) at the condition of 500 K and 1 atm. The resutls for other conditions can be found in the supplementary material. It is found that the high-temperature chemistry is not so different from the low temperature chemistry, thus it was not discussed explicitly here.

Figure 5. Time-resolved species profiles for the unimolecular decomposition of acetic anhydride at 500 K and 1 atm using both deterministic and stochastic (with different numbers of trials: 500, 1000 and 10000) approaches (1 atm = 0.1 MPa).

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Within the deterministic model, our eigenpair analysis showed that a mixing in eigenvalue spectrum, between the fastest chemically significant eigenvalues (CSEs) and the slowest internal energy relaxation eigenvalues (IEREs) where the difference is less than 1 order of magnitude, occurs at T ≥ 1000 K with P = 1.32×10-6 atm (c.f. Figure 6). In such a case, the derived phenomenological rate coefficients using the CSE approach, thus, can only be used with careful evaluation and the stochastic simulation can be alternatively carried out but with a sufficient number of trials. As the pressure increases, the merging regime occurs at a slightly higher temperature (e.g., T ≥ 1200 K at P = 1.32×10-3 atm and T ≥ 1400 K at P = 1.32×10-1 atm, cf. Figure S2); thus the mixing issue is less noticeable at high pressure. IEREs

CSEs

Figure 6. Eigenvalue spectra as a function of temperature for (CH3CO)2CO → CH2CO + CH3COOH (via both TS3 and TS4) at 1.32×10-6 atm. Only the eigenvalues with the smallest magnitude were presented: dashed and solid lines represent chemically significant eigenvalues (CSEs) and internal energy relaxation eigenvalues (IEREs) modes, respectively.

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It is seen in Figure 5 that the stochastic method with a trial number increased from 500 to 10000 is able to predict the profiles which are identical to those obtained from the deterministic framework; therefore, the number of 10000 trials can be concluded as statistically adequate at this condition, and this statistically adequate number is found to increase with the temperature. The computer time was found to increase with the temperature due to the increase of accessible energy levels. Details of the deterministic as well as stochastic simulations at different conditions were presented in Supplementary Figures S3. In short, we have demonstrated for the first time that the two approaches were systematically carried out within the solid ME/RRKM framework to complement each other in an attempt to confidently capture the correct chemistry/physics of this reaction. Rate coefficients k(T, P) as a function of pressure and temperature, calculated for temperature ranging between 300 and 1500 K and for pressures between 0.001 and 100 atm, were depicted in Figures 7 & 8. It can be seen that k(T, P) approaches the high-pressure limit at lower pressure when the temperature decreases. In other words, the fall-off region is shifted to the high pressure with temperature and this region is more noticeable at high temperature regime (e.g., T > 1000 K). The kinetic and thermodynamic data in the Chemkin format were provided in the supplementary Tables S2 & S3 in order to facilitate reactor modeling/simulation using this subkinetic model. As seen in Figure 9, our calculated rate coefficients, k(T, P), are in good agreement (i.e., within the experimental uncertainty) with the experimental data measured by Akao et al. (1996)5, Blake et al. (1971)56 and Blake et al. (1976)57 for both forward and reverse reactions at different pressures as a function of temperatures. The agreement in both directions implicitly reflects the validity of the calculated thermodynamic data for the species involved in this study. Note that the calculated forward rate coefficients also excellently matched with the

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older experimental data by Blake 19714 and Szwarc 19513 (cf. Figure 10) and the calculations were carried out using the full PES described in Figure 2 with no adjustment.

Figure 7. Calculated rate coefficients for unimolecular decomposition of (CH3CO)2O as a function of pressure at different temperatures (i.e., 300, 500, 700, 800, 900, 1000, 1200 and 1500 K). The calculations were carried out using the full PES described in Figure 3.

17



8 P = 0.001 atm P = 0.01 atm P = 0.1 atm P = 1 atm P = 10 atm P = 100 atm high-P limit

6 4

logk (1/s)

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2 0 -2 -4 -6 -8 -10 -12 -14 0.6

1.0

1.4

1.8 2.2 1000/T (1/K)

2.6

3.0

3.4

Figure 8. Calculated rate coefficients for unimolecular decomposition of (CH3CO)2O as a function of temperature at different pressures (i.e, 0.001, 0.01, 0.1, 1, 10, 100 atm and highpressure limit). The calculations were carried out using the full PES described in Figure 3.

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10-2 10-1

10-2

Figure 9. Comparison between calculated and experimental rate coefficients as a function of temperature at different pressures: (a) forward reaction, (CH3CO)2CO → CH2CO + CH3COOH; (b) reverse reaction, CH2CO + CH3COOH → (CH3CO)2CO. Experimental data are from the work of Akao and coworkers (Akao 19965) and Blake and coworkers (Blake 197156 and Blake 197657). 19



(a)

1.0

(CH3CO)2CO → CH2CO + CH3COOH (P =9.21×10-3 - 3.05×10-1 atm & T = 470 - 643 K)

logk (1/s)

0.0 -1.0 -2.0 expt'l (Blake 1971 - fitting) This work (P = 9.21× 10-3 atm)

-3.0

This work (P = 3.05×10-1 atm) -4.0 1.50

1.65

1.80

1.95

2.10

1000/T (1/K)

(b)

5.0

(CH3CO)2CO → CH2CO + CH3COOH (P = 1.68×10-2 - 1.79 ×10-2 atm & T = 553 - 923 K)

4.0 3.0 logk (1/s)

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

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2.0 1.0 0.0

expt'l (Szwarc 1951 - fitting)

-1.0

This work (P = 1.68×10-2 atm) This work (P = 1.79×10-2 atm)

-2.0 1.00

1.15

1.30

1.45

1.60

1.75

1000/T (1/K) Figure 10. Comparison between calculated and the earlier experimental rate constants (Blake 19714 and Szwarc 19513) for forward reaction, (CH3CO)2CO → CH2CO + CH3COOH as a function of temperature at different pressures. The calculations were carried out using the full PES described in Figure 3.

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The branching ratio of the two decomposition channels via two TSs (TS3:TS4) slightly decreases with temperature (e.g., ~ 999 at P = 1 atm and T = 300 – 1500 K, cf. Figure S4 (b)), reflecting the channel via a 6-membered-ring TS (TS3) dominates at the considered conditions. It is worth noting that if these two channels are treated independently (i.e., two separate simulations with each channel), the corresponding ratio is 24 (about 40 times smaller); thus, it is crucial to consider the full PES (as presented in Figure 2) in the kinetic analysis. The result also confirms the hypotheses in the previous experiment5 that the 4-membered-ring TS reaction pathway cannot compete or play any role even at high temperature when comparing with the 6-membered-ring TS pathway. The TS3:TS4 ratio is also found to decrease with pressure (e.g., 999 and 76 at 0.001 and 100 atm, respectively, at 1500 K; cf. Figure S4 (a) & (c)). Sensitivity analyses were also carried out to quantify the dependence of the ME solutions on the calculated ab initio input parameters in the model. Specifically, we examined the effects of the calculated barrier ∆V ‡ of the TS3 and TS4 channels and energy transfer ∆Edown on the timeresolved species mole fraction and the temperature-dependent rate coefficients. The normalized sensitivity coefficients for the species with respect to the barrier change of the TS3 channel (i.e., d(ln[X])/d(ln( ∆ V ‡ (T S 3) ) in Figure 11a) are negative for the reactants and TS3-via products (the products via the TS3 channel) but positive with larger magnitude for the TS4-via products. In other words, the increase of ∆ V ‡ (T S 3) decreased the mole fraction of the reactants and TS3-via products while it increased that of TS4-via products (with a larger normalized effect). Similarly, the increase of ∆ V ‡ (T S 4) basically had no effect on the TS3-via products (the coefficient is close to zero) while it decreased the mole fraction of the reactants and TS4-via products. Since there are two competing channels (i.e., TS3 vs. TS4), the sign as well as the magnitude of the sensitivity coefficients suggest that the TS3 pathway is the dominant channel. The sensitivity 21



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analysis was also carried out for the calculated rate constants (cf. Figure 11b). It was observed that the change of the TS3 barrier, ∆∆ V ‡ (T S3) , has an opposite effect on the TS3 rate constants while ∆∆ V ‡ (T S4) had no effect at all. It is interesting to find that both changes caused significant fluctuation of the rate constants for the TS4 channel, the minor channel. This observation can be explained by the competition between excitation/de-excitation and dissociation via different pathways which are time-dependent, thus it makes the kinetics of this system even non-equilibrium. Note that the perturbation has larger effect on the minor channel. It is also partially due to the large uncertainties of the corresponding calculated data which were calculated using the stochastic approach as discussed previously. The sensitivity analysis was also carried out with respected to the energy transfer Edown for the species mole faction as well as rate coefficients (provided in Figure S6). The results are consistent with those observed with the PES analysis about the detailed mechanism. In particular, the change of ∆E has negative effect on the reactant profile (i.e., negative value, cf. Figure S6-a) while it is more complicated for the product channels (both negative and positive, depending on the reaction time). Since the product channel via TS4 is a minor one, the sensitivity coefficient for this channel is larger and more fluctuating than that via TS3 for the temperature range of 3001500 K (cf Figure S6-b).

22


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(a)

T = 750 K, P = 0.025 atm 3.2E+06 2.8E+06 CH3COOH + CH2CO (via TS4)

d(ln[X])/d(ln∆ ∆V‡)

2.4E+06

+ Solid lines: ∆∆V‡(TS3)= + 1 kcal/mol + Dashed lines: ∆∆V‡(TS4)= + 1 kcal/mol

2.0E+06 1.6E+06

(CH3CO)2O

1.2E+06 8.0E+05

CH3COOH + CH2CO (via TS3)

4.0E+05 0.0E+00 -4.0E+05 0.E+00

2.E-02

(b)

4.E-02 Time (s)

6.E-02

8.E-02

T = 750 - 1000 K, P = 0.025 atm 8.E+05 6.E+05

d(lnk)/d(ln∆ ∆V‡)

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


via TS4

4.E+05 2.E+05

via TS3

0.E+00 -2.E+05 -4.E+05 750

800

850

900

950

1000

T (K) Figure 11. Normalized sensitivity coefficients for the species mole fraction [X] (a) and rate coefficients (b) with respect to the barrier height ∆ V ‡ of the TS3 (solid lines) and TS4 (dashed lines) channels. Note that the analysis was carried out with the full PES described in Figure 3.

23



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4. Conclusions In this study, the unimolecular decomposition of acetic anhydride, (CH3CO)2CO → CH2CO + CH3COOH, was investigated by using the high-level quantum chemical and state-ofthe-art integrated deterministic-stochastic statistical rate theory calculations. The results show that the reaction dominantly takes place via a 6-membered-ring transition state over the other two 4-membered-ring TSs in the considered T-P range. The temperature-pressure dependent rate coefficient calculations based on the RRKM/ME solutions were found to be in good agreement with scattered literature experimental data for both directions. The calculated thermodynamic data and rate coefficients, therefore, can be confidently used for various applications in the wide range of conditions (T = 300 – 1500 K and P = 0.001 – 100 atm).

Associated content *Supporting Information 0K

Table S1: The optimized geometries, electronic energies at 0 K ( Eelec ), zero-point energy (ZPE) corrections

and

vibrational

frequencies

of

the

species

involved,

calculated

at

CCSD(T)/CBS//B3LYP/CBSB7 level of theory for the title reaction. Table S2: Parameters obtained from the modified Arrhenius expression of the calculated values for the pressure-dependent rate coefficients over the temperature range of 500 – 1200 K. The calculation was carried out with the channel via TS3. Table S3: Detailed kinetic submechanism in Chemkin format for (CH3CO)2O → CH3COOH + CH2CO. Table S4: Rate constants and uncertainty for (CH3CO)2O → CH3COOH + CH2CO via both TS3 and TS4 at T = 750 – 980 K and P = 0.025 atm, using stochastic approach with 107 trials. Table S5: T1 diagnostic values for the decomposition of acetic anhydride computed at CCSD(T)/cc-pVXZ (X = D, T), using geometries at B3LYP/CBSB7.

24


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Figure S1: Hindrance potentials for AH[sp,sp], TS3, TS4 and CH3COOH at B3LYP/6-31G(d) level of theory. Figure S2: Eigenvalue spectra as a function of temperature for (CH3CO)2CO → CH2CO + CH3COOH (via both TS3 and TS4) at different pressures: (a) 1.32×10-3 atm and (b) 1.32×10-1 atm. Figure S3: Time-resolved species profiles for unimolecular decomposition of acetic anhydride (via TS3) at 1000 K (a) and 1500 K (b) at 1 atm using both stochastic and deterministic (with different numbers of trials: 500, 1000 and 10000) approaches. Figure S4: Branching ratios of acetic anhydride decomposition via two TSs, TS3 and TS4 at 0.001 atm (a) and 100 atm (b). The calculations were carried out using the full PES described in Figure 3. Figure S5: All possible pathways for the thermal decomposition of acetic anhydride calculated at CCSD(T)/CBS//B3LYP/CBSB7 level of theory (@ 0 K and including ZPE corrections). Figure S6: Normalized sensitivity coefficients for the species mole fraction [X] (a) and rate coefficients (b) with respect to the energy transfer ∆ = +100 cm-1. Note that the analysis was carried out with the full PES described in Figure 3. Text S1: Procedure of thermochemical calculations. This material is available free of charge via the Internet at http://pubs.acs.org. Author information Corresponding

Author:

Lam

K.

Huynh.

E-mail

address:

[email protected],

[email protected]. Tel: (84-8) 2211.4046 (ext 3233). Fax: (84-8)3724.4271.

Acknowledgements Computing resources and financial support provided by the Institute for Computational Science and Technology – Ho Chi Minh City and International University, VNU-HCM are gratefully 25



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acknowledged. LKH also acknowledges the Department of Science and Technology – Ho Chi Minh City for funding (Grant No. 1166/QĐ-SKHCN). KCL would like to express his gratitude to Ministry of Science and Technology in Taiwan for the financial support under Contract No. MOST 103-2221-E-110-073-MY2.

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