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A: Kinetics, Dynamics, Photochemistry, and Excited States

Chemical Kinetics of H-Atom Abstraction from Ethanol by H#2: Implication for Combustion Modeling Qian Zhao, Yingjia Zhang, Wuchuan Sun, Fuquan Deng, Feiyu Yang, and Zuohua Huang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b09074 • Publication Date (Web): 08 Jan 2019 Downloaded from http://pubs.acs.org on January 12, 2019

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The Journal of Physical Chemistry

Chemical Kinetics of H-atom Abstraction from Ethanol by HȮ2: Implication for Combustion Modeling Qian Zhaoa, Yingjia Zhanga, Wuchuan Suna, Fuquan Denga, Feiyu Yanga, Zuohua Huanga* a

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China. Abstract：As a renewable source of energy, ethanol has been widely used in internal combustion engines as either gasoline alternative fuel or fuel additive. However, as the chemical source term of computational fluid dynamics (CFD) simulation of combustors, it remains disagreement on understanding of chemical kinetic mechanism of ethanol. Reaction mechanism of ethanol + HȮ2 is well known a crucial reaction class in terms of predicting reactivity of ethanol as well as ethylene formation at engine relevant condition. However, the kinetic parameters of the reactions are basically extrapolated by analogy with n-butanol + HȮ2 system calculated by Zhou et al. (Zhou et al. International Journal of Chemical Kinetics, 2012, 44 (3), 155-164). The reliability of such the analogy remains to be seen, as no directly theoretical or experimental evidence is available in literature to date. In this study, thermal rate coefficients of H-atom abstraction reactions for ethanol + HȮ2 system were determined by using both conventional transitionstate theory and canonical variational transition-state theory, with the potential energy surface evaluated at the CCSD(T)/cc-pVTZ//M06-2x/def-TZVP level. The quantum mechanical effects were corrected by zero-curvature tunneling method at low temperatures (< 750 K), and difference schemes of two Eckart functions were fitted to optimize the minimum energy path curves. Torsional modes of the -CH3 and -OH groups were treated by using the hindered-internal-rotator approximation. Furthermore, the rate coefficients of the title reaction were calculated at both CCSD(T)/cc-pVTZ//M06-2x/def-TZVP and CCSD(T)/CBS//M06-2x/def-TZVP levels of theory with an uncertainty of a factor of 3. Similar to n

Corresponding author: Yingjia Zhang, [email protected], State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an

Jiaotong University, Xi’an 710049, People’s Republic of China. 1

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butanol + HȮ2 system, the title system is dominated by alpha site H-atom abstraction, but the rate coefficients of the three channels are slightly slower than that of n-butanol + HȮ2 system. Generally, the new calculations show only limited effect on ethanol reactivity at low pressures and high temperatures (over 1300 K) but it prevents the kinetic mechanisms to over-predict ignition delay times under engine relevant conditions.

2


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1. Introduction Ethanol is well-known one of the most promising sources of renewable energy for low-pollution engine application. Development of detailed kinetic mechanism of ethanol is therefore attractive for use as chemical source term of highly reliable combustor simulation. In the past few decades, a large number of experimental and modeling research of ethanol have been implemented and made lots of headway on understanding of ignition, oxidation and combustion of ethanol 1. For instance, Beeckmann et al.

2

measured the laminar burning velocity in a spherical combustion vessel at 10 bar but the comparison of the experimental data with the simulations showed that the kinetic mechanisms mostly have a deficit in correctly predicting the pressure effects. The kinetic models agreed to a certain extend with experimental data at ambient pressure, but it showed over-prediction at high pressures. Hashemi et al.

3

studied the

pyrolysis and oxidation of ethanol at 50 bar over the temperatures range of 600–900 K in a laminar flow reactor. Their proposed mechanism well predicted the ignition delay times over 900 K but it overpredicted the flame speeds. The sensitivity analysis also highlighted the importance of reaction, ethanol + hydroperoxyl radical (HȮ2), for predicting auto-ignition at high pressures and moderate temperatures. Hence they suggested that an accurate determination of the rate coefficients for ethanol + HȮ2 is crucial to improve the model ability. To verify the performance of literature kinetic mechanisms of ethanol, seven kinetic mechanisms, SD model 1a, LLNL model 1g, 4, Mittal et al. model 5, JetSurf 2.0 6, CRECK model 1c, Hashemi model 3 and Zhang et al. model 7 were chosen to simulate the ignition delay time for stoichiometric ethanol/air mixture at 30 bar over the temperature range of 650–1450 K with constant U, V approach, Fig. 1. Clearly, the literature models remain a large difference, especially at intermediate to low temperature regimes (700– 1000 K). Specifically, the kinetic models present more than five times differences in predicting ignition delay times at 750 K, and the discrepancy appears to be more prominent with decreasing temperature. It is meaning that the understanding of oxidation mechanism of ethanol does not reach a fairly good 3



consensus at present in the combustion community. This will thus provide a challenge to design next generation combustors using neat ethanol or gasoline/ethanol blending fuels relying on CFD simulation. 10

3

10

2

10

1

10

0

Ethanol/Air p = 30 atm  = 1.0

10

-1

10

-2

0.7

Ignition delay time (ms)


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(19)

Zhang et al. 2018 (15) Hashemi et al. 2017 (1) SD 2016 (3) CRECK 2014 (17) Mittal et al. 2014 (18) JetSurF2.0 2010 (16) LLNL 2004

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

10

2

1.25

1.30

1.35

1.40

1.45

-1

-1

1000/T (K )

1000/T (K )

Fig. 1. Comparison of ignition delay times predicted by literature kinetic mechanisms of ethanol at engine relevant conditions. Beeckmann et al. 2and Hashemi et al.

3

have clearly observed that the deviation between existing

kinetic mechanisms and experimental measurements for ethanol mainly occurred at high pressures and low temperatures. By corollary, HȮ2 radical, as the most important radical in ethanol oxidation at high pressures and low temperatures, should take the responsibility for the different ability of mechanisms. Sensitivity analyses performed in the most recent work of Hashemi et al. 3, Mittal et al. 5 and Zhang et al7 have indicated the dominant impact of ethanol + HȮ2 reactions on prediction of ignition delay times for ethanol at high pressures and lower temperatures. It follows that the accepted data appears to reach consensus in combustion kinetics community. Back in 1992 Norton and Dryer

8

estimated the kinetic

process of ethanol + HȮ2 by an analogous rate constant from methanol + HȮ2 measured by a turbulence flow reactor 9. Specifically, the A factor (2.70E+13) was evaluated by 2/3 of CH3OH + HȮ2 9 while the Ea (16 kcal/mol) was taken from Golden’s value10 of tertiary C-H bond + HȮ2 of butanol, due to the similar bond energies of H-(CH3CHOH) and H-(t-C4H9)

10.

Recently, Zhou et al.

11

carried out an ab-initio

calculation study for n-butanol + HȮ2 system at the CCSD(T)/cc-pVTZ//MP2/6-311G(d, p) level of theory coupled with variational transition state theory. Hereafter, almost all modelers, in a long time, adopted Zhou et al. 11 rate constants of butanol + HȮ2 to describe the kinetic process of ethanol + HȮ2 reaction in 4


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mechanism construction

1b, 1l, 1m, 2, 7, 12.

Obviously, it is controversial owing to the difference of the

molecular structure and bond dissociation energy between ethanol and n-butanol. Unfortunately, there are no experimental measurements or theoretical calculations are available in literature. With this in mind, the first aim of this study is to implement a high-level quantum chemistry calculation for the title reaction, and to provide an accurate rate coefficients for development of highfidelity kinetic mechanism. The second aim is to figure out whether it is reliable for the analogy with Zhou et al. calculation 11 to describe the kinetic mechanism of ethanol + HȮ2. 2. Theoretical method In order to ensure the comparability of computational accuracy for the title reactions, the CCSD(T)/cc-pVTZ, also adopted in the study of Zhou et al. 11, was used to calculated the single point energy. The M06-2X method with the def-TZVP basis set was used to optimize the structures of local minimum and frequencies owing to relatively more effective and accurate than MP2 method in most cases. The new pcs-n basis sets proposed by Frank13, display the lowest basis set errors at a given zeta quality level, and it is therefore suitable to both routine and benchmarked calculations using DFT methods in general. Moreover, Frank’s work also showed that the def-/def2-basis sets, developed by Weigend and Ahlrivhs14, display the comparable performance to the pcs-n, while the other basis sets including the Pople basis sets possess significantly larger errors relative to the basis set limit. Therefore, the reliability of the computational results with def-/def2-basis sets is more guaranteed compared to Pople basis sets used under the same calculated amount. It is concluded that the def-TZVP basis set is more applicable to DFT calculation relative to 6-311G** and it is thus adopted in this study. Moreover, an intrinsic reaction coordinate (IRC) calculation was performed for each transition state (TS) at the M06-2X/def-TZVP level of theory to identify whether the transition state belongs to the target reaction. To increase the accuracy, the CCSD(T) method with the cc-pVTZ and cc-pVQZ basis sets developed by Dunning

12b

was employed to compute the single point energies. The energies were 5



extrapolated to the complete basis set limit (CBS) level. Furthermore, the T1 diagnostic

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15

values were

found to be small enough (< 0.01 for the stable species and < 0.025 for the radical and TSs), suggesting that the single-reference method is acceptable. All of the quantum chemical calculations were performed by using the Gaussian 09 program 16. The conventional transition state theory (TST)

17

locates the TS at the saddle point, regardless of

temperature. However, the shortcoming is readily compensated by using the canonical variational transition-state theory (CVT) method 17. In fact, the CVT locates the TS at the maximum of the Gibbs free energy along the minimum energy path. In order to verify whether the first-order saddle point of VaG or the first-order saddle point of the MEP introduces a significant difference into the final calculation results, high-pressure limit of thermal rate coefficients were therefore performed by using the IVTST-0 algorithm of the RP-VTST method18 as well as Conventional TST method in this study. Both the methods were combined with zero-curvature tunneling (ZCT) method19 to correct quantum mechanical effects, especially the tunneling effect on the reaction rate constants at low temperatures. The different schemes of two Eckart functions were fitted to optimize the minimum energy path curves 18. The torsional modes of the -CH3 group and -OH group were treated using the hindered-internal-rotator approximation. A frequency scaling factor of 0.971 was used to correct zero point energy (ZPE). 3. Results and discussion 3.1. Potential energy surface For the ethanol + HȮ2 system, in general, hydrogen atom can be abstracted by HȮ2 radical from three sites, alpha (via TS2 with a barrier of 13.4 kcal/mol), beta (via TS1 with a barrier of 21.9 kcal/mol) and ȮH (via TS3 with a barrier of 18.9 kcal/mol) respectively, on ethanol molecular. Without exception, each reactant falls into a well first to form a Van Der Waals reactant-complex followed by its TS. Moreover, the formed TS yields a Van Der Waals product-complex before generating final product, Fig. 2. To easily 6


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distinguish these species, a detailed nomenclature is available in Table 1. Table 1 Abbreviations of reactions and species involved in this study. Remarks

Abbreviation

Explanation

Rxn1

H-atom abstraction from beta site

Rxn2

H-atom abstraction from alpha site

Rxn3

H-atom abstraction from hydroxyl site

R

Reactant

RC

Reactant-complex

TS

Transition state

PC

Product-complex

P

Product

Fig. 2. Detailed potential energy surface of ethanol +HȮ2 calculated at the CCSD(T)/cc-pVTZ level of theory at 0 K with considering the energy of reactants (C2H5OH+HȮ2) as the zero energy. Note that there are not real IRC results, but only the stable point energies with artistic interpolations. It is clearly that Rxn 1 possesses much higher energy of Van Der Waals reactant-complex than Rxn2 and Rxn3. In contrast, Rxn 2 and Rxn 3 have comparable Van Der Waals energies, meaning that the RCs of Rxn2 and Rxn3 are relatively stable. Furthermore, Rxn2 enters into a deep well (9.2 kcal/mol) after the reactants due to such the tendency to form hydrogen bonds. The similar phenomenon has also been found 7



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in the study of Zhou et al. 24 on same channel (9.32 kcal/mol). Likewise, Rxn3 enters into a deep well (9.0 kcal/mol) after the reactants. Notice that Rxn 2 and Rxn 3 have the deeper well than Rxn1 due to the formation of hydrogen bonds. To illustrate intuitively this characteristic, the weak interaction was analyzed by using Independent Gradient Model (IGM)20 with means of Multiwfn package21 and VMD software22, Fig. 3. Obviously, the Van Der Waals interaction is dominant in RC1 system. For RC2 system, however, the weak interaction in the complex is dominated by hydrogen bonds, and the Van Der Waals interaction presents only a negligible influence. The weak interaction of RC3 is also controlled by hydrogen bonds, and it presents the Van Der Waals interaction and steric hindrance. Clearly, it is consistent with the above analysis that the formation of hydrogen bonds has slightly stronger interaction than Van Der Waals force, resulting in the deeper well of Rxn2 and Rxn3 relative to Rxn1.

(a)

(b) 0.05

(c)

-0.05

Fig. 3. Iso-surface coloring graphs of RC1, RC2 and RC3 based on pro-molecular density with IGM analysis. Blue region indicates the extensive weak interaction of hydrogen bonds, green region denotes the quite weak interaction of Van Der Waals interaction, and red region represents the strong steric hindrance in the ring and cage. (a) Geometry of RC1; (b) Geometry of RC2; (c) Geometry of RC3. 8


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Moreover, Rxn2 has lower barrier and less heat absorption together with lower energy of product relative to Rxn1 and Rxn3. Combining consideration of reaction thermodynamics and kinetics therefore suggest that the Rxn2 is favorable compared to the other two. Details of single-point energies (SPEs) and nomenclature of corresponding species are listed in Table S2. Regarding the energy level, as mentioned above, the Rxn 1 possesses slightly higher barrier (21.9 kcal/mol) than Rxn3 (18.9 kcal/mol) but much higher than Rxn2 (13.4 kcal/mol). This phenomenon is in good agreement with the H-atom abstraction reaction at the corresponding position of n-butanol + HȮ2 system (13.10 kcal/mol for alpha site, 19.60 kcal/mol for delta site and 19.12 kcal/mol for ȮH site) calculated by Zhou et al.11. To generally understand the internal cause why the TS3 lies in a lower barrier than TS1, the distortion/interaction model

23

 E   Estrain  Eint was used to analyze the relative

  energies of TS3 and TS1. Among them, Estrain and Eint of TS1 are 18.20 kcal/mol and 6.15 kcal/mol

respectively, while they are about 30.86 kcal/mol and -22.01 kcal/mol for TS3. Though TS3 has remarkably higher strain energy, it also possesses quite high interaction energy. The compromise causes the slightly lower barrier of TS3 than that of TS1. Nevertheless, the Rxn 3 first enters a deeper well before entering the transition state, which makes it more difficult to cross the barrier. Moreover, the rate constants depend upon the activation barrier and the entropy cost in reaching the transition state, and strengthen the hydrogen bond formed in the transition state, the lower the activation entropy will be 11. Thus, the TS3 with stronger hydrogen bonds has less activation entropy than the TS1, leading to lower reaction rate of channel 3 than that of channel 1. Moreover, the barriers of Rxn1 and Rxn2 are higher than that of the corresponding channels in n-butanol + HȮ2 system. Therefore, all of the reaction channels exhibit such the tendency that the reaction rate coefficients of ethanol + HȮ2 are lower than that of n-butanol+ HȮ2. 3.2. Geometries of reactants, intermediate radicals, transition states and products The geometry optimization of the reactants, products, transition states, and the intermediate species 9



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of Rxn1, Rxn2 and Rxn3 channels was performed at the M06-2X/def-TZVP level of theory, Table S1. The optimized structural parameters are available in Figs. 4-6. 3.2.1 H-atom abstraction from beta site The optimized structures of RC1, PC1 and TS1 are illustrated in Fig. 4. Compared to the C-H bond on RC1 (1.091Å), the cleaving C-H bond (1.355Å) on TS1 is stretched by 24.2%, while the forming OH bond length on TS1 is (1.161Å), 19.7% longer than the value on equilibrium structure of PC1 (0.970Å), implying that TS1 possesses a “late”, product-like behavior. It can be thus inferred that Rxn1 is an endothermic reaction according to Hammond’s postulate 24. For example, if the two states, the transition state and the unstable intermediate, occur continuously during the reaction and contain almost the same energy content, the mutual transformation between them will only involve a small molecular structure restructure, namely the transition state is located structurally closer to higher energy side 24. Obviously, it is consistent with the PES illustrated in Fig. 2. Ethanol has three methyl C-H bond with a BDE of 103.4 kcal/mol calculated at the CBS-APNO level, and it is quite close to the literature value (103.2 kcal/mol) calculated at CBS-QB3 level 12a but 4 kcal/mol higher than the methyl C-H bond (99.4 kcal/mol) of n-butanol25. To implement the H-atom abstraction, kinetically accessible, the system needs to overcome a barrier of 21.9 kcal/mol, which is significantly higher than Zhou et al.

11

calculation (19.6 kcal/mol) on delta site of n-butanol. Thermally

accessible, however, this reaction needs to absorb 15.7 kcal/mol of heat. Through comparing BDE and reaction barriers between ethanol + HȮ2 and n-butanol + HȮ2, we thus have reason to suggest that the reaction rate constant of beta H-atom abstraction is slower in ethanol + HȮ2 system than that in n-butanol + HȮ2 system.

10


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1.428Å

1.311Å

0.970Å 2.762Å 2.320Å 1.420Å

1.421Å 1.517Å

1.091Å

1.487Å

PC1

RC1

1.392Å

1.161Å

1.355Å 1.424Å

1.504Å

TS1

Fig. 4. Optimized geometries of RC, PC and TS obtained at the M06-2X/def-TZVP level for beta site Hatom abstraction. 3.2.2 H-atom abstraction from alpha site The optimized structures of RC2, PC2 and TS2 are illustrated in Fig. 5. The cleaving C-H bond (1.293Å) is stretched by 18.4% relative to that in RC2 (1.092Å), while the forming O-H bond length on TS2 is 1.247Å which is 27.8% longer than that in equilibrium structure of PC2 (0.976Å), suggesting that TS2 exhibits reactant-like behavior. It can be seen from PES in Fig. 2, the Rxn2 is endothermic reaction. Therefore, the behavior violates Hammond’s postulate. Ethanol possesses two alpha C-H bonds with a BDE of 95.1 kcal/mol (95.3 kcal/mol reported by 11



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Sarathy et al. 12a) determined at the CBS-APNO level. Again, the calculated value is 2.1 kcal/mol higher than that in corresponding position of n-butanol (93 kcal/mol)25. Likewise, the system kinetically needs to overcome a comparable barrier of 13.4 kcal/mol to abstract Ḣ atom relative to n-butanol + HȮ2 system (13.10 kcal/mol). Furthermore, the process thermally needs to absorb 8.6 kcal/mol of heat. From the comparison of BDE and reaction barriers between ethanol + HȮ2 and n-butanol + HȮ2, the reaction rate constant of alpha H-atom abstraction is also slower than that in the corresponding position of n-butanol + HȮ2. Compared to the abstractions from beta and ȮH sites, the abstraction from alpha site dominates in both kinetics and thermodynamics.

1.311Å

1.362Å

2.876Å

1.429Å 2.210Å

1.483Å

1.437Å

0.976Å

1.511Å 1.092Å

PC2

RC2

1.379Å

1.499Å

TS2

1.293Å 1.390Å 1.247Å

Fig. 5. Optimized geometries of RC, PC and TS obtained at the M06-2X level with the def-TZVP basis set for alpha site H-atom abstraction. 3.2.3 H-atom abstraction from hydroxyl site The optimized structures of RC3, PC3 and TS3 are illustrated in Fig. 6. The cleaving O-H bond (1.263Å) is stretched by 30.7% relative to that in RC3 (0.966Å), while the forming O-H bond length in TS3 is 1.097Å, which is 12.5% longer than that in equilibrium structure of PC3 (0.975Å). Similar to beta 12


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H-atom abstraction, the TS3 presents a “late”, product-like behavior. According to Hammond’s postulate, again, the Rxn3 is endothermic reaction. Ethanol possesses only one hydroxyl O-H bond with the BDE of 105.3 kcal/mol calculated at the CBS-APNO level (105.4 kcal/mole in literature12a), which is 2.6 kcal/mol higher than that of O-H bond on n-butanol (102.7 kcal/mol25). Again, the system kinetically needs to overcome a barrier of 18.9 kcal/mol and thermally needs to absorb 17.5 kcal/mol of heat. It is different from two H-atom abstraction reactions above, the barrier is slightly lower than n-butanol + HȮ2 calculated by Zhou et al.

11.

In

conclusion, for the H-atom abstraction from ȮH site, the target reaction has a comparable barrier to nbutanol + HȮ2 system. Moreover, the target system has much higher BDE, meaning lower reaction rate coefficient of OH site abstraction, ethanol + HO2 than n-butanol + HȮ2.

1.429Å 0.975Å

2.439Å

1.899Å

1.309Å 0.966Å 1.374Å

1.430Å 1.520Å 1.515Å

PC3

RC3

13



1.097Å

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1.384Å

1.263Å

1.515Å

1381Å

TS3

Fig. 6. Optimized geometries of RC, PC and TS obtained at the M06-2X level with the def-TZVP basis set for hydroxyl site H-atom abstraction. 4. Analysis of reaction rate coefficient 4.1 Minimum energy path (VMEP) and adiabatic ground-state energy (VaG) Yang et al. 26 suggested that the frequently-used Euler steepest-descents algorithm is less accurate to determine minimum energy path and adiabatic ground-state energy. The reason is that the method searches linearly along the negative gradient direction, finds the lowest point of the energy, and then calculates the next step. The convergence becomes slowing down when near the vicinity of local minimum point, and even fluctuation occurs. With this in mind, the more accurate and stable Page-McIver method

27

was

applied in this study. Specifically, the values of 200 points for minimum energy path (VMEP) and adiabatic ground-state potential energy (VaG) were calculated at each end of saddle point with an interval of Δs = 0.01 amu1/2Bohr. Both the VMEP and VaG evaluated at the M06-2X/def-TZVP level for the title reactions at the range of -1.0 < s < 1.0 are illustrated in Fig. 7. For the H-atom abstraction reactions, none of these three channels shows well or well-like curves. Notice that the IRC calculations were performed over a narrow range of reaction coordinate s, the wells obtained in the IRC analysis are not the Van der Waals complex wells presented in Fig. 2. The zero point energy (ZPE) representing the overall energies contributed from each vibration mode is the difference between VMEP and VaG. The VaG enters the reactant14


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side and simultaneously the ZPE decreases gradually to a lower energy level and keep the minimum value in the vicinity of transition states. With the VaG depart from transition state to the product-side, the value of ZPE gradually increases, while this phenomenon is quite different from what stated by Yang et al. 26. In this study, as the ZPE does not decrease or increase sharply with the reaction coordinate, meaning that no red shift or blue shift occurs. Hence, there is no well or well-like curve, and the tunneling probability and rate coefficient almost remain unchanged. Unlike Rxn1, the VMEP of Rxn 3 is flatter at the product end and steeper at the reactant end. Moreover, the VMEP of Rxn2 exhibits a similar tendency to Rxn1 at the product end. Again, the VMEP of Rxn2 does not show a well or well-like curve with a steep slope at the reactant end. 15.0

78

70 68

10

VMEP G

Va 5

ZPE

66 64 62

G Va (kcal/mol)

15

-0.05

0.00

0.05

VMEP

7.5

60

62

ZPE

60 58

2.5

56 54

0.0

0.10

64

Va

G

5.0

56 -0.10

66

10.0

58 0

68

12.5

74 72

70

Rxn2

76

VMEP(kcal/mol)

20

72

80

Rxn1

G Va (kcal/mol)

25

VMEP(kcal/mol)

-0.10

-0.05

0.00

0.05

reaction coordinate (s)


0.10

80 20

78

Rxn3

76 72

15

VMEP G

Va

ZPE

10

70 68 66 64 62

G Va (kcal/mol)

74

VMEP(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


60

5

58 56 -0.10

-0.05

0.00

0.05

0.10


Fig. 7. VMEP and VaG evaluated at M06-2X/def-TZVP level of C2H5OH + HȮ2. 4.2. Reaction rate coefficients In order to ensure the comparability of computational accuracy for the title reactions, same method 15



with Zhou et al.

11,

Page 16 of 27

the conventional TST method with zero-curvature tunneling method was used to

calculated the rate constants. As mentioned in the section 2, the conventional TST provides only an approximate ‘‘true’’ rate constants, in part because it is a calculation in one-way flux through dividing surface, but it is just appropriate for small and classical vibrations around saddle point 28. Additionally, the dividing surface of conventional transition state is a hyper-plane perpendicular to MEP. Moreover, this dividing surface exhibits a strong re-crossing. It is generally believed that the conventional TST only presents upper limit of reaction rate coefficient. But in fact, part of active molecules likely crosses the barrier height and then turns around. It clearly violates the “no return” assumption in TST theory that the computational reacting flux is larger than the real net flux, meaning that a reasonable approach is necessary to solve the turnaround issue together with addressing the change of dividing surface located originally at the saddle point. The first way is to change the location of the dividing surface located at the saddle point in conventional TST

29.

More generally, other dividing surfaces need to be also considered and thus are defined as

generalized transition state30 except the conventional transition state dividing surface. Unlike conventional TST, CVT method attempts to find the best single compromise dividing surface for all energies contributing to the rate coefficient at each temperature. Here, the peak of ΔG has been chosen as the TS for each given temperature. It can be inferred from these considerations that CVT is better approximation relative to conventional TST. On the other hand, the CVT method maximizes the barrier on the free energy surface, resulting in lower or comparable rate constants, and the rate constants obtained by the CVT are equal to that calculated by the conventional TST when the maximum is located at the saddle point. That is why the rate coefficients with CVT method are not greater than TST ones 31. Nevertheless, the CVT method proves more prominent advantage than conventional TST in case of higher temperatures and lower barrier heights31b. For comparison, both the methods have been adopted in this study. It can be seen that the rate coefficients 16


Page 17 of 27

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

3

10

9

10

8

10

8

10

7

10

7

10

6

10

6

10

5

10

5

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10

4

10

3

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3

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10

2

10

1

10

1

10

0

10

0

5.5

TST/ZCT CVT/ZCT

0.0

0.5

1.0

1.5

2.0

1000/T (1/K)

-1 -1 3

3.0

3.5

4.0

4.5

5.0

5.5

1000/T (1/K) 11

11

kTST/ZCT (cm mol s )

2.5

-1 -1

10

alpha-C H-atom abstraction

3

-1 -1

-1 -1

10

9

10

10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10

10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10

-OH H-atom abstraction

TST/ZCT CVT/ZCT

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

-1 -1

1.0

11

10

11

10

3

0.5

10

10

kCVT/ZCT (cm mol s )

0.0


TST/ZCT CVT/ZCT

3

-1 -1 3

10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10

beta-C H-atom abstraction


11

11

10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10


obtained by both TST/ZCT and CVT/ZCT methods are quite consistent, in Fig. 8.


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


5.5

-1

1000/T (K )

Fig. 8. Comparison of the rate coefficients obtained from both TST/ZCT and CVT/ZCT methods. It means that the conventional TST is also able to well describe the rate coefficients of the target reactions due to the obvious potential energy barriers, Fig. 2. Moreover, the first-order saddle point of the VaG is generally close to that of the MEP, Fig.6. Although the CVT does not have evident competition superiority, it has more accurate in deed and can be as a benchmark for accuracy test by using conventional TST. Table 2 has listed the Arrhenius fitted parameters for individual rate coefficient with the formula of k  AT n exp

 Ea . RT

Table 2 Quasi-Arrhenius parameters of C2H5OH + HȮ2 reactions Reactions

A

n

Ea (kcal/mol)

Rxn1(CCSD(t)/cc-pVtZ)

2.307E-2

4.285

16.803


5.023E-2

4.047

8.945

17



Page 18 of 27


1.112E-1

3.874

16.416

Rxn1(CCSD(t)/CBS)

2.443E-2

4.278

15.699

Rxn2(CCSD(t)/CBS)

3.434E-2

4.092

8.697

Rxn3(CCSD(t)/CBS)

6.547E-2

3.937

17.011

Unit of rate coefficient is cm3molecule-1s-1.

Combining the uncertainty suggested by Zhou et al. 11, and the uncertainty in calculating energy and anharmonic vibration, the total uncertainty of the calculated rate coefficients is estimated to be a factor of 3. The rate coefficients of the title reactions are compared with the values of Zhou et al.11 as well as other literature recommendations1a-c, 1g, 4, Fig. 9. Not surprisingly, the current calculation results are generally slower than Zhou et al. calculations for all three sites, and it is consistent with the analysis above. Taking the beta H-atom abstraction reaction as an example, the rate coefficients obtained at the CCSD(T)/ccpVTZ level are 2.87 to 4.28 times slower than that calculated by Zhou et al. 11 at the temperature range of 500–2000 K. Nevertheless, Zhou et al. calculation is also close to the upper limit. Likewise, the rate coefficients obtained at the CCSD(T)/CBS level are also slower than that Zhou et al. calculations at the temperature over 625 K, but they are almost consistent at the temperature below 625 K, Fig. 9(a). By contrast, the recommendations from Marinov1g, SD1a and CRECK1c are excessively beyond the upper limit. For the alpha H-atom abstraction reaction, the calculations of Zhou et al. lie in the error bar at the entire temperatures, although it is slightly faster than the values calculated in this study at the temperature over 770 K. Note that it is different from the case of beta H-atom abstraction, the results performed at the CCSD(T)/CBS//M06-2X/def-TZVP level make no difference from that at the CCSD(T)/cc-pVTZ//M062X/def-TZVP level for the case of alpha H-atom abstraction, Fig. 9(b). Moreover, all the literature values lie in the error bar, meaning the previous kinetic description on the alpha site abstraction can be accepted. In addition, for the –OH site abstraction, Fig. 9(c), the rate coefficients obtained at the CCSD(T)/cc-pVTZ level are almost the same as those obtained at the CCSD(T)/CBS level at temperature above 1333 K. At 18


Page 19 of 27

temperature below 1333 K, however, the rate coefficients obtained at the CCSD(T)/CBS level are slightly slower. Zhou et al. calculations are close to the upper limit in the temperature range of 1220–2000 K, whereas it gradually deviates from the upper limit as an increase of temperatures. Almost all of the literature values lie in the error band, only the recommendation of Marinov

1g

is relatively low at the

temperature above 1700 K.

10

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(a) β-C H-atom abstraction

-1 -1

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(b) α-C H-atom abstraction

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k (cm mol s )

3

-1 -1

k (cm mol s )

Uncertainty limit 1 2 SD NUIG

0.50

0.75

Uncertainty 3 CRECK

1.00

cc-pVTZ 16 LLNL

1.25

1.50

CBS 23 Zhou

1.75

Marinov

2.00

7

2.25

0.25

Uncertainty Uncertainty limit 1 2 3 SD NUIG CRECK

0.50

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1.75

Marinov

2.00

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-1

1000/T (K )

k (cm mol 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


1000/T (K )

(c) -OH site H-atom abstraction

Uncertainty Uncertainty limit 1 2 16 SD NUIG LLNL

0.50

0.75

1.00

cc-pVTZ CBS 23 7 Zhou Marinov

1.25

1.50

1.75

2.00

2.25

-1

1000/T (K )

Fig. 9. Comparison of the rate coefficients for H-atom abstraction of ethanol by HȮ2 from beta, alpha and -OH sites. (a) Beta site H-atom abstraction; (b) alpha site H-atom abstraction; (c) –OH site H-atom abstraction. 5. Effect of rate coefficients on kinetic modeling To further explore the effect of the calculated rate coefficients on model performance of ethanol, two typical conditions, kinetic condition with fuel in argon mixture and engine relevant condition with fuel in air mixture, are selected for the comparison, Fig. 10. The current calculation values of Rxn1, Rxn2 and 19



Rxn3 at the CCSD(T)/cc-pVTZ level and literature values are respectively incorporated into the latest mechanism of ethanol proposed by Zhang et al. 7, to predict the ignition delay times. For the case at high temperature and low pressure, the rate coefficients obtained at both the CCSD(T)/cc-pVTZ level and the CCSD(T)/CBS level present only limited effect, Fig. 10(a). It happens that there is a similar observation from Zhou et al. 11 and other literature, and all of them show moderate agreement with the experimental data measured by Noorani et al. 32. It is no surprise because ignition delay time is more sensitive to ethanol + ȮH rather than ethanol + HȮ2 at high temperature and low pressure. Nevertheless, the discrepancy is still out there as decreasing temperatures (T < 1300 K). However, at high pressure and lower temperature, despite different rate coefficients use shows relative large deviation in prediction of the ignition delay times measured by Cancino et al.1e, all of them lie within the simulation band, Fig. 10(b). Note that the simulation results with the analogy to Zhou et al.

11

also lie within the calculated uncertainty band,

meaning the molecular structure analogy with n-butanol + HȮ2 system is generally appropriate to describe the kinetic process of ethanol + HȮ2 with considering the uncertainly. However, considering the upper limit of the calculated rate, the kinetic model still over-predicts slightly the experimental results. It thus suggested that the sub-mechanisms of ethanol oxidation mechanism such as acetaldehyde and vinyl alcohol need to be further studied for complementing the limitation.

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1

(a) EtOH in Argon p = 2.1 atm  = 1.0


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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

Page 20 of 27

0

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Range 2 NUIG

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(b) EtOH in Air p = 50 atm  = 1.0

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cc-pVTZ Noorani exp. 19 1 Zhang et al. SD

0.75

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Zhou et al.

0.90

Range 2 NUIG

23

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0.85

-1

Border 16 LLNL

0.90

CBS 7 Marinov

0.95

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cc-pVTZ Cancino 19 1 Zhang et al. SD

1.00

1.05

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Zhou et al.

1.15

23

1.20

-1

1000/T (K )

1000/T (K )

Fig. 10. Influence of kinetic parameters of beta H-atom abstraction of ethanol + HȮ2 on ignition delay time. (a) Kinetic condition with fuel in argon mixture; (b) engine condition with fuel in air mixture. 20


Page 21 of 27

To check the effect of newly-calculated rate coefficients on model performance in terms of predicting ignition delay time data of dual-fuel mixtures at low temperature range, two mixtures, ethanol/DME and ethanol/n-pentane proposed by Zhang et al.7 and Jin et al.33 respectively, were selected for comparison, Fig. 11. It can be seen that for pure ethanol, the newly-calculations significantly lengthen the ignition delay times for the both systems. With decreasing the content of ethanol, however, the effect becomes inconspicuous, and it can be neglected when the chemistry of mixtures goes in the NTC regime. In general, it only presents an obvious effect on the mixtures with chemistry governed by ethanol rather than by NTC fuels. 10

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1.0EtOH 0.7EtOH+0.3DME 0.5EtOH+0.5DME 0.3EtOH+0.7DME



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


Solid lines: Model with newly-calculations Dash lines: Original model

(a)

-1

0.7

p = 20 atm;  = 1.0 fuel in Air 0.8

0.9

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1.1

1.2

1.3

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p = 20 atm;  = 0.7 fuel in Ar

Solid lines: Model with newly-calculations Dash lines: Original model

(b)

-1

0.7

1.0EtOH 0.75EtOH+0.25NC5H12 0.5EtOH+0.5NC5H12 0.25EtOH+0.75NC5H12

0.8

-1

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1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

-1

1000/T (K )

1000/T (K )

Fig. 11. Effect of newly-calculated rate coefficients with ignition delay time data obtained at low temperature range. (a) Ethanol/DME mixtures; (b) Ethanol/n-Pentane mixtures. Zhang et al. model 7 and Jin et al. model33 were adopted for the calculations. To further examine the effect of newly-calculations on underlying species evolution, mole fraction analyses made by Zhang et al. model 7 were carried out for stoichiometric ethanol/air mixture at 20 atm and 1000 K, Fig. 12. It is clearly that the concentration of acetaldehyde obviously decreases while that of ethylene increases after combining the newly-calculations, but it shows only negligible effect on the vinyl alcohol, suggesting that further modification on the secondary mechanisms of ethanol is necessary.

21



0.018

Dash lines: Original model Solid lines: Model with new-calculations

0.015

0.0020 0.0016

0.012 C2H3OH

0.0012

C2H4

0.009

CH3CHO 0.006

0.0008 0.0004

0.003 0.000 1000

0.0024

Mole fraction

Mole fraction

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

Page 22 of 27

0.0000

1250

1500

1750

2000

2250

-0.0004 2500

Temperature/K

Fig. 12. Effect of newly-calculations on evolution of intermediate species in ethanol oxidation at 20 atm and 1000 K by using Zhang et al. 7 mechanism. 6. Concluding remarks In this work, the rate coefficients calculations for ethanol + HȮ2 system were performed by using both conventional TST and CVT with quantum effect considerations of ZCT. Two Eckart functions were used to correct the minimum energy path by different fitting method. Moreover, the torsional mode of the -CH3 and -OH groups were treated by using the hindered-internal-rotator approximation. It is found that there remains 1.288 times difference of the partition function for ethanol with and without considering the internal rotation, but it raises up to 1.44 times difference of the partition function for TSs. Combining both the effects, it is thus inferred that the uncertainty of the calculated rate constants caused from the effect of internal rotation is approximately a factor of 1.2. The reactants, products and transition states were optimized at the M06-2X/def-TZVP level and single point energy were computed at both the CCSD(T)/ccpVTZ level and the CCSD(T)/CBS level for comparison. For each reaction channel of ethanol + HȮ2 system, Van Der Waals complexes occur at both reactantend and product-end. Rxn1 possesses the shallowest well while Rxn2 and Rxn3 have the relatively deep well due to the formation of hydrogen bonds which makes more compact and stable. Although TS3 has remarkably higher strain energy, its interaction energy is also high compared to TS1, and it causes the slightly lower barrier for TS3 than TS1. But it falls into a deep well before arriving at the TS3, and it 22


Page 23 of 27 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


makes more difficult to cross the energy barrier. As a result, the stronger hydrogen bond makes lower activation entropy than Rxn1, resulting slower reaction rate of H-atom abstraction on OH site. Secondly, it only shows limited effect on Rxn 2 and total rate coefficients by using both the CCSD(T)/cc-pVTZ and CCSD(T)/CBS. Similar to n-butanol + HȮ2 system, the title system is dominated by alpha H-atom abstraction, but the rate coefficients of the three channels (either the CCSD(T)/cc-pVTZ level or the CCSD(T)/CBS level use) are slower than that of n-butanol + HȮ2 calculated by Zhou et al. 11. For beta H-atom abstraction, Zhou et al. 11 calculation is close to the upper limit proposed in this study. However, for the alpha H-atom abstraction, the values recommended by Zhou et al.11 and literature exactly lie in the uncertainty band. It is suggested that the previous analogy of ethanol + HȮ2 with n-butanol + HȮ2 is generally acceptable. The new calculations went over without much deviation in predicting ignition delay times for fuel in argon mixture at high temperature and low pressure, but they presented the noticeable effect for fuel in air mixture at lower temperature and high pressure. Despite considering the lower limit of the calculations, the kinetic model remains the over-prediction in the ignition delay times of both pure ethanol and ethanol/NTC binary fuels, suggesting that the secondary mechanisms of ethanol such as acetaldehyde and ethylene are valuable to further investigate from both sides, experimentally and theoretically. Supporting Information Frequencies, Zero-point energies, Rotational constants and structures from ab initio calculations at M062x/def-TZVP level. Moreover, single-point energies of species involved in title reactions at M06-2X and CCSD(T) level. Acknowledgments The authors would like to acknowledge the support from the National Natural Science Foundation of China (No. 91741115) and the Science Foundation of Shaanxi Province for Distinguished Young Scholars (No. 2018JC-002). 23



Page 24 of 27

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B. B. Reviews in Computational Chemistry. Wiley & Sons: 2010; Vol. 1-23. 32. Noorani, K. E.; Akihkumgeh, B.; Bergthorson, J. M. Comparative High Temperature Shock Tube Ignition of C1−C4 Primary Alcohols. Energy & Fuels 2010, 24 (24), 5834-5843. 33. Jin, H.; Pieper, J.; Hemken, C.; Bräuer, E.; Ruwe, L.; Kohse-Höinghaus, K. Chemical interaction of dual-fuel mixtures in low-temperature oxidation, comparing n -pentane/dimethyl ether and n pentane/ethanol. Combustion & Flame 2018, 193, 36-53.

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