ARTICLE pubs.acs.org/JPCA
Theoretical Investigations on Removal Reactions of Ethenol by H Atom Han-Bing Rao,*,† Xian-Yin Zeng,† Hua He,‡ and Ze-Rong Li*,§ †
College of Life and Science, Sichuan Agricultural University, Ya’an 625014, People’s Republic of China Animal Genetics and Breeding Institute of Sichuan Agricultural University, Sichuan YaAn 625014, People’s Republic of China § College of Chemistry, Sichuan University, Chengdu 610065, People’s Republic of China ‡
bS Supporting Information ABSTRACT: Ethenol is a recently identified combustion intermediate. However, its chemistry remains unclear. In present work, the removal reactions of ethenol by H atom are investigated. The geometries of all species involved in the reaction are optimized at B3LYP/6-311þþG(d,p), and their single point energies are extrapolated to the infinite-basis-set limit at the level CCSD(T). Energies are also calculated at G3B3, CBS-APNO, and CCSD(T)/6-311þþG(3df, 2p) for comparison. A total of six elementary reactions, including four abstractions and two additions, with explicit transition states are investigated. The results show that the reactions are selective: for abstractions, the hydrogen atom, linked to the oxygen atom, is the most reactive; while for additions, the preferred carbon site is the head “CH2d”. The rate constants are estimated in the temperature range 300-3000 K according to the conventional transition state theory with the Eckart tunneling model. The dominant channels are the two additions in the whole temperature range. The abstractions can be competitive at high temperature but still do not dominate. The calculated rate constants for the reverse reaction of (R6), synCH2dCHOH þ H T CH3 3 CHOH, are consistent with the available literature values. Finally, the Fukui functions are calculated to analyze the site reactivity.
1. INTRODUCTION Detailed chemical kinetic modeling for the combustion of hydrocarbon fuels is becoming more and more important. A chemical kinetic model generally includes a large number of elementary steps, which represent the intrinsic nature of the involved species and so are transferable from one model to another. In principle, the kinetic model should consist of all possible reaction pathways that involve all the chemical species. However, it is quite difficult and impractical. In fact, practical mechanisms are constructed on the basis of the available data. For example, previous kinetic models for the combustion of hydrocarbons contained no chemical species of the enol form,1-3 which were observed to be present in substantial concentrations in a wide range of hydrocarbon flames.4-6 Enols are minor components in flames, and their practical significance remains unclear. However, very little is known about the formation or consumption reactions of gas-phase neutral enols. For the formation of enols, Taatjes and co-workers6 found that the reaction of OH and ethene dominates ethenol production in ethene flames and speculated that the addition-elimination reactions of OH with other alkenes are also likely to be responsible for enol formation in flames. This suggestion has been explored theoretically by Zhou et al.,7 Huynh et al.,8 and r 2011 American Chemical Society
Izsak et al.,9 all for the reaction propene þ OH. Simmie et al.10 also did calculations with multilevel methods to determine the activation enthalpies for addition of 3 H, 3 CH3, and 3 C2H5 to CH2dCHX (X = H, OH, and CH3). Actually, the addition reactions to CH2dCH-OH are reverse to the formation of enols. In such a way, the rate constants for the formation of enols, which is endothermic, can best be obtained from the exothermic direction according to the microscopic reversibility. Very recently, Silva et al.11 found that vinyl alcohol is also an important (although minor) product in their R-hydroxyethyl þ O2 mechanism. For the consumption of enols, Taatjes et al.4 showed that removal of ethenol is not dominated by tautomerization to acetaldehyde and most likely proceeds instead by reaction with flame radicals, particularly OH and H. Zhou et al.12 investigated the mechanisms and kinetics of the OH hydrogen abstraction from propenols and found that different hydrogen atoms of the different conformations of propenols, including (E)-1-propenol, (Z)-1-propenol, and syn-propen-2-ol, possess different reactivities, which also depend on the temperature in the hydrogen abstractions. Received: October 13, 2010 Revised: January 22, 2011 Published: February 11, 2011 1602
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H atom is one of the most important active radicals in the combustion. Therefore, the reaction of H atom with ethenol (CH2dCHOH) might play an important role for the removal of ethenol. To assess such an importance, this work presents a theoretical investigation for the title reaction. The reaction mechanisms are concentrated on (R1)-(R6) with (R1)-(R4) as direct hydrogen abstractions and (R5),(R6) as hydrogen additions to the two carbon centers of the double bond, that is: syn-CH2 dCHOH þ H T CH2 dCH - O 3 þ H2
ðR1Þ
T CH2 dC 3 - OH þ H2
ðR2Þ
T ðZÞ- 3 CHdCH - OH þ H2
ðR3Þ
T ðEÞ- 3 CHdCH - OH þ H2
ðR4Þ
T 3 CH2 CH2 OH
ðR5Þ
T CH3 3 CHOH ðR6Þ The present work is organized as follows. In section 2, the computational methods are presented. Section 3 reports results and discussions of our geometries, mechanisms, electronic structures, and reactivities. Section 3 also reports the reaction kinetic parameters, which are calculated on the basis of the statistical transition state theory. Finally, the conclusions are presented in section 4.
2. COMPUTATIONAL METHODS Structure parameters for each stationary point along the potential energy surface (PES) were optimized at the level of B3LYP13,14/6-311þþG(d,p),15 except for TS6 in (R6), which struggles to locate transition states at this level (see details below). The B3LYP density functional theory has been shown to achieve accurate geometries, zero-point energies (ZPE),16 and frequencies17 while having a high computational efficiency.18,19 The harmonic vibrational frequencies were also calculated at the B3LYP/6-311þþG(d,p) level for each stationary point and served to compute the zero-point energies (ZPE, without scaling) and also to characterize the nature of the stationary points (minimum versus first-order saddle point). To verify whether the located transition state structures connected the expected minima, intrinsic reaction coordinate (IRC) calculations20 were carried out in both directions at the B3LYP/6-311þþG(d,p) level. To check the reliability of the B3LYP/6-311þþG(d,p) method in the geometrical optimization, B3LYP/6-31G(d) in G3B321 scheme and QCISD/6-311G(d,p) in CBS-APNO22 scheme were used for this purpose. Besides, transition state structures were reoptimized at MP2/6-31þG(d,p), QCISD/631G(d), and MP2/6-31G(d) to further testify the dependence of the transition states on the method and basis set. Because energy barriers affect the calculated rate constants exponentially, final energy estimates for the reactants, products, and transition states are extrapolated to the infinite-basis-set limit according to eq 1.23-27 corr Etot ¼ EHF ð1aÞ ¥ þ E¥ HF -RX EHF X ¼ E¥ þ Be
ð1bÞ
3 corr Ecorr ¥ ¼ EX þ A=ðX þ 1=2Þ
ð1cÞ
Figure 1. The optimized geometries of syn-CH2dCH-OH (Cs) and syn-CH2dCH-OH (Cs) at B3LYP/6-311þþG(d,p) (bond lengths in angstroms, angles in degrees).
where X is the maximum component of angular momentum in the cc-pVXZ basis set. In the present work, EHF ¥ was obtained on the basis of the single point energies at HF/cc-pVXZ with X = 2, was obtained from the correlation energies at 3, 4, and Ecorr ¥ CCSD(T)/cc-pVXZ with X = 2, 3. Furthermore, single point energies were also calculated at CCSD(T)/6-311þþG(3df, 2p), G3B3, and CBS-APNO for comparison. All electronic calculations in the present study were performed by using the Gaussion 03 program.28 Subsequent rate parameters were calculated by using the conventional transition state theory as shown below.
3. RESULTS AND DISCUSSION 3.1. Properties of the Stationary Points. The optimized geometries of all the stationary points along PES are presented in Table S1 of the Supporting Information, along with their Cartesian coordinates, vibrational frequencies with hindered rotation being considered (see Table S1; the vibration mode corresponding to the internal rotation is in bold and italic), and moments of inertia. For species with more than one conformation, internal rotor potential as a function of the corresponding dihedral angle was determined by relaxed-scanning the torsion angle in one period. In this way, the most stable conformation is determined, and it is used in the calculations of electronic structures and the subsequent kinetics, with the implicit assumption that conformation changes are very rapid relative to the chemical reactions. The internal rotation analyses at the B3LYP/ 6-311þþG(d,p) level are shown in Figures S1-S6 of the Supporting Information. The structure parameters for the conformer syn- and anti-CH2dCH-OH are presented in Figure 1. Both of the two conformers possess Cs symmetry, while the energy difference between the anti- and syn-forms is 1.27 kcal/ mol at the level of CCSD(T)/¥, or 1.39 kcal/mol at B3LYP/ 6-311þþG(d,p), with the adiabatic rotation barrier (syn f anti) 5.03 kcal/mol at B3LYP/6-311þþG(d,p). The syn-form contribution is then 89.5%, more preferred than the antiform 10.5% at 298.15 K according to the Boltzmann distribution rule. In this Article, the most stable conformers are concerned. The calculated structures in Figure 1 are consistent with the experimentally determined structures by the microwave spectroscopy method29 and the previous calculated ones.10,30-32 The C-C and the CH bond lengths are shortened in ethenol as compared to those of ethylene,33 while the CCO and CCH angles are larger. It should be noted that the DFT-based method can not locate the TS6. This has been shown in the work of Simmie and Curran.10 We investigated TS6 from the reverse direction by relaxed-scanning the distance between the carbon and the 1603
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Table 1. Geometry Parameters for the Transition States (TS1-TS6)a species TS1
coordinate HH
1.023
OH
1.117
OHH COHH TS2
TS3
QCISDc
1.118
168.8
168.0
85.4
92.3 0.864
0.867
0.839
0.875
1.462
1.435
1.462
1.451
CHH
179.8
CCHH HH
179.9 0.835 1.522 177.2
179.8
179.0
-179.6 0.839
-180.0 0.853
1.515
179.0 179.9 0.827
1.457
178.3
1.483
176.5
179.9 -173.0 0.864 1.464
4.5 0.837 1.493 177.1
-0.4
0.1
0.0
3.4
0.1
0.0
0.849
0.852
0.864
0.837
0.874
CH
1.507
1.503
1.453
1.480
1.464
177.0
1.472 179.9
177.6
CCHH
179.6
0.851
176.5
HH
178.5
MP2c
1.039
1.473
177.9
179.1
0.847 1.493 178.8
CCHH CH
0.0 1.931
0.0 1.923
0.0 1.853
0.0 1.768
-0.1 1.799
0.0 1.739
CC
1.352
1.357
1.363
1.348
1.367
1.354
CO
1.360
1.360
1.363
1.370
1.374
CCH CCOH
1.370
96.2
96.0
97.3
98.7
99.8
99.0
-106.0
-106.5
-107.3
-108.3
-110.1
-109.6
CH
1.997
1.846
1.906
1.807
CC
1.352
1.338
1.356
1.342
1.358 106.3
1.361 108.5
1.368 108.5
1.360 109.4
49.3
46.5
47.0
45.8
CO CCH CCOH a
MP2e
CH
CHH
TS6
QCISDd
0.857
CHH
TS5
B3LYPc
HH
CH
TS4
B3LYPb
Bond lengths in angstroms, angles in degrees. b 6-311þþG(d,p). c 6-31G(d). d 6-311G(d,p). e 6-31þG(d,p).
Table 2. PES for the Title Reaction Calculated at Various Levels of Theorya species
ZPEb
T1d
enolþH
35.3
0.012, 0.000
TS1
33.1
0.029
P1þH2
32.9
0.033, 0.005
TS2
33.1
0.030
P2þH2
33.1
0.035, 0.005
TS3
34.0
0.032
CCSD(T) e
CCSD(T)/¥ f
G3B3
CBS-APNO
0.0
0.0
0.0
13.3
12.7
10.2
0.0
-19.7
-18.5
-20.1
-20.0
16.9
16.2
15.8
14.9
4.8
5.0
3.7
3.9
18.5
17.7
17.5
16.4
P3þH2
33.0
0.033, 0.005
10.1
10.0
9.1
10.0
TS4 P4þH2
33.8 33.0
0.031 0.032, 0.005
17.7 8.7
16.8 8.6
16.8 7.6
15.6 8.7
TS5
36.4
0.030
5.8
P5
40.8
0.012
-27.1
TS6
37.9c
0.028
4.3
3.2
P6
41.2
0.015
-34.1
-35.3
5.2 (6.4g) -28.4 (-25.4g)
4.6
4.7
-27.8
-28.0
-34.7
-35.6
1.6
Energies (kcal/mol) are relative to the enol þ H including the corresponding ZPE corrections. b ZPE at B3LYP/6-311þþG(d,p) without scaling. ZPE at MP2/6-31þG(d,p) without scaling. d T1 diagnostic values calculated at CCSD(T)/6-311þþG(3df,2p). e Relative energies at CCSD(T)/6311þþG(3df,2p). f Relative energies based on eqs 1a-1c and Table S2 in the Supporting Information. g Reference 34 calculated at PMP2/aug-ccPVQZ//MP2/cc-PVTZ. a c
attaching hydrogen atom, and then found no maxima from products to reactants (see Figure S7 in the Supporting Information). However, TS6 can be located at MP2 and QCISD methods. The structures of TS6 at MP2/6-31þG(d,p) are used in this channel. In addition, TS1 cannot be located at methods of MP2/6-31þG(d,p), MP2/6-31G(d), QCISD/6-311G(d,p),
and QCISD/6-31G(d). Table 1 presents the structural parameters of the optimized transition states at various levels. One can see that the optimized transition states are not very sensitive to the methods. The geometry differences may be due to that the B3LYP wave functions have minor spin contamination as compared to the HF-based methods. The energetic data at 1604
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Table 3. Enthalpies of Activation and of Reaction at 298.15 K for (R5) and (R6) CCSD(T)/¥a
G3B3
CBS-APNO
ref
Enthalpies of Activation (kcal/mol) (R5)
4.07
(R6)
1.58
3.64
3.69
3.51,b 3.68c
0.71
0.72c
Enthalpies of Reaction (kcal/mol) (R5)
-29.37
-28.71
-28.88
-28.51,b -28.18c
(R6)
-36.32
-35.61
-36.45
-35.80,b -36.45c
a
Sum of the CCSD(T)/¥ electronic energy and thermal corrections to the enthalpies at 298.15 K at B3LYP/6-311þþG(d,p), except TS6 at MP2/6-31þG(d,p). b Reference 10 at CBS-QB3. c Reference 10 at CBSAPNO.
various levels in Table 2 show that the barrier height is not sensitive to the calculated geometries. 3.2. Reaction Mechanisms and PES. (R1)-(R4) channels take place via direct hydrogen abstractions through TS1-TS4, respectively. (R5) and (R6) channels are hydrogen additions to the CC double bond through TS5 and TS6, respectively. The first five channels have explicit transition states at B3LYP/6311þþG(d,p), while the (R6) channel does not at this method. However, TS6 can be located at methods MP2 and QCISD. The calculated energetic data (with ZPE correction) of these channels at various levels are listed in Table 2. One can see that the energetic data at these four methods agree well to each other, although with the largest discrepancy 3.1 kcal/mol in TS1. In other aspects, the relative energies of the products are consistent with each other (the differences range from 1.0 to 1.6 kcal/mol). In the following discussions, the energies extrapolating to the infinite basis set are used. To test the significance of the multireference character in the title reaction, T1 diagnostic analysis was done at CCSD(T)/6-311þþG(3df, 2p). Rienstra-Kiracofe et al.35 showed that for open-shell systems the multireference wave function is significant only if the T1 diagnostic value is greater than 0.044. As shown in Table 2, the T1 diagnostic values at the CCSD(T)/6-311þþG(3df, 2p) for all the open-shell species are smaller than 0.044; for the closed-shell species, ethenol and H2 in the present work, the T1 diagnostic values are smaller than 0.02. It indicates that the single reference-based ab initio methods used in this work should be applicable and the calculated results should be reliable. 3.2.1. Hydrogen Abstractions. (R1)-(R4) channels are direct hydrogen abstraction reactions. The four hydrogen atoms (H1-H4 see the labeling in Figure 1) have quite different bonding environments, so their reactivities are different. In (R1), the hydrogen atom H1, linked to the oxygen atom, is very reactive in the abstractions with the energy barrier 12.7 kcal/mol. As can be seen from the Supporting Information and Table 1, in TS1, the breaking O-H bond is enlarged by 0.152 Å, and the forming H-H bond is still 0.279 Å longer than the equilibrium H-H bond of the molecule H2. The reacting H 3 3 3 H 3 3 3 O geometry is nearly linear. Interestingly, TS1 is a little far away from a planar structure with the dihedral angle CCOH 45.2. It might result from the steric effect. The classical barrier height (i.e., without the ZPE correction) is 14.9 kcal/mol. The forward reaction energy of (R1) is -18.5 kcal/mol. In P1 (CH2dCH-O 3 ), the C-C bond is 1.424 Å, about 0.081 Å longer than that of ethenol, and the C-O bond is 1.235 Å, 0.128 Å shorter than that in ethenol.
The (R2) channel gives P2 (CH2dC-O 3 H) and H2. In TS2, the breaking C-H bond is stretched by 0.389 Å, and the forming H-H bond is 0.857 Å, which is still 0.113 Å longer than the equilibrium length of H2. The reacting H 3 3 3 H 3 3 3 C geometrical angle is almost linear. TS2 is nearly Cs symmetry. The barrier height of TS2 is 16.2 kcal/mol, which is 3.5 kcal/mol higher than that of TS1. The classical barrier height for (R2) is 18.4 kcal/mol. The (R3) channel gives P3 ((Z)- 3 CHdCH-OH, which is a syn-form) through TS3. The breaking C-H bond is 1.522 Å, which is stretched by about 40%. The forming H-H bond is 0.091 Å longer than that of H2. Evidently, TS3 is a product-like barrier. The reacting H 3 3 3 H 3 3 3 C angle is nearly linear. TS3 is almost Cs symmetry. The barrier height of TS3 is 17.7 kcal/mol. Very similarly, the (R4) channel gives P4 ((E)- 3 CHdCH-OH, which is a syn-form) through TS4. TS4 is also a product-like barrier with a linear H 3 3 3 H 3 3 3 C reacting angle and shows Cs symmetry. The TS4 barrier is 16.8 kcal/mol, which is 1.1 kcal/mol lower than that of TS3. From Table 2, it is obvious that the ZPE plays an important role in (R1)-(R4). The barriers for hydrogen abstracted by H atom in the title reaction are greater than that by OH in the propenol,12 with the H of O-H being the easiest way. 3.2.2. Additions. The hydrogen atom can attack the two carbon centers of the CC double bond. In (R5), the hydrogen atom attacks the carbon atom linked to the hydroxyl group via TS5 to give P5 ( 3 CH2CH2OH). In TS5, the forming C-H bond is 1.931 Å, which is 0.832 Å larger than the equilibrium length in P5 radical. The CC bond length is 1.352 Å, a little longer than that of ethenol, while the C-O bond length is shortened a little to 1.360 Å. The angle H 3 3 3 C 3 3 3 C is 96.2, nearly in a perpendicular direction. TS5 is a reactant-like barrier, with a small height 5.2 kcal/mol, as compared to the previous calculated barrier 6.4 kcal/mol at PMP2/aug-cc-PVQZ//MP2/cc-PVTZ.34 The forward reaction energy of (R5) is -28.4 kcal/mol. To compare with available literature values, enthalpies of activation and of reaction of (R5) and (R6) are summarized in Table 3. One can see that our calculated results are consistent with the literature values in ref 10 and references cited therein. In (R6), the hydrogen atom attacks the other carbon atom of the ethenol via TS6 to give P6 (CH3 3 CHOH). However, TS6 cannot be located at the B3LYP method, but can be located at the MP2 and QCISD methods. The MP2/6-31þG(d,p) structures for TS6 are used in the subsequent calculations. The forming C-H bond is 1.846 Å, which is quite larger than the equilibrium data in P6. The CC bond length is 1.338 Å, the CO bond length is 1.361 Å, and the angle H 3 3 3 C 3 3 3 C is 108.5. TS6 is also a reactant-like barrier, with a small height of 3.2 kcal/mol. This barrier height may be even lowered by about 1.5 kcal/mol if the frequencies at MP2/6-31þG(d,p) were scaled. Obviously, the addition to the “CH2” end through TS6 is easier than that to the “CHOH” end. This conclusion has been drawn by Simmie and Curran.10 The forward reaction energy of (R6) is -35.3 kcal/mol, which is 6.9 kcal/mol lower than that of the channel (R5). 3.3. Rate Constants. The forward and reverse rate constants of the six elementary reactions are determined by using the conventional transition state theory (TST) within the rigid rotor harmonic oscillator (RRHO) approximation, that is:36,37 kTST ¼ kðTÞ
σkB T Q TS ðTÞ expð-Ea =RTÞ h Q R ðTÞ
where κ is the tunneling factor; σ is the reaction symmetry number; Q represents the total partition function including 1605
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Table 4. TST Estimate of Elementary Rate Parameters for (R1)-(R6)a Af
nf -21
Ea,f
Ar -24
Ea,r
(R1)
2.453 10
3.077
7.23
3.721
24.60
(R2) (R3)
1.450 10-15 6.124 10-17
1.727 1.975
48.13 50.25
3.619 10-19 6.820 10-20
2.450 2.473
41.32 38.66
(R4)
4.109 10-17
2.030
15.18
6.943 10-20
2.498
5.06
1.577
3.67
9.964 108
1.395
32.52
1.432
1.20
8.693 108
1.441
36.90
-16
(R5)
5.005 10
(R6)
9.054 10-16
2.343 10
nr
Table 6. Calculated Local Softness for Ethenol at the Level B3LYP/6-311þþG(d,p)a 0
-1
S (au )
C1b
C2
H1
H2
H3
H4
0.788
0.276
0.521
0.258
0.347
0.438
a
See refs 39 and 40 for details; the raw data are given in the Supporting Information. b The subscripts are labeling numbers as shown in Figure 1.
k = AT exp(-Ea/RT); subscript “f”, forward; “r”, reverse; units: unimolecular reactions, s-1; bimolecular reactions, cm3 molecule-1 s-1; energy, kcal mol-1. a
n
Table 5. Eckart Tunneling Factors for (R1)-(R6) at Temperatures 300, 400, 500, and 600 K (R1)
(R2)
(R3)
(R4)
(R5)
(R6)
300 K
82.56
3.08
2.15
2.43
1.91
3.44
400 K
8.45
1.92
1.61
1.74
1.52
2.18
500 K
3.73
1.58
1.41
1.49
1.37
1.75
600 K
2.54
1.42
1.31
1.37
1.28
1.55
translation, vibration, rotation, and hindered rotation; Ea is the classical barrier height; and kB and h are Boltzmann’s and Planck’s constant, respectively. In this work, the Eckart tunneling correction was employed. The TST can give an estimate of the upper-limit for the rate constants as a function of the temperature. However, the TST is simple, and only information about the stationary points is necessary. Based on this little information, TST might give reliable estimations on the rate constants,38,39 especially for cases with significant barrier heights. Recent reaction class transition state theory (RC-TST) developed by Truong et al. employed the TST/Eckart method to estimate the rate constants of reaction classes, like O(3P) þ alkane f OH þ alkyl reaction class,40 CH3 þ alkane f CH4 þ alkyl reaction class,41 H þ alkene f H2 alkenyl reaction class,33 ROH þ H f RO 3 þ H2 reaction class,42 and so on. The differences of the results on these reaction classes between the barrier height group (BHG) and the explicit TST/Eckart are all acceptable. In addition, the energy parameters affect the rate constants exponentially. In this work, the energy parameters were obtained by a high level. So the TST can give reliable results based on little information, especially when the tunneling and variational effects are negligible. One can see that all six reaction channels involve significant barriers, so the variational effects might be negligible.43 The conventional TST is employed. The detailed rate constants with the temperature for (R1)-(R6) are given in the Supporting Information. For the practical use in the chemical kinetic modeling, the rate constants are fitted to the modified Arrhenius equation, k = ATn exp(-Ea/RT), in the temperature range 300-3000 K, as shown in Table 4. The rate constants were calculated using the kinetic module of the web-based Computational Science and Engineering Online (CSE-Online) environment.44 The calculated Eckart tunneling factors at low temperature in Table 5 show that the tunneling effect plays an important role particularly in the channel (R1) at 300 K. From the calculated rate constants (see also the Supporting Information), it shows that the forward rate constants of (R2) and (R3) are very small (76.3%) and (R5) (
