Theoretical Studies on the Unimolecular Decomposition of Ethylene

ARTICLE pubs.acs.org/JPCA

Theoretical Studies on the Unimolecular Decomposition of Ethylene Glycol Lili Ye,† Long Zhao,† Lidong Zhang,*,† and Fei Qi†,‡ † ‡

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, P. R. China State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China

bS Supporting Information ABSTRACT: The unimolecular decomposition processes of ethylene glycol have been investigated with the QCISD(T) method with geometries optimized at the B3LYP/6-311++G(d,p) level. Among the decomposition channels identified, the H2O-elimination channels have the lowest barriers, and the C
C bond dissociation is the lowest-energy dissociation channel among the barrierless reactions (the direct bond cleavage reactions). The temperature and pressure dependent rate constant calculations show that the H2Oelimination reactions are predominant at low temperature, whereas at high temperature, the direct C
C bond dissociation reaction is dominant. At 1 atm, in the temperature range 500
2000 K, the calculated rate constant is expressed to be 7.63  1047T
10.38 exp(
42262/T) for the channel CH2OHCH2OH f CH2CHOH + H2O, and 2.48  1051T
11.58 exp(
43593/T) for the channel CH2OHCH2OH f CH3CHO + H2O, whereas for the direct bond dissociation reaction CH2OHCH2OH f CH2OH + CH2OH the rate constant expression is 1.04  1071T
16.16 exp(
52414/T).

G2M (RCC2) level of theory.15 They predicted that the H2Oelimination process was the main reaction channel for the decomposition of C2H5OH at low temperature, whereas at high temperature the C
C bond cleavage became prevailing. Li et al.27 further studied the ethanol decomposition reactions with both experimental and theoretical methods. Their results showed that the dehydration reaction had a barrier height of 66.6 kcal/mol and was considered to be the dominant channel at low temperature as well, which agrees with previous studies15,29 very well. Meanwhile, the rate constant that they obtained for this channel was in excellent agreement with the shock-tube measurements by Herzler et al.30 For propanol, Bui et al.22 calculated the unimolecular decomposition of 2-propanol with a modified G2 method, and Shu et al.28 studied the decomposition of C3H7OH by the O(1D) + C3H8 reaction in crossed molecularbeam experiment. Bui et al. drew the same conclusion with ethanol that the H2O-elimination process was dominant at low temperature, whereas the C
C bond cleavage prevailed at high temperature. The results of Shu et al.28 also demonstrated that C
C bond cleavage was the main reaction among the direct bond dissociations for both 2-propanol and n-propanol. To sum up, from previous work of the unimolecular decomposition of monohydric alcohols, the H2O-elimination and the C
O bond cleavage processes are the two most important reactions for methanol, whereas the H2O-elimination and the C
C bond

1. INTRODUCTION With the rapid depletion of fossil fuels, biofuels have been recognized as one of the most potential alternative energy sources.1
5 As a typical class of biofuels, alcohols have aroused increasing interest in recent years. Alcohols have been widely used as alternative fuels or fuel additives, because they can effectively inhibit the formation of polyaromatic hydrocarbons (PAHs) and soot in combustion processes.6
9 As we know, bioethanol has already been blended with gasoline for use in combustion internal engines and biobutanol has even been directly used without blending.3,10 Although large amounts of investigations have been carried out on monohydric alcohols (such as methanol, ethanol, propanol and butanol),11
24 polyols gained less attention. Yet polyols are one of the principal components of plant matter, from which biofuels are derived. Hence the study of polyols should receive great emphasis.25,26 Investigations of unimolecular decomposition provide important reference for dynamic simulations and help to understand the chemical nature of molecules. Extensive experimental and theoretical studies on the unimolecular decomposition of alcohols, such as methanol, ethanol, and propanol, have been carried out.13,15,22,27,28 In 2001, Xia et al.13 studied the unimolecular decomposition pathways of CH3OH using ab initio calculations at the G2M level and calculated the rate constants for the dissociation processes using RRKM theory. Their results showed that the product branching ratios were strongly pressure-dependent, with the production of CH3 + OH and 1CH2 + H2O dominant under high and low pressure, respectively. Park et al. investigated the unimolecular decomposition of ethanol at the r 2011 American Chemical Society

Received: August 18, 2011 Revised: December 10, 2011 Published: December 12, 2011 55

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Table 1. Energies of Major Channels Calculated at Different Levels energies at different levels (Hartree) species

CBS-QB3

CBS-APNO

QCISD(T)/CBS//B3LYP/6-311++G(d,p)

CH2OHCH2OH


229.911542


230.172656


229.960330

CH2OHCHO


228.722435


228.982723


228.770534

CH2CHOH


153.564088


153.752460


153.593710

CH3CHO


153.582461


153.770772


153.611433

CH3OH


115.539942


115.670897


115.564626

CH2OH


114.888126


115.019347


114.913436

CHOH


114.259858


114.389643


114.284514


76.337482
1.166083


76.410617
1.165279


76.357777
1.164739

H2O H2 TS1


229.798607


230.060360


229.849693

TS2


229.797306


230.059838


229.848367

TS3


229.782258


230.044215


229.833383

TS4


229.782274


230.043341


229.831848

TS5


229.776116


230.037961


229.826127

cleavage processes are most significant for monohydric alcohols with more than two C atoms. Though a great many decomposition studies have been reported on monohydric alcohols, research on the decomposition of polyols is still lacking.31
33 Ethylene glycol (ETG), one of the simplest polyols, is an important model system for polyols fuels. A large number of investigations have been carried out on the conformation of ETG, especially in theory.34
44 Researchers found that the central O
C
C
O dihedral of ETG preferred to adopt a gauche conformation, which was convinced by calculations at various levels of theory.34
36 In 1973, Radom et al.34 studied the internal rotation of ETG using the linear-combination-of-atomicorbitals self-consistent-field (LCAO-SCF) method. They predicted that the two most stable conformations of this molecule were two gauche conformers tGg0 and gGg0 , in which an intramolecular hydrogen bond was present. In 1990, the two most stable conformers have been further studied by Cabral et al.,35 and the effects of electronic correlation were taken into account with MP2 method. They also constructed an intramolecular potential function related to the rotation around the C
C bond, showing a strong predominance of the gauche conformer in gas phase, which confirmed the experiment results and Radom’s prediction.34 The MP2/6-31G(d) calculations by Nagy et al.36 showed that the free energies of conformers without intramolecular hydrogen bond are higher by 3
4 kcal/mol than that of the most stable tGg0 conformer. Following the investigations of conformation analysis, some researchers made further efforts to investigate the nature and extent of intramolecular hydrogen bond in ETG.42,44 Although plenty of reports about ETG have been published, they mostly focus on the conformation analysis. There are, however, no studies on the unimolecular decomposition of ETG. Theoretical calculations on the unimolecular decomposition of ETG are necessary to understand the pryolysis and combustion chemistry of polyols fuels. In this work, we present comprehensive quantum chemistry and rate constant calculations for the unimolecular decomposition of ETG. A detailed mapping of the potential energy surface (PES) was built at a high precision ab initio level. The rate constants of the main reaction channels were computed subsequently. These will greatly contribute toward further understanding of

pyrolysis and combustion chemistry of polyols fuels and provide dynamic parameters for kinetic models.

2. COMPUTATIONAL METHODS 2.1. Ab Initio Calculations. The various conformers of ETG were optimized at the B3LYP/6-311G(d,p) level with the results provided in the Supporting Information (Figure S1 gives the optimized geometries and Table S1 gives the relative energy and enthalpy differences among various conformers). Among them the RC1 conformer is the most stable one. In this paper, we have only investigated the most stable conformer RC1. The unimolecular decomposition pathways of RC1 were first calculated with CBS-QB345,46 and CBS-APNO47 methods, two of the different complete basis set (CBS) methods. Previous studies12,48 validated the QCISD(T) (quadratic configuration interaction with singles doubles and perturbative inclusion of triples) method to be a high-precision level in building PESs of unimolecular decomposition reactions, which was also used in this work. For the QCISD(T) method, briefly speaking, the geometries of all the stationary points were optimized at B3LYP/6-311 ++G(d,p) level, and then single point energies were obtained by the QCISD(T) method with two basis sets: the correlationconsistent, polarized-valence, triple-ζ (cc-pVTZ) and quadruple-ζ (cc-pVQZ) basis sets of Dunning.12,49 The QCISD(T) energies were extrapolated to the complete basis set limit (CBS) via the expression

E½QCISDðTÞ=∞ ≈ E½QCISDðTÞ=cc-pVQZ þ fE½QCISDðTÞ=cc-pVQZ
E½QCISDðTÞ =cc-pVTZg  0:6938

ðE1Þ

The zero-point energy corrections were obtained from the B3LYP/6-311++G(d,p) optimizations. Table 1 lists energies of major channels calculated at different levels, showing subtle discrepancies among them. Energies, vibrational frequencies, and rotational constants obtained from QCISD(T)/CBS//B3LYP/ 6-311++G(d,p) method are adopted in following rate constant calculations. Uncertainty of this level in calculating barrier heights is estimated to be less than 1 kcal/mol. The intrinsic reaction 56

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Figure 1. Optimized geometries of saddle points at the B3LYP/6-311++G(d,p) level for the reaction channels. The units for bond lengths and bond angles are Å and degree, respectively.

coordinate (IRC) calculations at the B3LYP/6-311G(2d,d,p) level were used to confirm the connection between the designated transition states and the reactant or products.45 All the calculations were performed with the Gaussian03 program.50 2.2. Rate Constant Calculations. From a theoretical perspective, we could determine the reaction rate coefficients with potential energy surface of a reaction process, molecular properties of reactants, and transition states provided. Thereby the energies and molecular parameters obtained from the preceding ab initio calculations are applied in the rate constant calculations. The pressure- and temperature-dependent rate constants of the main channels in the decomposition processes of ETG were computed with the variable reaction coordinate-transition state theory (VRC-TST) and the Rice
Ramsperger
Kassel
Marcus (RRKM) theory using the Variflex program.51 Variflex code, which was developed on the basis of RRKM theory, is frequently employed to perform the rate constant calculations. Not only because Variflex has the most sophisticated and realistic treatment of loose transition states found in unimolecular reactions and reactions without a barrier but also due to the fact that the tight transition state theory and VRC-TST are implemented in this program package. For the tight transition states, the numbers of states were evaluated according to the rigid-rotor harmonicoscillator assumption.52 The rates are evaluated at the E/J (energy E and total angular momentum J) resolved calculation,53 in which the energy E covers the range from
29274.50 to 50625.50 cm
1 with an energy grain size of 100 cm
1, and the choice of total angular momentum J is consistent with our previous paper,54 spanning the range from 1 to 241 with a stepsize of 10 in the J-resolved calculation. The value 29274.50 cm
1 represents the energy to

go from the ground state of the desired electronic state of the complex to the ground states of the fragments for the first channel (corresponding to 83.7 kcal/mol of the bond cleavage channel in section 3.1.1). The energy E is specified to vary from
29274.50 cm
1 with a 100 cm
1 stepsize and an 800-step integration. The energy grain size of 100 cm
1 is consistent with previous papers,15,54 and this parameter has little impact on the final calculated results. Therefore, the section of rate calculation will only discuss the results of 100 cm
1. Onedimensional (1D) master equation calculations are used to account for the pressure dependence of rate constants. The master equation is solved by an eigenvalue-solver-based approach for the dissociation processes.55,56 Our rate calculations also include the tunneling corrections based on Eckart theory.57 Moreover, special consideration is given to lowfrequency vibrational modes, which correspond to internal hindered rotations.27 These modes are treated as hindered rotors by B3LYP/6-31G(d) hindrance potentials, which is fitted to Fourier functions according to the Variflex code. The hindrance potentials were obtained by relaxed scanning every 10 degrees. In the case of a simple bond cleavage process, no distinct transition state exists on the PES. This sort of process is regarded to be barrierless. In the present paper, for the barrierless decomposition process (CH2OHCH2OH f CH2OH + CH2OH), the Morse potential V ðRÞ ¼ De f1
exp½
βðR
R e Þg2

ðE2Þ

is applied to represent the potential energy along the reaction coordinate path (RCP). In this equation, De is the binding 57

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3. RESULTS AND DISCUSSION

energy, R is the reaction coordinate (i.e., the distance between the two C atoms, C 3 3 3 C), and Re is the equilibrium value of R. For the barrierless reaction, the VRC dividing surface is obtained by constraining the distance between two pivot points, one point in each of the fragments, to be fixed at some value. In the present paper, the pivot points are specified to be located at the two carbon atom center. And the reaction coordinate is defined as the distance between the C
C atoms involved in the breaking bond. The VRC approach employs various conservedtransitional mode convolution procedures, in which the conserved modes are treated as harmonic oscillators with a direct quantum sum for their contribution whereas the transitional mode contribution is estimated via the Monte Carlo integration.58,59

3.1. Potential Energy Surfaces. The decomposition of ETG can occur via many accessible product channels, as listed below. The optimized geometries of the saddle points for the reactions 1
10 at the B3LYP/6-311++G(d,p) level are shown in Figure 1. The PES obtained at the QCISD(T)/CBS//B3LYP/6-311+ +G(d,p) level are shown in Figures 2 and 3. Table 2 displays the vibrational frequencies and moments of inertia of all species used in the RRKM calculations.

CH2 OHCH2 OH

f f f f f f f f f f

CH2 OH þ CH2 OH CH3 CHO þ H2 O CH2 CHOH þ H2 O CH3 OH þ CHOH CH2 OHCHO þ H2 CH3 OH þ CH2 O CHOHCHOH þ H2 CH2 CH2 OH þ OH CH2 OHCHOH þ H CH2 OHCH2 O þ H

ð1Þ ð2Þ ð3Þ ð4Þ ð5Þ ð6Þ ð7Þ ð8Þ ð9Þ ð10Þ

We have calculated the enthalpies of reactions at 298 K for some important product channels, as displayed in Table 3. The predicted values are compared with the reference data taken from the NIST (National Institute of Standard and Technology) Chemistry WebBook60 (original papers for each piece of thermochmical data have been referenced61
66). As shown in Table 3, our results at the QCISD(T)/CBS//B3LYP/6-311++G(d,p) level agree quite well with the data from the NIST Chemistry WebBook, implying that the present method is reasonable for our calculations. 3.1.1. CH2OH + CH2OH Channel. This is a direct bonddissociation channel (Figure 2). In this barrierless path, the

Figure 2. Energy diagram for direct-bond-dissociation reactions at the QCISD(T)/CBS//B3LYP/6-311++G(d,p) level. ZPE is the zero point energy correction.

Figure 3. Calculated potential energy surface of small-molecular-elimination reactions at the QCISD(T)/CBS//B3LYP/6-311++G(d,p) level. ZPE is the zero point energy correction. 58

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Table 2. Vibrational Frequencies and Moments of Inertia of Species Used in Rate Constant Calculations of ETG νj (cm
1)

Ii (GHz)

species CH2OHCH2OH

15.37241, 5.54807, 4.58773

161, 253, 322, 430, 523, 872, 887, 1047, 1072, 1111, 1170, 1260, 1286,

CH2OHCHO

18.55728, 6.47503, 4.94747

195, 279, 377, 719, 761, 861, 1101, 1127, 1247, 1281, 1387, 1426, 1470,

CH2CHOH

64.04340, 10.41745, 8.96000

238, 482, 712, 857, 955, 972, 1134, 1281, 1347, 1435, 1719, 3142, 3161, 3252, 3869

CH3CHO

57.26968, 10.12804, 9.08797

154, 510, 776, 886, 1128, 1133, 1377, 1420, 1460, 1469, 1807, 2872, 3021, 3075, 3137

CH3OH

128.16658, 24.67021, 23.82241

302, 1044, 1071, 1168, 1356, 1480, 1494, 1505, 2989, 3036, 3113, 3847

CH2OH CHOH

193.57312, 29.85993, 26.07792 290.99124, 36.46674, 32.40569

406, 532, 1050, 1198, 1350, 1480, 3127, 3273, 3843 1097, 1215, 1319, 1503, 2859, 3716

1377, 1413, 1441, 1494, 1503, 2991, 2995, 3040, 3086, 3809, 3858 1792, 2929, 2978, 2992, 3724

H2O

823.85334, 430.03004, 282.54755

1603, 3816, 3921

H2

1810.977539

4418

TS1 (CH3CHO + H2O)

10.81101, 6.42353, 4.47439

788i, 251, 317, 426, 522, 547, 595, 808, 923, 1046, 1063, 1123, 1196, 1253,

TS2 (CH2CHOH + H2O)

15.27654, 4.38536, 3.91005

1977i, 177, 217, 292, 400, 453, 567, 723, 807, 900, 943, 1072, 1126, 1220, 1277, 1330,

TS4 (CH3OH + CHOH)

13.82462, 4.96870, 3.86764

953i, 154, 236, 374, 446, 524, 686, 755, 1023, 1069, 1125, 1154, 1164, 1193, 1371, 1409, 1471, 1508, 2129, 3049, 3062, 3141, 3667, 3807

TS5 (CH2OHCHO + H2)

15.03614, 5.89690, 4.77504

2062i, 191, 289, 496, 547, 763, 847, 894, 938, 1016, 1105, 1208, 1226, 1316, 1363,

1307, 1417, 1476, 1631, 2188, 2757, 2905, 3124, 3248, 3849 1412, 1522, 1593, 3098, 3161, 3267, 3741, 3847

1407, 1433, 1476, 1990, 2214, 2950, 2966, 3085, 3713

Table 3. Enthalpies of Reaction of Major Channels in the Decomposition of ETG (kcal/mol, 298 K) reactions

NIST Chemistry WebBook60

QCISD(T)/CBS//B3LYP/6-311++G(d,p)

CH2OHCH2OH f CH2OH + CH2OH CH2OHCH2OH f CH3CHO + H2O

86.1 ( 0.761,62
4.4 ( 1.063,64

85.5
3.9

CH2OHCH2OH f CH2CHOH + H2O

5.9 ( 0.765

6.8

18.5 ( 0.764,66

18.9

CH2OHCH2OH f CH3OH + CH2O

present level turns out to be 85.3 kcal/mol. From those data, the magnitude order of C
C bond dissociation energies in different molecules is ethane > ethanol > ETG. It can be inferred that it is easier to rupture the C
C bond in the molecule with the hydroxyl group involved in the molecule. The reaction coordinate path for the bond dissociation was computed at the CASPT2(2,2)/6-311G(d,p)//CAS(2,2)/6-311G(d,p) level,67,68 scanning along the dissociation bond length with 0.2 Å intervals (shown in Figure 4). We employed the active space including the C
C bond σ and σ* orbitals for CAS and CASPT2 calculations. From the calculations, the Morse potential energy function for the dissociation process from reactant to CH2OH + CH2OH was obtained with De = 78.8 kcal/mol, β = 2.219 Å
1, and Re = 1.538 Å. The potential for the dissociation process was used in all subsequent rate constant calculations. 3.1.2. CH3CHO + H2O Channel. In this channel (Figure 3), the OH group abstracts the H atom from the other OH group producing H2O, meanwhile one H-atom in the CH2O group migrates to the CH2 group to form a CH3 group. This reaction includes the C2
O2 and O1
H bond dissociation and O2
H (O1) bond formation; see Figure 1 for the label of atoms. The C2
O2, O1
H, and O2
H (O1) bond lengths in TS1 are 2.082, 1.669, and 1.022 Å, respectively. The C1
O1 bond changes from a single bond to a double bond during the reaction, and the C1
O1 bond lengths in CH2OHCH2OH, TS1, and CH3CHO are 1.421, 1.305, and 1.206 Å, respectively. This channel can produce aldehyde (CH3CHO) and H2O, via a five-member-ring

Figure 4. Calculated Morse curve for the direct decomposition process (CH2OHCH2OH f CH2OH + CH2OH) at the CASPT2(2,2)/ 6-311G(d,p)//CAS(2,2)/6-311G(d,p) level.

C
C bond directly ruptures to the product CH2OH. The predicted dissociation energy of C
C bond is 83.7 kcal/mol at QCISD(T)/CBS//B3LYP/6-311++G(d,p). We have compared the value of ETG with those of ethane and ethanol. With ethane, we calculated the C
C bond dissociation energy at the same level, with the result predicted to be 87.7 kcal/mol. Meanwhile for ethanol, the designated dissociation energy calculated at the 59

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84.2 kcal/mol, close to the barrier of CH3CH2OH f CH3CHO + H2 (86.1 kcal/mol at the G2M level by Park et al.15). Another pathway is the reaction CH2OHCH2OH f CH2OHCHO-2 + H2 with a five-member-ring transition state (TS6). Compared to case of the former pathway, the two eliminated H atoms come from the C2 and O1 atoms. The calculated barrier is 90.4 kcal/mol, which is 6.2 kcal/mol higher than that involving TS5. Due to the relatively high barrier of TS6, in these two pathways only the reaction CH2OHCH2OH f CH2OHCHO-1 + H2 is considered for the rate constant calculations. We also calculated other reaction channels consisting of H2 elimination (CHOHCHOH + H2) and CH3OH + CH2O channels, shown in Figure 3. The calculated barriers of these two channels are 96.4 and 91.7 kcal/mol, respectively, which are more than 20 kcal/mol higher than that of channel 1. The other direct bond dissociation channels include the C
O, C
H, and O
H bond cleavage (Figure 2). Their dissociation energies are relatively higher. The ordering of the dissociation energies is C
H ≈ C
O < O
H. The calculated dissociation energies are 94.1 (CH2OHCHOH-1 + H), 94.8 (CH2OHCHOH-2 + H), 94.5 (CH2CH2OH-1 + OH), 94.9 (CH2CH2OH-2 + OH), 104.9. (CH2OHCH2O-1 + H), and 106.6 (CH2OHCH2O-2 + H) kcal/mol, respectively. 3.2. Rate Constant Calculations. Among the pathways discussed above, the barriers and dissociation energies for channels 6
10 are relatively higher compared to those for channels 1
5. Here, we only calculate the rate constants for the five principal channels 1
5 for the decomposition process using the Variflex code.51 Our calculations cover a range of temperature from 500 to 2000 K, and pressure from 0.001 to 1000 atm with Ar as the bath gas. The interaction between reactant and bath gas is modeled by the Lennard-Jones potential. The Lennard-Jones pairwise parameters σ = 3.465 Å, ε/k = 78.89 cm
1 for Ar in previous literature69 are applied to our rate constant calculations. For the Lennard-Jones parameters of ETG, these values are estimated by the following equations:70

transition state (TS1). And the calculated energy barrier of TS1 is 69.4 kcal/mol, which is the lowest-energy reaction pathway. This H2O-elimination process is mainly attributed to the interaction between the two hydroxyl groups, i.e., the effect of intramolecular hydrogen bonding. The lowest energy barrier of this channel exhibits the great influence of the intramolecular hydrogen bonding on the decomposition of polyols. 3.1.3. CH2CHOH + H2O Channel. There are two possible formation pathways of CH2CHOH + H2O, as shown in Figure 3. The reaction that the OH radical abstracts one H atom from the other CH2 group occurs via a four-member-ring transition state (TS2). And the barrier is 70.3 kcal/mol, 0.9 kcal/mol above that of TS1. In the other pathway, the OH radical abstracts one H atom from the same C atom with a three-member-ring transition state (TS3). One H atom migrates from C1 to C2 in the latter pathway. The calculated barrier is 79.7 kcal/mol, which is 9.4 kcal/mol higher than that of TS2. In these two pathways, the former one with the transition state TS2 is more favorable for the H2O-elimination process. Thus for this process, only the rate constant of the reaction CH2OHCH2OH f TS2 f CH2CHOH + H2O is calculated. To further discover whether the number of hydroxyl groups has an effect on the H2O-elimination process, we compare the barrier of this channel with that of the ethanol dehydration reaction, which has the same water-elimination mechanism. With regard to ethanol, Sester and co-workers29 reported the barrier of H2O elimination to be around 67.1 kcal/mol at the MP2(FULL)/6-311G(d,p) level. Park et al.15 calculated this value by G2M(RCC2), which was 66.6 kcal/mol. Compared with that for ethanol, the barrier is higher for ETG (70.3 kcal/mol), which has one more hydroxyl group than ethanol in its molecular structure. The barriers of the channels 2 and 3 are very close to each other. As a result, both aldehyde and enol are easily formed. Whereas for the same products in ethanol decomposition, the formation of enol is much more difficult than the formation of aldehyde. 15 It should be noted that for ethanol, enol and aldehyde formation proceeds via the H2-elimination mechanism that is different from the ETG mechanisms. 3.1.4. CH3OH + CHOH Channel. The product CH3OH + CHOH can be produced via the process that one H atom of the CH2 group transfers to the other CH2 group and C
C bond cleavages, as the transition state TS4 shows in Figure 1. This reaction occurs via a three-member-ring transition state (TS4). In TS4, the C1
C2, C1
H, and C2
H bond lengths are 2.304,
, respectively. The imaginary frequency 1.229, and 1.400 Å associated with TS4 is calculated to be 953i cm
1. Analysis of the atomic motion along this vibration indicates that this transition state is mainly associated with the H transfer and C
C cleavage. The calculated barrier at the present level is 80.6 kcal/mol. 3.1.5. CH2OHCHO + H2 Channel. Two pathways have been identified for this process, as shown in Figure 3. For the channel with a relatively low barrier, H2 eliminates from the reactant (CH2OHCH2OH f CH2OHCHO-1 + H2) via a four-memberring transition state TS5, involving the H atom in the CH2 group and another H atom in the OH group attaching together. The C2
H and O2
H bond lengths in TS5 are 1.411 and 1.414 Å, respectively. They are 0.313 and 0.453 Å longer than those in ETG. The forming H
H bond length (0.978 Å, in TS5) is a little longer than the H2 molecular equilibrium bond length (0.744 Å calculated at the same level of theory). The imaginary frequency in TS5 is calculated to be 2062i cm
1, which corresponds to the motion of two H atoms. The calculated barrier for this channel is

σ ¼ 2:44ðTc =Pc Þ1=3

ðE3Þ

εA =kb ¼ 0:77Tc

ðE4Þ

In these equations, kb is the Boltzmann constant. The critical temperature and pressure for ETG are estimated using the method of Joback.71,72 With this method, the critical temperature and pressure Tc = 589.28 K, Pc = 66.53 bar are obtained. According to (E3) and (E4), the Lennard-Jones parameters we estimated for ETG are σ = 5.048 Å, ε/k = 315.35 cm
1. The energy transfer per downward collision is treated using an exponential-down model with ÆΔEdownæ = 125(T/300)0.85 cm
1 in Ar. This function form for the energy transfer parameter is quite reasonable, and similar forms have already been used in previous articles.12,73,74 Energies depicted in Figures 2 and 3, and the moments of inertia and vibrational frequencies presented in Table 2 are used in the rate constant calculations. The predicted rate constants at different pressures at the temperature range of 500
2000 K for channels 1
5 are listed in Table 4, expressed in modified Arrhenius equations. The rate constants have also been parametrized using Troe-type representations,75
77 with the fitting parameters displayed in Table 5. Troe’s formula usually results in fitting errors of more than 10% partially because of the transcendental functions and the empirical constants involved in it. For our data in Table 5, we conservatively estimate the fitting 60

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Table 4. Arrhenius Equations for Rate Constant (s
1) Predicted for Different Pressuresa

k1 k2 k3 k4 k5

0.001 atm

0.1 atm

1 atm

9.98  1073T
18.02 exp(
50907/T)

6.22  1073T
17.28 exp(
52206/T)

1.04  1071T
16.16 exp(
52414/T)

64
15.91

5.10  10 T

61
14.81

3.08  10 T

69
18.12

8.45  10 T

65
17.15

1.17  10 T

exp(
45427/T) exp(
44099/T) exp(
49900/T) exp(
48583/T)

57
13.46

2.10  10 T

53
12.30

8.89  10 T

66
16.64

5.92  10 T

62
15.78

2.67  10 T

10 atm 65
14.26

exp(
44575/T)

2.48  1051T
11.58 exp(
43593/T)

exp(
43252/T)

7.63  1047T
10.38 exp(
42262/T)

exp(
50641/T)

2.96  1062T
15.11 exp(
50444/T)

exp(
49700/T)

1.80  1058T
14.26 exp(
49622/T)

100 atm 57
11.57

k1

3.16  10 T

k2 k3

8.83  1043T
9.26 exp(
42207/T) 1.68  1040T
7.99 exp(
40855/T)

2.27  1035T
6.63 exp(
40477/T) 1.94  1031T
5.25 exp(
39069/T)

2.72  1026T
3.92 exp(
38570/T) 9.37  1021T
2.42 exp(
37091/T)

k4

4.21  1055T
12.85 exp(
49598/T)

1.27  1046T
9.84 exp(
47992/T)

6.87  1034T
6.37 exp(
45782/T)

k5

51
11.97

2.50  10 T

exp(
51945/T)

exp(
48858/T)

1.27  10 T

1000 atm 46
8.32

41
8.89

5.01  10 T

4.25  10 T

exp(
50666/T)

exp(
48655/T)

7.81  1029T
5.24 exp(
45021/T)

exp(
47291/T)

k1 to k5 correspond to reactions as follows, ETG f CH2OH + CH2OH (k1), ETG f CH3CHO + H2O (k2), ETG f CH2CHOH + H2O (k3), ETG f CH3OH + CHOH (k4), ETG f CH2OHCHO + H2 (k5). a

errors to be within a factor of 2. The high-pressure limit rate constant for the barrierless reaction CH2OHCH2OH f CH2OH + CH2OH has been calculated using the VRC approach. The reaction coordinate was defined as the distance between the C
C atoms involved in the breaking bond in our calculations. The transition state number of states was evaluated according to a version of variational transition state theory, which employs an assumed decoupling of the conserved and transitional modes.58,59 The results summarized in Tables 4 and 5 apparently exhibit the temperature and pressure dependency of rate constants and provide important data for future reference in kinetic modeling applications. The uncertainty of the rate coefficients using the VRC-TST method is pretty small and previous studies have reported the uncertainty to be within a factor of 2.12,48 Rate constants of channels 1
5 at the pressure of 0.001 and 1 atm are displayed in Figure 5. Figure 5a shows that for the direct bond dissociation channel 1 at 0.001 atm, k1 increases with temperature much more rapidly as compared with k2
k5, finally making channel 1 the most dominant reaction at high temperature. The PES in Figures 2 and 3 demonstrate that the dissociation energy of channel 1 is higher than the barriers of the channels 2 and 3. At low temperature, channel 1 presents smaller rate constants than those of channels 2 and 3, but when the temperature goes over 1075 K, channel 1 becomes the fastest channel. There are intersections for k1 with k2 and k3. Figure 5a shows that for channels 1 and 2, k1 > k2 over 715 K; for channels 1 and 3, k1 > k3 over 1075 K. For the small-molecule-elimination reactions (channels 2
5), the ordering of the rate constants is k3 > k2 > k4 > k5, and it remains unchanged across the temperature range of 500
2000 K. According to the energy profile (Figure 3), the barriers of TS2 for channel 3 and TS1 for channel 2 are lower than those of others, resulting in larger rate constants throughout the whole temperature range. For channels 2 and 3, both the barriers are very close (the energy difference is 0.9 kcal/mol). But k3 remains larger than k2 in the whole temperature range investigated, due to the fact that there are several processes leading to the same enol product. Figure 5a may be attributed to the combined effects of their barriers and transition states structures (i.e., the enthalpies and entropies of the TS’s). It should be pointed out that channel 2 (CH2OHCH2OH f CH3CHO + H2O) includes both the H2O elimination and hydrogen transfer, which is different from channel 3.

Table 5. Modified Troe Parameters of Major Channels for ETG Decomposition (T = 500
2000 K)b product

A∞ (s
1)

n∞

E∞ (K)

CH2OH + CH2OH

7.91  1025


2.06

44107

CH3CHO + H2O

7.48  1010

0.75

35041

CH2CHOH + H2O

1.78  105

2.60

33307

CH3OH + CHOH CH2OHCHO + H2

1.04  1011 3.32  103

0.82 2.73

40526 39239

A0 (cm3 molecule
1 s
1)

n0

E0 (K)

CH2OH + CH2OH

8.05  10

27


9.75

62009

CH3CHO + H2O

7.78  1048


10.68

43591

CH2CHOH + H2O

4.20  1056


12.59

33017

CH3OH + CHOH

1.43  1017


2.64

47910

CH2OHCHO + H2

4.19  1049


12.81

33315

product

a

product CH2OH + CH2OH CH3CHO + H2O CH2CHOH + H2O CH3OH + CHOH CH2OHCHO + H2 b

∞

∞

T*

T**

T***

0.734

4.325  10

4.188  10

3.486  100

3.170

4.948  10

5.689  10

4.039  100

4.374

1.615  10

1.418  10

4.047  100

6.052  10

4.337  10

1.853  101

1.761  10

4.379  10

2.741  100

224.7 3.358

2 2 2 1 2

3 4 4 4 3

∞

A , n , and E are the three Arrhenius parameters for high-pressurelimit rate constants, and A0, n0, and E0 are the three Arrhenius parameters for low-pressure-limit rate constants.

Figure 5b plots the rate constants for channels 1
5 at 1 atm. Compared to the rate constants at 0.001 atm, the magnitude sequences of k1
k5 are similar, except that the temperatures of intersections for k1 with k2 and k3 become smaller. Channel 3 producing CH2CHOH + H2O and channel 2 producing CH3CHO + H2O are dominant at low temperature; i.e., the H2O-elimination process plays a major role. At temperatures high above 625 K, however, the direct dissociation reaction leading to the formation of CH2OH + CH2OH becomes dominant. The general tendency is similar to the unimolecular decomposition of ethanol. With regard to ethanol, the H2Oelimination process is dominant below 10 atm in the temperature range 700
2500 K. At high pressure and high temperature, cleavage of the C
C bond producing CH3 + CH2OH is 61

dx.doi.org/10.1021/jp207978n |J. Phys. Chem. A 2012, 116, 55–63

The Journal of Physical Chemistry A

ARTICLE

’ ASSOCIATED CONTENT

bS

Supporting Information. B3LYP/6-311G(d,p) structures of various ETG conformers in Figure S1, corresponding energy and enthalpy differences in Table S1; reaction coordinate path in Figure S2; B3LYP/6-311G(d,p) geometries, vibrational frequencies, and rotational constants of various ETG conformers; B3LYP/6-311++G(d,p) geometries, vibrational frequencies, and rotational constants of the product fragments and stationary points on the ETG potential energy surface. This information is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Fax: +86-551-5141078. Tel: +86-5513607923.

’ ACKNOWLEDGMENT We are grateful for the great help of Dr. Stephen Klippenstein at Argonne National Laboratory for using Variflex. This work has been supported by grants from the Chinese Academy of Sciences and the Natural Science Foundation of China (Grant no. 10805047). ’ REFERENCES (1) Bull, S. R. Renewable Energy 1994, 5, 799–806. (2) Demirbas, M. F.; Balat, M. Energy Convers. Manage. 2006, 47, 2371–2381. (3) Kohse-H€oinghaus, K.; Osswald, P.; Cool, T. A.; Kasper, T.; Hansen, N.; Qi, F.; Westbrook, C. K.; Westmoreland, P. R. Angew. Chem., Int. Ed. 2010, 49, 3572–3597. (4) Balat, M. Energy Sources 2005, 27, 569–577. (5) Balat, M. Energy Sources, Part A 2009, 31, 1242–1255. (6) Kitamura, T.; Ito, T.; Senda, J.; Fujimoto, H. JSAE Rev. 2001, 22, 139–145. (7) Litzinger, T.; Colket, M.; Kahandawala, M.; Katta, V.; Lee, S. Y.; Liscinsky, D.; McNesby, K.; Pawlik, R.; Roquemore, M.; Santoro, R.; et al. Combust. Sci. Technol. 2009, 181, 310–328. (8) Ni, T.; Pinson, J. A.; Gupta, S.; Santoro, R. J. Appl. Opt. 1995, 34, 7083–7091. (9) Wu, J. T.; Song, K. H.; Litzinger, T.; Lee, S. Y.; Santoro, R.; Linevsky, M.; Colket, M.; Liscinsky, D. Combust. Flame 2006, 144, 675–687. (10) Nielsen, D. R.; Leonard, E.; Yoon, S. H.; Tseng, H. C.; Yuan, C.; Prather, K. L. J. Metab. Eng. 2009, 11, 262–273. (11) Rasmussen, C. L.; Wassard, K. H.; Dam-Johansen, K.; Glarborg, P. Int. J. Chem. Kinet. 2008, 40, 423–441. (12) Jasper, A. W.; Klippenstein, S. J.; Harding, L. B.; Ruscic, B. J. Phys. Chem. A 2007, 111, 3932–3950. (13) Xia, W. S.; Zhu, R. S.; Lin, M. C.; Mebel, A. M. Faraday Discuss. 2001, 119, 191–205. (14) Marinov, N. M. Int. J. Chem. Kinet. 1999, 31, 183–220. (15) Park, J.; Zhu, R. S.; Lin, M. C. J. Chem. Phys. 2002, 117, 3224–3231. (16) Park, J.; Xu, Z. F.; Lin, M. C. J. Chem. Phys. 2003, 118, 9990–9996. (17) Xu, Z. F.; Park, J.; Lin, M. C. J. Chem. Phys. 2004, 120, 6593–6599. (18) Li, Y. Y.; Wei, L. X.; Tian, Z. Y.; Yang, B.; Wang, J.; Zhang, T. C.; Qi, F. Combust. Flame 2008, 152, 336–359. (19) Moss, J. T.; Berkowitz, A. M.; Oehlschlaeger, M. A.; Biet, J.; Warth, V.; Glaude, P. A.; Battin-Leclerc, F. J. Phys. Chem. A 2008, 112, 10843–10855.

Figure 5. Rate constants for channels 1
5 at pressure 0.001 atm (a) and 1 atm (b), respectively.

predicted to be dominant.15 Furthermore, the main H2-elimination product for ethanol is aldehyde, whereas the formation of enol product is more favorable for H2O elimination from ETG. Figure 5 clearly shows that the formation of H2O is much more favorable than the formation of H2 and CHOH.

4. CONCLUSIONS The kinetics and mechanisms for the unimolecular decomposition of CH2OHCH2OH have been studied by high level ab initio theories and variational RRKM calculations. PES has been calculated at the QCISD(T)/CBS//B3LYP/6-311++G(d,p) level. For the direct bond dissociation reactions, the dissociation energy order is C
C < C
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O < O
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C bond dissociation reaction (CH2OHCH2OH f CH2OH + CH2OH) is dominant. Moreover, the main product of H2 elimination for ethanol is aldehyde, whereas the formation of enol product is more favorable due to the H2O elimination from ETG. The other small-molecule-elimination reactions, like H2-elimination and CHOH-elimination reactions, have relatively larger barriers, and they are not competitive throughout the temperature range investigated. The theoretical investigations in this work can help to better understand the pyrolysis and combustion chemistry of polyols fuels and provide reference data for kinetic models. 62

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