Theoretical Studies on the Unimolecular Decomposition of

Article pubs.acs.org/JPCA

Theoretical Studies on the Unimolecular Decomposition of Propanediols and Glycerol Lili Ye,† Feng Zhang,† 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

‡

S Supporting Information *

ABSTRACT: Polyols, a typical type of alcohol containing multiple hydroxyl groups, are being regarded as a new generation of a green energy platform. In this paper, the decomposition mechanisms for three polyol molecules, i.e., 1,2propanediol, 1,3-propanediol, and glycerol, have been investigated by quantum chemistry calculations. The potential energy surfaces of propanediols and glycerol have been built by the QCISD(T) and CBS-QB3 methods, respectively. For the three molecules studied, the H2O-elimination and C−C bond dissociation reactions show great importance among all of the unimolecular decomposition channels. Rate constant calculations further demonstrate that the H2O-elimination reactions are predominant at low temperature and pressure, whereas the direct C−C bond dissociation reactions prevail at high temperature and pressure. The temperature and pressure dependence of calculated rate constants was demonstrated by the fitted Arrhenius equations. This work aims to better understand the thermal decomposition process of polyols and provide useful thermochemical and kinetic data for kinetic modeling of polyols-derived fuel combustion.

1. INTRODUCTION Biofuel, as an environmental friendly source of renewable energy, has been regarded as one of the most promising alternative fuels nowadays.1−4 Typical biofuels, e.g., alcohols, ethers, and esters, contain oxygen in their molecular constitution, which distinguishes them from conventional hydrocarbon fossil fuels. Compared to the combustion of widely used fossil fuels, biofuels could effectively inhibit the formation of soot and its precursors in combustion processes,1−4 consequently reducing the climatic impact of fuel combustion. In order to intelligently select the feasible alternative fuels, scientific research is under way to pursue a profound understanding of biofuel combustion chemistry.5 Alcohols serve as important raw materials for biofuels. They can be used directly as a fuel or as an additive to internal combustion engines. Abundant investigations have been carried out on monohydroxy alcohols containing one hydroxyl group both experimentally and theoretically.6−16 At the same time, great emphasis is placed on the studies of polyols, which are becoming a new generation of green energy platform.17,18 As we know polyols can be obtained from biomass by pyrolysis and catalytic pyrolysis and can also be converted to biofuels and other chemicals.17,19 Propanediols (C3H8O2) and glycerol (C3H8O3), which contain two and three hydroxyl groups, respectively, have wide applications through chemical transformation to propylene glycol and acrolein20,21 and play important roles in biofuels’ production. In order to better © 2012 American Chemical Society

understand their combustion behaviors as fuels or additives, detailed studies on their decomposition mechanisms are needed. Many investigations have been carried out on propanediols and glycerol;22−26 yet, no reports were focused on their decomposition processes. In this work, we present comprehensive quantum chemistry and rate constant calculations for the unimolecular decomposition of propanediols (1,2-propanediol and 1,3-propanediol) and glycerol. We have proposed detailed reaction pathways for each molecule and built the potential energy surfaces (PES) by highly accurate methods. Rate constants were subsequently calculated for dominant channels of each molecule. We aim for a better understanding of the decomposition process of polyols by theoretical calculations. Meanwhile, rate constant computation can shed further light on the competition mechanisms among different reaction pathways and provide valuable data for developing and improving combustion kinetic models of analogous systems.

2. COMPUTATIONAL METHODS 2.1. Ab Initio Calculations. The reaction pathways of two propanediol isomers (i.e., 1,2-propanediol and 1,3-propanediol) were first optimized by the B3LYP/6-311++G(d,p) method. Received: February 13, 2012 Revised: April 17, 2012 Published: April 20, 2012 4457

dx.doi.org/10.1021/jp301424k | J. Phys. Chem. A 2012, 116, 4457−4465

The Journal of Physical Chemistry A

Article

without losing much accuracy. In the CBS-QB3 method, geometries and vibrational frequencies of the stationary points were first optimized at the B3LYP/CBSB7 level, and then CCSD(T)/6-31+G(d′), MP4(SDQ)/CBSB4, MP2/CBSB3, and CBS extrapolation calculations were conducted. The intrinsic reaction coordinate (IRC) calculations32 were performed to confirm the connection between the designated transition states and the reactant or products. The Gaussian 03 program33 was employed for all of the ab initio calculations. 2.2. Rate Constant Calculations. The rate constant of a reaction can be determined provided that the potential energy surface of the reaction and molecular properties of reactant and transition state including vibrational frequencies and rotational information are known. In this paper, the temperature and pressure dependent rate constants of major decomposition channels for propanediols and glycerol were calculated with the RRKM/Master Equation method. The temperature covers the range of 500−2500 K, whereas the pressure varies from 0.001 to 1000 atm. Collision energy transfer is treated using an exponentialdown model with ⟨ΔEdown⟩ = 150(T/300)0.85 cm−1, which has been proved as a reasonable model by various studies.34−36 The interaction between reactant and bath gas (argon used in this work) is assumed by the Lennard-Jones (L-J) pairwise potential. The L-J pairwise parameters of Ar (σ = 3.465 Å, ε/ k = 113.5 K) in the early literature37 are used. For 1,2propanediol, 1,3-propanediol, and glycerol, the L-J parameters are estimated by the empirical equations:38

Then single-point energies were corrected with the method of quadratic configuration interaction with singles, doubles, and perturbative inclusion of triples (QCISD(T)) with two large basis sets: the correlation-consistent, polarized-valence, triple-ζ (cc-pVTZ), and quadruple-ζ (cc-pVQZ) basis sets of Dunning.11,27 The QCISD(T) energies were extrapolated to the complete basis set limit (CBS)27 via the following expression: E[QCISD(T)/∞] ≈ E[QCISD(T)/cc‐pVQZ] + {E[QCISD(T)/cc‐pVQZ] − E[QCISD(T) /cc‐pVTZ]}0.6938

(E1)

The zero-point energy corrections were obtained from the B3LYP/6-311++G(d,p) optimizations. This composite method has proved its validity for many unimolecular decomposition reactions of similar systems.11,28,29 Furthermore, the Q1 diagnostics30,31 have been performed for the QCISD(T) calculations in order to assess the reliability of the singlereference correlation treatments, with the results presented in Table S1 in the Supporting Information. The small values of Q1 (smaller than 0.03) suggest the adequacy of QCISD(T) in the decomposition processes of propanediols. For glycerol, the decomposition pathways of this molecule were treated with the complete basis set-quadratic Becke3 (CBS-QB3) model32 considering the computational cost. We also conducted the CBS-QB3 calculations for major decomposition channels of propanediols and made a comparison between the results from QCISD(T) and CBS-QB3, shown in Table 1. Obviously, the two methods possess very close accuracy in building PES of propanediols. Therefore, it should be reasonable to treat glycerol with the CBS-QB3 method

reaction energies and barrier heights with different methods

CH2OHCHOHCH3 → CH3CHOH + CH2OH CH2OHCHOHCH3→ CH2OHCHOH + CH3 CH2OHCHOHCH3 → CH2OHCHCH2 + H2O (TS1) CH2OHCHOHCH3 → CH3COCH3 + H2O (TS2) CH2OHCHOHCH3 → CH3CHCHOH + H2O (TS3) CH2OHCHOHCH3 → CH3COHCH2 + H2O (TS4)

QCISD(T)/ CBS

CBS-QB3

83.7

84.7

85.1

85.9

14.3 (66.8)

15.1 (68.3)

−8.6 (68.9)

−8.2 (70.1)

8.4 (70.4)

9.2 (71.8)

3.1 (71.8)

3.8 (73.4)

reaction energies and barrier heights with different methods reactions of 1,3-propanediol HO(CH2)3OH → CH2OHCH2 + CH2OH HO(CH2)3OH → C2H4 + CH2O + H2O (TS5) HO(CH2)3OH → CH2OHCHCH2 + H2O (TS6)

QCISD(T)/ CBS

CBS-QB3

86.4 24.4 (62.0)

87.7 24.4 (63.1)

9.0 (66.5)

9.8 (67.7)

(E2)

εA /k b = 0.77Tc

(E3)

where kb is the Boltzmann constant, Tc is the critical temperature, and Pc is the critical pressure. The method of Constantinou and Gani39 is used to estimate the values of Tc and Pc for the three reactants. Thus the L-J values are computed to be σ = 5.580 Å and ε/k = 468.0 K for 1,2-propanediol, σ = 5.604 Å and ε/k = 474.1 K for 1,3-propanediol, and σ = 5.651 Å and ε/k = 515.2 K for glycerol. For calculating the rate constants of barrierless bond dissociation reactions, the variational transition state theory is required. The minimum energy pathways (MEPs) along the bond dissociation were stepwisely optimized with the step-size of 0.2 Å. Since the bond dissociation reaction possesses the multireference character, the multiconfiguration method CASPT2 was used to optimize geometries along the reaction coordinate. The active space is chosen as the σ and σ* orbitals involved in the bond breaking process with two electrons. Single-point energies for each point along the dissociation path were then scaled by the QCISD(T)/CBS reaction energies for propanediols and CBS-QB3 energies for glycerol. The location of the optimal transition state for a barrierless reaction was found to vary significantly with temperature. Therefore, we considered different positions along the MEPs for the transition state and calculated rate constants corresponding to each position at various temperatures. The minimum rate constants so obtained were what we want. This procedure for computing variational TST rate constants was proposed by da Silva and Bozzelli.40 Rate constants are computed using the ChemRate program.41

Table 1. Major Reaction Energies of Propanediols Calculated with Different Methodsa

reactions of 1,2-propanediol

σ = 2.44(Tc/Pc)1/3

a

The unit is kcal/mol, and data in brackets are the barrier heights of corresponding reactions. 4458



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3.1.1. Direct Bond Dissociation. For the three studied C3 molecules, each has two C−C bonds in the chemical structures. Table 2 lists the bond dissociation energies (BDEs) of the C−C bonds for the two propanediols at the QCISD(T)/CBS// B3LYP/6-311++G(d,p) level and glycerol at CBS-QB3. For 1,2-propanediol, the BDE is calculated to be 83.7 kcal/mol for the C1−C2 bond and 85.1 kcal/mol for the C2−C3 bond (see Figure 1 for atom labels), whereas for 1,3-propanediol, the two C−C bonds possess the same dissociation energy −86.4 kcal/ mol, and for glycerol, the BDEs of the two C−C bonds are predicted to be 84.1 (C1−C2) and 87.9 kcal/mol (C2−C3). In order to figure out the influence of hydroxyl group number on the BDEs of C−C bonds in different molecules, we have compared the results of propane and n-propanol with those of propanediols. The same QCISD(T)/CBS//B3LYP/6-311+ +G(d,p) method was used to perform the calculations. For propane, the BDE of the two C−C bonds is 87.0 kcal/mol, and for n-propanol, the BDEs of the two C−C bonds are computed to be 84.3 and 88.3 kcal/mol. The BDE of propane is larger than those of C3 alcohols; n-propanol has relatively larger BDEs than those of propanediols. Therefore, it can be concluded that the presence of hydroxyl groups makes it easier to dissociate the C−C bonds for alcohols than for alkanes, and the dissociation process gets more favorable with the increase of hydroxyl group number. No apparent transition state was shown for C−C bond dissociation reactions of the three polyols. As mentioned above, geometries on the dissociation reaction pathways were optimized by the CASPT2 method, and the energies were scaled according to dissociation energies computed by high level theory. The scaled factor varies from 0.93 to 1.05 for the five bond dissociation pathways. The scaled minimum energy pathways for these bond dissociation reactions were shown in Figure 5. 3.1.2. H2O-Elimination Reactions. With regard to 1,2propanediol, there are four accessible H2O-elimination pathways, as shown in Figure 2. The channel CH2OHCHOHCH3 → CH2OHCHCH2 + H2O (1c) with a four-member-ring transition state (TS1) has the lowest barrier height (66.8 kcal/ mol). The channel CH2OHCHOHCH3 → CH3COCH3 + H2O (1d) occurring via a five-member-ring transition state (TS2) has a barrier with 2.1 kcal/mol higher than that of channel (1c). One point worth noticing is that the H2Oelimination product of channel (1c) is enol, whereas acetone is formed from channel (1d). Channel (1d) via TS2 is mainly attributed to the effect of intramolecular hydrogen bonding. This reaction includes both H2O elimination and hydrogen transfer, which is different from channel (1c). The other two pathways producing CH 3 CHCHOH + H 2 O (1e) and CH3COHCH2 + H2O (1f) via four-member-ring transition states (TS3 and TS4) have barriers of 70.4 and 71.8 kcal/mol, respectively. Enols are also formed in these two pathways. Figure 3 shows three H2O-elimination pathways identified for 1,3-propanediol. The channel HO(CH2)3OH → C2H4 + CH2O + H2O (2b) has the lowest barrier height (62.0 kcal/ mol). This process can also be attributed to the intramolecular hydrogen bonding effect, in which a six-membered ring transition state (TS5) is formed. The other two pathways via TS6 and TS7 both produce CH2OHCHCH2 + H2O (2c), with energy barriers higher than that of channel (2b). Besides the enol product, ethene and formaldehyde are the other two significant species identified in the decomposition process of 1,3-propanediol.

3. RESULTS AND DISCUSSION 3.1. Potential Energy Surfaces. From our calculations, the C−C bond cleavage plays the dominant role among all direct bond dissociation channels, whereas the H2O-elimination reactions have relatively lower barriers among all the small molecular elimination channels for the three polyols decomposition. For this reason, we will mainly discuss these two sorts of reactions in present paper, i.e., the C−C bond cleavage and the H2O-elimination reactions. The major decomposition channels of the three molecules consist of the following reactions: For 1,2-propanediol

For 1,3-propanediol

For glycerol

Geometric structures of 1,2-propanediol, 1,3-propanediol, and glycerol are depicted in Figure 1. The computed PESs of

Figure 1. Geometric structures of 1,2- and 1,3-propanediol at B3LYP/ 6-311++G(d,p) level and glycerol at B3LYP/CBSB7 level (bond lengths and angles are given in Å and degree, respectively).

major channels for the three molecules are presented in Figures 2−4. Cartesian coordinates of the stationary points involved in above channels together with their vibrational frequencies and moments of inertia are included in the Supporting Information. The character of bond dissociation and H2O-elimination reactions for the three molecules will be discussed separately later. 4459



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Figure 2. Calculated potential energy surfaces for major pathways of 1,2-propanediol decomposition at the QCISD(T)/CBS//B3LYP/6-311+ +G(d,p) level.

Figure 3. Calculated potential energy surfaces for major pathways of 1,3-propanediol decomposition at the QCISD(T)/CBS//B3LYP/6-311+ +G(d,p) level.

Figure 4. Calculated potential energy surfaces for major pathways of glycerol decomposition at the CBS-QB3 level.

(3d), CH2OHCHOHCH2OH → CH2OHCOHCH2-1 + H2O (3e), CH2OHCHOHCH2OH → CH2OHCOHCH2-2+ H2O (3f), and CH2OHCHOHCH2OH → CH2OHCHCHOH-2 + H2O (3 g), all producing enols. Among the products above, CH2OHCHCHOH-1 and CH2OHCHCHOH-2 are isomers, with CH2OHCOHCH2-1 and CH2OHCOHCH2-2 being isomers as well. From the above, all of the H2O-elimination reactions of the three molecules give rise to the formation of enols. Due to the presence of multiple hydroxyl groups, the formation of enols is much easier in the decomposition of polyol molecules than in that of monohydroxy alcohols. Enols were formed through the H2O-elimination reactions in the polyols decomposition, which resulted from the H2 elimination in the decomposition of monohydroxy alcohols. In this work, the energy barriers of the enols formation pathways are in the range of 66.5−73.7 kcal/ mol for the three polyols, whereas with regard to monohydroxy alcohols, like ethanol and propanol,7,14 energy barriers are

Table 2. C−C BDEs of Several C3 Molecules Calculated with Different Methods (in kcal/mol) C−C BDEs Calculated With Different Methods molecules

QCISD(T)/CBS

CBS-QB3

1,2-propanediol 1,3-propanediol glycerol propane n-propanol

83.7, 85.1 86.4, 86.4

84.7, 85.9 87.7, 87.7 84.1, 87.9

87.0, 87.0 84.3, 88.3

Five possible H2O-elimination pathways are identified for glycerol. The channel CH 2 OH CHO HCH 2 OH → CH2OHCOCH3 + H2O (3c) via TS8 has the lowest energy barrier (68.3 kcal/mol). This process can be attributed to the intramolecular hydrogen bonding effect as well, and hydroxyacetone is formed in this process. The remaining four channels are CH2OHCHOHCH2OH → CH2OHCHCHOH-1 + H2O 4460



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generally greater than 100 kcal/mol for the enols formation paths via H2 elimination. What’s more, acetone and hydroxyacetone are formed in the dehydration process of 1,2-propanediol and glycerol, respectively, whereas ethene and formaldehyde are identified only for 1,3-propanediol. 3.2. Calculated Rate Constants. For the three molecules, only the predominant pathways discussed above, i.e., the direct bond dissociation and H2O-elimination reactions, are taken into consideration for the rate constant calculations. The direct bond dissociation channels consist of channels (1a−1b) for 1,2propanediol, channel (2a) for 1,3-propanediol, and channels (3a−3b) for glycerol, and the H2O-elimination channels involve channels (1c−1f) for 1,2-propanediol, channels (2b− 2c) for 1,3-propanediol, and channels (3c−3g) for glycerol. By applying the procedure proposed by da Silva and Bozzelli,40 we get the locations of optimal transition states varying with temperature for barrierless reactions. Here, we just take the calculation results of 1,2- and 1,3-propanediol for example. The minimum rate constants for channel (1a) result from the 3.548 Å transition state at 500−1000 K, the 3.148 Å transition state at 1100 K, and the 2.948 Å transition state for 1200−2500 K. The minimum rate constants for channel (1b) result from the 3.543 Å transition state at 500−700 K, the 3.343 Å transition state at 800−1000 K, the 2.943 Å transition state at 1100−2000 K, and the 2.743 Å transition state for 2100−2500 K. For channel (2a), the minimum rate constants result from the 3.751 Å transition state at 500−900 K, the 3.351 Å transition state at 1000−1700 K, the 3.151 Å transition state at 1800 K, and the 2.951 Å transition state for 1900−2500 K. Calculated rate constants at different pressures at the temperature range of 500−2500 K for different channels were fitted to modified Arrhenius equations. The parameters which can be directly used in combustion modeling are listed in Table

Figure 5. Calculated minimum energy pathways for the direct decomposition reactions of the three molecules at the CASPT2(2,2)/ 6-311G(d,p)//B3LYP/6-311G(d,p) level. Panel a was scaled by the QCISD(T) dissociation energies and panel b by CBS-QB3.

Table 3. Arrhenius Equations for Rate Constants of 1,2-Propanediol at Different Pressuresa k1a (s−1) A1a

pressure (atm) low-limit pressure 0.001 0.01 0.1 1 10 100 1000 infinite pressure

9.71 1.04 3.60 7.89 1.08 2.14 7.41 4.00 1.62

× × × × × × × × ×

n1a 1091 1089 1088 1084 1078 1068 1056 1045 1030

pressure (atm)

A1d

low-limit pressure 0.001 0.01 0.1 1 10 100 1000 infinite pressure

× × × × × × × × ×

1.50 2.17 7.35 1.01 1.43 5.97 5.32 2.79 1.48

20.67 22.24 21.77 20.41 18.15 15.12 11.64 8.27 3.70 k1d (s−1) n1d

77

10 1076 1071 1065 1056 1045 1034 1024 1011

16.82 19.36 17.80 15.58 12.81 9.63 6.30 3.23 −0.70

k1b (s−1) E1a 98 921 109 692 111 107 111 119 109 363 105 837 101 005 95 863 88 850

A1b 1.82 1.24 1.24 5.01 6.98 7.06 5.84 3.33 3.51

× × × × × × × × ×

E1d

A1e

78 921 95 044 94 612 92 770 89 665 85 486 80 639 75 867 68 387

× × × × × × × × ×

1.03 1.43 9.72 1.67 1.83 3.74 1.10 1.56 8.35

n1b 1092 1076 1078 1076 1071 1063 1053 1043 1028

20.75 18.51 18.75 18.03 16.35 13.81 10.72 7.64 3.20 k1e (s−1) n1e

78

10 1079 1074 1068 1059 1048 1037 1026 1011

17.04 19.89 18.39 16.16 13.34 10.06 6.57 3.33 −0.90

k1c (s−1) E1b 98 930 103 120 105 874 107 155 106 540 103 990 99 940 95 370 88 323

A1c 1.76 8.86 1.91 2.31 3.77 2.36 3.92 4.24 6.79

× × × × × × × × ×

E1e

A1f

80 284 97 194 97 091 95 467 92 457 88 241 83 236 78 230 71 273

× × × × × × × × ×

1.26 9.9 1.22 2.75 2.86 4.01 6.05 3.77 4.53

n1c 1075 1075 1071 1064 1055 1045 1034 1024 1011

79

10 1079 1076 1069 1060 1049 1037 1026 1011

16.33 18.83 17.23 15.00 12.26 9.14 5.90 2.92 −0.86 k1f (s−1)

E1c 75 865 93 084 92 451 90 485 87 333 83 180 78 425 73 786 67 542

n1f

E1f

17.32 20.25 18.81 16.60 13.76 10.42 6.84 3.49 −0.93

82 090 98 679 98 822 97 374 94 454 90 236 85 144 79 993 72 726

a The unit of low-limit pressure rate constants is cm3 molecule−1 s−1 and s−1 for other pressures; the unit of E is cal/mol. k1a to k1f correspond to reactions as follows, 1,2-C3H8O2 → CH3CHOH + CH2OH (1a), 1,2-C3H8O2 → CH2OHCHOH + CH3 (1b), 1,2-C3H8O2 → CH2OHCHCH2 + H2O (1c), 1,2-C3H8O2 → CH3COCH3 + H2O (1d), 1,2-C3H8O2 → CH3CHCHOH + H2O (1e), and 1,2-C3H8O2 → CH3COHCH2 + H2O (1f).

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Table 4. Arrhenius Equations for Rate Constants of 1,3-Propanediol at Different Pressuresa k2a (s−1) pressure (atm)

A2a

low-limit pressure 0.001 0.01 0.1 1 10 100 1000 infinite pressure

× × × × × × × × ×

2.41 2.64 3.55 1.67 1.06 4.52 7.14 7.84 8.75

n2a 89

10 1052 1063 1069 1068 1060 1049 1038 1025

−19.87 −12.16 −14.86 −16.02 −15.28 −12.85 −9.52 −6.22 −2.36

k2b (s−1) E2a

A2b

100 656 93 544 100 609 106 084 108 102 106 388 102 212 97 355 91 459

× × × × × × × × ×

1.88 5.08 5.92 3.17 1.54 4.02 9.39 5.13 3.86

n2b 71

10 1066 1062 1056 1048 1038 1028 1020 1011

−15.29 −16.26 −14.86 −12.81 −10.22 −7.30 −4.41 −1.96 0.74

k2c (s−1) E2b

A2c

70 123 84 088 83 933 82 339 79 368 75 383 71 040 67 130 62 622

× × × × × × × × ×

9.79 4.26 6.61 1.14 3.70 1.77 3.62 1.56 2.73

74

10 1070 1067 1062 1053 1043 1032 1023 1012

n2c

E2c

−16.26 −17.23 −16.09 −14.14 −11.46 −8.3 −5.08 −2.29 0.88

75 715 88 818 89 616 88 641 85 876 81 731 76 989 72 595 67 329

a The unit of low-limit pressure rate constants is cm3 molecule−1 s−1 and s−1 for other pressures; the unit of E is cal/mol. k2a to k2c correspond to reactions as follows, 1,3-C3H8O2 → CH2OHCH2 + CH2OH (2a), 1,3-C3H8O2 → C2H4 + CH2O + H2O (2b), and 1,3-C3H8O2 → CH2OHCHCH2 + H2O (2c).

Table 5. Arrhenius Equations for Rate Constants of Glycerol at Different Pressuresa k3a (s−1)

k3b (s−1)

k3c (s−1)

k3d (s−1)

A3a

n3a

E3a

A3b

n3b

E3b

A3c

n3c

E3c

A3d

n3d

E3d

low-limit pressure 0.001

7.16 × 1088

−19.90

93 022

1.55 × 1094

−21.26

8.27 × 1077

−17.10

−17.59

−20.46

2.86 × 1075

−18.33

1.08 × 1069

−16.95

1.05 × 1072

−17.67

0.01

4.05 × 1079

−19.24

1.67 × 1077

−18.41

5.77 × 1062

−14.91

8.14 × 1065

−15.66

0.1

5.26 × 1072

−16.97

4.83 × 1073

−17.03

3.56 × 1054

−12.35

3.74 × 1057

−13.04

1

7.01 × 1062

−13.89

4.49 × 1065

−14.42

8.97 × 1044

−9.42

4.08 × 1047

−9.99

10

2.25 × 1051

−10.40

108 881 109 631 108 055 104 500 99 667

6.00 × 1054

−11.06

6.88 × 1034

−6.37

9.28 × 1036

−6.78

100

9.13 × 1039

−6.99

94 487

1.47 × 1043

−7.55

2.29 × 1025

−3.55

7.86 × 1026

−3.77

1000

3.61 × 1030

−4.19

90 009

1.35 × 1033

−4.56

6.72 × 1017

−1.32

6.57 × 1018

−1.38

infinite pressure

7.66 × 1020

−1.35

85 326

1.42 × 1022

−1.35

93 171

9.87 × 1010

0.69

75 906 93 260 91 616 88 699 84 771 80 284 75 861 72 224 68 805

6.11 × 1079

4.58 × 1082

101 734 110 007 113 762 114 484 112 371 108 227 103 178 98 507

2.28 × 1011

0.82

78 591 96 415 95 026 92 190 88 189 83 514 78 840 74 952 71 221

pressure (atm)

k3e (s−1) A3e

pressure (atm) low-limit pressure 0.001 0.01 0.1 1 10 100 1000 Infinite pressure

1.00 1.01 8.11 3.64 3.64 7.30 5.34 3.88 1.11

× × × × × × × × ×

1080 1072 1065 1057 1047 1036 1026 1018 1011

k3f (s−1)

n3e

E3e

−17.65 −17.73 −15.72 −13.10 −10.03 −6.81 −3.78 −1.37 0.85

78 905 96 691 95 327 92 500 88 492 83 797 79 097 75 181 71 401

A3f 1.87 9.59 1.13 4.69 2.95 2.85 8.84 2.87 2.90

× × × × × × × × ×

1081 1073 1068 1059 1049 1038 1027 1019 1011

k3 g (s−1)

n3f

E3f

−17.98 −18.21 −16.23 −13.58 −10.45 −7.13 −3.99 −1.47 0.87

80 783 98 724 97 561 94 814 90 779 85 977 81 121 77 046 73 067

A3 g

n3 g

E3 g

× × × × × × × × ×

−18.27 −18.45 −16.49 −13.87 −10.76 −7.47 −4.38 −1.91 0.35

82 494 99 506 98 403 95 697 91 700 86 948 82 161 78 168 74 338

2.56 2.52 3.73 1.84 1.40 1.75 7.71 3.73 7.68

1082 1075 1069 1061 1051 1040 1029 1021 1013

The unit of low-limit pressure rate constants is cm3 molecule−1 s−1 and s−1 for other pressures; the unit of E is cal/mol. k3a to k3 g correspond to reactions as follows, glycerol → CH2OHCHOH-1 + CH2OH (3a), glycerol → CH2OHCHOH-2 + CH2OH (3b), glycerol → CH2OHCOCH3 + H2O (3c), glycerol → CH2OHCHCHOH-1 + H2O (3d), glycerol → CH2OHCOHCH2-1 + H2O (3e), glycerol → CH2OHCOHCH2-2+ H2O (3f), and glycerol → CH2OHCHCHOH-2+ H2O (3 g). a

increase with temperature and pressure, especially when the temperature and pressure get higher. For channels (1a) and (1b), k1a is dominant at low temperature while k1b plays the dominant role at high temperature. The ordering of k1c−k1f which can be expressed as k1c > k1e > k1f > k1d remains unchanged through the whole range investigated. According to the energy profile (Figure 2), the energy of TS1 for channel (1c), TS3 for channel (1e), and TS4 for channel (1f) has the order TS1 < TS3 < TS4, which can explain the result of k1c > k1e > k1f. The energy of TS2 for channel (1d) is smaller than

3 for 1,2-propanediol, Table 4 for 1,3-propanediol, and Table 5 for glycerol. We estimate that our rate constant calculations are accurate within a factor of 2.40,42 Computed rate constants versus pressure at four temperatures (i.e., 1000, 1500, 2000, and 2500 K) have been plotted in Figure 6 for 1,2-propanediol, Figure 7 for 1,3-propanediol and Figure 8 for glycerol. With 1,2-propanediol, the channels (1a)(1f) depicted in Figure 6 include two direct bond dissociation channels (1a) and (1b), and four dehydration channels (1c)(1f). From Figure 6, rate constants k1a-k1f of all the six channels 4462



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Figure 6. Calculated pressure-dependent rate constants for major channels of 1,2-propanediol decomposition at the temperature of 1000, 1500, 2000, and 2500 K.

Figure 7. Calculated pressure-dependent rate constants for major channels of 1,3-propanediol decomposition at the temperature of 1000, 1500, 2000, and 2500 K.

those TS3 and TS4, yet k1d is smaller than k1e and k1f. This can be attributed to the fact that the frequencies of TS3 and TS4 are lower than those of TS2. Figure 7 shows the rate constants of channels (2a−2c) at 0.001−1000 atm at different temperatures for 1,3-propanediol. Similar with 1,2-propanediol, rate constants of the three channels increase with temperature and pressure. Particularly,

k2a of the direct-bond-dissociation channel increases with pressure much more significantly compared with those of the two dehydration channels (k2b and k2c). From Figure 3, the energy of TS5 for channel (2b) is smaller than that of TS6 for channel (2c), yet k2b < k2c, which is also due to the fact that the frequencies of TS6 are lower than frequencies of TS5. 4463



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Figure 8. Calculated pressure-dependent rate constants for major channels of glycerol decomposition at the temperature of 1000, 1500, 2000, and 2500 K.

the H2O-elimination reactions are predominant at low temperature and pressure, whereas the direct C−C bond dissociation reactions are dominant at high temperature and pressure. Calculated rate constants at different pressures at 500−2500 K for different channels were fitted to the modified Arrhenius equations. What’s more, enol is the common product of the H2O-elimination process for the three molecules. Acetone and hydroxyacetone are produced in the dehydration process of 1,2-propanediol and glycerol respectively, whereas ethene and formaldehyde are identified for 1,3-propanediol.

Figure 8 plots the rate constants of channels (3a−3g) for glycerol. Rate constant computations have been conducted for seven channels, including two direct bond dissociation channels (3a) and (3b), and five dehydration channels (3c−3g). k3a and k3b increase much more rapidly than the rate constants of other five channels. At 1000 K, k3b remain smaller than k3a through the whole pressure range 0.001−1000 atm, whereas k3b becomes the largest at T > 2000 K. Channels (3d) and (3e) have very close barrier heights (70.5 and 70.7 kcal/mol); however, we get the result k3d > k3e. This is because channel (3d) has a degeneracy twice that of channel (3e). Rate constants of k3d−k3f are very close, which may be attributed to the combined effect of the barriers and transition state structures. What’s more, the channel (3g) producing CH2OHCHCHOH-2 + H2O is faster than the other H2Oelimination reactions, and its rate constants k3g is larger than k3c−k3f through the whole range investigated, which may be caused by the much lower frequencies of its transition state structure than others. From the rate constants depicted in Figures 6−8, one common point has been demonstrated for the three molecules: the H2O-elimination reactions play the controlling role at low temperature and pressure while the direct C−C dissociation reactions become dominant at high temperature and pressure.

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ASSOCIATED CONTENT

S Supporting Information *

Geometric structures, vibrational frequencies, and rotational constants of species at QCISD(T)/CBS//B3LYP/6-311+ +G(d,p) level for propanediols and at CBS-QB3 level for glycerol. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +86-551-5141078. Tel: +86551-3607923. Notes

The authors declare no competing financial interest.

4. CONCLUSIONS The decomposition mechanisms for three multiple-hydroxylradical molecules 1,2-propanediol, 1,3-propanediol and glycerol, have been investigated theoretically. For propanediols, the PESs have been constructed with the QCISD(T)/CBS// B3LYP/6-311++G(d,p) method, while the PES of glycerol has been built at the CBS-QB3 level. For the three molecules studied, the C−C bond breaking and dehydration reactions are predicted to be most important processes in their unimolecular decomposition. Further rate constant calculations indicate that

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ACKNOWLEDGMENTS Authors are grateful for the funding supports from Chinese Academy of Sciences, Natural Science Foundation of China under Grant No. 10805047.

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REFERENCES

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Theoretical Studies on the Unimolecular Decomposition of

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