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Kinetics of the Hydrogen Abstraction Reaction from 2-Butanol by OH Radical Jingjing Zheng, Gbenga Oyedepo, and Donald G. Truhlar J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b06121 • Publication Date (Web): 08 Sep 2015 Downloaded from http://pubs.acs.org on September 15, 2015

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The Journal of Physical Chemistry

August 29, 2015 Revised for J. Phys. Chem. A

Kinetics of the Hydrogen Abstraction Reaction From 2-Butanol by OH Radical Jingjing Zheng, Gbenga A. Oyedepo, and Donald G. Truhlar* Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, MN 55455, USA Abstract. The kinetics of the hydrogen abstraction from 2-butanol by hydroxyl radical have been studied using multi-path variational transition state theory with the multidimensional small curvature tunneling approximation. The rate constants for each of the five hydrogen abstraction sites (C1, C2, C3, C4, and O) and the overall reaction have been computed by direct dynamics based on M08-HX/6-311+G(2df,2p) electronic structure calculations. We show that multistructural torsional anharmonicity, anharmonicity differences of high-frequency modes between the transition structures and the reactants, and reaction-path dependence of multiple reaction paths are all important factors for determining accurate reaction rates and branching fractions for this problem. The reaction barrier heights for abstraction from various sites follow the order C2 < C3 < C4 < C1 < O, but the reactivities of the various sites do not precisely follow the inverse order of barrier heights, and the order of reactivities depends on temperature. The abstractions from C2 and C3 have the largest contribution to the total reaction rate from 200 to 2000 K.

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1. Introduction The exhaustibility of supplies of oil, petroleum, and natural gas necessitate the exploration of alternative energy sources that are renewable. One source of candidate replacement fuels or fuel additives is alcoholic biofuels, especially bio-butanol.1 Ethanol, the currently dominant biofuel in the market, suffers from a number of significant shortcomings; the two most important of which are that it only has 65% of the energy density of gasoline, and it possesses high hygroscopicity that makes it very corrosive.2 Bio-butanol has very low solubility in water with 90% of the energy density of gasoline and higher cetane number (compared to ethanol) therefore miscible with diesel fuel.2,3 Although, 1-butanol is the most widely studied of the three butanol isomers (1-butanol, 2-butanol, and 2-methyl-1-propanol or isobutanol) that could be produced via biological pathways (2-methyl-2-propanol and tert-butanol are petrochemical products), the remaining two isomers have one common advantage over the former; in particular, they have higher octane numbers with better anti-knocking indexes.4 2-Butanol has a particular unique edge over the others due to its favorable lower boiling point (99.5o C), which indicates that less heat energy is expended to recover it from aqueous fermentation broth during production.4,5 This motivates the quantitative prediction of the fundamental kinetics of the combustion of 2-butanol to better understand its performance and benefits in the design and optimization of transportation engine technology. Hydrogen abstraction by small radicals like H, OH, HO2, and CH3 is an important class of reactions in combustion, especially at ignition temperatures (600-1200 K). At combustion temperatures, the OH radical, one of the most reactive oxidizing species, is the most prolific hydrogen abstractor,6 and its reaction with 2-butanol is the focus of the present study. The abstraction reactions from 2-butanol can occur at five different reaction sites:


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CH3CH2CH(OH)CH3 + OH → CH3CH2Ċ(OH)CH3 + H2O

(C2)

→ CH3ĊHCH(OH)CH3 + H2O

(C3)

→ ĊH2CH2CH(OH)CH3 + H2O

(C4)

→ CH3CH2C(OH)ĊH2 + H2O

(C1)

→ CH3CH2CH(O·)CH3 + H2O

(O)

The rate constant for the overall reactions is called the total rate constant and is equal to the sum of the five individual reaction rate constants, i.e., ktotal = kC2 + kC3 + kC4 + kC1 + kO

(1)

Note that 2-butanol has a chiral carbon that cause it to have two enantiomers, R and S. The transition structures of C3 create an additional chiral center at the hydrogen abstraction site. Therefore C3 transition structures have four different optical isomers, namely (R, R), (S, S), (R, S), and (S, R). Quantitative knowledge of the branching fractions (ki/ktotal; i = C2, C3, C4, C1, O) defining the selectivity for H-atom abstraction from the five chemically non-equivalent sites of 2-butanol is necessary for modeling the combustion mechanism, and yet experimental kinetics studies usually measure just ktotal, so information about the branching is unavailable experimentally. There are three previous experimental studies of the rate constant for the reaction of 2butanol with hydroxyl radical as a function of temperature. Jiménez et al. determined the absolute overall rate coefficients for the reaction of OH with 2-butanol as a function of temperature (263-354 K) using the pulsed laser photolysis/laser-induced fluorescence technique.7 They observed negative temperature dependence of the rate constants at the low temperatures studied, and they fit their results to the Arrhenius expression. McGillen et al.8 measured the rate constant over the temperature range from 223-381 K, and they found significant non-Arrhenius behavior at the lower temperatures. Pang et al. recently utilized the shock tube ignition delay technique to measure the overall rate constant for the reaction of OH with 2-butanol over the high temperature range 888-1178 K, where the rate constant is an increasing function of



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temperature.9 Combustion models for the oxidation of 2-butanol have been published by Sarathy et al.,10 Frassoldati et al.,11 and Moss et al.12 There are no published measurements of the branching ratios, but McGillen et al.8 combined their rate constants with an analysis involving room temperature reaction end-product yields and high-temperature structure-activity relationships from previous work to derive estimates of site-specific reaction rate coefficients at temperatures up to 2000 K. The aim of the present work is to calculate the rate constants and branching fractions over a very wide temperature range for the five hydrogen abstraction sites by using multi-path canonical variational transition state theory13,14,15,16,17,18,19,20 (MP-CVT). This theory allows the transition state hypersurface to be orthogonal to the conformation-specific reaction coordinate at each of the saddle point conformations of each of the five reactions by allowing the variational transition state to be a multi-faceted dividing surface.13,15,21 To account for quantum mechanical effects on reaction-coordinate motion, the multidimensional small-curvature tunneling (SCT) approximation, which incorporates the coupling between the reaction coordinate and the transverse vibrational modes, has been employed.22 2. Computational method 2.1. Electronic structure calculations Density functional theory and wave function theory calculations were carried out using the Gaussian 0923 and Molpro 201024 quantum mechanical programs respectively. Restricted openshell Hartree-Fock orbitals are used for all the coupled-cluster calculations where only the valence electrons are correlated. The integration grid employed for all the density functional calculations except anharmonic calculations, using our locally modified Gaussian 09 versions MN-GFM6.225 has 99 radial shells and 974 angular points per shell, which is denoted as (99, 974); the default grid in Gaussian 09 (75, 302) has been demonstrated to be inadequate for frequency calculations using meta density functionals in a previous work.26 The M08-HX density functional27 in combination with the 6-311+G(2df,2p) basis set (hereafter referred to as MG3S)


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was utilized, having been validated in previous studies28 to give good performance, to optimize the geometries of all the conformers of the reactant, transition state, and product. The nature of each stationary point was confirmed by vibrational analysis. Because high-order numerical derivatives are very sensitive to the precision of analytic Hessians, a very fine grid was used in anharmonic calculations; this grid has 96 radial shells around each atom and a spherical product angular grid having 32 θ points and 64 ϕ points in each shell. In addition to the already mentioned M08-HX, three other density functionals including M08-SO,27 M1129 and M11-L30 in combination with both MG3S and 6-31+G(d,p) basis sets were also used and their results are given in the supporting information. 2.2. Partition Functions The multi-structural method with torsional anharmonicity (MS-T) was used for stationary points partition function calculations.31,32 In the MS-T calculations, each of the translational and electronic partition functions is separable from the conformational-rotational-vibrational partition function, but the latter is coupled, especially by the presence of multiple torsional degrees of freedom in the polyatomic molecules, which leads to many conformational structures in reactants and the transition states. The existence of multiple conformational structures increases the partition functions and therefore affects the computed rate constants. We define the multistructural torsional anharmonicity factor FαMS-T (T) of species α, which may be called the MS-T anharmonicity factor, Q MS-T α (T ) FαMS-T = con-rovib, SS-HO Qrovib, α (T )

(2)

MS-T where Qcon-rovib, α (T ) denotes the conformational-rotational-vibrational partition function SS-HO calculated by the MS-T method, and Qrovib, α (T ) is the single-structure rotational-vibrational

partition function obtained from the global minimum structure using the rigid-rotor harmonic oscillator approximation. The species α may be a reactant molecule or a transition state. Both



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MS-T SS-HO Qcon-rovib (T ) and Qrovib (T ) were calculated from the geometries, energies, and Hessians

obtained using the M08-HX/MG3S method. 2.3. Dynamics We calculate the reaction rate constants under the assumption that the system is in the lowpressure plateau region where the pressure is low enough for isolated binary collisions to be the reaction mechanism and there are no collision-stabilized pre-transition-state complexes33 (that could cause the rate constant to be pressure dependent) but high enough that reactant states are in local equilibrium with each other during the reaction. The rate constant calculated by the multi-path canonical variational transition state theory with small curvature tunneling (MP-CVT/SCT) is P

k T k MP−CVT/MT = γ B h

T,‡ ‡ Qelec ∑ Qk

Φ

k=1 MS-T, R

exp(−βV ‡ )

(3)

‡ where γ is generalized transmission coefficient, kB is the Boltzmann’s constant, Qelec is

electronic partition function, P is number of reaction path calculated (less or equal to the total T, ‡ number of reaction paths), Qk is rovibrational partition function of saddle point k with

torsional potential anharmonicity (T), Φ MS-T, R is the bimolecular reactants’ partition function per unit volume (with its zero of energy at the potential energy of the lowest-energy reactant structure), and V ‡ is the classical barrier height (defined as the change in the potential energy from the zero of energy used for the reactants partition function to the zero of energy used for the transition state partition function, where the zero of energies are defined as the lowest energy of all conformations of reactants and transition state respectively). Note that when number of reaction paths P involved in eq 3 is reduced to one, the MP-CVT/SCT reaction rate is also called MS-CVT/SCT13 rates. The generalized transmission coefficient γ is defined as


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7 P

T,‡

Qk ∑ κ k Γ CVT k

γ = k=1 P T,‡ ∑ Qk

(4)

k=1

where κ k is tunneling transmission coefficient of path k, Γ CVT is the CVT recrossing k transmission coefficient that is calculated as

Γ CVT k

=

QkT,CVT QkT,‡

.

(5)

T, CVT where Qk is the rovibrational partition function that includes torsional anharmonicity at the

canonical variational transition state along the reaction path the saddle point. The variational transition state expressions derived above include both variational effects and quantum mechanical effects on the reaction-coordinate motion. Quantum mechanical effects on reaction-coordinate motion include both tunneling at energies below the vibrationally adiabatic barrier and nonclassical reflection at energies above it. Because we use multidimensional tunneling, the tunneling calculation also corrects to some extent for the assumption in transition state theory that the reaction coordinate is separable. Neglecting the quantum effects on reaction-coordinate motion (which corresponds to setting all κ k equal to unity) yields what we usually call a quasiclassical calculation (in older work it was called a hybrid calculation). A “variational effect” is defined as a deviation of a quasiclassical variational transition state theory rate constant from a quasiclassical conventional transition state theory rate constant, where conventional transition state theory corresponds to placing the transition state dividing surfaces at the saddle point normal to the imaginary-frequency normal mode. Direct dynamics calculations were performed using the POLYRATE34 and GAUSSRATE35 programs. For each of reaction sites, the reaction paths were followed using the Page-McIver integrator36 in coordinates scaled to a reduced mass of 1 amu with a step size of 0.002 Å. The Hessians were computed at the non-stationary geometries along the MEP every 9 steps. The



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reorientation of the dividing surface (RODS) algorithm37,38 was used to maximize the standardstate free energy at each point of the reaction path and thus to eliminate unphysical dips on the vibrationally adiabatic potential energy curves arising from the strong coupling of highfrequency modes to the reaction coordinate. 3. Calculations and discussion 3.1. Barrier heights We prefer to use density functional theory for the full dynamics calculations because of its excellent performance/cost ratio, but for very high accuracy, it is preferable to reassess the approximate density functionals by comparison to more accurate results at stationary points of the reactions of interest. The first step in assessing approximate density functionals for these reactions is to obtain best estimates of barrier heights. For this purpose, we used the coupledcluster approximation with single and double excitations, quasi-perturbative inclusion of connected triple excitations, and explicit correlation by the F12a or F12b method. We carried out such calculations with the jun-cc-pVTZ basis set39 and the CCSD(T)-F12a and CCSD(T)-F12b coupled cluster approximations 40,41,42 at M08-HX/MG3S optimized geometries. In previous work43 on a database of 48 barrier heights and reaction energies, it was found that CCSD(T)F12a/jun-cc-pVTZ has a mean unsigned error of only 0.44 kcal/mol with respect to very accurate results. Therefore it is reasonable to take the CCSD(T)-F12a/jun-cc-pVTZ results as our reference for our best estimates. Tables 1 lists the calculated zero-point-exclusive classical forward barrier heights calculated by the CCSD(T)-F12a/jun-cc-pVTZ and M08-HX/MG3S methods. It is obvious that the M08-HX/MG3S agree with the CCSD(T)-F12a/jun-cc-pVTZ very well (mean unsigned deviation of only 0.15 kcal/mol) for these reaction barrier heights and this conclusion also agrees with our previous studies for similar hydrogen abstraction reaction of alcohol by OH radical.15,44 The barriers for abstraction at the various sites increase in the order C2 < C3 < C4 < C1 < O.


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3.2. Anharmonicity of high-frequency modes In a previous study44 of a similar reaction, namely hydrogen abstraction from isobutanol by OH radical, it was shown that the anharmonicities of high-frequency modes of the reactant and the transition state is sufficiently different that accounting for this difference in rate calculations is critical. In the present work we treat the anharmonicity of high-frequency modes by the quasiharmonic approximation, by which we mean using the harmonic oscillator formulas for partition functions but with effective frequencies. One way to obtain the effective frequencies to scale the directly calculated frequencies by scale factors optimized against a database of accurate zero-point energies.45 Such a procedure mainly improves the anharmonicity of high-frequency modes (because high-frequency modes make the largest contribution to the zero-point energies in polyatomic molecules), and because the populations of high-frequency modes are dominated by their zero-point levels, it improves their partition functions. A scaling factor that is parameterized to reproduce accurate zero-point energy ( λ ZPE ) can be written as45

λ ZPE = λ H λ Anh

(6)

where λ H accounts the inexactness of a model chemistry for harmonic oscillator frequencies and

λ Anh represent the correction for the anharmonicity of the zero point level. Therefore the λ H is supposed to only depend on the model chemistry, but λ Anh depends on the specific species. The

λ H for M08-HX/MG3S has been determined to be 0.984,45 and this value is used here. The determination of λ Anh is discussed next. To calculate λ Anh , we first used the hybrid 46 degeneracy-corrected 47 secondorder48,49,50,51 vibrational perturbation theory (HDCVPT2) to calculate the anharmonic zeroAnh pointe energies ( EZPE ) of 2-butanol and transition structures using the MPW1K/6-31+G(d,p)

method. The λ Anh for a given structure is calculated as



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E Anh λ Anh = ZPE H EZPE

(7)

H where EZPE is the zero-point energy calculated by the harmonic-oscillator approximation. (In Anh H eq 7, both EZPE and EZPE were evaluated with the same exchange-correlation functional and

basis without scaling, although we could have equally well calculated them both with the λ H scale factor for the employed exchange-correlation functional.) The reason that we chose the MPW1K exchange-correlation functional for the calculation of λ Anh is because it is a hybrid generalized gradient approximation with good performance for barrier height calculations,52 and also it is more numerically stable for high-order derivatives than meta functionals (e.g., M08-HX used for other aspects of the present work). The HDCVPT2 calculations were performed by the Gaussian 09 program (revision D.01). The calculated λ Anh and λ ZPE for the M08-HX/MG3S method for each species are given in Table 2. We label these λ ZPE as specific-reactionparameter (SRP) scaling factors, although we note that they are species-specific (different for reactants and transition state), not just reaction specific. In summary, we started with the M08HX frequencies, multiplied them by the general λ H and then multiplied them by an SRP value of λ Anh determined by MPW1K, just as in our previous work44 on isobutanol. The λ ZPE value of 2-butanol 0.971 is quite close to the standard scaling factor 0.973 for M08-HX/MG3S method. The key finding though is that the λ ZPE scaling factors for transition states are smaller than the standard values for equilibrium structures, just as we found for the isobutanol + OH reactions that we studied before.44 Although the differences between standard and SRP scaling factors are between 0.012 and 0.006, these small differences can change the zero-point energies of transition states by about 0.5 – 0.9 kcal/mol, which affects the reaction rate constants and branching ratios significantly., as will be shown below.


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For testing purpose, we also calculated λ ZPE for each structure of the C2 transition state. The SRP λ ZPE of all C2 transition structures are basically the same (either 0.967 or 0.966). The SRP λ ZPE for the lowest-energy transition structure of C2 are 0.967 and 0.968 by using the N12SX/6-31+G(d,p) and B3LYP/6-31+G(d,p) respectively.

3.3. Conformational structures and torsional anharmonicity Table 3 lists the convention for labeling conformational structures. Table 4 lists the global minima conformational structures of the reactant (2-butanol) and transition states obtained from each of the five hydrogen abstraction reactions above (C1, C2, C3, C4, and O) on their respective potential energy surfaces. There are 18 distinguishable structures (9 pairs of mirror images) for 2-butanol, generated by two torsions (Figure 1), i.e. C-C-C-C and C-C-O-H. The lowest energy structures, labeled as T-G- and T+G+, are a pair of mirror images based on the C-C-C-C and H-CO-H dihedral angles represented on Figure1. The energy difference between the global minimum and highest energy conformer is 0.90 kcal/mol and it indicates that all the conformers have significant thermal distribution and should therefore be included in the computed partition function for the reactant and the eventual rate constant. Figure 2 plots the minimum energy structures of the transition states for all five reactions. Four of the five listed structures (H abstraction from C sites) are stabilized by moderate to weak hydrogen bonding, as identified using the criteria specified by Jeffrey; 53 the C2 transition structures are stabilized in a H-bonded five-member ring, while the C1 and C3 transition states are stabilized in H-bonded six-member rings and the C4 transition state is stabilized in a sevenmember ring. The O···H bond lengths in the cyclic transition structures for the C2, C3, C4, and C1 reaction sites are 2.60, 2.16, 2.01, and 2.20 Å, respectively. The stabilizations of the transition states are factors contributing to the low-energy barriers and thus to increasing the reaction rates. However, the ring-like structures of the H-bonding stabilized structures decrease



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the entropy, which is a factor leading to smaller reaction rates. The final rate constants reflect both factors. As can be seen in Figure 3, the F MS-T factor of eq 2 has a significant effect on the calculated partition functions. The F MS-T factor increases the partition functions for all five transition states and reactant 2-butanol. The calculated rate will be affected by the ratio of MS-T MS-T FTS to F2-butanol . For most temperature, the transition state (except O site abstraction)

F MS-T is larger than that of 2-butanol, therefore the multi-structural torsional anharmonicity increases the reaction rates except for the O site abstraction. 3.4. Selection of multiple reaction paths The existence of multiple transition structures for each reaction implies that each of the five reactions has multiple reaction paths. In a full multipath calculation, one would calculate variational effects and tunneling transmission coefficients for all reaction paths. However, the number of reaction paths in this study is quite large, e.g., 43 pairs of transition structures for the C4 transition state corresponding to 43 pairs of reaction paths. When the number of transition structures is very large, it is often impractical to calculate all reaction paths due to the high computational effort, but it may be unnecessary to calculate all reaction paths explicitly since many of them may have negligible influence on the transmission coefficients. Therefore we employ a criterion to select the reaction paths to be calculated explicitly to obtain transmission coefficients. The overall generalized transmission coefficient is a weighted average of those for all reactions paths (see eq 4), and the weight of each transition structure is its partition function. Hence a reasonable criterion is to choose the reaction paths of the transition structures with the largest partition functions. Note that partition function is temperature dependent, and one could choose the reaction paths with the largest partition function of transition structures for the interested temperature range. For example, the C2 and C3 reactions dominate the overall reaction for low temperature as calculated by the MS-CVT/SCT method (in which only one reaction path


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is used, see Fig. 5 a), and the C4 reaction dominates at high temperature; therefore, we include the reaction paths of the C2 and C3 reactions that have largest partition functions at low temperature and the reaction paths of the C4 reaction with largest partition functions at high temperature. We choose 6, 5, 4, and 4 pairs of reaction paths for the C2, C3 (R, R), C3 (R, S), and C4 reactions channels, respectively, and only one reaction path for the other reaction channels (which is the same as using the lowest pair of optical-isomer reaction paths). As examples of the weights, we note that the partition functions of the transition structures of the six selected C2 reaction paths contribute from 11% to 2% of the total partition function. 3.5. Rate constants, branching fractions, and activation energies The rate constants were calculated in several different ways, and the total rate constants calculated in four different ways are shown in Figure 4. The MS-CVT/SCT calculations with general scaling factors are shown as a red dashed line in Fig. 4, one reaction path associated with the lowest-energy transition structure for each reaction is used to calculate the variational effects and tunneling transmission coefficients, and the frequencies are scaled by the standard scaling factor for M08-HX/MG3S (0.973). Figure 4 shows that these general-scaling MS-CVT/SCT rates are much lower than the experimental data for both high and low temperatures. In Section 3.2, we obtained SRP scaling factors for each reaction, and they show that the transition structures are more anharmonic than would be predicted by applying the general scaling factor. Applying these SRP scaling factors within the context of MS-CVT/SCT yields the black solid line in Fig. 4; the rate constants are increased by factors from 2 to 9 in 250 – 2400 K temperature range. They agree well with the experimental rates at high temperature, and they are in better agreement with experiment at low temperatures, but still too small. The next theoretical curve in figure 4 is the MP-CVT/SCT result, shown by a blue curve. This improves the agreement with experiment at low T, but worsens the agreement at high T. As assessed in a previous study,32 the MS-T method with a coupled torsional potential has considerable uncertainty for a very strongly coupled system. In ref. 44, we considered the ratio of



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the multi-structural reference classical (MS-RC) partition function ( Q MS-RC ) to the fully coupled classical (FCC) phase space integral ( Q FCC ) for the transition state of the hydrogen abstraction reaction of ethanol with hydroxyl radical, and we denote this temperature-dependent ratio as g ≡ Q MS-RC / Q FCC (see Figure 7 in Ref. 44 and see supporting information for the polynomial fitting of g as function of T). We fit this error estimate to the following functional form:

g = 0.286396 + 6.51847 ×10−3 T − 7.63994 ×10−6 T 2 + 4.26822 ×10−9 T 3 −1.19099 ×10−12 T 4 +1.32662 ×10−16 T 5

(8)

This comparison of the MS-T method to the fully coupled classical phase space integral is one way to assess possible systematic errors in MS-T, and we next assume that the MS-T partition functions of transition structures in the current study have the same errors as estimated by this means for the ethanol + OH reactions. The reason for this assumption is that fully coupled classical phase space integrals are unavailable for larger systems, but the 2-butanol and ethanol molecules are similar enough that assuming the correction is the same as for ethanol is probably closer to the truth than assuming the correction is not needed. Therefore the MP-CVT/SCT rate constants with SRP scaling are divided at each temperature by the factor g; these rates are shown as a solid green line in Fig. 4 and are taken as our final estimate. These final rate constants (kfinal) are in excellent agreement with the high-temperature experimental data and agree with the lowtemperature experimental data within a factor of 2. At 250 K, a factor of 2 underestimate of the rate is roughly equivalent to an overestimate of the barrier height by 0.3 kcal/mol, and this is well within the reliability of our barrier height calculations. The four theoretical curves in Fig. 4 illustrate how the calculated reaction rates are affected by various factors, in particular the anharmonicity difference between the transition state and the reactant, the dependences of transmission coefficients reaction paths, and the uncertainty of the MS-T partition function for strongly coupled torsions.


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The calculated site-specific and total rate constants for the hydrogen abstraction reactions have been fitted to the following four-parameter function15,54 for the temperature range between 250 and 2400 K:

( E(T + T ) + ! T + T0 $n 0 k = A# & exp *− " 300 % *) R(T 2 + T02 ) -,

(8)

where k is the rate constant, T is the temperature, R is the gas constant, and A, T0, n, and E are fitting parameters. The parameters are given in Table 5, and reaction rate constants at a series of temperatures are given in Table 6. The rather low values of T0 obtained for the present reactions imply that, except for the lowest temperature range, the more customary fitting function (which is obtained from eq 8 by setting T0 equal to zero) would have fit the data almost as well. Figure 5 shows the branching fractions for each of the hydrogen abstraction sites using MS-CVT/SCT with SRP scaling and MP-CVT/SCT with SRP scaling respectively. The difference between these two sets set of results is that the latter includes variational effects and tunneling from multiple reaction paths; the figure shows that including these effects gives quantitatively different branching fractions. The MP-CVT/SCT calculations predict that the C2 and C3 reactions are the dominant reactions through the whole temperature region, while MSCVT/SCT calculations show that branching fraction of C4 reaction increases rapidly and becomes the dominant one at temperature higher than 1400 K. The reactivity of each hydrogen abstraction site depends on the temperature and it does not always agree with the order of classical barrier heights. We calculated the activation energies (Ea), which are proportional to the local slopes of the Arrhenius plots, as functions of temperature; analytic differentiation of eq 8 yields



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16

Ea = E

T 4 + 2T0T 3 − T02T 2

(

T02 + T 2

)

2

+ nR

T2 T + T0

(9)

The calculated Ea values are in Table 7 and they show non-Arrhenius behavior (i.e., nonconstant Ea) not only for the total rate constant but also for all the site-specific ones. The C2 and C3 reactions have negative activation energy at temperatures of 350 K and lower. Table 8 compares site-specific rate constants and branching ratios (defined as the ratios of the site-specific rate constants to the total rate constant) from the present work to those estimated by McGillen et al.8 There are some points of interesting qualitative agreement; for example both studies predict the order of site-specific rate constants to be C2 > (C1+C4) > C3 > O at low T, and that the C3 rate constant becomes larger than the C2 rate constant between 381 and 1000 K. But quantitatively there is only fair agreement. The reasons why the two sets of results differ may be analyzed as follows. Our branching ratios are directly calculated, including multiple structures, anharmonicity, and multiple reaction paths each including multidimensional tunneling, whereas their estimates are based on combining three kinds of data, and especially on the extrapolation of SARs originally intended for use at high temperature down to the lowtemperature regime. In assessing possible errors in the present calculations, we emphasize that although there have been great strides forward in making theoretical predictions quantitatively reliable, there are still uncertainties, and in the present case we believe these are most likely due to the inexactness of the exchange-correlation functional and the methods used to treat anharmonicity. However, there is no simple explanation in terms for barrier heights. For example, the largest deviation of the site-specific barrier heights used here from the CCSD(T)F12a/jun-cc-pVTZ results is for C1, where M08-HX/MG3S predicts a lower barrier height (which, ceteris paribus, would lead to a larger rate constant), and yet our predicted branching ratio for C1 is smaller than the estimate of McGillen et al. at low temperature, where the results should be most sensitive to barrier height and where competing entropic effects are smallest. In assessing the possible errors in the SAR estimates, we note that the SAR analysis does not take


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17

explicit account of the multiple structures, the temperature dependence of torsional anharmonicity, or the fact that the order of the reactivities of each hydrogen abstraction site does not always agree with the order of classical barrier heights. When one looks at the details of the present calculations, as discussed above, such as (to mention just one aspect) the differing entropic effects at hydrogen-bonded and non-hydrogen-bonded transition states, it is hard to have confidence that all the subtle and complex effects that influence the full calculations can be incorporated in a SAR analysis that does not take explicit account of multiple structures. 3.6. Temperature dependence The rate constants shown in Fig. 4 have inverse temperature dependence at low temperatures, i.e., the rate decreases when temperature increases. Here we make an analysis of this temperature dependence. It is important to include both tunneling and variational effects to calculate quantitative rate constants and branching ratios. But these are not the factors causing the inverse temperature dependence at low T, and so they are neglected in the present discussion. Thus, to simplify the discussion and calculations, this discussion is based on conventional transition state theory (all calculations at stationary points) with generic scaling factors and g = 1, but we do use MS-T partition functions. A bimolecular reaction rate is then given by

# ΔG,‡ & k T (( k = B  exp %% − hC $ kBT ' # ΔH ,‡ ΔS ,‡ & kBT (( = exp %% − + k T k hC  B B ' $

(10)

where C  is the gas-phase concentration under standard-state conditions (in molecules per unit volume, it equals P°/ kBT , where P° = 1 bar), ΔG,‡ is standard-state free energy of activation,

ΔH ,‡ is standard state enthalpy of activation, and ΔS ,‡ is standard-state entropy of activation. All the thermodynamic functions are relative to the values of reactants. The logarithm of reaction rate gives



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18

(

)

ΔG,‡ kBT

)

ΔH ,‡ ΔS ,‡ + kBT kB

ln k = ln kBT / hC 0 −

(

= ln kBT / hC 0 −

(

)

The logarithm of rate constant is decomposed three components, a pre-factor ln kBT / hC 0 ,

ΔH ,‡ ΔS ,‡ − , and . To illustrate the temperature dependence of all these quantities, Figure 6 kBT kB

(

) (

ln kBT / hC 0 − ln kBT / hC 0

plots

ΔS ,‡ ΔS ,‡ − kB kB

) T =2500 K

, ln k − ln k T =2500 K , and − T =2500 K

,

−

ΔG,‡ ΔG,‡ + kBT kBT

ΔH ,‡ ΔH ,‡ + kBT kBT

, T =2500 K

vs. 1000/T. Since the T =2500 K

free energy and enthalpy also include the contribution from the barrier height V ‡ , Fig. 6 also plots −

(ΔG,‡ −V ‡ ) (ΔG,‡ −V ‡ ) + kBT kBT

vs. 1000/T to illustrate the effect of the classical T =2500 K

barrier height on the standard-state free energy of activation. The transition state of a bimolecular reaction has six more vibrational modes than are present at reactants; therefore the enthalpy and entropy of the transition state relative to those of reactants will increase usually when temperature increases. But the contributions of the enthalpy and the entropy to the free energy have different signs, so it is normal that the change of free energy of activation without including barrier height is curved as illustrated by the dotted green lines ( −

(ΔG,‡ −V ‡ ) ΔG,‡ vs. 1000/T) in Fig. 6. The inverse temperature dependence of − is kBT kBT

enhanced by the negative barriers as in the C2 and C3 reactions and is diluted by the positive barriers as in the C4, C1, and O reactions (this is why an inverse temperature dependence of rate

(

constants is hardly ever observed for high-barrier reactions). The pre-factor ln kBT / hC 0

)


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19

further dilutes the effect of the inverse temperature dependence of −

ΔG,‡ . Note that the factor kBT

ln kBT / hC 0 is proportional to lnT 2 . As a consequence of these considerations, only the C2

(

)

and C3 reactions have low enough barriers for their rate constants to have inverse temperature dependence. Since the C2 and C3 reactions dominate the total reaction at low temperature, the total rate constants have inverse temperature dependence at low temperatures.

4. Concluding Remarks Accurate prediction of the barrier heights of a chemical reaction is central to quantitative theoretical prediction of its kinetics. For reactions involving small molecules, reliable ab initio methods, such as those involving the coupled-cluster calculations with basis sets of near complete-basis-set (CBS) quality or that can be extrapolated to the CBS limit, have been used successfully to predict barrier heights and thus their rate constants. Density functional calculations can be validated both in general and for specific reactions by comparison to such wave function calculations, and the density functional calculations can be used for direct dynamics calculations of the reaction rates including multiple conformations, anharmonicity, and multidimensional tunneling. This is the strategy employed here. Multi-path canonical variational transition state theory, including the multidimensional treatment of tunneling by the small-curvature approximation, has been used to determine the rate constants for hydrogen abstraction from the various sites of 2-butanol by OH radical in the lowpressure plateau regime and over a wide temperature range. We show that multistructural torsional anharmonicity, anharmonicity differences of high-frequency modes between the transition structures and the reactants, variational effects, and tunneling contributions from multiple reaction paths are all important factors for determining accurate reaction rates and branching fractions. Effects of multiple reaction paths are also shown to be important for accurately predicting the reaction rates and branching fractions.



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20

At low temperatures, the calculated reaction rates decrease with temperature, in agreement with previous experimental studies by Jiménez et al.7 The overall rate constants calculated by the MP-CVT/SCT method with SRP scaling factors are in reasonable agreement with the experimental results at both low and high temperature. The reaction barrier heights for abstraction from various sites follow the order C2 < C3 < C4 < C1 < O, but the reactivities of the various sites do not precisely follow the inverse order of barrier heights, and the predicted order of reactivities depends on temperature.

! ASSOCIATED CONTENT Supporting Information. Structures, additional tables of energetic quantities, and further discussion of the inverse temperature dependence at low T. This material is available free of charge via the Internet at http://pubs.acs.org. ! AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. ! ACKNOWLEDGMENTs The authors are grateful to James Burkholder for assistance in correcting Table 9 of Ref. 8. Our work on biofuel combustion is supported in part by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, as part of the Combustion Energy Frontier Research Center under Award Number DE-SC0001198, and our work on gas-phase reaction kinetics is funded by the U. S. Department of Energy, Office of Basic Energy Sciences, under grant no. DEFG02-86ER13579.


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21

Table 1. Calculated zero-point-exclusive forward barrier heights ΔV ‡ (kcal/mol) and zeropoint-inclusive forward barrier heights ΔH  (0) (kcal/mol) of the hydrogen abstraction reaction of 2-butanol by OH radical

a

Method

C1 b

C3

C4

O

ΔV ‡

-1.33 -0.49 0.64 2.80 -1.36 -0.69 0.64 2.73 zero-point-inclusive forward barrier heights c 0.40 -2.29 -2.04 -0.83 0.75 CCSD(T)-F12a/jun-cc-pVTZ c -0.05 -2.32 -2.24 -0.83 0.68 M08-HX/MG3S a The zero-point-exclusive barrier height is also called the classical barrier height; it is the potential energy at the lowest-energy saddle point minus the potential energy at the lowestenergy equilibrium structure of the reactant. The zero-point-inclusive barrier height is obtained CCSD(T)-F12a/jun-cc-pVTZ M08-HX/MG3S

b c

1.66 1.21

C2

by adding the change in zero point energy; it equals the enthalpy of activation ΔH ! (T ) at temperature T = 0. M08-HX/MG3S geometries were used. Zero-point energies were calculated using M08-HX/MG3S with the SRP frequency scaling factors shown in Table 2.



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22

Table 2. Scaling factors λ ZPE and λ Anh for 2-butanol and transition statesa ______________________________________________________________________________ 2-butanol

C1-TS

C2-TS

C3-TS (R, R)

C3-TS(R, S)

C4-TS

OH-TS

______________________________________________________________________________

λ Anh

0.987

0.982

0.982

0.978

0.977

0.981

0.979

λ ZPE

0.971

0.966

0.967

0.962

0.961

0.965

0.964

______________________________________________________________________________ a

The lowest-energy structure of each species is used. (The transition states for the various

reactions are considered as different species, each with more than one structure, but the λ Anh values are taken to be the same for all structures of a given species.) Note that the second row of this table is equal to 0.984 times the first row.


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23

Table 3. Conventions for labeling conformations Naming convention trans

Label T

Dihedral angle range (degrees) 180

trans±

T±

±150, ±180

anti±

A±

±105, ±150

±

±90, ±105

±

±75, ±90

±

±30, ±75

±

±0, ±30 0

a gauche±

g

G cis± cis

C C



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24

Table 4. Global minima structures on the potential energy surfaces of the reactant, products and transition state species Torsion angle labels Species Global minimum Mirror image Number of structures 2-butanola Transition State

T-G+G+

T+G-G-

18

C2c

T-G+G+C-

T+G-G-C+

26

C3c

T-G+G+C+

T+G-G-C-

34

c

-

C4

+

+

+

+ +

+

-

TG G C

c

C1

TTGC

+

-

-

-

86

+

98

T GGC - -

-

TTGC

Od T-G-G+GT+G+G-G+ 34 The consecutive torsion labels in the reactant and products indicate C-C-C-C, C-C-O-H and CC-C-O dihedral angles. b The torsion label indicate C-C-C-C, C-C-C-H and C-C-C-O dihedral angles. c The torsion labels indicate C-C-C-C, C-C-O-H, C-C-C-O and C-H-O-H dihedral angles. d The torsion label indicate C-C-C-C, C-C-O-H, C-C-C-O and O-H-O-H dihedral angles. a


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25

Table 5. The parameters fitted to the MP-CVT/SCT rate constants kfinal a using eq 8 kC2 A (cm3molecule-1s-1) n

kC3

1.985×10-13 2.168

kC4

kC1

kO

Total

7.620×10-14 1.189×10-14 4.131×10-15 5.722×10-14 2.776 3.447 3.593 1.574

2.033×10-13 2.750

E (kcal/mol)

-1.203

-1.658

-0.05461

-0.8064

0.740

-1.533

T0 (K)

38.23

34.12

176.1

93.67

333.8

35.80

a The MP-CVT/SCT rate constants use SRP scaling factor and include best estimate of the

systematic error in the MS-T method

Table 6. MP-CVT/SCT rate constants kfinal (cm3 molecule-1 s-1) with the SRP scaling factor and including the best estimate of the systematic error in the MS-T method T (K) 298 400 600 1000 1500 2400

C2 2.43E-12 2.31E-12 2.93E-12 5.53E-12 1.05E-11 2.33E-11

C3 2.14E-12 1.89E-12 2.57E-12 5.84E-12 1.28E-11 3.27E-11

C4 6.84E-14 1.06E-13 3.38E-13 1.33E-12 4.63E-12 1.97E-11

C1 5.84E-14 7.37E-14 1.72E-13 6.91E-13 2.31E-12 9.40E-12

O 5.46E-14 8.51E-14 1.69E-13 3.83E-13 7.24E-13 1.63E-12

Total 4.75E-12 4.46E-12 6.18E-12 1.38E-11 3.10E-11 8.67E-11



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26

Table 7. Arrhenius activation energies (kcal/mol) T (K) C2 C3 C4 C1 O Total 200 -0.78 -1.11 0.69 0.04 0.31 -0.98 250 -0.54 -0.79 0.96 0.30 0.52 -0.67 298 -0.31 -0.49 1.23 0.60 0.73 -0.37 350 -0.06 -0.17 1.53 0.94 0.97 -0.06 400 0.18 0.13 1.84 1.29 1.19 0.24 500 0.64 0.72 2.46 2.00 1.61 0.82 600 1.09 1.30 3.11 2.72 1.98 1.40 700 1.54 1.87 3.76 3.44 2.33 1.96 800 1.98 2.44 4.42 4.16 2.66 2.52 900 2.42 3.01 5.09 4.88 2.97 3.08 1000 2.86 3.57 5.76 5.59 3.28 3.64 1100 3.30 4.13 6.43 6.31 3.58 4.19 1200 3.73 4.69 7.10 7.03 3.88 4.75 1300 4.17 5.25 7.78 7.75 4.18 5.30 1400 4.61 5.80 8.45 8.47 4.48 5.85 1500 5.04 6.36 9.13 9.18 4.78 6.40 1800 6.34 8.03 11.17 11.33 5.67 8.05 2000 7.21 9.13 12.53 12.76 6.28 9.15 2400 8.94 11.35 15.25 15.63 7.49 11.35 a Based on the MP-CVT/SCT rate constants k final with the SRP scaling factor and including the best estimate of the systematic error in the MS-T method.


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27

Table 8. Comparison to the state-selected rate constants estimated by McGillen et al. T (K) C2 C3 -12 3 rate constants - McGillen et al. (10 cm molecule s-1) 250 7.8 1.5 298 5.6 1.5 381 4.3 1.7 1000 5.9 6.8 1800 13.2 22.3 -12 3 -1 rate constants - present (10 cm molecule s ) 250 2.8 2.7 298 2.4 2.2 381 2.3 1000 5.5 1800 14.2 ratio of rate constants - present/McGillen et al. 250 0.36 298 0.43 381 0.54 1000 0.93 1800 1.08 branching ratios- McGillen et al. 250 0.66 298 0.58 381 0.47 1000 0.24 1800 0.19 branching ratios - present 250 0.47 298 0.51 381 0.51 1000 0.40 1800 0.31 a

a

C1+C4

O

total

1.8 1.9 2.2 8.5 26.8

0.6 0.7 0.9 3.1 8.5

11.7 9.7 9.1 24.3 70.8

0.09 0.12

0.05 0.06

5.6 4.8

2.0 5.6 18.6

0.18 2.0 11.9

0.08 0.4 1.0

4.5 13.6 45.8

1.84 1.46 1.16 0.82 0.83

0.05 0.06 0.08 0.24 0.45

0.07 0.08 0.09 0.12 0.12

0.48 0.49 0.50 0.56 0.65

0.13 0.16 0.19 0.28 0.32

0.15 0.19 0.24 0.35 0.38

0.06 0.07 0.10 0.13 0.12

1.00 1.00 1.00 1.00 1.00

0.19 0.46 0.44 0.41 0.41

0.24 0.03 0.04 0.15 0.26

0.10 0.01 0.02 0.03 0.02

1.00 1.00 1.00 1.00 1.00

computed from the fits in their Table 9 after correcting a tabulation error (23 should be -398).



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17 18 19 20

21

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Truhlar, D. G.; Garrett, B. C. Variational Transition-State Theory. Acc. Chem. Res. 1980, 13, 440–448. Truhlar, D. G.; Isaacson, A. D.; Garrett, B. C. Generalized Transition State Theory. In Theory of Chemical Reaction Dynamics; Baer, M., Ed.; CRC Press: Boca Raton, FL, 1985; Vol. 4, pp 65–137. Jackels, C. F.; Gu, Z.; Truhlar, D. G. Reaction-Path Potential and Vibrational Frequencies in Terms of Curvilinear Internal Coordinates. J. Chem. Phys. 1995, 102, 3188–3201. Fernandez-Ramos, A.; Ellingson, B. A.; Garrett, B. C.; Truhlar, D. G. Variational Transition State Theory with Multidimensional Tunneling. In Reviews in Computational Chemistry; Lipkowitz, K. B., Cundari, T. R., Eds.; Wiley-VCH: Hoboken, NJ, 2007; Vol. 23, pp. 125–232. Bao, J. L; Meana-Pañeda, R.; Truhlar, D. G. Multi-Path Variational Transition State Theory for Chiral Molecules: The Site-Dependent Kinetics for Abstraction of Hydrogen from Hydroperoxyl Radical, Analysis of Hydrogen Bonding in the Transition State, and Dramatic Temperature Dependence of the Activation Energy. Chem. Sci. 2015, online as Advance Article: dx.doi.org/10.1039/C5SC01848J (accessed Aug. 29, 2015). Liu, Y.–P.; Lynch, G. C.; Truong, T. N.; Lu, D.–h.; Truhlar, D. G. Multi-path Variational Transition State Theory for Chemical Reaction Rates of Complex Polyatomic Species: Ethanol + OH Reactions. J. Am. Chem. Soc. 1993, 115, 2408–2415. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. Werner, H.–J.; Knowles, P. J.; Manby, F. R.; Schütz, M.; Celani, P.; Knizia, G.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G. et al. Molpro, University of Birmingham, Birmingham, 2010.1, 2010. Zhao, Y.; Peverati, R.; Yang, K.; Truhlar, D. G. MN-GFM version 6.2 computer program modules, University of Minnesota, Minneapolis, 2011. Zheng, J.; Yu, T.; Papajak, E.; Alecu, I. M.; Mielke, S. L.; Truhlar, D. G. Practical Methods for Including Torsional Anharmonicity in Thermochemical Calculations of Complex Molecules: The Internal-Coordinate Multi-Structural Approximation. Phys. Chem. Chem. Phys. 2011, 13, 10885–10907. Zhao, Y.; Truhlar, D. G. Exploring the Limit of Accuracy of the Global Hybrid Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions. J. Chem. Theory Comput. 2008, 4, 1849–1868. Xu, X.; Alecu, I.M.; Truhlar, D. G. How Well Can Modern Density Functionals Predict Internuclear Distances at Transition States? J. Chem. Theory Comput. 2011, 7, 1667-1676. Peverati, R.; Truhlar, D. G. Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation. J. Phys. Chem. Lett. 2011, 2, 2810–2817. Peverati, R.; Truhlar, D. G. M11-L: A Local Density Functional that Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics. J. Phys. Chem. Lett. 2012, 3, 117–124. (a) Zheng, J.; Mielke, S. L.; Clarkson, K. L.; Truhlar, D. G. MSTor: A Program for Calculating Partition Functions, Free Energies, Enthalpies, Entropies, and Heat Capacities of Complex Molecules Including Torsional Anharmonicity. Computer Phys. Commun. 2012, 183, 1803-1812. (b) Zheng, J.; Meana-Pañeda, R.; Truhlar, D. G. MSTor version



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2013: A New Version of the Computer Code for the Multistructural Torsional Anharmonicity with A Coupled Torsional Potential. Computer Phys. Commun. 2013, 184, 2032-2033. Zheng, J.; Truhlar, D. G. Quantum Thermochemistry: Multi-Structural Method with Torsional Anharmonicity Based on a Coupled Torsional Potential. J. Chem. Theory Comput. 2013, 9, 1356-1367. (a) Benson, S. W.; Dobis, O. Existence of Negative Activation Energies in Simple Bimolecular Metathesis Reactions and Some Observations on Too-Fast Reactions. J. Phys. Chem. A 1998, 102, 5175-5181. (b) Alecu, I. M.; Gao, Y.; Hsieh, P-C.; Sand, J. P.; Ors, A.; McLeod, A.; Marshall, P. Studies of the Kinetics and Thermochemistry of the Forward and Reverse Reaction Cl + C6H6 = HCl + C6H5. J. Phys. Chem. A 2007, 111, 3970-3976. (c) Greenwald, E. E.; North, S. M.; Georgievskii, Y.; Klippenstein, S. J. A Two Transition State Model for Radical−Molecule Reactions:   A Case Study of the Addition of OH to C2H4. J. Phys. Chem. A 2005, 109, 6031-6044. Zheng, J.; Zhang, S.; Lynch, B. J.; Corchado, J. C.; Chuang, Y.–Y.; Fast, P. L.; Hu, W.–P.; Liu, Y.–P.; Lynch, G. C.; Nguyen, K. A. et al. Polyrate version 2015, University of Minnesota, Minneapolis, 2015. Zheng, J.; Zhang, S.; Corchado, J. C.; Chuang, Y.-Y; Coitiño, E. L.; Ellingson, B. A.; Truhlar D. G. Gaussrate version 2015, University of Minnesota, Minneapolis, MN 554550431, USA. Page, M.; McIver, J. W., Jr. On Evaluating the Reaction-Path Hamiltonian. J. Chem. Phys. 1988, 88, 922-935. González-Lafont, A.; Villá, J.; Lluch, J. M.; Bertrán, J.; Steckler, R.; Truhlar, D. G. Variational Transition State Theory and Tunneling Calculations with Reorientation of the Generalized Transition States for Methyl Cation Transfer. J. Phys. Chem. A. 1998, 102, 3420-3428. Villá, J.; Truhlar, D. G. Variational Transition State Theory Without the Minimum Energy Path. Theor. Chem. Acc. 1997, 97, 317-323. Papajak, E.; Truhlar, D. G. Convergent Partially Augmented Basis Sets for Post-HartreeFock Calculations of Molecular Properties and Reaction Barrier Heights. J. Chem. Theory Comput. 2011, 7, 10-18. Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479-483. Adler, T. B.; Knizia, G.; Werner, H.-J. A Simple and Efficient CCSD(T)-F12 Approximation. J. Chem. Phys. 2007, 127, article no. 221106. Knizia, G.; Adler, T. B.; Werner, H.-J. Simplified CCSD(T)-F12 Methods: Theory and Benchmarks. J. Chem. Phys. 2009, 130, article no. 054104. Papajak, E.; Truhlar, D. G. What are the Most Efficient Basis Set Strategies for Correlated Wave Function Calculations of Reaction Energies and Barrier Heights? J. Chem. Phys. 2012, 137, article no. 064110. Zheng, J; Meana-Pañeda, R.; Truhlar, D. G. Prediction of Experimentally Unavailable Product Branching Ratios for Biofuel Combustion: The Role of Anharmonicity. J. Am. Chem. Soc. 2014, 136, 5150-5160.


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TOC graphic



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-

Figure 1. Minimun-energy structure (T-G ) of 2-butanol.


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Figure 2. Lowest-energy transition structures for abstraction from various sites: (a) C2, (b) C3, (c) C4, (d) C1, (e) O.



30

75

C2 C3 (R, R) C3 (R, S) C1 C4 O 2-butanol

65 55 45

F MS-T

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500

800

1100

1400

T (K)

1700

2000

2300

Figure 3. Multi-structural torsional anharmonicity factors (FMS-T) as functions of temperature (T) for abstraction transition states of various sites and for the reactant 2-butanol.


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Figure 4. Calculated overall forward total rate constant (using M08-HX/MG3S method) and corresponding experimental results (denoted as symbols) as functions of reciprocal temperature for the hydrogen abstraction reaction from 2-butanol by OH radical. The rate constants of McGillen et al. are for 223, 298, and 381 K and are calculated from the fits in their Table 9 after correcting a tabulation error (23 should be -398). The four room temperature experimental results on the plots cannot all be seen well because they are on top of one another.



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Figure 5. Branching fractions as functions of reciprocal temperature.


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(

) (

Figure 6. Plots of ln k − ln k T =2500 K (black solid line), ln kBT / hC 0 − ln kBT / hC 0 (maroon long dash dot line), −

(ΔG,‡ −V ‡ ) (ΔG,‡ −V ‡ ) − + kBT kBT dash line), and

ΔS ,‡ ΔS ,‡ − kB kB

ΔG,‡ ΔG,‡ + kBT kBT

T =2500 K

) T =2500 K

(green solid line), T =2500 K

ΔH ,‡ ΔH ,‡ + (green dash dot line), − kBT kBT

(red T =2500 K

(blue dotted line). All calculations are based on the M08T =2500 K

HX/MG3S potential energy surfaces.


Kinetics of the Hydrogen Abstraction Reaction ... - ACS Publications

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