Effects of Water Molecule on CO Oxidation by OH: Reaction Pathways

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Effects of Water Molecule on CO Oxidation by OH: Reaction Pathways, Kinetic Barriers and Rate Constants Linyao Zhang, Li Yang, Yijun Zhao, Jiaxu Zhang, Dongdong Feng, and Shaozeng Sun J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 14 Jun 2017 Downloaded from http://pubs.acs.org on June 15, 2017

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The Journal of Physical Chemistry

Effects of Water Molecule on CO Oxidation by OH: Reaction Pathways, Kinetic Barriers and Rate Constants

Linyao Zhang#, Li Yang§, Yijun Zhao#, Jiaxu Zhang*,§, Dongdong Feng#, Shaozeng Sun*,#

#

School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China

§

School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China

Corresponding Authors E-mail: [email protected], [email protected]

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Abstract The water dilute oxy-fuel combustion is a clean combustion technology for near-zero emission power; and the presence of water molecule could have both kinetic and dynamic effects on combustion reactions. The reaction OH + CO → CO2 + H, one of the most important elementary reactions, has been investigated by extensive electronic structure calculations. And the effects of a single water molecule on CO oxidation have been studied by considering the pre-formed OH(H2O) complex reacts with CO. The results show little change in the reaction pathways, but the additional water molecule actually increases the vibrationally adiabatic energy barriers (VG a ). Further thermal rate constant calculations in the temperature range of 200 to 2000 K demonstrate that the total low-pressure limit rate constant for the water assisted OH(H2O) + CO → CO2 + H2O + H reaction is 1 - 2 orders lower than that of the water unassisted one, which is in consistency with the change of VG a . Therefore, the hydrated radical OH(H2O) would actually slow down the oxidation of CO. Meanwhile, comparisons show that the M06-2X/aug-cc-pVDZ method gives a much better estimation in energy and thus is recommended to be employed for direct dynamics simulations.

Key words: CO oxidation, effects of water, VTST-ISPE, rate constants

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1. Introduction Oxy-fuel combustion with steam (H2O) added to moderate the flame temperature has many advantages, such as higher efficiency and near-zero emission, in power generation processes.1 The high water vapor concentration is the main difference between air combustion and O2/H2O-fuel combustion. Besides the thermodynamic effects caused by water, the additional H2O molecules could directly affect the H2O involved chemical reactions or act as high efficient third-body collision partners to change the reaction paths.2,3 The oxidation of carbon monoxide (CO) by hydroxyl radical (OH), which is the final oxidation step for all hydrocarbon fuels4, is considered to be the second most important reaction5 in combustion chemistry and also plays an essential role for the conversion of CO to CO2 in atmospheric chemistry6. It is well-known that the OH + CO reaction is not a simple bimolecular reaction and is actually included the HOCO7-9 complex-forming process10. And very recently, the existence HOCO radical and its formation mechanism had been confirmed under thermal conditions by time-resolved direct frequency comb spectroscopy (TRFCS) experiments11. As schematically shown in this scheme,

(1)

that the chemically activated complex (HOCO*) can either dissociate into products, revert to reactants, or be deactivated to yield a stable (but highly reactive) HOCO complex through collision with a third body (M).

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Crossed molecule beam studies12 of the OH + CO reaction at 14.1 kcal/mol collision energy had shown that the products angular distribution exhibited a quite broad backward-forward structure with a forward bias which suggested the existence of short-lived HOCO intermediate living to about one rotational period. The not particularly long lifetime of the HOCO radicals have led to a strong non-statistical behavior and thus dynamics is important13. Therefore, this four-atom system has also attracted extensive theoretical investigations, with numerous well-built analytic potential energy surfaces (PESs) followed by quasi-classical trajectory calculations (QCT) and/or quantum dynamics (QM) studies14-25 performed on these PESs to reveal its dynamics features. Recently, based on a very large number of high-level ab initio energies, Guo and coworkers developed26 and improved27 a global PES by the permutation invariant polynomial (PIP) fitting method. Subsequently, Chen et al.28 developed a global PES by neural networks (NN) fitting method and further improved29 using a new PIP neural network (PIP-NN) approach. The results of the follow-up QCT and QM studies26-31 on these global PESs show well consistency, but still cannot fully reproduce the crossed beam experiments, such as the forward bias reactive differential cross section (DCSs). The reasons for these discrepancies between the theory and experiment still remain unclear, thus further studies are still needed. The collisional stabilization of the chemically activated HOCO* radical with a third-body (M) have been recognized to be important at both low temperatures and high pressures4,11,32. Water molecule (H2O) had been experimentally shown to be an

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efficient third body collider to stabilize the HOCO* complex by Paraskevopoulos and Irwin10 early in 1984, but the detail collisional energy transfer features are still not well understood. Meanwhile, HOCO and H2O could also form weakly bound compounds. Aloisio and Francisco33 predicted a cyclic H2O-cis-HOCO complex with two hydrogen-bond using density functional theory (DFT) and suggest that the H2O-HOCO complex may play an important role in the OH + CO reaction in the presence of water. Oyama et al.34 identified the existence of H2O-trans-HOCO complex using spectral method and observed its pure rotational spectra and suggested that H2O molecule could strongly affect the properties of the HOCO radical through the formation of H2O-HOCO complex. Water molecule could also act as a reactant to directly participate in the reaction. In a recent study, Tachikawa et al.35 obtained the PESs for the OH + CO and OH + CO + H2O reactions and investigated the effects of single water molecule on the reaction barrier through ab initio calculations. By comparing the energies relative to the summation of reactants (OH + CO and OH + CO + H2O asymptotic limit, respectively), they claimed that the existence of water could decrease activation energies and accelerate the CO2 formation. However, termolecular reaction is rare and water molecule is more likely to influence the reaction through a pre-formed hydrated substance, e.g., the hydrated hydroxyl radicals OH(H2O)36-39. The pre-reaction complex has also shown to be an important factor to affect the rate constants and branching ratios.40 Therefore, the reaction pathways, kinetic barriers, rate constants, and reaction dynamics for the oxidation of CO via OH(H2O) radical are desirable to

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reveal the effects of water molecule through the pre-formed hydrated radical. The direct dynamics41,42 with energies and gradients calculated on-the-fly with electronic structure calculations is an effective though time-consuming method to go deep into the reaction and energy transfer dynamics. For example, Jasper and coworkers43-46 had successfully obtained detail energy transfer features for the decomposition of CH4 in H2O and eight other bath gases through extensive direct dynamics trajectory calculations. It is widely known that the accurate PESs are required for any reaction kinetics and dynamics studies. And for direct dynamics simulations, a chemical accuracy as well as computational efficiency electronic structure calculation method is needed in the first place. In this study, stationary point properties along the OH + CO reaction pathways are calculated with different theories and compared with benchmark ab initio calculations. The preferred method is then used to characterize the reaction pathways for the OH(H2O) + CO reaction and confirmed to be also accurate for the hydrated reaction as compared with CCSD(T) results. Subsequently, thermal rate constants are calculated for both reactions using variational transition state theory (VTST) plus a modified competitive canonical unified statistical (CCUS) model. Single-level calculations for the OH + CO reaction are first performed to verify the suitability of the modified model. Dual-level (X//Y) calculations for the OH(H2O) + CO reaction, with energy profiles improved with interpolated single-point energy (ISPE)47 method by employing energy corrections, are performed to obtained more accurate quantitative results. The kinetic barriers along the reaction paths and rate constants

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over the temperature range of 200 - 2000 K are obtained and discussed.

2. Computational methods The MP2 (second-order Møller-Plesset perturbation theory)48 and DFT (M06-2X49 and ωB97XD50 functionals) theories with triple-ζ 6-311++G(d,p) (abbreviated to G**) and Dunning’s correlation consistent augmented basis sets (aug-cc-pVXZ, X = D and T, and abbreviated to AVXZ for simplicity)51,52 are employed to determine stationary point properties for the OH + CO reaction. The M06-2X/AVDZ

method

gives

the

best

agreement

with

the

full

coupled-cluster/complete basis set (FCC/CBS)20 results and is selected to perform the calculations for OH(H2O) + CO reaction. The stationary nature of the structures is confirmed by harmonic vibrational frequency calculations, that is, the potential minima possess all real frequencies, whereas the transition state possesses only one imaginary frequency. The harmonic zero-point energy (ZPE) is obtained at all the above levels of theory. To ensure that the transition states connect designated minima, the minimum energy path (MEP) is obtained by the intrinsic reaction coordinate (IRC)53 theory for both directions off the saddle point. In order to identify the feasibility of the method as well as obtain more reliable energies, benchmark single-point energies for the OH(H2O) + CO reaction system are calculated at CCSD(T) (coupled cluster with inclusion of single and double excitations and perturbative inclusion of triple excitations)54 level of theory with AVXZ (X = T and Q) basis sets based on M06-2X/AVDZ minimum geometries.

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Further improvements are made with the same FCC/CBS method for the OH + CO reaction proposed by Yu et al.20. In the extrapolation, the basis set truncated errors are corrected with55

ECCSD(T) ( x ) ≈ ECCSD(T) ( ∞ ) + Ax−3

(2)

where ECCSD(T) ( x ) and ECCSD(T) ( ∞) represent the energies calculated with AVxZ basis set and at the complete basis set (CBS) limit, respectively. A is variable to be determined. By employing the AVTZ (x = 3) and AVQZ (x = 4) basis sets and adding T / 5 ), the FCC/CBS energies are written the CI truncation error correction ( ECCSD(T)/TZ

as

EFCC/CBS ≈ ECCSD(T)/AVQZ +

27 ×  ECCSD(T)/AVQZ − ECCSD(T)/AVTZ  37 

1 T + ECCSD(T)/AVTZ 5

(3)

T where ECCSD(T)/AVTZ is the perturbational energy of the connected triple excitations

calculated at CCSD(T)/AVTZ level, which accounts for about 75-80% of the full triple- and higher-order contributions56. The Gaussian 09 program package57 is used to perform the above electronic structure calculations as well as the IRCs, and the “int=ultrafine” keyword is used for all DFT calculations to employ high quality DFT integration grid.

3. Results and discussion 3.1. Potential Energy Surface of the OH + CO reaction The potential energy curve of the OH + CO reaction with energies relative to the summation of reactants at M06-2X/AVDZ and FCC/CBS//CCSD(T)/cc-pVTZ20 8


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levels is presented in Fig. 1. The optimized structures of the stationary points as well as available experimental values for the HOCO intermediates are depicted in Fig. S1 of the Supporting Information (SI). As discussed in Section 1, that the oxidation of CO by OH proceeds through trans- and cis-HOCO isomers that lie in deep wells. The two HOCO isomers are both planar structures with energies nearly degenerate and can be interconverted by the rotation of the HOCO dihedral angle through a transition state. There are two possible entrance channels for the formation of highly energized HOCO* complex, the trans and cis entrance channels, where the reactants pass through weakly bound linear OH--CO and OH--OC complex, respectively. The trans entrance channel leading to the trans-HOCO isomer has a slightly negative transition state barrier (trans-TS1), while the cis channel forming the cis-HOCO isomer has a positive barrier (cis-TS1). Therefore, the trans entrance channel is the energetically preferred one to drop into the HOCO deep well. And there also exist two exit channels for the HOCO intermediate complex to generate the H and CO2 products. We can see that the cis exit channel is directly an H-atom-detachment process through the broken of the H-O bond in cis conformation of H-OCO. The trans exit channel, however, would first undergo a H-atom-transfer process (from O-atom to C-atom) followed by the H-atom-detachment process from C-atom in H-CO2. The overall barrier of the cis exit channel is much lower than that of the trans channel, which makes the cis exit channel dominant. But, the HOCO intermediates have more chances to give back to the reactants rather than approach to the products because of the relatively lower barrier from the reactants side.

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Notably, all the stationary points mentioned above have been easily located with all the selected methods except for the cis-TS1 transition state. Despite numerous attempts in our calculations, cis-TS1 can only be identified using M06-2X functional with AVDZ and AVTZ basis sets by fixing the HOCO dihedral angle to zero, while other methods would obtain a geometry with two imaginary frequencies using the same restricted optimization strategy. And if the HOCO dihedral angle is free during the transition state (TS) searching process for cis-TS1, all calculations would lead to

trans-TS1. This phenomenon is somewhat identical with the work of Lester et al.58 and Nguyen et al.59, who found the cis configuration of TS1 to be a second-order saddle point on the torsional potential surface with the rotation of H-atom around the O-C axis. In their kinetics studies, however, the cis conformer was implicitly included because the torsional motion was treated as a separable one dimensional hindered internal rotor. We also notice that cis-TS1 and its corresponding entrance channel were explicitly included in the famous full dimensional HOCO PESs developed by Yu20, Guo and coworkers26-29

based on high level CCSD(T) ab initio calculations.

Therefore, cis-TS1 is explicitly included in our PES and the kinetic studies. The energies of the stationary points relative to the summation of reactants calculated with MP2 and DFT functionals, employing the G**, AVDZ, and AVTZ basis sets are summarized in Table 1. FCC/CBS energies based on CCSD(T)/AVTZ geometries20 as well as UCCSD(T)-F12/AVTZ26 results are also listed. We can see that the discrepancies between two high-level values are less than 1 kcal/mol for most cases and the mean unsigned error (MUE) is 0.6 kcal/mol, which illustrates the

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consistency of the CCSD(T) calculations. In present study, we choose the FCC/CBS values as energy benchmark because they have taken the finite basis set and CI truncated errors into account. MUEs of different methods as compared with FCC/CBS values are given in Table 1. The deviations between the relative energies obtained in this study using different methods and the benchmark FCC/CBS values together with a fitted normal distribution curve for each histogram are shown in Fig. 2. The position of the maximum of the fitted curve corresponds to the mean signed error (m or MSE) whereas the half-width at half-maximum (HWHM) is the standard deviation (s) that quantifies the dispersion of the errors. The standard deviations predicted by the MP2 perturbation theory, ωB97XD functional, and M06-2X functional are 3.1, 2.8, 3.2 kcal/mol, 1.5, 1.8, 1.9 kcal/mol, and 0.5, 0.5, 0.8 kcal/mol, when employing the G**, AVDZ and AVTZ basis sets, respectively. Overall, the M06-2X functional gives relatively smaller error distributions as compared with benchmark values than the other theories, which means it is energetically preferred for the particular OH + CO reaction. And the MSEs and MUEs for M06-2X functional employing G**, AVDZ, and AVTZ basis sets are +0.5, 0.0, −0.5 kcal/mol and 0.5, 0.4, 0.7 kcal/mol, respectively, indicate the AVDZ basis set has the lowest systematic errors, while G** tend to overestimate and AVTZ is likely to underestimate the single-point energies. The principal unsigned energy differences (see Table 1) between M06-2X/AVDZ and FCC/CBS values lie in the cis-HOCO and HCO2 intermediate, for which the energies given by M06-2X/AVDZ are 0.9 kcal/mol lower than and 0.8 kcal/mol higher than

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the corresponding FCC/CBS values. As the HOCO isomers play an important role in the conversion of CO to CO2 reaction6, it has attracted extensive special attentions4,6,7,11,60,61. From Fig. S1 of the SI we can see that the HOCO geometric structures of the trans and cis configurations given by M06-2X/AVDZ are all in good agreement with the results from a recent work60 by combining the spectrum experiment and CCSD(T) theory. The differences of bond length and bond angle are less than 0.04 Å and 0.7°. Table S1 of the SI summarizes the harmonic frequencies for all species at M06-2X level as well as CCSD(T) values and selected experimental results for the two HOCO isomers. In general, for the trans- and cis-HOCO isomers, the M06-2X/AVDZ frequencies give overall good agreement with CCSD(T) and experiment values with relative discrepancies less than 5% and 12%, respectively. As for the spin contamination, Table S1 of the SI also shows that the values for the doublet range from 0.750 to 0.764 before annihilation, very closed to the expected value of the pure double state 0.75, which means the wave function was not severely contaminated by higher multiplicity states. From the discussions above, it is clear that the combination of M06-2X functional with double-ζ AVDZ basis set proves to be a chemical accuracy method for the OH + CO reaction. On the one hand, the M06-2X functional, which is a high nonlocality functional that highly recommended for main-group thermochemistry and kinetics and noncovalent interactions49. On the other hand, the coincidence accuracy of the low level M06-2X/AVDZ calculation is likely due to a cancellation of errors

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arising from the inaccurate exchange-correlation functional and the finite basis sets44. Considering the amount of computation of DFT methods and the fact that DFT direct dynamics simulations42 had be successfully used in the identification and explanation of non-MEP62,63 and non-traditional64,65 reaction pathways, M06-2X/AVDZ is recommended for direct dynamics simulations for this particular reaction system.

3.2. The oxidation of CO by pre-formed OH(H2O) radical Formation of hydrogen-bonded water complexes OH(H2O)n is an important process in the atmosphere66. The weakly bound radical with one water molecule, OH(H2O), had been predicted to be a stronger oxidizing agent than free OH radical67. Previous studies36-39 had identified the OH(H2O) complex with different minimum-energy structures and the most stable one concerned in this study is shown in Fig. 3 and Fig. 4, which is of Cs symmetry where hydroxyl acts as a proton donor and the unpaired electron orbital lies in the reflection plane39. In our study, M06-2X/AVDZ method is used to calculated the stationary point properties of the hydrated OH(H2O) + CO reaction system and its accuracy has been validated against FCC/CBS energies obtained from CCSD(T) results with the extrapolation method described in Section 2. Meanwhile, to verify the multi-reference feature of the wave function for stationary points in open shell system, T1 diagnostics68 for all reactants, products,

transition

states,

and

intermediates

are

performed

at

the

CCSD/AVTZ//M06-2X/AVDZ level of the theory. As evident in Table 2, the T1 diagnostic values are found to be in the range of 0.010 to 0.038, with values less than

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0.04569 for all the species, indicating single-reference methods like CCSD(T) used for the present calculations is reliable. Fig. 3 presents the potential energy diagram with relative energies corresponded to the summation of OH(H2O) and CO reactants at M06-2X/AVDZ level together with values obtained at FCC/CBS//M06-2X/AVDZ and CCSD(T)/AVQZ//MP2/G**35 level of theories. The calculated single-point energies and ZPEs are listed in Table 2 and the SCF together with correlation energies from MP2, CCSD, and perturbative triple excitations are summarized in Table S2 of the SI. The results at CCSD(T)/AVQZ level show well consistency with previous studies35 that based on MP2/G** geometries. The energy deviations of CCSD(T)/CBS values are within 0.9 kcal/mol compared with the CCSD(T)/AVQZ values, which shows good convergence toward the complete basis set limit CCSD(T) energies. The correlation energy correction due to CI truncation is found to converge within 0.07 mHartree when using T

perturbative triple excitations at AVQZ basis set ( ECCSD(T)/QZ ). And the MUE between FCC/CBS and CCSD(T)/CBS values is 0.6 kcal/mol with the maximum difference of 1.3 kcal/mol at wHCO2. The statistical histogram of deviations between M06-2X/AVDZ and benchmark FCC/CBS values with a fitted normal distribution curve is depicted in Fig. S2 of the SI. The MUE and standard deviation between M06-2X/AVDZ and FCC/CBS values are 0.9 and 0.8 kcal/mol, respectively. The negative MSE of −0.8 kcal/mol indicates the DFT functional tends to underestimate the barriers. The maximum unsigned energy discrepancies (2.1 and 1.6 kcal/mol) appear in the two exit channels at the transition state of wTS2_3 and wTS3_1, but the

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energy barriers of the two exit channels are nearly degenerate at both levels of theory. From Fig. 1 and Fig. 3, it can be found that the PESs for the OH + CO and OH(H2O) + CO reactions are similar and the additional water molecule does not have significant impacts on the reaction pathways where the oxidation of CO by OH(H2O) still undergoes a complex-forming process just resemble to the water-free one. The hydrated HOCO complexes still have two, trans and cis, possible configurations. For the trans conformation, H2O molecule bounds with the HOCO complex through a hydrogen bond between the oxygen on the water and the hydrogen on HOCO (H2O--H-OCO). The cis isomer is a cyclic structure including six atoms except one of the hydrogens from water with two weak interactions which was also found by Aloisio and Francisco33 using the B3LYP functional. And the principal interaction is between the oxygen on the water and the hydrogen on HOCO (H2O--H-OCO), while the other one is between the hydrogen on the water and the terminal oxygen on HOCO (HOCO-HOH). There are two isomerization channels with different transition states in the presence of water molecule, while only one exists in the HOCO system for the two isomers. The additional water molecule decreases the energy gap between the two isomers and makes them almost degenerate in energy. But the main trans-cis isomerization barrier height is nearly the same for both reactions. The entrance channels that lead to the deep-well intermediates are somewhat different with the water unassisted reaction. Before passing through the entrance barriers, two weakly bound pre-complexes, OH(H2O)CO_1 and OH(H2O)CO_2, could be formed. And the water molecule seems like could either inserting into the

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OH--CO hydrogen bond or attach onto the OH--CO compound. For the energetically stable one, the water molecule acts as a bridge to link the OH and CO with retaining the H2O--HO interaction and forming a new weak bond between one of the hydrogen on H2O and the carbon on CO. While, the other pre-complex is a ring-like planer structure with one of the H-atoms on water interacts with the O-atom on OH and the C-atom on CO bonds with both the H-atoms of OH and the O-atoms on H2O. Unlike the water-free reaction, the structures of the H-O-C-O atoms of the two transition states (wTS1_1 and wTS1_2) in the entrance channels are both in trans configuration similar with trans-TS1 and both channels would lead to trans-HOCOw intermediate with no direct channel link to the hydrated cis-HOCOw isomer. The exit channels are similar for the isomers to reach the products, that the (hydrated) cis-isomer could reach the products directly through an H-atom-detachment process while the (hydrated) trans-isomer would first undergo an H-atom-transfer process before the H-atom detachment from complex. But the participation of water molecule makes the overall barrier of the two exit channels almost degenerate, in contrast to the water-free system where cis-exit channel energetically dominates. The obtained PES for the OH(H2O) + CO system discussed above is also similar with a recent study by Tachikawa et al.35, but they actually considered a tri-molecular reaction with stationary point energies corresponded to the summation OH, CO, and H2O asymptotic limit and concluded the decrease of the energy barrier. In our study, the hydration energy is taken into account in the reactants which draws a quite different conclusion in energy barrier. Meanwhile, the IRC calculations (performed at

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M06-2X/AVDZ and double checked at MP2/G** level) make a revision to the connection relationship for the entrance channel, which is different from Tachikawa’s study35, as shown in Fig. S3 of the SI. The optimized geometries for the stationary points as well as available experimental and theoretical values are marked in Fig. 4. We can see that the relevant geometries of stationary points indicate that the water molecule mainly interacts with the H-atom from OH radical through weak hydrogen bonds. The geometries obtained at M06-2X/AVDZ level also show well consistence with other theoretical and experimental results, as shown in Fig. 4. The length of the hydrogen bond on OH(H2O) is 1.892 Å in present study and 1.910 Å at CCSD(T)/AVTZ39 level. The principal hydrogen bond of the cis-HOCOw isomer is 1.731 Å identified by Aloisio and Francisco33 at B3LYP/6-311++G(3df,3pd) level, which is 1.723 Å at M06-2X/AVDZ level. The hydrogen bond in the trans-HOCOw isomer is 1.754 Å in our study, and the value determined by Oyama et al.34 was 1.794 Å from spectral experiments and 1.751

Å by CCSD(T)/AVTZ calculations. Table S3 of the SI summarizes the harmonic frequencies and values of stationary points at M06-2X/AVDZ level, and the values in range of 0.750 to 0.765 before annihilation also demonstrate the spin contamination is not a problem for the hydrated reaction. From the above discussions, the M06-2X/AVDZ method is also indicated to be a preferred method that shows well chemical accuracy for the hydrated OH(H2O) + CO system and will be employed in the following kinetics and future dynamics studies.

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3.3. Kinetic barriers and rate constants To reveal more intuitive kinetics information, the thermal rate constants are calculated with the variational transition state theory (VTST)70-73 theory. The canonical form of variational transition state theory (CVT)73 where the rate constant is minimized as a

function of

reaction coordinates (s) by

searching

the

temperature-dependent dividing surface can be expressed as

k T k CVT (T ) =  B  h

 −∆G GT,0 (T , s )     + ,0 K min exp    s  RT     

(5)

where kB is Boltzmann’s constant, h is Planck’s constat, K+,0 is the reciprocal of concentration in the standard-state for bimolecular reactions or unity for unimolecular GT,0 reactions, s is the coordinate along the reaction path, and ∆G (T , s ) is the

standard-state Gibbs free energy of activation at temperature T for the reaction coordinate s. The results discussed in the previous sections show that the OH + CO and OH(H2O) + CO reactions undergo similar complex-forming process with short-lived intermediates lie in deep well. For these reactions, more precise approach should be used to account for the collision energy transfer and intermolecular vibrational energy redistribution (IVR), e.g., the Rice-Ramsperger-Kassel-Marcus (RRKM) theory or the most recent system-specific quantum Rice-Ramsperger-Kassel (SS-QRRK)74,75 theory, which is beyond the scope of this study. Instead, we use a simplified dynamical model with canonical approach (canonical unified statistical76,77 (CUS) theory) to account for the complex-forming case and the competitive CUS (CCUS)78 model to deal with the 18


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branching of the reaction paths. The CUS model was originally formulated for the case shown in Fig. 5a71,76,78,79, where *1A and *2A represent the local maximum points and C represents the intermediate complex in the deep well. For present reactions with branching channels are much more complicate, however, we can first simplify the reaction channels. (a) According to the study by Valero and Kroes80, the rate constants from the reactants to the hydrogen-bond complexes in the entrance channel are much larger and can be neglected. (b) The isomerization process of the two intermediate complexes is very fast in low-pressure limit (~106 to ~107 s−1 at 298 K) makes the two isomers can be treated as one complex during the kinetics analysis. (c) The present reactions are sufficiently exergonic that we can neglect the product side complexes and the association bottlenecks for the reverse reactions78. So, the overall reactions with and without water molecule in this study both can be simplified as schematically shown in Fig. 5b, where *1A, *2A, *1B and *2B represent the local maximum points of

trans-TS1, cis-TS2, cis-TS1 and trans-TS4, respectively, for OH + CO reaction and wTS1_1, wTS3_1, wTS1_2 and wTS2_3, respectively, for OH(H2O) + CO reaction and C represents the local minimum of the intermediate complex. Let ki denote the flux coefficient (partial rate constants) for a dividing surface at a location i of local maximum or local minimum as if the corresponding maximum or minimum was the only kinetics bottleneck for the reaction77,80, i = *1A, *2A, *1B, *2B, or C. The CUS rate constant kCUS for the case shown in Fig. 5a is given by80 1 1 1 1 = − + k CUS k*1A kC k*2A 19


(6)


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The CCUS rate constant kCCUS for the case in Fig. 5b can be obtained by applying the procedures for combining fluxes in parallel and series, which yields78

1 k

CCUS

=

1 1 1 − + ( k*1A + k*1B ) kC ( k*2A + k*2B )

(7)

The intermediate complex is at least 30 kcal/mol lower in energy than both the reactants and the transition states, so the 1/kC term in equation (6) and (7) can be neglected. The TST rate constant (kTST) and CVT rate constant (kCVT) together with small-curvature tunneling (SCT)73 correction (kCVT/SCT) were obtained simultaneously at low-pressure limit where bimolecular collisions were not influenced by third bodies. All calculations were carried out with the Polyrate 2016-2A program81 with energies, gradient, and Hessians calculated on the fly using Gaussian 09 program package57 interfaced by Gaussrate 2016 program82. All the properties (geometries, energies, gradient, and Hessians et al.) along the MEP are obtained on the fly with electronic structure calculations at selected level. The MEP (from s = −1.6 bohr to s = 1.6 bohr) following method is Page-McIver integrator (pagem) and the curvature components are calculated using a quadratic fit to obtain the derivative of the gradient with respect to the reaction coordinate (dgrad method). The length step ∆s of the MEP is chosen to make the calculation converged with ∆s = 0.05 bohr for OH + CO reaction and ∆s = 0.025 bohr for OH(H2O) + CO reaction. For all calculations, the symmetry number of the forward reaction is 1 [SIGMAF=1]. The degeneracies and energies of the 2Π3/2 and 2Π1/2 states of OH (∆E=140 cm−1)80,83 and 2A' and 2A" states of OH(H2O) (∆E=112 cm−1)38 are used in the calculation of electronic partition functions [ELEC]. A frequency scale factor 20


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0.97184 is used in all computations [FREQSCALE]. For OH(H2O) + CO reaction, the potential energy profiles are further improved with interpolated single-point energy (ISPE)47 method by employing FCC/CBS//M06-2X/AVDZ energy corrections for the exoergicity and barrier height of some extra points along each reaction path. The classical potential energy VMEP curves and the ground-state vibrational adiabatic potential energy VG a curves together with the zero-point energy ZPE curves (VG a = VMEP + ZPE) as functions of the reaction coordinate s are used to represent the main properties of the reaction paths. As limited high-level information could be used for OH + CO reaction, single-level kinetics calculations are carried out using VTST approach with MEP calculated at M06-2X/AVDZ level and to verify the accuracy of the CCUS model. While for the OH(H2O) + CO reaction, dual-level (with energy corrections based on our FCC/CBS//M06-2X/AVDZ results) kinetics calculations are performed using the VTST-ISPE approach. Fig. S4 of the SI shows the VMEP and VG a curves for the hydrated reaction with and without ISPE corrections and it is clear that both the maximum point and its location have been shifted. So, it is necessary to employ high-level energies as the rate constants are very sensitive to the properties of the reaction paths. The VMEP, VG a , and ZPE curves are depicted in Fig. 6, for the main trans entrance (trans-TS1 and wTS1_1) and cis exit (cis-TS2 and wTS1_2) channels of the two reactions with rest channels shown in Fig. S5 of the SI. The ZPE curves are practically constant as s varies and the VMEP and VG a curves are similar in shape. The 1/2 location of the maximum on the VG a curve shift to s 0.12 and −0.55 (amu) bohr for

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the two main entrance channels, respectively, implying the variarional effect on the calculation of the rate constants is large. For the main energy barriers, although the VMEP barrier of the entrance channel for OH + CO reaction is lower, the VG a barriers that directly affect the rate constant are much higher than the hydrated OH(H2O) + CO reaction. So, the additional water molecule would actually reduce the total reaction rate constant, which is further confirmed by the following rate constant calculations. The kCVT/SCT results for the partial and total rate constants at low-pressure limit are summarized in Table 3 and Table 4, with detail information of each step along with the variational effects (kCVT/kTST) and tunneling effects (kCVT/SCT/kCVT) listed in Excel Tables of the SI. The kTST, kCVT and kCVT/SCT values against the reciprocal of temperature for the overall reactions are shown in Fig. 7 along with available experimental values and wildly used Arrhenius expressions. We can see from Fig. 7a that the kCVT/SCT obtained with CCUS model could well duplicate the strong non-Arrhenius behavior of the reactions which means the statistical model is appropriate. And the kCVT/SCT values provide a better agreement with the recommended Arrhenius expression proposed by Senosiain et al.85 in the temperature range from 800 to 2000 K, but about 1.5 times higher than that of Joshi et al.9 in the temperature range from 200 to 2000 K. The obtained values somewhat overestimate the experimental rate constants86,87 and the discrepancy become larger at low temperatures. The differences are not unexpected as rate constants are very sensitive to energy barriers and the reaction pathways are being simplified in our CCUS model.

22


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Notably, the main exit channel (k*2A in Table 3) shows slightly negative temperature effect at 200−400 K. This phenomenon is in agreement with the results of Valero and Kroes80 calculated on YMS20 PES and is resulted from the strong tunneling effect at low temperature for this channel (see Excel Tables of the SI). Overall, it is reasonable to expect that the results obtained with CCUS model are reliable for the two reactions studied in our study. For the OH(H2O) + CO → CO2 + H2O + H reaction, Fig. 7b shows that the CVT and CVT/SCT rate constants are almost superposed when the temperature higher than 900 K, which indicates that the tunneling effect are small at high temperatures. For the main entrance channel, the variational effect is considerable at low temperatures (see Table 3, Table 4 and the Excel Tables of the SI) and this is in consistency with the analysis of the VG a curves where the maximum point shift to s −0.55. The

kCVT/SCT/kCVT values for the total reaction are 653, 100, 31 and 14 at 200, 250, 298, and 350 K, suggesting that the tunneling effect is more significant at low temperatures. Quantitative results show that the rate constants drop shapely with the participation of water molecule and are only 1/190 and 1/8 of the water-free reaction at 200 and 2000 K. Therefore, the hydrated OH radical would actually slow down the oxidation of CO and this is consistent with the change in free energy barriers. Even though there is no previous studies for the OH(H2O) + CO reaction, we hope that our study may provide prediction for future research. It should be noticed that, in present study, we focus on the effects of the pre-reaction hydrated OH(H2O) complex on CO oxidation rather than the water

23



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catalysis filed where water molecule is free on both reactant and product sides. As OH radical can even react with the H2O molecule at high temperatures, the significance of the pre-formed OH(H2O) complex on the CO oxidation depends on the extent to which the OH(H2O) complex could exist. Buszek et al.88 have shown that the atmospheric concentration of the OH(H2O) radical is about 2.87 × 104 molecule/cm3 based on the corresponding equilibrium constant. In our calculation, the binding energy of the OH(H2O) complex is 3.8 kcal/mol and the equilibrium constant is 1.19 × 10−19, 3.95 × 10−20, 1.35 × 10−22 cm3/molecule at 200, 298, and 2000 K, respectively (Table S4 of the SI, the values are in consistent with the results of Buszek88). Taking into account the measured concentration of OH89-91 in hydrocarbon combustion flame of 1011 - 1015 molecules/cm3 and ~1019 molecules/cm3 of H2O (50% mole fraction in the mixture) in the water dilute oxy-fuel combustion system, the concentration of the OH(H2O) complex is estimated to be 108 - 1012 molecules/cm3 at 2000 K. Therefore, the oxidation of CO by hydrated OH(H2O) radical is somewhat important. However, the atomic-level dynamics may deviate substantially from that suggested by the stationary points and the corresponding MEP. Hence, the detailed dynamics studies are needed to probe more detail reaction mechanisms to reveal the atomic-level effects of water molecule on the CO oxidation.

4. Conclusions In this work, electronic structure calculations of MP2 and DFT functionals (M06-2X and ωB97XD) with three different basis sets have been performed on the

24


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OH + CO reaction. M06-2X/AVDZ has shown to be a chemical accuracy method as compared with high-level FCC/CBS results with MUE of 0.4 kcal/mol. The influences of single water molecule on the CO oxidation mechanism are probed at FCC/CBS//M06-2X/AVDZ level of theory by considering the pre-formed hydrated complex OH(H2O) react with CO. The obtained PESs show that the additional water molecule would actually affect the main energy barriers, but have little effects on the reaction pathways of CO oxidation. We have further carried out kinetics studies using VTST theory combine with a simplified dynamical CCUS model for the water assisted and unassisted CO oxidation reactions. Single-level calculations at M06-2X/AVDZ level for OH + CO → H + CO2 reaction validate the suitability and accuracy of the CCUS model, which could fully reflect the strong non-Arrhenius behavior. For the OH(H2O) + CO → CO2 + H2O + H reaction, dual-level kinetic calculations are obtained using the VTST-ISPE approach based on the MEP at FCC/CBS//M06-2X/AVDZ level. The results show that the additional water molecule would increase the free energy barriers and lower the rate constants by 1 - 2 orders in the temperature range of 200 - 2000 K and the Tunneling effects are more important for the hydrated reaction at low temperatures. Our studies provide intuitive kinetic information of the effects of single water molecule on the CO oxidation by OH, the method can be used to study the elementary reactions in the water added oxy-fuel combustion system. However, the atomic-level dynamics may be quite different from that suggested by the MEP and the other effects of water molecule, such as the collisional energy

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transfer features, are still not clear. Hence, the detailed chemical dynamic simulations are necessary to probe the effects of water molecule on the CO oxidation from atomistic level which has seldom been performed.

Acknowledgments We greatly thank Regents Professor Donald G. Truhlar for providing the Polyrate 2016-2A and Gaussrate 2016 programs. The financial support of this research is provided by the National Natural Science Foundation of China (Grant No. 51536002, No. 21573052), and the Open Project of Beijing National Laboratory for Molecular Sciences (No. 20150158).

Supporting Information The calculated and experimental frequencies, values, and geometries of the stationary points for OH + CO reaction. The calculated frequencies, values, SCF and correlation energies, equilibrium constants, selected IRC diagrams, histograms of energy differences, and additional VMEP, VG a and ZPE curves for OH(H2O) + CO reaction. Excel Tables of partial and total thermal rate constants for the above reactions.

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Table 1. Relative Energies (in kcal/mol) of Stationary Points for OH + CO Reaction at Different Level of Theories. Species OH+CO OH--OC OH--CO cis-TS1a trans-TS1 trans-HOCO trans-TS4 tor-TS HCO2 cis-HOCO cis-TS2 C2v-TS3 H+CO2 MUE

G** 0.0 −1.0 −2.1 \ 4.2 −28.3 12.0 −17.9 −12.7 −26.0 5.0 −10.5 −30.3 2.5

MP2 AVDZ 0.0 −1.2 −2.5 \ 2.5 −29.6 10.2 −19.3 −15.0 −27.6 4.0 −12.5 −30.4 1.8

AVTZ 0.0 −1.2 −2.6 \ 1.9 −33.5 5.5 −23.3 −18.4 −31.5 −0.4 −15.8 −33.1 3.0

G** 0.0 −1.1 −2.1 \ −1.6 −33.1 4.7 −23.3 −18.8 −31.1 −1.2 −12.3 −26.4 2.1

ωB97XD AVDZ AVTZ 0.0 0.0 −1.0 −0.8 −2.2 −2.2 \ \ −1.5 −1.4 −34.0 −34.0 3.7 3.4 −24.1 −24.2 −19.6 −19.3 −32.0 −32.0 −1.2 −1.8 −12.5 −12.7 −25.8 −26.8 2.4 2.5

G** 0.0 −1.4 −2.0 \ −0.4 −29.7 9.1 −20.5 −13.2 −28.2 2.0 −8.7 −22.9 0.5

M06-2X AVDZ 0.0 −1.2 −2.0 3.2 −0.7 −30.7 8.0 −21.3 −13.7 −29.1 1.2 −9.6 −23.2 0.4

AVTZ 0.0 −1.1 −2.1 3.2 −0.8 −31.5 6.9 −22.4 −14.4 −30.0 0.2 −10.2 −24.1 0.7

FCC/ CBSb 0.00 −1.13 −2.20 2.62 −0.96 −30.10 7.86 −20.78 −14.58 −28.25 1.44 −9.84 −23.39 −

F12b/ TZc 0.00 −1.22 −2.26 3.12 −0.58 −29.59 8.78 −20.29 −13.64 −27.82 2.41 −8.71 −22.62 0.6

a: cis-TS1 can only be located at M06-2X/AVDZ and M06-2X/AVTZ level by fixing the HOCO dihedral angle to zero (see the text). b: Energies from Ref.20 using an extrapolated full coupled-cluster/complete basis set (FCC/CBS) method. c: Energies from Ref.26 at UCCSD(T)-F12b/AVTZ level of theory.

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Table 2. Relative Energies (in kcal/mol) of Stationary Points for OH(H2O) + CO Reaction at Different Level of Theories. Species

T1a

0.010 OH + H2O + CO 0.018 0.010 OH(H2O) + CO 0.010 OH(H2O)CO_1 0.015 OH(H2O)CO_2 0.014 wTS1_1 0.021 wTS1_2 0.022 trans-HOCOw 0.019 wTS2_1 0.019 wTS2_2 0.019 wTS2_3 0.021 cis-HOCOw 0.019 wHCO2 0.038 wTS3_1 0.022 wTS3_2 0.019 0 H + CO2(H2O) 0.016

M06-2X ZPE AVDZ

CCSD(T)b AVTZ AVQZ CBS

FCC/ CBS

Ref c

22.114

6.0

5.9

5.8

5.8

5.8

5.8

24.019 25.101 25.031 25.445 25.555 28.712 27.366 27.105 25.612 28.955 25.991 22.856 23.463

0.0 −3.0 −1.8 −0.4 0.7 −34.2 −24.8 −18.0 3.0 −34.3 −14.3 3.5 −9.1

0.0 −2.1 −1.5 −0.3 1.0 −30.6 −21.9 −14.5 7.8 −30.4 −10.3 7.8 −4.3

0.0 −1.9 −1.3 −0.4 1.0 −31.7 −22.9 −15.5 6.9 −31.5 −11.2 6.7 −5.5

0.0 −1.7 −1.1 −0.5 0.9 −32.5 −23.6 −16.3 6.3 −32.3 −11.8 5.9 −6.4

0.0 −1.8 −1.2 −0.9 0.5 −33.1 −24.2 −16.8 5.1 −32.9 −13.2 4.8 −7.5

(0.0) \ −1.3 −1.5 \ −32.0 −23.0 \ 6.9 −31.3 −11.2 5.5 −5.9

22.040

−20.6

−17.5

−18.9 −19.8 −20.6 −18.9

a: T1 diagnostic values, CCSD/AVTZ. b: Based on geometries at M06-2X/AVDZ level. c: Energies from Ref.35 at CCSD(T)/AVQZ//MP2/6-311++G** level and are relative to OH(H2O) + CO asymptotic limit energy calculated in this study at the same level.

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Table 3. Partial CVT/SCT and Total CCUS/SCT Thermal Rate Constants (in cm3 molecule−1 s−1) as a Function of Temperature Derived from PES at M06-2X/AVDZ Level for the OH + CO → CO2 + H Reaction. T(K) 200 250 298 350 400 500 700 900 1000 1200 1500 1800 2000

k*1A 3.76E−13 4.91E−13 6.04E−13 7.28E−13 8.51E−13 1.10E−12 1.65E−12 2.22E−12 2.52E−12 3.14E−12 4.10E−12 5.09E−12 5.76E−12

Partial kCVT/SCT k*2A k*1B 3.61E−13 7.19E−17 3.07E−13 5.58E−16 2.81E−13 2.19E−15 2.67E−13 6.50E−15 2.62E−13 1.44E−14 2.69E−13 4.57E−14 3.19E−13 1.85E−13 4.00E−13 4.27E−13 4.50E−13 5.83E−13 5.66E−13 9.56E−13 7.79E−13 1.64E−12 1.03E−12 2.45E−12 1.23E−12 3.05E−12

k*2B 2.82E−17 3.09E−17 3.97E−17 6.11E−17 1.03E−16 3.05E−16 1.78E−15 6.12E−15 9.93E−15 2.20E−14 5.43E−14 1.08E−13 1.57E−13

CCUS/SCT

k 1.84E−13 1.89E−13 1.92E−13 1.96E−13 2.01E−13 2.18E−13 2.73E−13 3.52E−13 4.01E−13 5.14E−13 7.28E−13 9.89E−13 1.20E−12

a: Variational effect (kCVT/kTST) of the total reaction. b: Tunneling effect (kCVT/SCT/kCVT) of the total reaction.

42


Total Va 0.90 0.91 0.91 0.91 0.91 0.91 0.90 0.88 0.88 0.86 0.85 0.83 0.82

Tb 2.11 1.73 1.53 1.38 1.29 1.18 1.07 1.02 1.00 0.98 0.95 0.92 0.92

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Table 4. Partial CVT/SCT and Total CCUS/SCT Thermal Rate Constants (in cm3 molecule−1

s−1)

as

a

Function

of

Temperature

Derived

from

PES

at

FCC/CBS//M06-2X/AVDZ Level for the OH(H2O) + CO → CO2 + H2O + H Reaction. T(K) 200 250 298 350 400 500 700 900 1000 1200 1500 1800 2000

kCVT/SCT k*1A 6.32E−14 8.45E−14 9.92E−14 1.16E−13 1.32E−13 1.59E−13 2.12E−13 2.69E−13 2.99E−13 3.59E−13 4.44E−13 5.44E−13 6.12E−13

k*2A 9.75E−16 1.11E−15 1.31E−15 1.62E−15 2.02E−15 3.15E−15 7.19E−15 1.45E−14 1.97E−14 3.40E−14 6.72E−14 1.18E−13 1.63E−13



CCUS/SCT

k 9.61E−16 1.10E−15 1.29E−15 1.60E−15 1.99E−15 3.10E−15 7.01E−15 1.40E−14 1.88E−14 3.19E−14 6.08E−14 1.03E−13 1.39E−13

a: Variational effect (kCVT/kTST) of the total reaction. b: Tunneling effect (kCVT/SCT/kCVT) of the total reaction.

43


Total Va 0.74 0.75 0.76 0.75 0.75 0.74 0.72 0.70 0.69 0.67 0.65 0.63 0.61

Tb 653 99.6 31.3 13.5 7.71 3.78 1.94 1.44 1.32 1.17 1.05 0.99 0.95


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Page 44 of 51

Fig. 1. Schematic PES for OH + CO reaction with relative energies (in kcal/mol) corresponded to the summation of OH and CO without ZPE at M06-2X/AVDZ level and FCC/CBS//CCSD(T)/cc-pVTZ20 values in parentheses.

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Fig. 2. Histograms of signed energy errors between values calculated with a) MP2; b) ωB97XD functional; c) M06-2X functional, employing the G**, AVDZ, and AVTZ basis sets, and the FCC/CBS results. All located stationary point energies are included in the histograms and each is fit with the normal distribution of error curve. The fitting parameters are shown in figures with m represents the mean signed error (MSE) and s represents the standard deviation. cis-TS1 is not located for all MP2, ωB97XD calculations and M06-2X/G** method (see text). 45



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Page 46 of 51

Fig. 3. Schematic PES for OH(H2O) + CO reaction with relative energies (in kcal/mol) corresponded to

summation

of

OH(H2O)

and

CO

without

ZPE

at

M06-2X/AVDZ

level

with

FCC/CBS//M06-2X/AVDZ values in parentheses and CCSD(T)/AVQZ//MP2/G** values35 in square brackets.

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Fig. 4. Geometries of stationary points for OH(H2O) + CO reaction obtained at M06-2X/AVDZ level with available theoretical and experimental values in parentheses(a from Ref. 39; b and c from Ref. 34; d from Ref. 33). Bond distances are in angstroms and angles in degrees.

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Fig. 5. Schematic diagrams of the simplified standard-state (0) generalized transition-state (GT) free energy profiles vs. reaction coordinates. (a) original form, (b) revised form for present study.

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Fig. 6. Classical potential energy curve (VMEP), ground-state vibrationally adiabatic 1/2 energy curve (VG bohr a ), and zero-point energy curve (ZPE) as functions of s (amu)

around (a) trans-TS1, (b) cis-TS2 for OH + CO reaction and (c) wTS1_1, (d) wTS3_1 for OH(H2O) + CO reaction.

49



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Fig. 7. Computed TST, CVT, and CVT/SCT rate constants using CCUS model as a function of 1000/T between 200 and 2000 K and widely used Arrhenius expressions for OH + CO → CO2 + H reaction. (a) Expression 19: k=1.17×10−19T2.053exp(139/T)+9.56×10−12T−0.664exp(−167/T) (b) Expression 285: k=10−18.8T 2.02exp(747/T ) (c) Experimental values between 250 and 1040 K at 50 Torr in Ar86 (d) Experimental values at high temperature in Ar87

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TOC

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Effects of Water Molecule on CO Oxidation by OH: Reaction Pathways

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