Article pubs.acs.org/JPCB
Product Translational and Vibrational Distributions for the OH/OD + CH4/CD4 Reactions from Quasiclassical Trajectory Calculations. Comparison with Experiment. Joaquin Espinosa-Garcia and Jose C. Corchado*
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Departamento de Química Física, Universidad de Extremadura, Avenida de Elvas S/N, 06071 Badajoz, Spain ABSTRACT: For the OH + CH4/CD4 hydrogen abstraction reactions, the methyl radical (CH3 and CD3) product translational distributions and the water (H 2 O and HOD) product vibrational distributions experimentally reported by Liu’s group are reproduced by quasi-classical trajectory (QCT) calculations on an analytical full-dimensional potential energy surface when a quantum spirit is included in the analysis. Our simulations correctly predict: (i) the vibrational excitation of the water product, (ii) the inversion of the water vibrational population, and (iii) the propensity of transfer from reactant kinetic energy to product translational energy. These reactions therefore present a marked isotopic effect. In addition, the water product vibrational distributions for the OH/OD + CH4 reactions agree reasonably well with Butkovskaya and Setser’s experiments for a similar alkane reaction. The theory/experiment agreement is better for the HOD than for the H2O product due to the mode coupling in the H2O molecule, which is absent in the HOD stretching modes, which show a more “local” character. In summary, for polyatomic systems with many degrees of freedom (15 in the present reaction), QCT calculations analyzed with a quantum spirit represent a useful alternative to quantum scattering methods.
I. INTRODUCTION The OH + CH4 (and its isotopic analogues) hydrogen abstraction reaction is a benchmark system at low temperatures because it constitutes the major process for the removal of methane in atmospheric chemistry and at high temperatures because of its importance in combustion processes. So these reactions have received much attention, both experimental and theoretically. In 2005, Liu et al.1−3 published a series of studies on the dynamics of the OH + CD4 → HOD + CD3 and isotopic analogues, using crossed-beam experiments over collision energies in the range 5−16 kcal mol−1. They found that correlated with the methyl radical vibrational ground-state, CD3(v = 0), which is the dominant product state, the HOD coproduct appears almost exclusively stretch-excited, ∼90%, with an inversion of the vibrational distribution that peaks at ν(OD) = 2. As for the H2O coproduct in the analogous OH + CH4 → H2O + CH3 reaction, 70% shows as stretch-excited and also presents an inverted vibrational distribution peaking at ν(OH) = 1. Thus, in both reactions, the vibrational excitation of the coproduct, HOD and H2O, is mostly localized in the newly formed bond, OD and OH, respectively. These authors studied the dynamics of these reactions by analyzing the methyl product translational distribution (PTD), the water product vibrational distribution (PVD), and the product angular (PAD) distribution. Butkovskaya and Setser4 performed a series of experiments at room temperature for several OH/OD + RH → H2O/HOD + © XXXX American Chemical Society
R reactions, analyzing the vibrational distributions of the nascent water product molecule. They found that most (80− 85%) of the vibrational energy is released to the local mode associated with the new OH stretching mode. These authors did not study the title reaction, and as a first approximation to the problem we will use the similar OH/OD + C2H6 → H2O/ HOD + C2H5 hydrogen abstraction reaction for comparison. Recently, for this system our group5 developed an analytical full-dimensional potential energy surface, PES-2014, improving our previous PES-2000 surface.6 The new PES-2014 surface is fitted exclusively to high-level ab initio calculations, is symmetric with respect to the permutation of the four methane hydrogen, and provides analytically energy and energy first derivatives (gradients), which constitutes a computational advantage. This surface presents a barrier height of 6.4 kcal mol−1, an exothermicity of −13.3 kcal mol−1, and intermediate complexes in the entrance and exit channels, stabilized by 0.4 and 1.1 kcal mol−1 with respect to the reactants and products, respectively. In addition, it reproduces the topology of the reactive system, in excellent agreement with high-level ab initio calculations. Using the PES-2014 we performed an exhaustive dynamics study5 using quasi-classical trajectory (QCT) Special Issue: Bruce C. Garrett Festschrift Received: May 5, 2015 Revised: June 5, 2015
A
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
Figure 1. Energetic profile of the OH+ CH4/CD4 → H2O/HOD + CH3/CD3 reactions using the PES-2014 surface, where the reactant complex, product complex, and saddle point are included. Energy values in kcal mol−1. Ab initio values from ref 5. The saddle-point geometry is also included.
Vstretch consists of four London−Eyring−Polanyi (LEP) stretching terms and depends on 12 fitted parameters; Vharm represents the valence binding terms and depends on 16 parameters; Vop denotes the harmonic out-of-plane potential depending on four fitted parameters, and finally Vwater is the potential describing the water product, which is a combination of a Morse potential and a harmonic bending potential and depends on three fitting parameters. In addition, it includes a series of switching functions whose main aim is to change smoothly from the tetrahedral structure in methane to the planar structure in methyl. This VB-MM functional form with adjustable parameters gives great flexibility to the PES. A total of 35 parameters were fitted exclusively to high-level ab intio calculations, representing the overall topology of the hydrogen abstraction reaction potential energy surface. In this case, the “infinite basis” (IB) method was used,10,11 which extrapolates the energies from the cc-pVDZ and cc-pVTZ basis sets.12 A schematic profile of this reaction with the PES-2014 is shown in Figure 1, together benchmark theoretical results for comparison. Standard QCT calculations were performed on the PES-2014 surface using the VENUS code,13 where a Monte Carlo approach is used to select the scattering parameters (impact parameter, vibrational phases, and spatial orientation of the initial reactants), first at a collision energy of 10 kcal mol−1 for a direct comparison with Liu’s experiment1−3 and second at room temperature for comparison with Setser’s related experiment.4 The trajectories were initiated and stopped in asymptotic regions, where the molecular interactions are negligible, with the two reactants or products separated by at least 10 Å. In the first case, for each reaction, OH + CH4 and OH + CD4, 100 000 trajectories were run, where the maximum impact parameter, bmax, was obtained using small batches of trajectories (10 000) with trial values until no reactive trajectories were found. The values of bmax were 2.8 and 2.4 Å, respectively. The large number of trajectories run in each reaction leads to small or negligible statistical errors ( 3) two polyatomic products are formed, and the mode coupling and the intramolecular vibrational energy redistribution makes the analysis much more difficult. This is the case of the present seven-atom bimolecular reaction, OH + CH4 → H2O + CH3, where two products of three and four atoms are formed. We begin by analyzing the H2O PVD in the perprotio reaction, OH + CH4. Given the available energy, 24.9 kcal mol−1, the OH stretching mode can be excited up to one quantum, and several stretching−bending combinations are also possible, in accordance with the experiment.3 The H2O PVD obtained with QCT/NMA calculations is shown in Figure 3, using two binning approaches, SB and 1GB, together with experimental results3 for comparison. Both binning techniques reproduce the experimental finding that the (01*0) state is the most populated, with an appreciable population of the (01*1) state; however, the SB approach shows populations in the (000) and (02*0) states, which are not experimentally detected. The small population in the vibrational ground-state (000), 4%, is explained because in this approach the quantum numbers in the range [−0.5, +0.5], which includes trajectories with mechanically forbidden negative quantum actions, contribute to the ground-state population. The population in
Table 1. Product Energy Partitioning (In Percentage) for the OH + CH4 and OH + CD4 Reactions at 10 kcal mol−1 OH + CH4 QCT f V(methyl) f R(methyl) f V(water) f R(water) fT
OH + CD4
exp.
a
0 10 53 3 34
exp.a
QCT
b
b
0 11 54 3 32
47 6 47
58 4 38
Ref 3. bExperimentally, the methyl radical (CH3 or CD3) is considered as a structureless particle.
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a
f T are the energy fractions as vibration, rotation, and translation, respectively, and the methyl (CH3 or CD3) coproduct is considered in its vibrational ground-state. The heavy−light−heavy kinematics of these reactions favors transfer T → T′ (reactant kinetic energy to product translational energy); however, while the methyl (CH3 or CD3) coproduct is experimentally treated as a structureless particle, and therefore zero value for the methyl coproduct internal energy is assumed, theoretically ∼10% of the methyl energy we obtain is rotational energy. This behavior was already observed by Bass et al.,23 who analyzed different Cl + alkane reactions and concluded that the alkyl coproduct internal energy must be taken into account (in the Cl + C2H6 → HCl + C2H5 reaction, obtained a ∼0.22), which can modify the dynamics. Therefore, we hope that future experimental studies on the present reactions can confirm this finding. The total available energy, Eav, is given by Eav = Ecoll + ΔHR (0 K)
(9) −1
which represents 24.9 and 24.1 kcal mol at Ecoll = 10 kcal mol−1 for CH4 and CD4, respectively. Taking into account this energy and the difference in vibrational frequencies between OH and OD, 3806 and 2767 cm−1, it is possible to populate up to one quantum the OH stretching level in H2O and up to two quanta the OD stretching level in HOD, which is in agreement with the experimental evidence. Another important averaged dynamics property is the vibrational distribution of the water product as pure stretching, pure bending, and a combination of these, which has been experimentally reported3 for the methyl coproduct in its vibrational ground state. Table 2 lists the experimental and QCT results for both reactions, where in the QCT calculations we used the NMA and the FFT algorithms, with the SB and 1GB approaches. First, in general, for both reactions, the NMA Table 2. Probabilities for Vibrational Excitation in the Water Product as Pure Stretching, Ps, Combination Mode, Pc, and Pure Bending, Pb, at 10 kcal mol−1 OH+CH4 NMAa Pgsd Ps Pc Pb
OH+CD4
FFTb
SB
1GB
SB
1GB
4 80 14 2
1 72 21 5
6 71 17 6
1 71 23 3
exp.c 0 71 24 4
NMAa
FFTb
SB
1GB
SB
1GB
1 80 18 0
0 78 22 0
1 80 19 0
0 76 24 0
exp.c 0 85 15 0
a
Normal mode analysis, NMA. Ref 10. bFast-Fourier-transformed, FFT. Ref 9. cExperimental values from ref 3. dGround-state probability. D
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
Figure 2. Product speed distributions of the OH + CH4/CD4 → H2O/HOD + CH3(v = 0)/CD3(v = 0) reactions at 10 kcal mol−1. QCT results on the PES-2014 surface (left panels) and experimental measures1−3 (right panels). The error bar is ±0.2 km s−1, representing ±1 standard deviation.
respective ZPE and are the consequence of a flux of energy between modes that quantum mechanics would forbid. The 1GB approach corrects the two previous issues: It removes the (000) population and largely diminishes the (02*0) population. In this way, it improves agreement with the experiment by introducing a quantum spirit in this analysis. The HOD PVD in the deuterated reaction, OH + CD4, obtained with a similar methodology, QCT/NMA-SB/1GB, is plotted in Figure 4. The experimental results3 are also included for comparison. Both binning techniques give the correct order of population, (200) > (100), in accordance with the experiment; however, as previously noted, the SB method overestimates the (300) state, 9%, and underestimates the most populated state (200). The quantum spirit introduced with the 1GB approach corrects these deficiencies and better reproduces the experiment. In general, the agreement with the experiment is better for the OH + CD4 → HOD + CD3 reaction than for the perprotio analogue, OH + CH4 → H2O + CH3. This behavior had already been found in a previous study24 on the OH + NH3 → H2O + NH2 reaction, and it can be explained because a major limitation of the NMA algorithm is the presence of coupling between modes. So, while the H2O product presents two similar stretching modes, 3806 and 3762 cm−1, with possible strong coupling, the HOD product presents a more “local” character, associated with different stretching modes, 2767 and 3801 cm−1. In addition, the H and D hydrogen abstraction
Figure 3. Populations of the vibrational states of the H2O product, in the OH + CH4 reaction, labeled (n,m,l), where n and m represent the quantum numbers for the OH symmetric (ν1) and asymmetric (ν3) stretch modes and l represents that for the bending mode (ν2), as computed using the NMA method with the SB and 1GB binning approaches. Experimental values from ref 3.
the (02*0) state can also be due to the classical nature of the QCT method. Thus, part of the energy required to excite the stretch mode to v = 2 comes from the fact that the other two vibrational modes can have an energy lower than their E
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
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in eq 4). This diminishes the quantum character of the calculation but reduces the statistical error. As was shown in the first part of the present work, the SB and 1GB methods give similar results, and this is the expected behavior at room temperature. In addition, in previous works20,26−30 the 1GB method has been tested for similar hydrogen abstraction reactions, finding that SB and 1GB provide qualitatively similar vibrational distributions, although the HB method overestimates the population of some vibrational states due to the ZPE violation problem in one of both products, and this deficiency is corrected by the 1GB method, which includes a more quantum spirit. Table 3 lists some QCT-averaged properties together with experimental results (OH/OD + C2H6) for comparison. The Table 3. H2O/HOD Product-Averaged Properties for the OH/OD + Alkane → H2O/HOD + Alkyl Radical Reactions at 298 K
Figure 4. Same for the HOD product in the OH + CD4 reaction. Now the (n,m,l) labels represent the quantum number for the OD stretch mode (ν1), m represents that for the OH stretching mode (ν3), and l represents that for the bending mode (ν2). Experimental values from ref 3.
H2O QCT P(0:1:2)c d d
reactions present different tunnelling quantum effects; therefore, a more appropriate treatment by quasi-classical trajectories is expected for the OH + CD4 reaction. Unfortunately, the GB approach cannot handle this quantum effect; however, because of the high collision energy one can expect that tunnelling will not play a crucial role in either of the isotopic substitutions. III.B. QCT Results at Room Temperature. Comparison with Experiment. Butkovskaya and Setser4 carried out a series of experiments for water-forming reactions at T = 298 K for various families of compounds, including saturated hydrocarbons among others. They reported results for the water product in the OH/OD + C2H6 reaction, but not for the title reaction, OH/OD + CH4. Setser25 pointed out that this reaction was not studied because (i) at room temperature it is too slow to allow for a good experimental study and (ii) the available energy is rather low and so only a few vibrational levels could be observed. In addition, he suggested that the results from the OH + ethane should be representative for OH + primary alkanes with an adjustment of the available energy for each reaction. Thus, to complete the present QCT study at a given energy, in this section we perform QCT calculations at room temperature for the OH/OD + CH4 reactions and compare the results with the experimental data reported by the OH/OD + C2H6 reactions.4 The aim is two-fold: first, to report for the first time theoretical results for the title reactions at T = 298 K, which await experimental confirmation, and second, to confirm Setser’s suggestion about the behavior of OH + primary alkanes. At this temperature, the reaction cross section is σR = 0.028 ± 0.001 Å2, as compared with σR = 1.877 ± 0.021 Å2 at Ecol=10 kcal mol−1, that is, a reactivity a factor of ∼65 lower. This result justifies Setser’s comment on the difficulties of experimentally studying the title reaction at room temperature. This very low reactivity implies a higher statistical error in the vibrational energy calculations, which is even more important when the 1GB approach is used. (One would need a large number of reactive trajectories, which are very scarce under the chosen thermal conditions.) To circumvent this problem we decided to increase the number of trajectories with respect to the previous section and the width of the Gaussian function used to compute the weight in the 1GB calculation (by diminishing α
e /
a
55:36:8 57 89
HOD exp.
b
21:65:14 51 81
QCT
exp.
34:58:8 60 60
31:55:14 47 81
11
17
12
14
0.12
0.21
0.20
0.21
a QCT results for the OH/OD + CH4 reactions. bExperimental results4 for the OH/OD + C2H6 reactions. cPopulations P1,2 for the H2O product in the ν1 and ν2 levels, which cannot be experimentally separated. Population P2 for the HOD product. dMean fraction of vibrational energy in the H2O/HOD product: /. eMean fraction of vibrational energy in the ν2 mode: /. fMean fraction of vibrational energy in the ν3 mode: /.
mean fractions of vibrational energy, , , and , reproduce the experimental tendency, where the majority of vibrational energy is deposited in the new OH stretching mode, ν2; however, large discrepancies are found in the populations of the new OH bond formed, P(0:1:2), especially in the case of the H2O product. Nevertheless, it should be noted that this theory/experiment comparison is not straightforward because the QCT calculations were performed for the OH + CH4 reaction while the experimental data correspond to the OH + C2H6 reaction. In this comparison, therefore, one must take into account these differences. So, the OH + C2H6 reaction is more exothermic than the OH + CH4 reaction, ΔH0 = −18.6 versus −14.9 kcal mol−1. This results in a different topology of the PESs with a stronger fall in the exit channel for the ethane reaction and therefore the possibility of higher vibrational excitation in the water product. The isotopic variant OD + alkane reaction shows a significantly better agreement with the experiment, which can be explained by the more “local” character in the OH and OD vibrational modes as compared with the two similar OH stretching in H2O; however, we again find an underestimation of the excitation to v = 2, which may be due to the differences in the exothermicity of both reactions. Figure 5 plots the QCT results for the H2O PVD together with the Butkovskaya and Setser4 experimental results, once again for the OH + C2H6 reaction for comparison. Remember that in the case of the H2O product, ν1,2 = 1 means that either mode 1 or mode 2 could have one quantum of excitation because these modes present similar energy. Thus, the following pairs of states present similar energy: (100) and F
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Figure 5. Vibrational state distribution of the H2O(n,m,l) product at 298 K. QCT calculations on the PES-2014 surface for the OH + CH4 reaction computed using the NMA method with the SB and 1GB binning approaches. Experimental values from ref 4 for the OH + C2H6 reaction.
Figure 6. Same as Figure 5 but for the HOD(n,m,l) product.
due to the limitations of the classical method, and it is partially corrected when the 1GB method is employed. Note that the theoretical results shown in the present section have a predictive character to be confirmed by future experimental studies. In any case, they seem to confirm Setser’s suggestion that the results obtained for the reactions with ethane are representative of the behavior of the primary alkanes.
(010), (101) and (011), (102) and (012), (200) and (020). Taking into account the differences previously noted between OH + CH4 and OH + C2H6 reactions, we consider that the QCT calculations on the PES-2014 simulate reasonably well the dynamics of the title reaction. It has to be noted that, as previously discussed, the SB and 1GB methods give similar results, although the population of the (100) and (01*0) states is significantly overestimated. With SB, we obtained a population of 35% in the (020) state (two quanta in the OH stretching modes), reduced to 25% when the 1GB method is applied. The available energy, = −ΔH0o + Ea + 4RT, was larger for the OH + C2H6 reaction, 23.1 kcal mol−1, than for the OH + CH4, 20.6 kcal mol−1. With this available energy it was possible to populate the second stretch level, ν1,2 = 2, in the case of the OH + C2H6 reaction, but only the first stretch level, ν1,2 = 1, for the OH + CH4 reaction. Because the available energy was not enough to populate this state, this is clearly an overestimation as a result of the method used. As discussed in the previous section, this is due to an incorrect flux of energy between modes whose effect can largely be reduced by using binning techniques that introduce a quantum spirit in the classical calculation. Thus, the 1GB method partially corrects this problem, although as a result it increases significantly the population of the lower (100) and (01*0) states, Therefore, although the agreement with experiment worsens, the results are more physically reasonable. From a qualitative point of view, our calculations agree with experiment in the flux of energy mainly to the stretching modes. Next, we analyze the PVD for the HOD product. Figure 6 shows the QCT results for the OD + CH4 reaction, together with the experimental data4 for comparison. Note first that in HOD these authors reported the following normal-mode frequencies: ν1(OD) = 2723 cm−1, ν2(OH) = 3707 cm−1, and ν3(bending) = 1403 cm−1. The ν1 and ν3 are coupled by collisions through the ν1 = 1 and ν3 =2 levels. Thus, the following pairs of states present similar energy: (100) and (002), (200) and (004), and (110) and (012). Second, with the available energy it is possible to populate two quanta in the ν1(OD) stretching mode but only one in the ν2(OH) mode. The QCT results reasonably simulate the dynamics description of the title reaction, where again the (020) state population is
IV. CONCLUSIONS In 2005, Kopin Liu’s group reported a series of experimental results analyzing water product translational (PTD) and vibrational (PVD) distributions in the OH + CH4 and OH + CD4 bimolecular reactions. In the present work, we have reproduced these delicate experiments by using QCT calculations where the vibrational analysis was performed using the NMA and FFT algorithms. The influence of the inclusion of a quantum spirit in the classical calculations was analyzed using two binning approaches: standard binning (SB) and Gaussian binning model 1 (1GB). The following conclusions can be highlighted: With respect to the theoretical tools used, (i) the NMA and FTT algorithms give similar results, but while the FFT algorithm is developed only for triatomic molecules, the NMA algorithm is general for any polyatomic system, and (ii) The 1GB binning technique includes better quantum corrections to the classical calculations than the SB approach. With respect to the theory/experiment comparison, the PTD and PVD experiments are reproduced when the QCT/NMA/ 1GB approach is used. Thus, the vibrational energy is mostly deposited in the new OH and OD bonds formed, and the vibrational population peaks at v = 1 and 2 for the H2O and HOD products, respectively, marking a clear isotope effect. Because of the more “local” character in the HOD stretching modes and the lesser tunnelling effect in the OH + CD4 reaction the agreement with the experiment is better than that for the H2O product. Finally, in the PVD analysis at room temperature we compared the QCT results for the OH/OD + CH4 reactions with the available experimental data4 for the OH/OD + C2H6 reactions. We found that first the product vibrational distribution of the H2O and HOD products is reasonably simulated, where the majority of available energy appears as H2O/HOD product vibrational energy, mainly in the new OH stretch mode formed, and second, that the results from the OH G
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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Varandas, A. J. C.; Wang, H.; Wolf, R. J. VENUS96: A General Chemical Dynamics Computer Program. QCPE Bull. 1996, 16, 43. (14) Monge-Palacios, M.; Gonzalez-Lavado, E.; Espinosa-Garcia, J. Quasi-classical Trajectory Study of the Effect of Antisymmetric Stretch Mode Excitation on the O(3P) + CH4(3 = 1) OH + CH3 Reaction on an Analytical Potential Energy Surface. Comparison with Experiment. J. Chem. Phys. 2014, 141, 094307. (15) Duchovic, R.; Schatz, G. C. The FFT Method for Determining Semiclassical Eigenvalues: Application to Asymmetric Top Rigid Rotors. J. Chem. Phys. 1986, 84, 2239−2246. (16) Schatz, G. C. A Program for Determining Primitive Semiclassical Eigenvlaues for Vibrating/Rotating Triatomic Molecules. Comput. Phys. Commun. 1984, 51, 135−147. (17) Corchado, J. C.; Espinosa-Garcia, J. Product Vibrational Distributions in Polyatomic Species Based on Quasiclassical Trajectory Calculations. Phys. Chem. Chem. Phys. 2009, 11, 10157−10164. (18) Bonnet, L. The Method of Gaussian Weighted Trajectories. III. An Adiabaticity Correction Proposal. J. Chem. Phys. 2008, 128, 044109. (19) Bonnet, L. Classical Dynamics of Chemical Reaction in a Quantum Spirit. Int. Rev. Phys. Chem. 2013, 32, 171−228. (20) Czakó, G.; Bowman, J. M. Quasiclassical Trajectory Calculations of Correlated Product Distributions for the F+CHD3(v1=0,1) Reactions Using an Ab initio Potential Energy Surface. J. Chem. Phys. 2009, 131, 244302. (21) Bonnet, L.; Espinosa-Garcia, J. The Method of Gaussian Weighted Trajectories. V. On the 1GB Procedure for Polyatomic Processes. J. Chem. Phys. 2010, 133, 164108. (22) Czakó, G. Gaussian Binning of the Vibrational Distributions for the Cl + CH4(v4/2 = 0, 1) → H + CH3Cl(n1n2n3n4n5n6) Reactions. J. Phys. Chem. A 2012, 116, 7467−7473. (23) Bass, M. J.; Brouard, M.; Vallance, C.; Kitsopoulos, T. N.; Samartzis, P. C.; Toomes, R. L. The Dynamics of the Cl+C2H6→ HCl(v′,j′)+C2H5 Reaction at 0.24 eV: Is Ethyl a Spectator? J. Chem. Phys. 2003, 119, 7168−7178. (24) Espinosa-Garcia, J.; Corchado, J. C.; Bonnet, L. Quasi-classical Trajectory Study of the Water Vibrational Distribution for the Polyatomic OH/OD+NH3 Reactions. Comparison with Experiment. Chem. Phys. Lett. 2015, 620, 56−60. (25) Setser, D. W., Private communication. Kansas State University: Manhattan, KS, 2014. (26) Espinosa-Garcia, J. Quasi-classical Trajectory Study of the Hydrogen Abstraction F + CHD3 Reaction: A State-to-state Dynamics Analysis. Chem. Phys. Lett. 2008, 454, 158−162. (27) Czako, G.; Liu, R.; Yang, M.; Bowman, J. M.; Guo, H. Quasiclassical Trajectory Studies of the O(3P) + CX4 → OX(v) +CX3 [X=H and D] Reactions on an Ab initio Potential Energy Surface. J. Phys. Chem. A 2013, 117, 6409−6420. (28) Gonzalez-Lavado, E.; Corchado, J. C.; Espinosa-Garcia, J. The Hydrogen Abstraction Reaction O(3P) + CH4: A New Analytical Potential Energy Surface based on Fit to Ab initio Calculations. J. Chem. Phys. 2014, 140, 064310. (29) Czako, G.; Bowman, J. M. Reaction Dynamics of Methane with F, O, Cl and Br on Ab initio Potential Energy Surfaces. J.Phys.Chem. A 2014, 118, 2839−2864. (30) Li, J.; Corchado, J. C.; Espinosa-Garcia, J.; Guo, H. Final Stateresolved Mode Specificity in HX + OH → X + H2O (X = F and Cl) Reactions: A Quasi-classical Trajectory Study. J. Chem. Phys. 2015, 142, 084314.
+ ethane should be representative for OH + primary alkanes with an adjustment for the available energy for each reaction. It is of interest to note that in the last case tunnelling is quite significant, and ∼75% of the reactivity at 298 K can be attributed to tunnelling for both the OH and OD reactions; however, in the pair OH/OD + ethane reactions we reached similar conclusions as the OH + CH4/CD4 pair at a relatively high collision energy, for which tunnelling was much smaller (especially in the CD4 case). Therefore, we can conclude that the description of the HOD product is better than that for the H2O product because of the dynamical properties and approximations used rather than the absence of tunnelling effects. In summary, in the absence of state-to-state full-dimensional quantum-mechanical calculations, in this theory/experiment comparison the PES, the QCT, and the NMA algorithms are being tested, and the agreement obtained for the dynamics properties analyzed in the present work leads us to state that this classical approach is an affordable and useful alternative to current prohibitive quantum scattering studies for polyatomic reactions.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Phone: +34 924289787. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Zhang, B.; Shiu, W.; Lin, J. J.; Liu, K. Mode Correlation of Product Pairs in the Reaction OH + CD4 → HOD + CD3. J. Chem. Phys. 2005, 122, 131102. (2) Zhang, B.; Shiu, W.; Liu, K. Imaging the Reaction Dynamics of OH + CD4.2. Translational Energy Dependencies. J. Phys. Chem. A 2005, 109, 8983−8988. (3) Zhang, B.; Shiu, W.; Liu, K. Imaging the Reaction Dynamics of OH + CD4.2. Isotope Effects. J. Phys. Chem. A 2005, 109, 8989−8993. (4) Butkovskaya, N. I.; Setser, D. W. Infrared Chemiluminiscence from Water-forming Reactions: Characterization of Dynamics and Mechanisms. Int. Rev. Phys. Chem. 2003, 22, 1−72. (5) Espinosa-Garcia, J.; Corchado, J. C. QCT Dynamics Study of the Reaction of Hydroxyl Radical and Methane Using a New Ab initio Fitted Full-dimensional Analytical Potential Energy Surface. Theor. Chem. Acc. 2015, 134, 1−10. (6) Espinosa-Garcia, J.; Corchado, J. C. Potential Energy Surface for a Seven-atom Reaction. Thermal Rate Constants and Kinetic Isotope Effects for CH4+OH. J. Chem. Phys. 2000, 112, 5731−5739. (7) Yu, H.-G. A Five-dimensional Quantum Scattering Model for the Type AB+XCD3⇌ABX+CD3 Reaction in Hyperspherical Coordinates: Application to OH+CH4⇌H2O+CH3. J. Chem. Phys. 2001, 114, 2967−296. (8) Song, H.; Lee, S.-Y.; Yang, M.; Lu, Y. Six-dimensional and Sevendimensional Quantum Dynamics Study of the OH + CH4 → H2O + CH3 Reaction. J. Chem. Phys. 2013, 139, 154310. (9) Song, H.; Li, J.; Jiang, B.; Yang, M.; Lu, Y.; Guo, H. Effects of Reactant Rotation on the Dynamics of the OH + CH4 → H2O + CH3 Reaction: A Six-dimensional Study. J. Chem. Phys. 2014, 140, 084307. (10) Truhlar, D. G. Basis Set Extrapolation. Chem. Phys. Lett. 1998, 294, 45−48. (11) Fast, P. L.; Sanchez, M. L.; Truhlar, D. G. Infinite Basis Limits in Electronic Structure Theory. J. Chem. Phys. 1999, 111, 2921−2926. (12) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992, 96, 6796−6806. (13) Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D-h.; Peslherbe, G. H.; Swamy, K. N.; Van de Linde, S. R.; H
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Product Translational and Vibrational Distributions for the OH/OD + CH4/CD4 Reactions from Quasiclassical Trajectory Calculations. Comparison with Experiment. Joaquin Espinosa-Garcia and Jose C. Corchado*
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Departamento de Química Física, Universidad de Extremadura, Avenida de Elvas S/N, 06071 Badajoz, Spain ABSTRACT: For the OH + CH4/CD4 hydrogen abstraction reactions, the methyl radical (CH3 and CD3) product translational distributions and the water (H 2 O and HOD) product vibrational distributions experimentally reported by Liu’s group are reproduced by quasi-classical trajectory (QCT) calculations on an analytical full-dimensional potential energy surface when a quantum spirit is included in the analysis. Our simulations correctly predict: (i) the vibrational excitation of the water product, (ii) the inversion of the water vibrational population, and (iii) the propensity of transfer from reactant kinetic energy to product translational energy. These reactions therefore present a marked isotopic effect. In addition, the water product vibrational distributions for the OH/OD + CH4 reactions agree reasonably well with Butkovskaya and Setser’s experiments for a similar alkane reaction. The theory/experiment agreement is better for the HOD than for the H2O product due to the mode coupling in the H2O molecule, which is absent in the HOD stretching modes, which show a more “local” character. In summary, for polyatomic systems with many degrees of freedom (15 in the present reaction), QCT calculations analyzed with a quantum spirit represent a useful alternative to quantum scattering methods.
I. INTRODUCTION The OH + CH4 (and its isotopic analogues) hydrogen abstraction reaction is a benchmark system at low temperatures because it constitutes the major process for the removal of methane in atmospheric chemistry and at high temperatures because of its importance in combustion processes. So these reactions have received much attention, both experimental and theoretically. In 2005, Liu et al.1−3 published a series of studies on the dynamics of the OH + CD4 → HOD + CD3 and isotopic analogues, using crossed-beam experiments over collision energies in the range 5−16 kcal mol−1. They found that correlated with the methyl radical vibrational ground-state, CD3(v = 0), which is the dominant product state, the HOD coproduct appears almost exclusively stretch-excited, ∼90%, with an inversion of the vibrational distribution that peaks at ν(OD) = 2. As for the H2O coproduct in the analogous OH + CH4 → H2O + CH3 reaction, 70% shows as stretch-excited and also presents an inverted vibrational distribution peaking at ν(OH) = 1. Thus, in both reactions, the vibrational excitation of the coproduct, HOD and H2O, is mostly localized in the newly formed bond, OD and OH, respectively. These authors studied the dynamics of these reactions by analyzing the methyl product translational distribution (PTD), the water product vibrational distribution (PVD), and the product angular (PAD) distribution. Butkovskaya and Setser4 performed a series of experiments at room temperature for several OH/OD + RH → H2O/HOD + © XXXX American Chemical Society
R reactions, analyzing the vibrational distributions of the nascent water product molecule. They found that most (80− 85%) of the vibrational energy is released to the local mode associated with the new OH stretching mode. These authors did not study the title reaction, and as a first approximation to the problem we will use the similar OH/OD + C2H6 → H2O/ HOD + C2H5 hydrogen abstraction reaction for comparison. Recently, for this system our group5 developed an analytical full-dimensional potential energy surface, PES-2014, improving our previous PES-2000 surface.6 The new PES-2014 surface is fitted exclusively to high-level ab initio calculations, is symmetric with respect to the permutation of the four methane hydrogen, and provides analytically energy and energy first derivatives (gradients), which constitutes a computational advantage. This surface presents a barrier height of 6.4 kcal mol−1, an exothermicity of −13.3 kcal mol−1, and intermediate complexes in the entrance and exit channels, stabilized by 0.4 and 1.1 kcal mol−1 with respect to the reactants and products, respectively. In addition, it reproduces the topology of the reactive system, in excellent agreement with high-level ab initio calculations. Using the PES-2014 we performed an exhaustive dynamics study5 using quasi-classical trajectory (QCT) Special Issue: Bruce C. Garrett Festschrift Received: May 5, 2015 Revised: June 5, 2015
A
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
Figure 1. Energetic profile of the OH+ CH4/CD4 → H2O/HOD + CH3/CD3 reactions using the PES-2014 surface, where the reactant complex, product complex, and saddle point are included. Energy values in kcal mol−1. Ab initio values from ref 5. The saddle-point geometry is also included.
Vstretch consists of four London−Eyring−Polanyi (LEP) stretching terms and depends on 12 fitted parameters; Vharm represents the valence binding terms and depends on 16 parameters; Vop denotes the harmonic out-of-plane potential depending on four fitted parameters, and finally Vwater is the potential describing the water product, which is a combination of a Morse potential and a harmonic bending potential and depends on three fitting parameters. In addition, it includes a series of switching functions whose main aim is to change smoothly from the tetrahedral structure in methane to the planar structure in methyl. This VB-MM functional form with adjustable parameters gives great flexibility to the PES. A total of 35 parameters were fitted exclusively to high-level ab intio calculations, representing the overall topology of the hydrogen abstraction reaction potential energy surface. In this case, the “infinite basis” (IB) method was used,10,11 which extrapolates the energies from the cc-pVDZ and cc-pVTZ basis sets.12 A schematic profile of this reaction with the PES-2014 is shown in Figure 1, together benchmark theoretical results for comparison. Standard QCT calculations were performed on the PES-2014 surface using the VENUS code,13 where a Monte Carlo approach is used to select the scattering parameters (impact parameter, vibrational phases, and spatial orientation of the initial reactants), first at a collision energy of 10 kcal mol−1 for a direct comparison with Liu’s experiment1−3 and second at room temperature for comparison with Setser’s related experiment.4 The trajectories were initiated and stopped in asymptotic regions, where the molecular interactions are negligible, with the two reactants or products separated by at least 10 Å. In the first case, for each reaction, OH + CH4 and OH + CD4, 100 000 trajectories were run, where the maximum impact parameter, bmax, was obtained using small batches of trajectories (10 000) with trial values until no reactive trajectories were found. The values of bmax were 2.8 and 2.4 Å, respectively. The large number of trajectories run in each reaction leads to small or negligible statistical errors ( 3) two polyatomic products are formed, and the mode coupling and the intramolecular vibrational energy redistribution makes the analysis much more difficult. This is the case of the present seven-atom bimolecular reaction, OH + CH4 → H2O + CH3, where two products of three and four atoms are formed. We begin by analyzing the H2O PVD in the perprotio reaction, OH + CH4. Given the available energy, 24.9 kcal mol−1, the OH stretching mode can be excited up to one quantum, and several stretching−bending combinations are also possible, in accordance with the experiment.3 The H2O PVD obtained with QCT/NMA calculations is shown in Figure 3, using two binning approaches, SB and 1GB, together with experimental results3 for comparison. Both binning techniques reproduce the experimental finding that the (01*0) state is the most populated, with an appreciable population of the (01*1) state; however, the SB approach shows populations in the (000) and (02*0) states, which are not experimentally detected. The small population in the vibrational ground-state (000), 4%, is explained because in this approach the quantum numbers in the range [−0.5, +0.5], which includes trajectories with mechanically forbidden negative quantum actions, contribute to the ground-state population. The population in
Table 1. Product Energy Partitioning (In Percentage) for the OH + CH4 and OH + CD4 Reactions at 10 kcal mol−1 OH + CH4 QCT f V(methyl) f R(methyl) f V(water) f R(water) fT
OH + CD4
exp.
a
0 10 53 3 34
exp.a
QCT
b
b
0 11 54 3 32
47 6 47
58 4 38
Ref 3. bExperimentally, the methyl radical (CH3 or CD3) is considered as a structureless particle.
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a
f T are the energy fractions as vibration, rotation, and translation, respectively, and the methyl (CH3 or CD3) coproduct is considered in its vibrational ground-state. The heavy−light−heavy kinematics of these reactions favors transfer T → T′ (reactant kinetic energy to product translational energy); however, while the methyl (CH3 or CD3) coproduct is experimentally treated as a structureless particle, and therefore zero value for the methyl coproduct internal energy is assumed, theoretically ∼10% of the methyl energy we obtain is rotational energy. This behavior was already observed by Bass et al.,23 who analyzed different Cl + alkane reactions and concluded that the alkyl coproduct internal energy must be taken into account (in the Cl + C2H6 → HCl + C2H5 reaction, obtained a ∼0.22), which can modify the dynamics. Therefore, we hope that future experimental studies on the present reactions can confirm this finding. The total available energy, Eav, is given by Eav = Ecoll + ΔHR (0 K)
(9) −1
which represents 24.9 and 24.1 kcal mol at Ecoll = 10 kcal mol−1 for CH4 and CD4, respectively. Taking into account this energy and the difference in vibrational frequencies between OH and OD, 3806 and 2767 cm−1, it is possible to populate up to one quantum the OH stretching level in H2O and up to two quanta the OD stretching level in HOD, which is in agreement with the experimental evidence. Another important averaged dynamics property is the vibrational distribution of the water product as pure stretching, pure bending, and a combination of these, which has been experimentally reported3 for the methyl coproduct in its vibrational ground state. Table 2 lists the experimental and QCT results for both reactions, where in the QCT calculations we used the NMA and the FFT algorithms, with the SB and 1GB approaches. First, in general, for both reactions, the NMA Table 2. Probabilities for Vibrational Excitation in the Water Product as Pure Stretching, Ps, Combination Mode, Pc, and Pure Bending, Pb, at 10 kcal mol−1 OH+CH4 NMAa Pgsd Ps Pc Pb
OH+CD4
FFTb
SB
1GB
SB
1GB
4 80 14 2
1 72 21 5
6 71 17 6
1 71 23 3
exp.c 0 71 24 4
NMAa
FFTb
SB
1GB
SB
1GB
1 80 18 0
0 78 22 0
1 80 19 0
0 76 24 0
exp.c 0 85 15 0
a
Normal mode analysis, NMA. Ref 10. bFast-Fourier-transformed, FFT. Ref 9. cExperimental values from ref 3. dGround-state probability. D
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
Figure 2. Product speed distributions of the OH + CH4/CD4 → H2O/HOD + CH3(v = 0)/CD3(v = 0) reactions at 10 kcal mol−1. QCT results on the PES-2014 surface (left panels) and experimental measures1−3 (right panels). The error bar is ±0.2 km s−1, representing ±1 standard deviation.
respective ZPE and are the consequence of a flux of energy between modes that quantum mechanics would forbid. The 1GB approach corrects the two previous issues: It removes the (000) population and largely diminishes the (02*0) population. In this way, it improves agreement with the experiment by introducing a quantum spirit in this analysis. The HOD PVD in the deuterated reaction, OH + CD4, obtained with a similar methodology, QCT/NMA-SB/1GB, is plotted in Figure 4. The experimental results3 are also included for comparison. Both binning techniques give the correct order of population, (200) > (100), in accordance with the experiment; however, as previously noted, the SB method overestimates the (300) state, 9%, and underestimates the most populated state (200). The quantum spirit introduced with the 1GB approach corrects these deficiencies and better reproduces the experiment. In general, the agreement with the experiment is better for the OH + CD4 → HOD + CD3 reaction than for the perprotio analogue, OH + CH4 → H2O + CH3. This behavior had already been found in a previous study24 on the OH + NH3 → H2O + NH2 reaction, and it can be explained because a major limitation of the NMA algorithm is the presence of coupling between modes. So, while the H2O product presents two similar stretching modes, 3806 and 3762 cm−1, with possible strong coupling, the HOD product presents a more “local” character, associated with different stretching modes, 2767 and 3801 cm−1. In addition, the H and D hydrogen abstraction
Figure 3. Populations of the vibrational states of the H2O product, in the OH + CH4 reaction, labeled (n,m,l), where n and m represent the quantum numbers for the OH symmetric (ν1) and asymmetric (ν3) stretch modes and l represents that for the bending mode (ν2), as computed using the NMA method with the SB and 1GB binning approaches. Experimental values from ref 3.
the (02*0) state can also be due to the classical nature of the QCT method. Thus, part of the energy required to excite the stretch mode to v = 2 comes from the fact that the other two vibrational modes can have an energy lower than their E
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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in eq 4). This diminishes the quantum character of the calculation but reduces the statistical error. As was shown in the first part of the present work, the SB and 1GB methods give similar results, and this is the expected behavior at room temperature. In addition, in previous works20,26−30 the 1GB method has been tested for similar hydrogen abstraction reactions, finding that SB and 1GB provide qualitatively similar vibrational distributions, although the HB method overestimates the population of some vibrational states due to the ZPE violation problem in one of both products, and this deficiency is corrected by the 1GB method, which includes a more quantum spirit. Table 3 lists some QCT-averaged properties together with experimental results (OH/OD + C2H6) for comparison. The Table 3. H2O/HOD Product-Averaged Properties for the OH/OD + Alkane → H2O/HOD + Alkyl Radical Reactions at 298 K
Figure 4. Same for the HOD product in the OH + CD4 reaction. Now the (n,m,l) labels represent the quantum number for the OD stretch mode (ν1), m represents that for the OH stretching mode (ν3), and l represents that for the bending mode (ν2). Experimental values from ref 3.
H2O QCT P(0:1:2)c d d
reactions present different tunnelling quantum effects; therefore, a more appropriate treatment by quasi-classical trajectories is expected for the OH + CD4 reaction. Unfortunately, the GB approach cannot handle this quantum effect; however, because of the high collision energy one can expect that tunnelling will not play a crucial role in either of the isotopic substitutions. III.B. QCT Results at Room Temperature. Comparison with Experiment. Butkovskaya and Setser4 carried out a series of experiments for water-forming reactions at T = 298 K for various families of compounds, including saturated hydrocarbons among others. They reported results for the water product in the OH/OD + C2H6 reaction, but not for the title reaction, OH/OD + CH4. Setser25 pointed out that this reaction was not studied because (i) at room temperature it is too slow to allow for a good experimental study and (ii) the available energy is rather low and so only a few vibrational levels could be observed. In addition, he suggested that the results from the OH + ethane should be representative for OH + primary alkanes with an adjustment of the available energy for each reaction. Thus, to complete the present QCT study at a given energy, in this section we perform QCT calculations at room temperature for the OH/OD + CH4 reactions and compare the results with the experimental data reported by the OH/OD + C2H6 reactions.4 The aim is two-fold: first, to report for the first time theoretical results for the title reactions at T = 298 K, which await experimental confirmation, and second, to confirm Setser’s suggestion about the behavior of OH + primary alkanes. At this temperature, the reaction cross section is σR = 0.028 ± 0.001 Å2, as compared with σR = 1.877 ± 0.021 Å2 at Ecol=10 kcal mol−1, that is, a reactivity a factor of ∼65 lower. This result justifies Setser’s comment on the difficulties of experimentally studying the title reaction at room temperature. This very low reactivity implies a higher statistical error in the vibrational energy calculations, which is even more important when the 1GB approach is used. (One would need a large number of reactive trajectories, which are very scarce under the chosen thermal conditions.) To circumvent this problem we decided to increase the number of trajectories with respect to the previous section and the width of the Gaussian function used to compute the weight in the 1GB calculation (by diminishing α
e /
a
55:36:8 57 89
HOD exp.
b
21:65:14 51 81
QCT
exp.
34:58:8 60 60
31:55:14 47 81
11
17
12
14
0.12
0.21
0.20
0.21
a QCT results for the OH/OD + CH4 reactions. bExperimental results4 for the OH/OD + C2H6 reactions. cPopulations P1,2 for the H2O product in the ν1 and ν2 levels, which cannot be experimentally separated. Population P2 for the HOD product. dMean fraction of vibrational energy in the H2O/HOD product: /. eMean fraction of vibrational energy in the ν2 mode: /. fMean fraction of vibrational energy in the ν3 mode: /.
mean fractions of vibrational energy, , , and , reproduce the experimental tendency, where the majority of vibrational energy is deposited in the new OH stretching mode, ν2; however, large discrepancies are found in the populations of the new OH bond formed, P(0:1:2), especially in the case of the H2O product. Nevertheless, it should be noted that this theory/experiment comparison is not straightforward because the QCT calculations were performed for the OH + CH4 reaction while the experimental data correspond to the OH + C2H6 reaction. In this comparison, therefore, one must take into account these differences. So, the OH + C2H6 reaction is more exothermic than the OH + CH4 reaction, ΔH0 = −18.6 versus −14.9 kcal mol−1. This results in a different topology of the PESs with a stronger fall in the exit channel for the ethane reaction and therefore the possibility of higher vibrational excitation in the water product. The isotopic variant OD + alkane reaction shows a significantly better agreement with the experiment, which can be explained by the more “local” character in the OH and OD vibrational modes as compared with the two similar OH stretching in H2O; however, we again find an underestimation of the excitation to v = 2, which may be due to the differences in the exothermicity of both reactions. Figure 5 plots the QCT results for the H2O PVD together with the Butkovskaya and Setser4 experimental results, once again for the OH + C2H6 reaction for comparison. Remember that in the case of the H2O product, ν1,2 = 1 means that either mode 1 or mode 2 could have one quantum of excitation because these modes present similar energy. Thus, the following pairs of states present similar energy: (100) and F
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
Figure 5. Vibrational state distribution of the H2O(n,m,l) product at 298 K. QCT calculations on the PES-2014 surface for the OH + CH4 reaction computed using the NMA method with the SB and 1GB binning approaches. Experimental values from ref 4 for the OH + C2H6 reaction.
Figure 6. Same as Figure 5 but for the HOD(n,m,l) product.
due to the limitations of the classical method, and it is partially corrected when the 1GB method is employed. Note that the theoretical results shown in the present section have a predictive character to be confirmed by future experimental studies. In any case, they seem to confirm Setser’s suggestion that the results obtained for the reactions with ethane are representative of the behavior of the primary alkanes.
(010), (101) and (011), (102) and (012), (200) and (020). Taking into account the differences previously noted between OH + CH4 and OH + C2H6 reactions, we consider that the QCT calculations on the PES-2014 simulate reasonably well the dynamics of the title reaction. It has to be noted that, as previously discussed, the SB and 1GB methods give similar results, although the population of the (100) and (01*0) states is significantly overestimated. With SB, we obtained a population of 35% in the (020) state (two quanta in the OH stretching modes), reduced to 25% when the 1GB method is applied. The available energy, = −ΔH0o + Ea + 4RT, was larger for the OH + C2H6 reaction, 23.1 kcal mol−1, than for the OH + CH4, 20.6 kcal mol−1. With this available energy it was possible to populate the second stretch level, ν1,2 = 2, in the case of the OH + C2H6 reaction, but only the first stretch level, ν1,2 = 1, for the OH + CH4 reaction. Because the available energy was not enough to populate this state, this is clearly an overestimation as a result of the method used. As discussed in the previous section, this is due to an incorrect flux of energy between modes whose effect can largely be reduced by using binning techniques that introduce a quantum spirit in the classical calculation. Thus, the 1GB method partially corrects this problem, although as a result it increases significantly the population of the lower (100) and (01*0) states, Therefore, although the agreement with experiment worsens, the results are more physically reasonable. From a qualitative point of view, our calculations agree with experiment in the flux of energy mainly to the stretching modes. Next, we analyze the PVD for the HOD product. Figure 6 shows the QCT results for the OD + CH4 reaction, together with the experimental data4 for comparison. Note first that in HOD these authors reported the following normal-mode frequencies: ν1(OD) = 2723 cm−1, ν2(OH) = 3707 cm−1, and ν3(bending) = 1403 cm−1. The ν1 and ν3 are coupled by collisions through the ν1 = 1 and ν3 =2 levels. Thus, the following pairs of states present similar energy: (100) and (002), (200) and (004), and (110) and (012). Second, with the available energy it is possible to populate two quanta in the ν1(OD) stretching mode but only one in the ν2(OH) mode. The QCT results reasonably simulate the dynamics description of the title reaction, where again the (020) state population is
IV. CONCLUSIONS In 2005, Kopin Liu’s group reported a series of experimental results analyzing water product translational (PTD) and vibrational (PVD) distributions in the OH + CH4 and OH + CD4 bimolecular reactions. In the present work, we have reproduced these delicate experiments by using QCT calculations where the vibrational analysis was performed using the NMA and FFT algorithms. The influence of the inclusion of a quantum spirit in the classical calculations was analyzed using two binning approaches: standard binning (SB) and Gaussian binning model 1 (1GB). The following conclusions can be highlighted: With respect to the theoretical tools used, (i) the NMA and FTT algorithms give similar results, but while the FFT algorithm is developed only for triatomic molecules, the NMA algorithm is general for any polyatomic system, and (ii) The 1GB binning technique includes better quantum corrections to the classical calculations than the SB approach. With respect to the theory/experiment comparison, the PTD and PVD experiments are reproduced when the QCT/NMA/ 1GB approach is used. Thus, the vibrational energy is mostly deposited in the new OH and OD bonds formed, and the vibrational population peaks at v = 1 and 2 for the H2O and HOD products, respectively, marking a clear isotope effect. Because of the more “local” character in the HOD stretching modes and the lesser tunnelling effect in the OH + CD4 reaction the agreement with the experiment is better than that for the H2O product. Finally, in the PVD analysis at room temperature we compared the QCT results for the OH/OD + CH4 reactions with the available experimental data4 for the OH/OD + C2H6 reactions. We found that first the product vibrational distribution of the H2O and HOD products is reasonably simulated, where the majority of available energy appears as H2O/HOD product vibrational energy, mainly in the new OH stretch mode formed, and second, that the results from the OH G
DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
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+ ethane should be representative for OH + primary alkanes with an adjustment for the available energy for each reaction. It is of interest to note that in the last case tunnelling is quite significant, and ∼75% of the reactivity at 298 K can be attributed to tunnelling for both the OH and OD reactions; however, in the pair OH/OD + ethane reactions we reached similar conclusions as the OH + CH4/CD4 pair at a relatively high collision energy, for which tunnelling was much smaller (especially in the CD4 case). Therefore, we can conclude that the description of the HOD product is better than that for the H2O product because of the dynamical properties and approximations used rather than the absence of tunnelling effects. In summary, in the absence of state-to-state full-dimensional quantum-mechanical calculations, in this theory/experiment comparison the PES, the QCT, and the NMA algorithms are being tested, and the agreement obtained for the dynamics properties analyzed in the present work leads us to state that this classical approach is an affordable and useful alternative to current prohibitive quantum scattering studies for polyatomic reactions.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Phone: +34 924289787. Notes
The authors declare no competing financial interest.
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REFERENCES
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DOI: 10.1021/acs.jpcb.5b04290 J. Phys. Chem. B XXXX, XXX, XXX−XXX
