Mode and Bond Selectivities in Methane ... - ACS Publications

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Mode and Bond Selectivities in Methane Dissociative Chemisorption: Quasi-Classical Trajectory Studies on Twelve-Dimensional Potential Energy Surface Bin Jiang and Hua Guo* Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States ABSTRACT: The mode and bond selectivities in methane dissociative chemisorption on Ni(111) are studied using a quasi-classical trajectory (QCT) method on a twelve-dimensional global potential energy surface based on a large number of density functional theory points. The calculated reaction probabilities near and above the reaction barrier reproduced the general trends observed in experimental investigations of various vibrationally excited CH4, CHD3, and CH2D2 species on nickel surfaces. The mechanism of these mode and bond selectivities is analyzed using the recently proposed sudden vector projection model.

I. INTRODUCTION The dissociative chemisorption of methane on transition-metal surfaces, which leads to adsorbed methyl and hydrogen species, has attracted much attention in the past decades, not only because of its key role in the industrial production of syngas via steam reformation1 but also for its fundamental importance as a prototypical system for gas−surface reactions.2 It has been established for some time that methane dissociation on transition-metal surfaces is activated by both the translational energy along the surface normal and vibrational excitation of methane.3−8 More recently, quantum state resolved studies, mostly from the groups of Utz and Beck, have revealed clear mode and bond-selectivities in dissociative chemisorption of methane and its isotopomers.9−25 On the Ni(100) surface, for example, it was demonstrated that the symmetric stretching excitation of CH4 is the most effective in promoting the reaction, more so than the same amount of translational energy.17 It is followed by the asymmetric stretching modes, which are about as effective as translational energy,9 while the umbrella bending mode is the least effective.16 Similarly strong mode selectivity has been observed on the Ni(111) surface: Although the enhancement by the symmetric stretching excitation has not been reported, the asymmetric stretching excitation of CH4 has been found to be more effective than translational energy,15 while the umbrella bending mode is lower in its efficacy.16 Mode selectivity has also been reported for CH2D2 on Ni(100), in which a two-quantum excitation in one C−H bond was found to promote the reaction more than single-quantum excitations in both C−H bonds.14 In addition, bond selectivity has been uncovered in the dissociation of CHD3 on the Ni(111) surface19 and more recently on the Pt(111) surface.25 To this end, it was found that the excitation of C−H stretching mode in CHD3 promotes the cleavage of C−H bond which leads to the adsorbed CD3 product. We note © 2013 American Chemical Society

in passing that the mode and bond selectivities observed in these gas−surface processes bear striking similarities with the X + CH4 (X = H, F, O, Cl) type reactions in the gas phase.26 These aforementioned experiments provided unprecedented details for this gas−surface reaction, underscoring the fact that energy flow among the relevant degrees of freedom may be far from the statistical limit as assumed by statistical models.27,28 To understand the mode and bond selectivities, it is thus vital to understand the reaction dynamics. However, this is a much more challenging problem than the extensively studied and already complex hydrogen dissociative chemisorption29,30 as fifteen degrees of freedom are needed to describe the fulldimensional dynamics of methane on a rigid surface. Early efforts were based on pseudodiatomic quantum models with empirical potential energy surfaces (PESs), which shed much light on the general trends.31−33 Subsequently, reduceddimensional quantum models with more degrees of freedom were proposed by several authors, providing more dynamical details.34−39 It is worth noting that the rigid surface approximation in these earlier studies was removed and the importance of surface effects were extensively investigated by Jackson and co-workers.40−45 Because of the reduced-dimensional nature of these dynamical models, however, none was able to treat all four vibrational modes of CH4. Very recently, a full-dimensional quantum dynamical model has been proposed by Jackson and Nave46,47 based on the reaction path Hamiltonian approach.48 Although the Hamiltonian is still approximate in nature, this full-dimensional model sheds valuable light on the multidimensional dynamics in methane dissociative chemisorption. Received: June 10, 2013 Revised: July 15, 2013 Published: July 16, 2013 16127

dx.doi.org/10.1021/jp405720c | J. Phys. Chem. C 2013, 117, 16127−16135

The Journal of Physical Chemistry C

Article

DFT calculations.61 The permutation symmetry of the four H atoms is explicitly taken into account in the fitting, which is vital for studying mode and bond selectivities in this reaction. It has been shown that the DFT reaction path and stationary points are faithfully reproduced by the PES. Since details of the PES have been given in our recent work,61 only the general features related to the QCT calculations are discussed here. Similar to our recent work on the H2O dissociative chemisorption on Cu(111),66,67 our 12D PES for the CH4/ Ni(111) system was computed within the rigid surface approximation.61 The neglect of the lateral coordinates (X, Y) is justified by the observed “normal energy scaling” in methane dissociative chemisorption on transition-metal surfaces,2 namely, the fact that the initial sticking probability depends only on the kinetic energy along the surface normal. The azimuthal angle (ϕ) about the surface normal (Z) is also neglected because the surface corrugation is found to be quite small. This amounts to a flat surface approximation that has been widely used in earlier H2 dissociative chemisorption studies.35,68−70 It should also be noted that the PES is less accurate in the product channel, due to its reduced-dimensional nature.61 In spite of these approximations, however, this 12D PES includes all rotational and vibrational degrees of freedom for methane, in addition to the scattering coordinate (Z). As a result, it is ideal for studying mode and bond selectivities. Because of its polynomial form, the evaluation of the PES is very fast, which is a necessary prerequisite for QCT calculations. In addition, the PES is very smooth, which allows the conservation of energy for trajectories. In Table 1, the potential energies and vibrational frequencies for CH4, CHD3, and CH2D2 are listed in the reactant asymptote and transition state. Note that, in the latter two cases, there are two nonequivalent transition states corresponding to the C−H and C−D bond cleavages. B. QCT Calculations. The QCT calculations were carried out using VENUS,71,72 in which Ni(111) was treated as a flat surface, dictated by the limitations of our 12D PES. Unlike the few hundred trajectories computed in the recent transition-state sampled direct dynamics work of Sacchi et al.,58−60 a large number of trajectories were initiated with free methane 5.0 Å above the metal surface. The initial coordinates and momenta for all atoms in CH4 and all deuterated methane were determined with the standard normal mode sampling,73,74 assuming either quantized energies or thermal conditions. The maximal impact parameter (bmax) was fixed at zero due to the fact that the impact site on the Ni(111) surface is fixed in our model. The gradient of the PES was obtained using a finitedifferencing method, and the propagation time step of 0.10 fs was sufficient to converge the energy better than 10−3 kcal/mol. The trajectories were terminated if the C−H or C−D bond reached a separation of 2.0 Å (2.2 Å was tested and no change was found) beyond the saddle point which is located at rC−H/C−D = 1.57 Å. These trajectories were counted as reactive ones. Otherwise, trajectories in which the CH4 was scattered back beyond Z = 5.0 Å were terminated and counted as nonreactive ones. The reaction probability is given by the ratio between the number of reactive trajectories (Nr) and total number of trajectories (Ntotal):

A major bottleneck in understanding the dynamics of methane dissociative chemisorption is the lack of an accurate global PES. While many plane-wave density functional theory (DFT) calculations have been performed on this system,49−53 most have focused on the saddle point along the reaction path. The reaction path Hamiltonian extends the description of the PES near the minimum energy path (MEP) with a harmonic approximation of all orthogonal vibrational modes,45−47,54,55 but it might lose accuracy away from the MEP. A fulldimensional PES has recently been reported by Kroes and coworkers39 based on a modified Shepard (MS) interpolation56 of DFT points, but the evaluation of high-dimensional MS PESs is known to be extremely slow and the accuracy of the PES has not be extensively tested. An alternative to PES is the direct dynamics or ab initio molecular dynamics approaches,57 in which the potential energy is calculated on the fly. For methane dissociative chemisorption, it is still too expensive to run a large number of trajectories from the reactant channel in order to get satisfactory statistics for reaction probabilities. As a result, the trajectories in such studies were initiated from the saddle point and information about mode and bond selectivities was collected by analyzing trajectories in the reactant asymptote.52,58−60 Very recently, we have developed a twelve-dimensional (12D) PES for methane dissociative chemisorption on rigid Ni(111), ignoring the two lateral coordinates (X, Y) along the surface plane and the azimuthal angle (ϕ) around the surface normal.61 The PES was fit to more than 35,000 DFT (PW9162) points using the permutation invariant polynomial approach63 and is smooth and very fast to evaluate. An eight-dimensional (8D) quantum model has been used on this PES to explore the dynamics and mode selectivity in CH4 dissociative chemisorption.61 After correcting surface effects, the calculated initial sticking probabilities for various methane vibrational states were found to agree semiquantitatively with the experimental results, thus confirming the reliability of the PES.61 Unfortunately, however, this reduced-dimensional quantum model64,65 requires the preservation of C3v symmetry in the nonreactive methyl group and, thus, cannot be used to study bond selectivity in molecules such as CHD3 and CH2D2. In the present work, we address the experimentally investigated mode and bond selectivities in the dissociative chemisorption of CH4, CHD3, and CH2D2 on the Ni(111) surface, using a quasi-classical trajectory (QCT) method on our 12D PES. In addition to confirming the mode selectivity in CH4, the relative ratio between the C−H and C−D bond cleavages has been calculated for the first time for various vibrational states of CHD3 and CH2D2, which is found consistent with available experimental data. The mode and bond selectivities are rationalized by the recently proposed sudden vector projection (SVP) model. These theoretical results provide insights into the complex reaction dynamics in these systems. This publication is organized as follows. Section II outlines the PES and QCT method used in this work. Section III presents the calculated results and compares them with the experimental data, and section IV discusses mechanistic issues with the SVP model. Finally, we conclude in section V.

II. COMPUTATIONAL DETAILS A. Potential Energy Surface. A 12D global PES has been recently constructed for the dissociative chemisorption of methane on a rigid Ni(111) surface, based on a large number of

Pr = Nr /Ntotal

(1)

and the standard error is given by Δ = [(Ntotal − Nr)/Ntotal/ Nr]1/2. 16128



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small hydrocarbons have shown that the IVR is not particularly strong,75−79 at least during the short reaction time, due apparently to the low density of vibrational states. In addition, the recent direct dynamics calculations of methane dissociative chemisorption58−60 provided further evidence that IVR is not overly fast during the scattering dynamics. Finally, we note that our model allows neither sampling of impact sites nor the inclusion of surface motion. Although these effects can be included approximately by scaling the reaction probability curve,40−44,46 as we did in our recent quantum work,61 such corrections were not attempted here due to the lack of probabilities at low energies. As a result, we are more interested in this work in overall trends, rather than a quantitative comparison with experiment. A. CH4 Dissociation. Let us first discuss the dissociative chemisorption of CH4 on Ni(111), which serves as a test for treating mode selectivity with QCT. As shown in Table 1, the ZPE corrected barrier for CH4 dissociation on Ni(111) is 22.47 kcal/mol on our PES; we therefore performed QCT calculations near or above this energy. As shown in Figure 1,

Table 1. Comparison of the Vibrational Frequencies of Reactants (CH4, CHD3, and CH2D2) and Transition States (CH3−H−Ni, CD3−H−Ni/CHD2−D−Ni, and CHD2−H− Ni/CH2D−D−Ni) on the Potential Energy Surfacea

species

modeb

v1 v2 v3 v4 v5 v6 v7 v8 v9 ZPE transition v1 state v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 vi ZPE ZPE corrected barrier reactant

CHD3

CH2D2

H + CD3 /D + CHD2

H + CHD2 /D + CH2D

2929 1496 3048 1279

3022 2114 975 2254 1258 1004

27.04 3127 3091 2951 1660 1435 1395 1161 777 700 406 116 1017i 24.04 22.37

21.68 2321/2963 2224/2321 2167/2223 1631/1274 1039/1265 1020/1064 880/961 601/640 546/525 373/375 100/85 998i/747i 18.44/19.58 22.14/23.25

2994 2158 1400 1002 1295 3047 1061 2255 1204 23.53 3102/3109 2271/2958 2169/2271 1633/1401 1262/1270 1119/1175 944/1056 653/714 579/573 386/389 104/89 1001i/750i 20.33/21.44 22.17/23.28

CH4

a Frequency is in cm−1; zero point energy (ZPE) and barrier height are in kcal/mol. bThe vibrational modes of CH4/CHD3/CH2D2 reactant are labeled in the traditional spectroscopic representation of normal modes, which follows the frequency noncrossing rule.87 The vibrational frequencies at transition state are labeled in the decreasing order.

Figure 1. Dissociation probabilities for CH4 on Ni(111) in its ground vibrational state (black ○) and first excited states in the symmetric stretching (v1, purple ◇), asymmetric stretching (v3, blue △), rock bending (v2, green □), and umbrella bending (v4, red ▽) modes.

The QCT calculations were carried out at multiple collision energies for both ground and excited vibrational states of methane and its two isotopomers. The rotational effects are not investigated because the experimental evidence suggested a minor role in the reaction.11,23 At low energies, over 106 trajectories are needed to achieve reasonable statistical error (below 1%), but the statistics improve as energy increases.

excitations in all vibrational modes are found to promote the reaction comparing to the ground vibrational state at given collision energies. Interestingly, the symmetric (v1) and asymmetric (v3) stretching modes have comparable and largest enhancements, while the two bending modes (v2 and v4) only increase the reactivity slightly. (The choice of the specific asymmetric stretching mode is unimportant as the three degenerate modes scramble quickly.) Our results are generally consistent with the available experimental data2 and also consistent with recent quantum46,47,61 and classical analysis.58,59 However, we note in passing that the QCT vibrational efficacies are generally smaller than experimental values and those obtained in our earlier quantum calculations. This difference has been noted before in other systems.80 A part of the difference is due to the tunneling nature of the reaction, but the classical representation of the dynamics presumably also plays a role. B. CHD3 Dissociation. Due to the inequivalence of the C− H and C−D bonds, none of the existing reduced-dimensional models is capable of treating bond-selective reactions in the dissociative chemisorption of CHD3. However, this inequivalence presents no problem in our 12D QCT model. To be consistent with the recent bond-selective experiment of Killelea et al.,19 we first calculated the dissociation probability of CHD3

III. RESULTS It should be noted at the onset that QCT is based on Newtonian mechanics, thus incapable of treating tunneling. Thus, it is only appropriate to study reactive events above the vibrationally adiabatic barrier. Although most existing experimental energies are below the barrier,2 in which tunneling is the dominant mechanism, it is our belief that the reaction mechanism and mode/bond selectivity should not change qualitatively above the barrier. The second concern about QCT is the so-called zero-point energy (ZPE) leaking due to classical intramolecular vibrational energy redistribution (IVR) that is more efficient than that in quantum mechanics. In other words, the vibrational energy deposited in a specific vibrational mode of the reactant may flow to other degrees of freedom before colliding with the surface. However, recent QCT studies of reactions involving 16129



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with its internal states thermalized at several temperatures, which serve as the baseline for bond selectivity. As shown in Table 2, the ratio of the CD3/CHD2 products is close to the

On the other hand, exciting both the CD3 symmetric and asymmetric stretching modes (v2 and v4) promotes the cleavage of the C−D bond, as shown in Table 2. Interestingly, the C− D:C−H ratios in this case are significantly larger than the C− H:C−D ratio when v1 is excited. This is similar to that in the HOD dissociation on Cu(111) studied earlier.81 In addition, the symmetric stretching mode (v2) is slightly more effective in enhancing the C−D bond cleavage than the asymmetric stretching mode (v4), which has a frequency that is 100 cm−1 larger. Unfortunately, there has been no experiment exploring these particular excitations, but our results are consistent with the recent ab initio direct dynamics analysis initiated from transition state, in which the final energy distribution in v2 mode is slightly larger than that in v4 mode considering degeneracy.60 Figure 2 compares the enhancement in the two different channels with excitations of various vibrational modes of

Table 2. Energies and Relative Product Yields for StateResolved and Thermal Ensembles of CHD3 Eviba ground state

v1 = 1

v2 = 1

v4 = 1

Tnozzle Tnozzle Tnozzle Tnozzle Tnozzle

= = = = =

550 600 700 830 900

K K K K K

0 0 0 0 0 statistical 8.64 8.64 8.64 8.64 8.64 8.64 6.04 6.04 6.04 6.04 6.04 6.04 6.44 6.44 6.44 6.44 6.44 6.44 1.07 1.41 2.20 3.44 4.21

Etransa

Etotala

22 22 24 24 26 26 30 30 33 33 proportion H:D 20 28.64 22 30.64 24 32.64 26 34.64 30 38.64 33 41.64 20 26.04 22 28.04 24 30.04 26 32.04 30 36.04 33 39.04 20 26.44 22 28.44 24 30.44 26 32.44 30 36.44 33 39.44 27.57 28.64 27.23 28.64 26.44 28.64 25.20 28.64 24.43 28.64

CD3/CHD2 ratio 0.145 0.173 0.196 0.206 0.209 0.333 9.33 5.34 3.32 2.22 1.23 0.896 0.0479 0.0725 0.100 0.118 0.142 0.161 0.0415 0.0583 0.0619 0.0953 0.124 0.147 0.260 0.265 0.270 0.280 0.287

a

Evib is the vibrational energy relative to the ground vibrational state, Etrans is the translational energy normal to the surface, Etotal is the total energy, and the unit is kcal/mol. The vibrational energies for thermal ensembles are taken from experiments.19

statistical limit of H:D (1:3), but slightly favorable to the CHD2 product. This is in good agreement with experiment, where no obvious preference of either the C−H or C−D bond cleavage was found under thermal conditions.19 The slight preference toward the C−D bond cleavage is somewhat surprising, although the effect is not so large. From the energetic perspective (Table 1), the C−H bond is expected to be slightly more reactive due to its lower ZPE-corrected barrier. This anomaly, which has also been seen in our earlier quantum mechanical study on the dissociative chemisorption of HOD on Cu(111),81 is difficult to understand at present. When the C−H stretching mode (v1) was excited to its first overtone, as shown in Table 2, there is a significant preference toward the C−H bond cleavage. At the translational energy of 20.0 kcal/mol, for example, the v1 excitation yielded a C−H:C− D cleavage ratio about 10:1. This is consistent with the recent ab initio direct dynamics study,60 in which the trajectories are started near the transition state, and with the experimental ratio of 30:1, although the latter was measured at a much lower collision energy.19

Figure 2. Dissociation probabilities for CHD3 on Ni(111) in its ground vibrational state (black ○) and first excited states in the C−H stretching (v1, blue ◇), CD3 symmetric (v2, red ▽), and asymmetric (v4, green □) stretching modes. Probabilities for the CD3 product and for the CHD2 product are shown in the upper and lower panels, respectively.

CHD3. It is clear that the C−H stretch (v1) excited state shows significant enhancement for the C−H bond cleavage, yielding the CD3 product. However, it barely changes the reactivity for the CHD2 channel and even inhibits this channel at high energies. Similarly, the CD3 stretch (v2 and v4) excited states significantly increase the reactivity for the C−D bond cleavage, but this results in almost no enhancement for the C−H bond cleavage. Supplying strong evidence of the bond selective nature of this reaction, our results share some similarities with previous investigations on the gas phase H + HOD80,82 and H/ Cl + CHD3 reactions.83 16130



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C. CH2D2 Dissociation. CH2D2 is an asymmetric top with nine vibrational normal modes, but its vibration is better described in the local mode picture.84 To this end, the vibrational basis set can be denoted as |n1n2n3n4⟩ with the quantum numbers for the C−H1, C−H2, C−D1, and C−D2 vibrations. Beck et al. have experimentally quantified the difference in reactivity for two nearly isoenergetic C−H stretching vibrational states of CH2D2, namely, the |1100⟩ and |2000⟩ states, on Ni(100).14 As expected, both states were shown to have a large reactivity increase over the ground state of CH2D2, especially at low energies.14 More interestingly, the sticking probability of |2000⟩ is several times larger than that of |1100⟩. This mode selectivity is striking, given the fact that | 2000⟩ is the less energetic of the two states. Similar observations have been also reported by Zare and co-workers on the Cl + CH2D2 reaction.85 The dissociation probabilities of CH2D2 in its |0000⟩, |1100⟩, and |2000⟩ states are compared in Figure 3. The enhancement

suggesting mode and bond selectivities are intrinsic properties of these reactions. The results presented in this work are particularly significant for bond selectivity because few quantum dynamical studies have been reported about the branching between two possible reaction channels. How then can these mode and bond selectivities be understood? In a pioneering publication, Halonen, Bernasak, and Nesbitt55 proposed a vibrationally adiabatic model to rationalize the mode selectivity in methane dissociative chemisorption. These authors demonstrated that localization near the transition state transforms the symmetric and triply degenerate antisymmetric stretching modes of CH4 into the proximal and distal C−H local modes. The former lowers its frequency significantly near the transition state due to “mode softening”, while the latter maintain their frequencies as spectator modes. Hence, excitation in the symmetric stretching mode will adiabatically lead to a lower effective barrier than that for the ground vibrational state, resulting in higher reactivity. Excitation in the antisymmetric stretching modes, however, can also promote the reaction, but only by vibrationally nonadiabatic transitions. While this adiabatic model provides valuable insights into the mode selectivity in the dissociative chemisorption of methane, it offers no quantitative information on the relative efficacy between the symmetric and antisymmetric stretching modes. More recently, Jackson and Nave have advanced this idea further by performing wave packet calculations using the reaction path Hamiltonian, which allowed a semiquantitative description of the mode selectivity in methane dissociative chemisorption.46,47 We have recently proposed the sudden vector projection (SVP) model,86 which offers an alternative perspective of the mode and bond selectivities in both gas phase and surface reactions. In contrast to the adiabatic model of Halonen et al.,55 our SVP model is based on the sudden approximation, in which the collision partners are assumed to have no IVR until impact. This is a reasonable approximation as the collision time is relatively short for direct reactions at the energy of interest. This sudden assumption is also borne out in QCT calculations of X + CH4 reactions77−79 and ab initio direct dynamics studies of methane dissociative chemisorption.58,59 In Figure 4, the C− H bond distance is plotted as a function of time, which shows very little change in the vibrational amplitude until CHD3 reaches the surface, no matter if the trajectory is reactive or

Figure 3. Total dissociation probabilities for CH2D2 on Ni(111) in its |0000⟩ (black ○), |1100⟩ (red ▽), and |2000⟩ (green □) states.

for the C−H bond cleavage by both excited states is quite large, in qualitative agreement with experiment.14 In addition, the |2000⟩ state is more efficient than the |1100⟩ state at low energies, again in good accord with experimental observations. At Ec = 10 kcal/mol, for example, the probability of the former is about two times larger than that of the latter. However, the difference diminishes as the collision energy increases. This trend is consistent with experiment, despite the fact that the difference there is more pronounced than what we found here. Another cautionary note, our calculations have been done on Ni(111) without correcting for tunneling and lattice effects while the experiment was carried out on Ni(100).14 The branching ratio between the C−H and C−D bond cleavages, which was not measured in the experiment of Beck et al.,14 is also obtained in our QCT calculations. As found in the Cl + CH2D2 reaction,85 the |1100⟩ and |2000⟩ states almost lead exclusively to the C−H bond broken product, namely, CHD2, at low energies. Again, the probability for CDH2 increases as the energy increases, in accord with the fact that IVR becomes larger at high energies.

IV. DISCUSSION In section III, the mode and bond selectivities in the dissociative chemisorption of CH4 and two partially deuterated methanes have been investigated using QCT on a DFT based global PES. Although not at the experimental energies, the QCT results capture the major trends in these systems. They are also consistent with the existing quantum dynamic models,

Figure 4. The variance of the C−H bond length as a function of reaction time in a few representative trajectories in the QCT simulation of the CHD3 (v1 = 1) dissociation on Ni(111). The black and red lines represent respectively reactive trajectories with C− H and C−D bond cleavage, while the blue line represents a nonreactive trajectory. The barrier region is indicated in the figure. 16131



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The CHD3 results can also be rationalized by the SVP model. As listed in Table 3, the overlap between the v1 mode of CHD3 and the reaction coordinate is 0.77 for the H + CD3 channel while it is 0.02 for the D + CHD2 channel. This large difference compares favorably with the QCT results that the C−H bond is selectively broken upon the excitation of the v1 mode. Similar consistency can be found for the CD3 stretching modes (v2 and v4) in CHD3. In particular, we note that the slightly higher efficacy of the symmetric stretching v2 mode is predicted by the SVP model as evidenced by the larger overlaps for this mode in both channels. It is interesting to note the SVP prediction that the umbrella bending mode (v3) and the CD3 rock mode (v6) show different enhancements in the H + CD3 and D + CHD2 channels, respectively, implying the bond selectivity may also exist for these two modes. Not surprisingly, the CH2D2 results can also be understood with the SVP model. For example, both the symmetric and asymmetric CH2 stretch modes (v1 and v6) of CH2D2 have significant overlaps with the reaction coordinate, with the former slightly larger. Although the relative efficacies of |1100⟩ and |2000⟩, which are respectively the first overtones of v6 (2v6) and the combination of v1 and v6 (v1+v6), cannot be directly predicted by the SVP model, the (v1+v6) state is expected to be more reactive than the 2v6 state due to the larger overlap of the v1 mode than that of v6. In addition, the preferential cleavage of C−H bond via the excitation of C−H vibration is also evidenced by the large v1/v6 differences of overlaps in the H + CHD2 and D + CH2D channels. It is interesting to point out that our SVP model predicts that the CD2 stretch modes would have properties similar to those of the CH2 stretch modes discussed above.

nonreactive, indicating that the vibrational energy is well localized in the C−H bond before arriving the barrier region. Within this sudden model, we proposed that the mode/bond selectivity is largely determined by the projection of the reactant vibrational vector onto the vector of the reaction coordinate at the transition state, namely, the mode associated with the imaginary frequency. This idea that “initial excitation of a motion that has a large component along the reaction coordinate should accelerate the reaction”26 is of course not new, but the SVP model provides a simple method to quantify the projections as discussed in our recent work.86 If the two vectors align well, its promotional effect is expected to be large. On the other hand, the promotional effect would be absent if the vectors are orthogonal. This SVP model has recently been tested for several atom−diatom reactions86 and successfully applied to the dissociative chemisorption of CH4 on Ni(111).61 A distinct feature of the SVP model is that both the symmetric and asymmetric stretching modes of CH4 are found to promote its dissociative chemisorption with comparable efficacies,61 in excellent agreement with experimental observations.2 As shown in Table 3, this makes sense as both modes are strongly coupled with the reaction coordinate. Table 3. Projections of the Reactant Vibrational and Translational Modes onto the Reaction Coordinate at the Transition State mode

a

v1 v2 v3 v4 v5 v6 v7 v8 v9 translational

CHD3

CH2D2

CH4

H + CD3/D + CHD2

H + CHD2/D + CH2D

0.40 0.24 0.31 0.21

0.77/0.02 0.08/0.44 0.06/0.42 0.007/0.36 0.35/0.23 0.04/0.15

0.55/0.03 0.07/0.53 0.27/0.06 0.04/0.31 0.39/0.33 0.53/0.004 0.08/0.32 0.01/0.51 0.33/0.03 0.23/0.29

0.24

0.23/0.28

V. CONCLUSIONS In this work, we have examined mode and bond selectivities in the dissociative chemisorption of methane and two of its partially deuterated isotopomers on Ni(111). Due to the formidable computational costs associated with a full-dimensional quantum treatment, the dynamics is characterized by quasi-classical trajectories on a twelve-dimensional potential energy surface developed with a large number of density functional theory points. Despite the inability of the classical model to characterize dynamics below the reaction barrier, our results are in qualitative agreement with all available experimental data on mode and bond selectivities, thus confirming the accuracy of the potential energy surface. In addition, these results are rationalized by the newly proposed sudden vector projection model, which attributes the efficacy of a particular reactant vibrational mode in promoting the particular reaction pathway to its projection onto the reaction coordinate at the corresponding transition state. These theoretical studies provide in-depth understanding of the mode and bond selectivities in this important heterogeneous reaction.

a

The vibrational modes of CH4/CHD3/CH2D2 reactant are defined as in Table 1.

It is our opinion that the adiabatic and sudden models provide complementary viewpoints of the mode selectivity in reactions. However, the methane dissociation reaction discussed here is probably closer to the sudden limit due to the slow IVR in methane. In contrast to the adiabatic model, nonadiabatic transitions are not needed in the SVP model to explain the comparable efficacies of the two stretching modes in promoting the reaction. In fact, the necessity to invoke strong nonadiabaticity to explain the experimental finding argues against the vibrational adiabaticity that forms the very basis of the adiabatic model. The recent direct dynamics studies also led Sacchi et al. to conclude that nonadiabatic coupling is not necessary to explain the mode selectivity.58,59 We have applied the SVP model to the three systems studied here, and the results are summarized in Table 3. As mentioned earlier, the stretching modes of CH4 give the largest overlaps with the reaction coordinate mode at the transition state, while the bending modes have relatively small overlaps. The slightly smaller overlap for the v4 mode, which is consistent with experimental observations,2 is due to the average over its three degenerate modes.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 16132



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ACKNOWLEDGMENTS This work was funded by the National Science Foundation (CHE-0910828 to H.G.).

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