and Bond-Selective Chemistry on Metal Surfaces: The Dissociative

Article pubs.acs.org/JPCC

Mode- and Bond-Selective Chemistry on Metal Surfaces: The Dissociative Chemisorption of CHD3 on Ni(111) Han Guo and Bret Jackson* Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003, United States ABSTRACT: A quantum approach based on an expansion in vibrationally adiabatic eigenstates is used to explore CHD3 dissociation on Ni(111). Symmetric stretch vibrations are shown to have larger efficacies for promoting reaction and bond selectivity than antisymmetric stretches. Mode softening, associated with a localization of vibrational energy on the reacting bond, correlates adiabatically with the symmetric stretch. This lowers the barrier on that vibrationally adiabatic reaction path. At energies below these barriers, reaction occurs via nonadiabatic transitions to lower-energy vibrational states at the avoided crossings. This sudden behavior preserves energy localization on the reactive bond and converts vibrational energy into bond breaking. One of the antisymmetric stretches can typically not couple to the other states due to symmetry, eliminating these pathways. The ν1 stretch has a large efficacy and can give 100% C−H cleavage selectivity. Both CD3 stretches have reasonable efficacies, and both promote C−D relative to C−H cleavage. These effects are stronger for the symmetric stretch. We observe some minor surface-induced intramolecular vibrational energy redistribution (IVR), where excitation of C− H or C−D stretches can promote C−D or C−H cleavage, respectively. Our results are consistent with experiment with regard to the magnitude of the dissociative sticking and the increase in selectivity with excitation of the ν1 stretch.

I. INTRODUCTION Controlling the outcome of chemical reactions is a major theme of chemistry. One way to do this is to selectively excite different types of vibrational motion in the reactant molecules. In gasphase reactions of H with HOD, for example, it was demonstrated that laser excitation of either the O−H or O− D stretch would selectively, and almost exclusively, break that bond, forming H2 + OD or HD + OH products, respectively.1,2 Another well-studied polyatomic molecule exhibiting laserinduced bond selectivity is methane.3 Experimental studies of the gas-phase reactions of CHD3, CH2D2, and CH3D with Cl have demonstrated that excitation of different vibrational modes in the methane molecule can selectively break bonds and modify product state distributions.3−11 In this paper we focus on bond selectivity in the dissociative chemisorption of methane on the surface of a metal. As the rate-limiting step in the steam reforming of natural gas,12 this reaction has received considerable scientific scrutiny.12−15 Experiments have demonstrated that when CH4 dissociatively chemisorbs on Ni(111) a single C−H bond breaks as the molecule collides with the surface, leaving chemisorbed H and CH3 fragments.16,17 Electronic structure studies based on density functional theory (DFT) find that the barriers to this reaction are large, on the order of 1 eV for smooth Ni surfaces.18−22 Thus, the probability that methane chemisorbs on a bare surface, S0 (the zero-coverage sticking probability), can be very small at typical collision energies, and S0 increases strongly with increasing translational energy. DFT studies have also shown that the barrier for dissociative chemisorption can vary with the vibrational displacement of the metal atom over which the methane dissociates,20−23 and this has been related to the strong variation in S0 with substrate temperature observed in experiments.13−15 Vibrational excitation of the © XXXX American Chemical Society

incident methane can also significantly enhance S0 for this strongly activated late-barrier system, and this behavior is nonstatistical.13−15 For example, on Ni(100), adding 0.36 eV to the molecule by exciting the symmetric stretch leads to a greater increase in reactivity than putting the same amount of energy into the incident translational energy,24 Ei. Adding 0.37 eV by exciting the antisymmetric stretch increases S0 by a smaller amount than if the same amount of energy were put into translation.25 These effects are often expressed in terms of a vibrational efficacy η=

E (0, S0) − E i(v , S0) ΔE i = i ΔEv ΔEv

(1)

where ΔEi is the increase in Ei necessary to give the same S0 as increasing the vibrational energy by ΔEv. In eq 1, Ei(v, S0) is the incident translational energy giving a sticking probability of S0 for an initial vibrational state v, and v = 0 is the ground state. On Ni(100), η = 1.4 and 0.94 for the symmetric and antisymmetric vibrations, respectively.24,25 In addition to this mode specificity, bond-selective chemistry has been observed for these reactions. For the dissociative chemisorption of CHD3 on Ni(111), excitation of the ν1 stretch preferentially breaks the C−H bond relative to a C−D bond by more than a 30:1 ratio.26 Similarly, laser excitation of the C−H stretching modes of CHD3, CH2D2, and CH3D leads to a selective breaking of that bond for dissociation on Pt(111).17 Special Issue: Steven J. Sibener Festschrift Received: January 28, 2015 Revised: March 5, 2015

A

DOI: 10.1021/acs.jpcc.5b00915 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

in the harmonic approximation. We write our PES, in the reaction path coordinates s and {Qk}, as

We have recently developed a quantum mechanical approach that allows us to compute S0 for this reaction. On the basis of the Reaction Path Hamiltonian27,28 (RPH), our method treats all 15 degrees of freedom (DOFs) of the methane molecule and includes the effects of lattice motion. This has allowed us to compare directly with experiment for the first time, helping to elucidate the origins of the vibrational enhancement, mode specificity, and the strong variation in S0 with substrate temperature observed for these reactions.29−33 In combination with other recent high-dimensional quantum studies34 and QCT35,36 (quasi-classical trajectory) and AIMD37−40 (ab initio molecular dynamics) studies, much has been learned about these reactions in the past few years. In this paper we use our methods to examine bond selectivity in the dissociative chemisorption of CHD3 on Ni(111). Our approach has several unique features that make it a good choice for this study. First, the full dimensional treatment of the vibrational modes of methane allows us to distinguish between their different behaviors, e.g., the differing efficacies of symmetric vs antisymmetric stretches. Our quantum approach allows for a rigorous treatment of the large amount of vibrational zero point energy (ZPE) in the molecule. Our vibrationally adiabatic basis allows us to observe how these vibrational modes evolve as the molecule moves along the reaction path, and the nonadiabatic couplings describe how vibrational energy moves between different modes of the molecule. In Section II we briefly describe our quantum model for dissociative chemisorption. All parameters describing our potential energy surface (PES) and the phonon coupling are computed via DFT. In Section III we use this to examine the dissociative chemisorption of CHD3 on Ni(111). The effects of vibrational excitation on S0 and C−H vs C−D bond cleavage are examined. Our results are summarized in Section IV.

14

V = V0(s) +

k=1

ℏ H=K+V=− 2

∑ i=1

(3)

14

xi = ai(s) +

∑ Li ,k(s)Q k

(4)

k=1

where the ai(s) describe the geometry of the molecule on the reaction path at point s. Converting to our reaction path coordinates, the quantum form of our Hamiltonian is28 H=

1 2 1 ps + V0(s) + H vib − (bssps2 + 2ps bssps + ps2 bss) 2 4 1 − (ps πs + πsps ) (5) 2

where 14

H vib =

⎤ ⎡1 2 1 2 Pk + ωk (s)Q k2 ⎥ ⎦ 2 2 k=1

∑ ⎢⎣

(6)

the momenta conjugate to s and Qk are ps and Pk, respectively, and 14

bss =

14

14

∑ Q kBk ,15(s) and πs = ∑ ∑ Q kPB j k , j (s ) k=1

(7)

k=1 j=1

The vibrationally nonadiabatic couplings are given by 15

Bk , j (s) =

∑ i=1

2

∂ + V (x1 , x 2 , ..., x15) ∂xi2

1 2 ωk (s)Q k2 2

Our first approximation is thus to ignore any anharmonic terms in V. The eigenvectors from our normal mode calculations, Li,k(s), define the transformation between the xi and our reaction path coordinates

II. REACTION PATH MODEL FOR DISSOCIATIVE CHEMISORPTION For a rigid surface, our Hamiltonian is 2 15

∑

dLi , k ds

Li , j(s)

(8)

To derive eq 5, we expand H to first order in bss and πs. The operator πs describes energy flow between all modes k and j, through the Coriolis couplings Bk,j. The operator bss describes energy flow between the vibrational modes k and motion along the reaction coordinate, due to the curvature, with couplings Bk,15. Our “15th eigenvector” is the normalized gradient vector describing motion along the MEP (the “mode” with the imaginary frequency at the TS). An earlier study that included in H all terms through second order in bss showed these higherorder terms to be unimportant.32 This was consistent with a classical study that found similar results when comparing the exact with the first-order form of the RPH kinetic energy operator.50 We use a close-coupled wave packet approach to describe our total molecular wave function, writing 29,30,32

(2)

where the xi are the mass-weighted Cartesian coordinates of the CH4 nuclei. To construct our PES, V, we first locate the reaction path, or minimum energy path (MEP), from the transition state (TS) to the reactant and product configurations. We use the DFT-based Vienna ab initio simulation package (VASP), developed at the Institut für Materialphysik of the Universität Wien,41−45 to compute total energies. A four-layer 3 × 3 supercell with periodic boundary conditions represents the metal as an infinite slab, with a large vacuum space above the slab to separate the repeated images. This supercell, larger than in our previous studies, corresponds to a methane coverage of 1/9 ML. The interactions between the ionic cores and the electrons are described by fully nonlocal optimized projector augmented-wave (PAW) potentials,45,46 and exchange-correlation effects are treated using the Perdew−Burke−Ernzerhof (PBE) functional.47,48 Additional details can be found in earlier work.22,49 The distance along the MEP is s, where (ds)2 = 2 ∑15 i=1(dxi) , and s = 0 at the TS. At several points along s we compute the total energy, V0(s). We also compute and diagonalize the force-projected Hessian to find the 14 normal vibrational coordinates Qk and corresponding frequencies ωk(s) that describe displacements orthogonal to the reaction path at s,

Ψ(t ) =

∑ χn (s; t )Φn({Q k}; s) n

(9)

where the Φn are eigenfunctions of Hvib, with eigenvalues ∑k ℏωk(s) (nk + (1/2)), and n labels the vibrational state corresponding to the set of quantum numbers {nk}. These vibrationally adiabatic Φn are products of one-dimensional harmonic oscillator eigenfunctions that depend parametrically on s. Given Ψ(t) and our Hamiltonian of eq 5, the coupled B


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The Journal of Physical Chemistry C equations of motion for the wave packets, χn(s; t), are of the form29 iℏχ0̇ (s ; t ) =

the ground, 1-quantum, and 2-quanta states add up to a total of 78 coupled channels. Finally, we note that our notation is a bit different from earlier papers. Commutation of the operators in eqs 10 and 11 leads to our earlier form. Initially, all of the wave packets χn are zero, except for the one corresponding to the initial state, ni. Standard techniques29,30 are used to propagate the wave packets in time, and the reactive flux at large positive s is Fourier transformed in time on each channel n, giving both vibrational-state-resolved and energy-resolved reaction probabilities for all incident energies Ei included in the initial wave packet.52,53 The methane is initially in the vibrational ground state or has one or two quanta of vibrational energy in one of the nine asymptotically bound modes. The asymptotically unbound modes, corresponding to X and Y, which give the location of the molecular center of mass over the surface unit cell, and molecular rotation follow the MEP in the entrance channel. X and Y remain almost directly over the top site (X = 0 and Y = 0 in our coordinate system), where the barrier is lowest, up to the TS. The result of our wave packet calculation is thus the rigidsurface top-site reaction probability, which we denote P0(Ei, ni; X = Y = 0), with the rotation of the molecule in the entrance channel treated adiabatically. To compute S0 we average P0 over surface impact sites, correct the rotational treatment, if necessary, and include the effects of lattice motion. Motion along X and Y is slow on collision time scales, given the relatively large total molecular mass, the large collision energies, and our normal incidence conditions. Assuming that there is no steering of the incident methane along X and Y, we average P0 over all impact sites in the surface unit cell, using the following “energy-shifting” approximation to estimate P0 for impacts away from the top site

⎛1 2 ⎞ ⎜ p + V ⎟ eff,0⎠χ0 (s ; t ) ⎝2 s ℏ2 ⎡ d 2 d d d2 ⎤ + ∑ ⎢fk 2 + 2 fk + 2 fk ⎥χk (s ; t ) 4 ⎣ ds ds ds ds ⎦ k (10)

iℏχk̇ (s ; t ) = +

⎛1 2 ⎞ ℏ2 ⎡ d 2 d d ⎜ p + V ⎟χ + ⎢fk 2 + 2 fk k eff, ⎝2 s ⎠k 4 ⎣ ds ds ds

d2 ⎤ f ⎥χ (s ; t ) + ds 2 k ⎦ 0

⎡

∑ ⎢⎣gkq d q

ds

+

d ⎤ g ⎥χ + ... ds kq⎦ q

(11)

The subscript n = 0 denotes the vibrationally adiabatic ground state, and the subscripts n = k and n = q label excited states with a single quantum of vibrational excitation in mode k or q, respectively. We also include in our basis all states with two vibrational quanta excited, χkq. In eq 11 we have not explicitly written the terms describing the coupling of χk to the χkq or the equations of motion for the two-quanta wave packets, χkq, because they are lengthy and straightforward to derive. The coupling function f k, where fk (s) =

ℏ Bk,15(s) 2ωk(s)

(12)

links states differing by one quantum of energy in ωk, while gkq, where ⎡ ℏ2 ⎢ ωq(s) Bk , q (s) − gkq(s) = 4 ⎢⎣ ωk(s)

⎤ ωk(s) Bq , k (s)⎥ ⎥⎦ ωq(s)

P0(E i , n i ; X , Y ) ≈ P0[E i − ΔV (X , Y ), n i ; X = Y = 0]

(13)

(15)

couples states with the same number of excited vibrations but exchanges mode k for q. The wave packets evolve on coupled vibrationally adiabatic potentials 14

Veff, n(s) = V0(s) +

⎛

∑ ℏωk(s)⎝nk + ⎜

k=1

1 ⎞⎟ 2⎠

ΔV is the increase in barrier height at (X, Y) relative to the top site. We can use eqs 3 and 4 to compute ΔV for small displacements away from the reaction path at the TS or simply translate the molecule and recompute the total energy. The results are similar for small displacements, and the barrier height increases rapidly with this displacement. Recent AIMD studies confirm this sudden behavior and our methods.32 These same studies also suggest that rotational dynamics in the entrance channel are closer to sudden than adiabatic.32,37 We have developed an approach for estimating S0 in the rotationally sudden limit that is similar to our treatment of X and Y, and we consider that limit in this paper.32 Finally, our methods for introducing the effects of lattice motion are well documented elsewhere.54,55 We average P0 over all displacements and momenta normal to the surface of the metal atom over which the methane dissociates, for a substrate temperature T. Displacement of the metal atom changes the height of the barrier to dissociation, and DFT is used to determine the magnitude of this effect. The momentum of the metal atom determines the relative collision velocity.

(14)

where, for example, Veff,0 is simply the MEP with ZPE corrections. The parametric dependence of the Φn on s results in couplings that depend upon the momentum and kinetic energy of the molecule, and curve crossing becomes increasingly likely at higher velocities, as well as for larger values of the coupling functions. In earlier studies our basis set expansion treated only the nine modes that were bound asymptotically in the reactant channel, i.e., the bends and stretches of gas-phase methane. The remaining five modes have ωk(−∞) = 0 and describe translation parallel to the surface and rotation of the molecule when it is far from the metal. Nearer the TS they become hindered types of motion. In this study we now also include the two modes with the highest frequencies near the TS in our basis. The remaining three modes have frequencies close to zero over most of the reaction path and correspond to motions like the azimuthal orientation of the reacting C−H bond or rotation of the nonreacting methyl group. Our DFT studies have shown that the PES varies weakly with these types of motion.22 Our PES, eq 3, is thus “flat” along these coordinates, and we ignore them, consistent with some recent quantum studies by other groups.34,51 Given these 11 vibrational modes,

III. RESULTS On Ni(111), at the TS for methane dissociation, the carbon atom is roughly over the top site; the dissociating hydrogen is angled toward the surface, 133° from the surface normal; and the nonreacting methyl group is angled away from the surface. The barrier height is V† = V0(0) = 1.005 eV, relative to the energy of the molecule and metal slab at infinite separation. C


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The Journal of Physical Chemistry C There are four possible, equally probable, orientations of CHD3 at the TS, illustrated in Figure 1.

Figure 1. Four possible orientations of CHD3 at the transition state on Ni(111). C is gray; D are blue; H is white; and the Ni are green.

In Figures 2 and 3 we plot the ωq(s) along the reaction path for these configurations, as well as for CH4, for comparison. Figure 3. Energies of the normal modes of CHD3, for the symmetric and asymmetric C−D cleavage configurations, along the reaction path s, for dissociation on Ni(111).

D cleavage of CHD3, the reaction path is symmetric with respect to reflection through a plane lying perpendicular to the surface and along the dissociating bond, and the normal modes are either symmetric (A′) or antisymmetric (A″) with respect to reflection through this plane. We label the A′ modes 1′−8′ and the A″ modes 1″−6″. This symmetry is important, as f k is only nonzero for the A′ modes, and the gkq only connect states of the same symmetry. For asymmetric C−D cleavage (configurations 3 and 4), there is no symmetry, and the f k and gkq are in general nonzero. However, the two cases are related by this reflection and thus have identical ωq(s), couplings, and behavior. It is useful to consider the mode softening that occurs as the molecule approaches the TS. For CH4 far above the metal, the 4 equiv C−H stretches can be combined into four normal modes with similar energies: one symmetric stretch (3′) and three antisymmetric stretches (1′, 2′, 1″). As the molecule approaches the TS, the reactive C−H bond, angled toward the metal, weakens. In the local mode picture we then have one unique lower-frequency C−H stretch and three relatively unperturbed higher-frequency C−H stretches. In the normal mode picture these four vibrations combine to give a single lower frequency mode comprised primarily of the softened vibration, while the three relatively unperturbed stretches combine to form three approximately degenerate nonlocal stretches. The vibration of the softened mode is thus localized on the reacting C−H bond, and this mode correlates adiabatically with the singly degenerate symmetric stretch. For the three higher-frequency near-degenerate modes, the vibration is localized on the nonreacting methyl group, and these modes correlate adiabatically with the triply degenerate antisymmetric stretch. This behavior is typical of CH4 dissociation on the Pt and Ni surfaces we have examined33 and was initially described in a simple model for methane dissociation on a flat surface.56 It has

Figure 2. Energies of the normal modes of CH4 and the symmetric C−H cleavage configuration of CHD3, along the reaction path s, for dissociation on Ni(111).

When the molecule is far above the surface (large negative s), nine of the frequencies are nonzero. For CHD3 these are the C−H symmetric stretch, ν1, the doubly degenerate CD3 antisymmetric stretch, ν4, the CD3 symmetric stretch, ν2, and the bending modes, ν5, ν6, and ν3. The interaction with the surface removes all degeneracies. The remaining five (asymptotically unbound) modes, similar for all four configurations, are shown only for the case of symmetric C−H cleavage. For the symmetric C−H cleavage and symmetric C− D


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This softening also modifies the barrier heights, Veff,n(0), along the excited-state vibrationally adiabatic pathways.58 In Table 1 we see that for molecules in the ν1 state the barrier to cleavage of the C−H bond is significantly less than those for C−D cleavage, which remain similar to the ground-state values. Thus, in the absence of any vibrationally nonadiabatic effects, we expect that excitation of the ν1 symmetric C−H stretch should significantly enhance C−H cleavage relative to C−D cleavage and thus also increase S0. Excitation of the ν2 symmetric C−D stretch should also significantly enhance S0 in the vibrationally adiabatic limit, but by increasing both C−D cleavage and C−H cleavage. The antisymmetric stretches do not significantly soften, for reasons discussed, and the vibrationally adiabatic barriers for ν4 are similar to those in the ground state. In general, these effects are larger for C−H cleavage than C−D cleavage: as the C−H vibrational frequencies are larger than the C−D frequencies by roughly √2, so are mode softening and the decrease in activation energy. In Figures 4 and 5 we plot P0 as a function of the incident translational energy, Ei, for the C−H cleavage and symmetric

also been observed in studies of the gas-phase Cl + CH3D reaction.6,8 We see the same behavior here for CHD3, for both C−D cleavage configurations of Figure 3: the single symmetric CD3 stretch correlates with the breaking C−D bond and the ν2 mode softens, while the two relatively unperturbed C−D bonds correlate with the doubly degenerate ν4 antisymmetric CD3 stretch. For the C−H cleavage configuration in Figure 2, the ν1 stretch (1′) is already localized, asymptotically, on the reactive bond, and it softens, trivially. Thus, as the molecule approaches the surface, the symmetric stretches evolve from nonlocal modes into vibrations entirely localized on the reactive bond. At the same time, the reactive bond ceases to contribute to the antisymmetric stretches. This localization is preserved as we transition between vibrationally adiabatic states at the avoided crossings. For example, for the C−H cleavage configuration for CHD3, the 2′ mode corresponds to vibration of the reactive C−H bond between the 1′−2′ and 2′−3′ crossings. The 3′ becomes the reactive C− H stretch between the 2′−3′ and 3′−4′ crossings, etc. Thus, within our adiabatic representation, the Coriolis couplings, Bqk, preserve this energy localization on the reactive bond as we approach the TS and play a major role in reactivity. Mode softening lowers the activation energy for dissociation, Ea. This is the ZPE-corrected barrier height, equal to Veff,n evaluated at the TS (s = 0), for the vibrationally adiabatic ground state. For dissociation on Ni(111), Ni(100), Pt(111), Pt(100), and the stepped Pt(110)-(1 × 2), we have found that this mode softening lowers the activation energy by more than 0.1 eV relative to V†.22 For CH4 on Ni(111), Ea = 0.866 eV, and in Table 1 we list Ea for the three reaction configurations of Table 1. Activation Energies for CHD3 Dissociative Chemisorptiona activation energy (eV)

ground state

ν1

ν4

ν2

symmetric C−H symmetric C−D asymmetric C−D

0.860 0.907 0.905

0.762 0.904 0.904

0.857, 0.838 0.907, 0.891 0.903, 0.890

0.780 0.796 0.793

a

Equal to Veff,n(0). For ν4, results are given for both components.

Figure 4. Single-site rigid-lattice reaction probabilities, for the symmetric C−H cleavage configuration of CHD3 dissociation on Ni(111). Results are shown for the ground state (gs) and four excited states, as indicated, and several levels of nonadiabatic coupling: no coupling (solid), Bq,15 only (filled circles), Bq,k only (open circles), and full (xxx).

CHD3. We see that the ZPE-corrected barrier for C−H cleavage is lower than that for C−D cleavage by about 0.05 eV. This is roughly the difference between the ZPE in the C−H stretch (ν1) and the ZPE in either of the CD3 stretches (ν2 or ν4). Thus, the C−H bond is more reactive than the C−D bonds, and we expect the ratio of C−H:C−D cleavage for ground-state CHD3 to be somewhat larger than a statistical 1:3. This has been observed experimentally for CHD3 on Ni(111), where the “laser off” cleavage ratio increases from the statistical 1:3 as the nozzle temperature is lowered, and ground-state molecules contribute more to S0.26 We note that our activation energies are consistent with those in the QCT study of Guo and co-workers,35 accounting for the fact that their barriers are about 0.1 eV larger than ours due to their use of a smaller 2 × 2 supercell.21 As we increasingly deuterate methane, S0 for the vibrational ground state should decrease, due to the decrease in ZPE. For CD4 on Ni(111), we find that Ea = 0.905 eV, higher than for CH4. This is consistent with experimental measurements on Ni(111)16 and Pt(111),57 where the sticking curves for CD4 are shifted to higher energies relative to those for CH4. We note that QCT studies reproduce this behavior,36 which is due to the change in ZPE with deuteration, and not tunneling.

C−D cleavage configurations of CHD3, respectively. In many cases the behavior of the reacting molecules is clearly not vibrationally adiabatic, and we consider various levels of coupling in the figures to illustrate this. Results are shown for the vibrationally adiabatic limit, where we set both Bq,15 and Bq,k equal to zero. The shifts between the curves along the energy axis for different initial states correspond to the differences in Veff,n(0) in Table 1. The reaction probability drops rapidly for Ei below these activation energies, as tunneling becomes the only mechanism for reaction. When we add the curvature couplings, Bq,15, we couple the vibrationally excited states to the adiabatic ground state, converting the asymptotic vibrational energy ωq(−∞) into translational motion along the reaction path. This corresponds to bond breaking at the TS, and over-the-barrier reaction is possible for energies down to Ei = Veff,q(0) − ωq(−∞). This low-energy tail in P0 is clearly seen for the 1′ and 3′ states in Figure 4, but the values for P0 can be small. Bq,15 also couples the ground and the 1-quantum states to 1- and 2E


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up over-the-barrier pathways for reaction. A molecule that follows this cascading pathway preserves the energy localization on the reactive C−H or C−D bond. For example, for C−H cleavage, if we initially excite the ν1 (1′) mode, a local C−H stretch, following the 1′ to 2′ to 3′ to 4′, etc. pathway keeps the vibrational energy localized on this reacting bond, enhancing C−H cleavage. This is vibrationally sudden behavior. For the C−D cleavage configurations, if we excite ν2, the nonlocal symmetric C−D stretch, the vibrational energy localizes on the reactive C−D bond, which softens, as we move along the reaction path. Hopping to the next lowest surface at the avoided crossings keeps the vibrational energy localized on this reacting bond, giving enhanced C−D cleavage. Note that for the symmetric C−H and C−D cleavage configurations the A″ modes cannot participate in the low Ei reaction mechanisms due to the curvature couplings, as these are equal to zero. The Coriolis terms do allow for transitions between the A″ states, but these are few and widely separated. For the 1″ initial state, we see enhancement at low Ei and a deviation from adiabatic behavior, only for values of P0 around 10−3 and smaller. Before combining and averaging over the configurations of Figure 1, it is useful to consider the impact site and latticeaveraged sticking for each configuration separately. In Figures 7

Figure 5. Single-site rigid-lattice reaction probabilities, for the symmetric C−D cleavage configuration of CHD3 dissociation on Ni(111). Results are shown for the ground state (gs) and four excited states, as indicated, and both full-coupling and the adiabatic limit.

quanta states, respectively, and the result is a decrease in P0 at higher Ei as amplitude is transferred to these states, i.e., as motion along the reaction path is converted into vibration orthogonal to the path. This is the dominant effect of the curvature coupling for all CHD3 configurations and also for CH4 dissociation. When we add the Coriolis couplings, Bq,k, amplitude can be transferred between different vibrationally adiabatic states. For a molecule in a vibrational state n, an important mechanism for reaction at Ei below Veff,n(0) is to convert vibrational energy into translational motion along the reaction path, by transferring amplitude from one vibrationally adiabatic state to another of lower energy. In Figure 6 we plot some of the Bq,k(s)

Figure 7. Dissociative sticking probabilities for CHD3 in either the 1′ or the ground state (gs), on Ni(111), for three of the transition state configurations of Figure 1.

Figure 6. Coriolis couplings for the C−H cleavage configuration of CHD3/Ni(111).

for the case of symmetric C−H cleavage. This coupling is largest at the avoided crossings, where the two modes involved exchange character, and we focus on these in Figure 6. As a molecule in the ν1 (1′) state approaches the surface, it can “hop” to the 2′ component of ν4, for s ≈ −1.3 amu1/2 Å. After this crossing, the 2′ vibration resembles the C−H stretch. We can then have transitions from 2′ to 3′, 3′ to 4′, and so on. This “cascade” effect can convert a significant amount of energy into bond breaking at the TS. It is clear in Figures 4 and 5 that this mechanism can significantly increase P0 at lower Ei by opening

Figure 8. Dissociative sticking probabilities for CHD3 in the 1″, 2′, 3′, or the ground state (gs), on Ni(111), for two of the transition state configurations of Figure 1. F


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The Journal of Physical Chemistry C and 8 we plot S0 for three TS configurations, for molecules initially in either the ground or one of the stretch vibrational states, for CHD3 incident on Ni(111) at 90 K. The groundstate dissociative sticking probabilities behave as the activation energies of Table 1 would suggest: the sticking is roughly the same for the C−D cleavage configurations, while the sticking probability for C−H cleavage is larger and essentially shifted to lower Ei by about 0.05 eV, the difference in Ea. At large collision energies C−H and C−D cleavage probabilities become about the same (per bond). In Figure 7 the expected enhancement of C−H cleavage with excitation of the ν1 stretch (1′) is clearly seen, for the reasons discussed. In Figure 8, we see similar behavior for ν2: excitation of the CD3 symmetric stretch (3′) significantly enhances the probability for C−D cleavage. The effect appears to be much stronger for C−H stretch excitation, but the amount of energy in the vibration is larger. At S0 = 10−4, the efficacies for ν1 promoting C−H cleavage for the C−H cleavage configuration and for ν2 promoting C−D cleavage for the symmetric C−D cleavage configuration are similar: η = 0.85 and 0.81, respectively. The 2′ component of the antisymmetric CD3 stretch also increases S0 for C−D cleavage by a substantial factor. This arises from the B2′,3′ Coriolis coupling that transfers amplitude to the highly reactive 3′ state, where the vibration becomes localized on the dissociating C−D bond. We also see surface-induced IVR. In Figure 7 we observe a minor enhancement of C−D cleavage with excitation of ν1, which is initially localized on the C−H stretch. In Figure 5 this clearly results from a small Coriolis coupling between ν1 and the CD3 stretches. This only becomes important at very low Ei where S0 ≈ 10−4 or less. At higher energies, the C−D sticking for molecules initially in the ν1 state follows more adiabatic behavior. In Figure 8 we see a similar enhancement in C−H cleavage with excitation of the 2′ and 3′ CD3 stretches. Again, there is adiabatic behavior at higher energies, and these surfaceinduced IVR effects become important only at smaller values of Ei and S0, where there are no over-the-barrier adiabatic pathways available. This surface-induced IVR is stronger for the CD3 stretches than for the C−H stretch because the corresponding Coriolis couplings are larger. This can be seen in Figure 2 where the 2′ and 3′ modes are on the “cascading pathway” for C−H cleavage, while in Figure 3 the 1′ mode is not on the pathway for C−D cleavage. Symmetry is clearly very important. Molecules excited to the A″ states exhibit vibrationally adiabatic behavior at most energies, and given minimal mode softening, there is little increase in S0 relative to the ground-state value. At very low Ei, where S0 is small, there is some enhancement due to nonadiabatic transitions to lower-energy A″ states. This contributes to the tendency for symmetric stretches to have larger efficacies for promoting reaction than the antisymmetric stretches. First, the singly degenerate symmetric combination correlates with the softened mode, where the vibration becomes localized on the reactive bond. The antisymmetric combinations are 2- and 3-fold degenerate for CHD3 and CH4, respectively. One of these is typically of A″ symmetry and does not significantly couple to the reaction coordinate.29,30,32,33 Another component typically couples strongly to the symmetric stretch through the Coriolis coupling. For CH4 in Figure 2, this is the 2′ state, which couples strongly to the 3′ state early in the entrance channel, around s = −4.5 amu1/2 Å.29,30,32,33,59 This coupling is responsible for the relatively large vibrational efficacy observed for the antisymmetric stretch state. For CH4, the third antisymmetric component couples to the symmetric

stretch less strongly. The result, when the degeneracy is averaged over, is that the vibrational efficacy for the antisymmetric stretch is smaller than for the symmetric stretch, though typically still substantial. Our earlier calculations have predicted that the symmetric stretches have larger efficacies than antisymmetric stretches for promoting dissociation of CH4 on Ni(100)29 and Ni(111),30 and this has been observed experimentally on Ni(100).24,25 Guo’s Sudden Vector Projection (SVP) model,60 when applied to these metals, also predicts a larger enhancement for the symmetric over the antisymmetric stretch.32,34 Similar behavior has been observed in gas-phase reactions of Cl with CH461 and CH3D.6 In Figure 9 we plot the sticking probability for either C−H cleavage or C−D cleavage, for ground-state CHD3 and three

Figure 9. Sticking probability for either C−H or C−D cleavage, for CHD3 molecules in either the ground state (gs) or one of the vibrationally excited states indicated.

vibrationally excited states. For C−H cleavage, this is just the symmetric C−H configuration result divided by 4. For C−D cleavage this is the sum over the three C−D configurations, divided by 4. The results for ν4 are an average of the two component modes. For molecules initially in the ground state, we see that at high energies C−D cleavage is favored over C−H cleavage, approaching the statistical ratio of 3:1. However, at lower Ei, the smaller activation energy for C−H cleavage becomes important, and it is more likely that that bond will break. As expected, excitation of the ν1 C−H stretch significantly enhances C−H cleavage. Near saturation, at high energies, C−D cleavage is still favored; however, at energies below the vibrationally adiabatic barrier heights the effect is large, and we see almost 100% C−H selectivity. Excitation of the ν2 and ν4 C−D stretches greatly increases the probability for C−D cleavage relative to the ground state, by several orders of magnitude at lower energies. This effect is larger for ν2 over ν4, for the reasons discussed. Also, as predicted, the increase in both reactivity and selectivity for ν1 and C−H is larger than for ν2, ν4, and C−D. This bond selectivity is clearer in Figure 10, where we plot the C−H:C−D cleavage ratio for the cases in Figure 9. Utz and co-workers have measured this ratio for CHD3 molecules incident on a 90 K Ni(111) surface, at Ei = 0.6 eV. For molecules excited to the ν1 state, they report that the C−H:C− D cleavage ratio is greater than 30:1, and our results are clearly consistent with this measurement. In the absence of laser G


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molecule and is almost entirely localized on the C−H stretch, and IVR is slow. What is surprising is that both QCT studies predict that the C−D bond is more reactive than the C−H bond for CHD3 molecules in the ground vibrational state. As discussed, because of ZPE effects, our quantum approach gives a C−H:C−D cleavage ratio larger than 1:3, only approaching this statistical value at very high energies. Guo and co-workers, on the other hand, find a ratio below this value at all energies, and Shen et al. similarly report a ratio of about 1:4 for CHD3/Pt(111), for Ei between 0.6 and 1.0 eV.36 We agree with Guo and co-workers that this “is difficult to understand at present”. On the other hand, Guo and co-workers predicted that excitation of either of the CD3 stretches would significantly enhance S0 and C−D cleavage selectivity, and we see similar behavior. They found that the increase in S0 was slightly larger for the symmetric over the antisymmetric stretch, but only at the lowest energies, and the C−H:C−D cleavage ratios in Figure 10 are similar for ν2 and ν4. In contrast, we find that the increase in both S0 and C− D selectivity is much larger for ν2 than for ν4. Finally, for the CD3 stretch states, the magnitude of the C−D selectivity is larger in the QCT study than in the quantum, although relative to the ground-state results, the changes are similar. In Figure 11 we plot the total dissociative sticking probabilities (both C−H and C−D cleavage) for CHD3 in

Figure 10. C−H:C−D cleavage ratio, for CHD3 molecules in either the ground state (gs) or one of the vibrationally excited states indicated. The lines are from this work, and the circles are from the QCT studies of Guo and co-workers.35

excitation, Utz and co-workers report a ratio of 1:3 at 0.6 eV.26 While our ground-state results predict much more C−H cleavage, the laser-off experiments were done at very high nozzle temperatures, where vibrationally excited molecules in the beam contribute to S0. In fact, Utz and co-workers report 25% C−H cleavage only at nozzle temperatures above 800 K, and this increases to 40% as the nozzle temperature is lowered to 550 K. Our ground-state results correspond to a nozzle temperature of 0 K, and the Utz results are consistent with our observation that the C−H bond is more reactive than the C−D bond in this limit. We also note that at this low collision energy several tenths of an electronvolt below the ZPE-corrected static surface barrier the sticking probabilities are very small and sensitive to errors in our model for how the barrier height changes with lattice motion. From Figure 9 it is clear that the values for C−H:C−D at these energies are ratios of very small numbers and are thus suspect. Overall, however, our results for bond selectivity are consistent with experiment. We see in Figure 10 that excitation of either C−D stretch should enhance C−D selectivity relative to the ground state, but the effect is weaker than for the ν1 enhancement of C−H selectivity. Again, the symmetric stretch is more efficacious for this than the antisymmetric stretch. Finally, we begin to lose selectivity at very small values of S0, where surface-induced IVR becomes important. Our results are mostly consistent with recent QCT studies, with some interesting differences. Guo and co-workers examined the dissociative chemisorption of CH4, CHD3, and CH2D2 on a rigid flat Ni(111) surface, using a global 12-DOF PES.35 Their PES was fit to many thousands of DFT energies, computed using the PW91 functional, and thus their potential should be similar to ours, except for the higher barrier noted earlier. We plot their results for CHD3 in Figure 10. The agreement is good for molecules in the ν1 state. The quantum and QCT methods both reproduce the high C−H selectivity observed at lower collision energies, and both approach a statistical value at high energies. We note that Shen et al., in their QCT study of CHD3 on Pt(111), report very similar behavior for molecules in the ν1 state.36 They also use a global PES fit to many thousands of DFT calculations but include the full dimensionality of the molecule and allow the surface atoms to move. This agreement, like the C−H selectivity, is perhaps not surprising, as the ν1 excitation adds about 0.4 eV to the

Figure 11. Lines are theoretical sticking probabilities for CHD3 molecules in either the ground state (gs) or one of the vibrationally excited states indicated. Circles are experimental data (exp) from ref 26. Our laser-off estimate is described in the text.

several initial states and compare with available experimental data from the Utz group.26 The efficacies of the stretch modes for promoting reaction are reasonably large, considering our methods tend to underestimate η.29,30,33 At S0 = 10−4, η ≈ 0.82, 0.67, and 0.51 for ν1, ν2, and ν4, respectively. As discussed, the effects are larger for C−H relative to C−D excitations and symmetric relative to antisymmetric stretches. Our results are in reasonable agreement with experiment for the dissociative sticking of molecules in the ν1 state. On the other hand, our ground-state S0 significantly deviates form the laser-off data at low energies. As noted, however, the nozzle temperatures are very high in these experiments, 550−900 K for the data plotted, and vibrationally excited molecules likely make significant contributions to S0. We estimate the magnitude of this effect using a simple method described elsewhere,30,31 where we assume that all excited vibrational states have the same efficacy η. The results in Figure 11, for η = 0.7, give us a crude estimate H


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localized on those bonds during the collision; i.e., surfaceinduced IVR should be minor. We observe some surfaceinduced IVR in this study: excitation of the C−H stretch can increase C−D cleavage, and excitation of the C−D stretches can increase C−H cleavage. However, these effects occur only at lower energies where other pathways for reaction are unavailable, and thus the probabilities for these processes are small. Second, the vibrational state should have a relatively large efficacy for promoting reaction. The ν1 stretch of CHD3 has a large efficacy and can lead to 100% C−H cleavage selectivity at energies below saturation. Given that this mode is initially already localized on the single C−H bond, none of this is surprising, given the relatively minor IVR. More interestingly, both CD3 stretches, ν2 and ν4, have reasonable efficacies, and both promote C−D relative to C−H cleavage. The effect is much stronger for the symmetric stretch, for the reasons discussed. Our results are consistent with experiment with regard to both the magnitude of the dissociative sticking and the increase in selectivity with excitation of the ν1 stretch.

of the overall effect of the large nozzle temperatures. Overall, the agreement with experiment is reasonable, given the complexity of the system.

IV. CONCLUSIONS We have examined both mode specificity and bond selectivity in the dissociative chemisorption of CHD3 on Ni(111) using a quantum model based on the Reaction Path Hamiltonian. As methane approaches the metal surface, the reacting bond weakens, while the other three bonds remain relatively unperturbed. In the normal mode picture we thus have one vibration localized on the reacting bond and three modes localized on the nonreacting methyl group. In our vibrationally adiabatic description of CH4, the symmetric stretch correlates adiabatically with the mode localized on the reactive bond, while the triply degenerate antisymmetric stretches correlate with the modes on the methyl group. For CHD3 we see similar behavior. For the C−D cleavage configurations the symmetric C−D stretch softens as the vibration becomes localized on the dissociating bond, while the two antisymmetric stretches become localized on the nonreacting C−D bonds, with the frequencies relatively unperturbed. This localization of energy on the reacting bond is preserved as we transition between modes at the avoided crossings. Vibrational time scales and reaction/collision time scales are very similar for this system, ranging between roughly 10 and 40 fs. Neither adiabatic nor sudden behavior dominates the overall dynamics. At energies above the vibrationally adiabatic barrier heights the reaction probabilities are large, and mode softening, which lowers the corresponding adiabatic barrier, favors the symmetric stretch states. At energies below the adiabatic barrier heights, over-the-barrier pathways for reaction exist via nonadiabatic transitions at the avoided crossings to states of lower vibrational frequency, converting vibrational energy into motion along the reaction path of the new state. We find that the Coriolis couplings are far more important than the curvature couplings for facilitating reaction at lower energies. Thus, while the overall dynamics are not necessarily sudden, the small fraction of molecules that do react at energies below Veff,n(0) do so via vibrationally sudden (diabatic) pathways that preserve the localization of energy on the reacting bond. Perhaps this is why Guo’s SVP model is qualitatively consistent with observed mode specificity; the only over-the-barrier pathways available for reaction at typical experimental energies, at least for this system, are sudden/diabatic. We thus expect the symmetric stretch to have a larger efficacy for promoting reaction than the antisymmetric stretches. Interestingly, we find that one of the antisymmetric stretch components typically has a reactivity similar to that of the symmetric stretch, as these modes mix via a strong Coriolis coupling in the entrance channel. However, the other components of the antisymmetric stretch have smaller reactivities, for the reasons discussed. In addition, one of the antisymmetric stretches can often not couple to the ground state or the A′ states due to symmetry, and the reaction probability drops off rapidly below the vibrationally adiabatic barrier. Overall we find the symmetric stretch states to be more effective at promoting reaction, and any corresponding bond selectivity, consistent with available experimental data for these and similar reactions. Laser-induced bond selectivity can occur when two conditions are met. First, a vibrational state initially localized on one or more equivalent bonds should remain relatively

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 1-413-545-2583. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS B. Jackson gratefully acknowledges support from the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S. Department of Energy, under Grant # DE-FG02-87ER13744.

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REFERENCES

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