H2 Dissociation on H Precovered Ni(111) Surfaces: Coverage

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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H2 Dissociation on H Precovered Ni(111) Surfaces: Coverage Dependence, Lattice Motion, and Arrangement Effects Huali Zhao,† Ying He,† Yi Zhao,‡ and Wenji Wang*,† †

College of Chemistry & Pharmacy, Northwest A&F University, Yangling, 712100, Shaanxi Province, P. R. China State Key Laboratory for Physical Chemistry of Solid Surfaces and Fujian Provincial Key Lab of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, P. R. China

‡

S Supporting Information *

ABSTRACT: Hydrogen molecule dissociation on metal surfaces is a prototype reaction to study the gas−surface interaction. The dissociation rate constants of H2 on H atom precovered Ni(111) surfaces are calculated using the quantum instanton method in full dimensionality. Four different arrangements of the preadsorbed H and the dissociated H2, in which the preadsorbed H is located at the nearest (H2/H1−Ni(111)), second-nearest (H2/H2−Ni(111)), third-nearest (H2/H3−Ni(111)), and fourth-nearest (H2/H4−Ni(111)) neighbor sites of the bridge site where the H2 is dissociated, are considered. Compared to the dissociation rates of H2 on a clean Ni(111) surface (H2/Ni(111)), the dissociation rates of H2/H1−Ni(111) are much smaller. For instance, the former is 5.22 times larger than the latter at 300 K. This is because there is a strong repulsive interaction between the preadsorbed H and H2, which hinders the dissociation of H2. The dissociation rates of the four arrangements increase in the order of H2/H1−Ni(111), H2/H2−Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111). For example, the rate constants ratio of H2/H2−Ni(111) to H2/H1−Ni(111) is 4.40 at 300 K. This situation further reveals that the repulsive interaction decreases quickly with the increase of the distance between the preadsorbed H and H2. For the process of H2/H1−Ni(111), the dissociation rates on the mobile lattice are larger than those on the rigid lattice. For instance, the lattice motion enhances the dissociation rate by 29% at 300 K. The calculated kinetic isotope effects are larger than 1, and increase rapidly with decreasing temperature, which demonstrates that the quantum tunneling effect is remarkable. All of the kinetic isotope effects for H2/Ni(111), H2/H1−Ni(111), H2/H2−Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) are close to each other, which indicates that surface coverage, lattice motion, and arrangement effects affect the kinetic isotope effect a little.

1. INTRODUCTION Dissociation of hydrogen on metal surfaces represents one of the most extensively investigated topics in the past few decades.1,2 This reaction not only has catalytic performance in hydrogenation but also is considered to be very suitable for the foundation study on adsorption. Although lots of information has been obtained from both experimental measurements and theoretical simulations,3−20 the investigation on the surface coverage effect21,22 is scarce. The coverage dependence is important because the catalyst surface is usually covered by reaction intermediates under real conditions of heterogeneous catalytic reactions.23,24 Up to now, only a few experiments have been carried out to reveal the coverage dependence of hydrogen molecule dissociation on metal surfaces. Christmann et al.25 studied the adsorption of hydrogen on Ni(111), (100), and (110) surfaces with low energy electron diffraction, electron energy loss spectroscopy, and the laser-induced thermal desorption technique. Their measured work function which determined the activation energy of desorption was proportional to the hydrogen coverage. Norton and co-workers26 used microanalysis to measure the absolute coverage of adsorbed D on Pt(111), and found that there was a repulsive interaction at nearest neighbor distance. Poelsema et al.27 also observed a © XXXX American Chemical Society

strong repulsive interaction between the adsorbed hydrogen atoms by means of thermal energy atom scattering and thermal desorption spectroscopy. Later, Poelsema and co-workers28 further investigated the dissociative adsorption of hydrogen on the Pt(111) surface with the thermal energy helium atom scattering method. The result exhibited a strong decay of the sticking probability with increasing coverage. Gudmundsdottir et al.29 demonstrated that the binding energy and activation energy for desorption of hydrogen on Pt(110)-(1 × 2) depended strongly on hydrogen coverage by using the temperature-programmed desorption technique, and the activation energy for desorption decreased from 0.7 to 0.32 eV with the increase of surface coverage. Theoretically, Panczyk and Rudzinski30 applied a semiempirical equation to describe the coverage dependence of the chemical potential of the adsorbed H atoms, and the equation gave the correct value of the adsorption energy. Lozano and co-workers31 employed classical molecular dynamics simulations to study H-coverage effects on H2 dissociative adsorption on Pd(100), and found that, for a given initial Received: October 13, 2017 Revised: November 29, 2017 Published: December 11, 2017 A

DOI: 10.1021/acs.jpcc.7b10166 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

processing of the Boltzmann operator, whereas the Boltzmann operator can be calculated using the path integral Monte Carlo technique, and therefore, this method can be applied to complex systems with large degrees of freedom. The quantum instanton method has been successfully applied to gas phase49−51 and surface reactions,52−56 and it gives accurate estimates of the rate constants and kinetic isotope effects.57−59 This paper is set up as follows: Section 2 describes the potential energy surface, the framework of the quantum instanton method, and computational details. Section 3 gives the numerical results of dissociation rates and kinetic isotope effects. Section 4 is the conclusion.

coverage, the dissociative adsorption probability of H 2 molecules could vary by a factor of 5 depending on the particular arrangement of the adsorbed H atom on the surface. On the basis of reactive force fields and a molecular dynamics (MD) method, Xiao and Dong32 developed a strategy to make a thorough investigation of the surface coverage effect of the H2/H−Pd(111) system. The results demonstrated that the relative sticking coefficient decreased rapidly with the increase of surface coverage. German et al.33 used a model in the framework of the precursor mediated dissociation mechanism to study the activated hydrogen dissociation on metal surfaces, and concluded that, for different metals, the coverage dependence of rate constants was different. Groβ and coworkers34,35 presented ab initio molecular dynamics (AIMD) simulations of the adsorption of H2 on hydrogen precovered Pd(100), and found that not only the hydrogen coverage but also the arrangements of the adsorbed H atoms could strongly affect the dissociative adsorption probability. Their finding also showed that there was a strong dependence of the sticking probability on the recoil of the substrate atoms, which suggested that the surface temperature effect should not be ignored. However, due to the high computational cost, the surface temperature effect was not considered in their simulations. The incorporation of the surface temperature effect in dynamics simulations is a nontrivial task. Mills et al.36,37 investigated the dissociative sticking coefficient of H2 on Cu(110) with the quantum transition state theory, in which all of the degrees of freedom of H2 and eight Cu surface atoms were treated quantum mechanically. The calculated free energy barriers based on the reversible work evaluation showed that the lattice dynamics assisted the reaction by lowering the entropic barrier. Mondal et al.38 performed quantum and quasi-classical dynamics calculations of H2 on Cu(111), and found that surface thermal expansion of the lattice led to a considerable decrease of reaction barrier height. Donald and Harrison39 used a dynamically biased precursor-mediated microcanonical trapping model to predict the effect of surface temperature for H2 dissociation on Cu(111), and the results revealed that dynamical effects suppressed the dissociative sticking coefficient by nearly 2 orders of magnitude as compared to statistical expectations. Nattino et al.40 performed ab initio molecular dynamics calculations for dissociative adsorption of hydrogen on Cu(111), which included effects of surface atom motion, and the AIMD results were better than those on the static surface when compared with experiment. However, the surface temperature effect on the precovered surface has not been reported yet. The present paper focuses on two goals. One is to reveal how a preadsorbed H atom and the arrangement of this preadsorbed H atom affect the dissociation of H2 on Ni(111). The other is to exam the lattice motion effect on the H precovered Ni(111) surface. The dissociation rate constants of H2 on the H precovered Ni(111) surface are calculated by using the quantum instanton method,41−43 which is developed by Miller et al. from the rigorous quantum mechanics rate formula.44 This method has the following advantages. First, it uses the concept of instanton45−48 to calculate the quantum tunneling probability, which takes into account all possible tunneling paths and weights each path by the Boltzmann factor, so it takes full account of the quantum tunneling effect, especially in the tunneling dominated low temperature zone. Second, the quantum instanton method mainly involves the

2. METHOD 2.1. Potential Energy Surface and Lattice Model. The embedded diatomics-in-molecules potential energy surface (PES) constructed by Truong et al.60,61 is employed in the present work. On this PES, there are four possible dissociation paths, atop-to-bridge (with a classical potential energy barrier of 5.09 kcal/mol), atop-to-center (5.09 kcal/mol), bridge-tocenter (1.82 kcal/mol), and double-bridge-to-center (2.10 kcal/mol). It is clear that the preferred path is the bridge-tocenter. However, this case is in conflict with the finding of Kresse,62 who calculated the dissociation barrier of H2 on Ni(111) with spin-polarized gradient corrected density functional theory, and showed that the dissociation barrier over the top site (0.34 kcal/mol) was the lowest and the barrier over the bridge site (4.61 kcal/mol) was relatively high. Experimentally, Robota et al.63 reported a barrier of 2.3 kcal/ mol, and Steinruck et al.64 estimated that the activation energy was in the range 1−2 kcal/mol. Although the adopted PES is semiempirical, its barrier height is closer to these experimental measurements than that based on spin-polarized gradient corrected density functional theory. Under this circumstance, we expect that the calculations based on this PES can give qualitative conclusions. Moreover, this PES has several merits. First, it is a full-dimensional potential energy surface, which involves all of the degrees of freedom of hydrogen and nickel atoms. Second, it is capable of describing the interaction between the metal and one, two, or three H atoms, which is suitable to reveal the surface coverage effect. Third, the interaction is sensitive to the arrangements of the preadsorbed H and H2, which is expected to predict the adsorbate arrangement effect. In order to get insight into the dissociation dynamics on the precovered surface, we prepare a hydrogen atom precovered Ni(111) lattice which consists of 301 nickel atoms with 6 layers. On a clean Ni(111) surface, the gas-phase H2 first reaches the surface, then it is dissociated at a bridge site with a classical potential energy barrier of 1.82 kcal/mol, finally, two separated H atoms reside at two adjacent 3-fold hollow sites. On a H precovered Ni(111) surface, four different arrangements of the preadsorbed H and the dissociated H 2 corresponding to the same coverage are adopted, as depicted in Figure 1. The structures in parts a, b, c, and d denote that the preadsorbed H is located at the nearest neighbor site (an hcp site) (H2/H1−Ni(111)), second-nearest neighbor site (an fcc site) (H2/H2−Ni(111)), third-nearest neighbor site (an fcc site) (H2/H3−Ni(111)), and fourth-nearest neighbor site (an hcp site) (H2/H4−Ni(111)) of the bridge site where H2 is dissociated, respectively, and the corresponding classical potential energy barriers are 3.33, 2.21, 1.99, and 1.90 kcal/ mol. In order to better understand the influence of lattice B


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The Journal of Physical Chemistry C ΔH(β) = ℏ

̈ (0) −Cdd 2Cdd(0)

(5)

with ̂

̂

̂

̂

Cdd(t ) = tr[e−βH /2Δ̂(ξa(r ))e ̂ −βH /2eiHt / ℏΔ̂(ξb(r )) ̂ e−iHt / ℏ] (6)

Here, Δ(ξa(r̂)) and Δ(ξa(r̂)) are generalized delta-functions, which have the following form N

∑

Δ(ξγ(r )) ̂ = δ(ξγ(r )) ̂

i=1

1 (∇i ξγ(r )) ̂ 2 mi

(γ = a , b) (7)

where ∇i = ∂/∂ri. The dividing surfaces ξa(r) and ξb(r) are defined as follows, in which there are adjustable parameters (ξγ, γ = a, b) that shift the locations of the dividing surfaces. ξγ(r ) =

− [R x(Ha − Hb) − R(Ha − Hb)]

(2)

Here, β is the inverse temperature 1/(kBT), F̂ a and F̂ b are the flux operators, and Ĥ is the Hamiltonian operator of the H2/ H−Ni(111) system 3

∑ i=1

pi 2̂ 2mi

N

+

∑ j=1

Pĵ

F(ξa , ξb) = −kBT log[Cdd(ξa , ξb)]

(10)

and the free energy profile along the reaction path is given by F(ξ) = −kBT log[Cdd(ξ , ξ)]

2

2Mj

b

where Z(H ) and Z(H ) are the coordinates of the z-axis (normal to the Ni(111) surface) for the two hydrogen atoms (Ha and Hb) of the dissociated H2, respectively. R(X−Y) denotes the interatomic distance between atoms X and Y. The subscripts R and TS denote the values at the reactant region (H2 is far away from the Ni(111) surface) and the transition state geometry, respectively. With the above definition, if ξγ = 0, sR(r) = 0, the dividing surface is located at the reactant domain, if ξγ = 1, sTS(r) = 0, the dividing surface is fixed at the transition state region, and as ξγ changes from 0 to 1, the dividing surface moves smoothly from the reactant domain to the transition state region. The free energy surface, which can exhibit the dissociation barrier, is defined as

In the above formula, Qr is the reactant partition function per unit volume and Cff(0) is the zero time value of the flux− flux correlation function

Ĥ =

(x = R, TS) (9)

a

(1)

̂ ̂ ̂ ̂ Cff (t ) = tr[e−βH /2Fâ e−βH /2eiHt / ℏFb̂ e−iHt / ℏ]

(8)

Zx(Ha) + Zx(Hb) Z(Ha) + Z(Hb) − 2 2

sx =

motion on the dissociation rate, we further set a mobile lattice for H2/H1−Ni(111), in which 7 (closest to the preadsorbed H and the dissociated H2, 5 in the first layer and 2 in the second layer) and 24 (near the above-mentioned 7 Ni atoms) Ni atoms are treated as quantum mechanical and movable particles, respectively. 2.2. Quantum Instanton Theory. For H2 dissociation on a H atom precovered Ni(111) surface, the dissociation rate constant can be calculated by the quantum instanton formula41−43 π ℏ Cff (0) Q r 2 ΔH(β)

(γ = a , b)

Here,

Figure 1. Arrangements of the preadsorbed H and H2 on Ni(111).

k QI =

s R (r ) − ξγ = 0 sR (r ) − s TS(r )

+ V̂ (ri ̂ , R̂ j)

(11)

with ξ = ξa = ξb. A discretized path integral description of the Boltzmann operator can be obtained by invoking the standard procedure

(3)

where r̂i, mi, p̂i and R̂ j, Mj, P̂ j denote the coordinates, masses, and momenta of the ith H and jth Ni atoms, respectively, V(ri, Rj) is the potential energy, and N is the number of Ni atoms. F̂ a and F̂ b are defined by i Fγ̂ = [Ĥ , h(ξγ(r )) ̂ ] (4) ℏ with γ = a, b, h is the Heaviside function, r represents a collection of the Cartesian coordinates of H atoms, and ξa(r) and ξb(r) stand for two separate dividing surfaces. ΔH(β), in eq 1, is a specific type of energy variance related to the zero time value and second time derivative of the delta− delta correlation function Cdd(t)

̂

̂

̂

̂

e−βH /2 ≈ (e−βV /2P e−βT / P e−βV /2P )P /2

(12)

where P is the number of time slices. Under this circumstance, all of the quantities in eq 1 can be readily evaluated using the imaginary time path integral Monte Carlo65 and adaptive umbrella sampling techniques.66 The detailed derivations have been given in previous works.42,67,68 2.3. Computational Details. In our path integral Monte Carlo simulation, the numbers of time slices for H atoms (PH) and quantized nickel atoms (PNi) are different. The value of PH is chosen to be large enough to obtain a converged rate constant at a given temperature on the rigid lattice, while the C


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The Journal of Physical Chemistry C value of PNi is adopted according to the criterion of Markland and Manolopoulos.69 Concretely speaking, (PH, PNi) is set to (120, 10), (100, 10), (80, 8), (60, 6), (50, 5), (40, 4), (32, 4), and (20, 4) at 200, 250, 300, 400, 500, 600, 800, and 1000 K, respectively. The number of the Monte Carlo cycle is about (4−8) × 106 for computing a single ensemble average. It converges most of the rate constants within 10% statistical errors.

surface and readies to dissociate, it will encounter a repulsive interaction from the preadsorbed H, which raises the dissociation barrier. Our normal-mode analysis shows that the repulsive effect raises the classical potential energy barrier by 1.51 kcal/mol, and zero-point energy correction further increases the difference of potential energy barriers to 1.63 kcal/mol (as seen in Table S2 in the Supporting Information). This situation can also be confirmed by the difference of free energy barriers. As seen in Figure 3, the dissociation free energy barrier of H2/H1−Ni(111) is higher than that of H2/ Ni(111) by 0.96 kcal/mol at 300 K.

3. RESULTS AND DISCUSSION 3.1. Surface Coverage and Lattice Motion Effects. We first calculate the dissociation rate constants of H2/H1− Ni(111) with the quantum instanton method over the temperature range 200−1000 K on the rigid lattice, in which the preadsorbed H is located at the nearest neighbor site of the bridge site where H2 is dissociated. In order to get insight into the effect of lattice motion on the precovered surface, we further obtain the dissociation rates on the mobile lattice. The calculated dissociation rates are listed in Table S1 (in the Supporting Information), in which we also tabulate the values of H2 dissociation on a clean Ni(111) surface68 (H2/Ni(111)). The corresponding Arrhenius plots are drawn in Figure 2.

Figure 3. Free energy profiles along the reaction path for H2/Ni(111) and H2/H1−Ni(111) at 300 K. The solid, dashed, and dotted lines represent the free energy profiles on the clean rigid Ni(111) surface and the H precovered rigid and mobile Ni(111) surfaces, respectively.

As is shown in Figure 2, the difference between the rates of H2/H1−Ni(111) and H2/Ni(111) becomes larger and larger with decreasing temperature. For instance, on the rigid lattice, the dissociation rates of H2/Ni(111) are 5.22 and 1.98 times as large as those of H2/H1−Ni(111) at 300 and 800 K, respectively. This trend indicates that the activation energies are different for these two processes. By fitting the rate constants to the Arrhenius form, we obtain the activation energies. The calculated activation energies for H2/H1− Ni(111) and H2/Ni(111) are 2.81 and 2.07 kcal/mol in the temperature range 500−1000 K. The Arrhenius plot of H2/ Ni(111) deviates from linearity much greater than that of H2/ H1−Ni(111), from which we can infer that the quantum tunneling effect of H2/Ni(111) is much more substantial than that of H2/H1−Ni(111). This situation is caused by the fact that, as illustrated in Figure 3, the free energy barrier of H2/ Ni(111) is much lower than that of H2/H1−Ni(111), and there is a deep well between the reactant and transition state for H2/Ni(111), which makes the barrier thinner and easier to get through. Due to the much more rapid increase of the quantum tunneling effect for H2/Ni(111) with decreasing temperature, the dissociation rates ratio of H2/Ni(111) to H2/ H1−Ni(111) becomes very large at low temperatures. In addition, it can be seen from Figure 3 that, although there is an obvious well between reactant and transition state when H2 dissociates on the clean Ni(111) surface, which is corresponding to the physisorbed state, this physisorbed state becomes rather weak when H2 dissociates on the present H precovered Ni(111) surface. This phenomenon indicates that the physisorbed state depends on surface coverage.

Figure 2. Arrhenius plots of rate constants for H2/H1−Ni(111) and H2/Ni(111). The solid, dashed, dotted, and dash-dotted lines stand for H2 dissociation rates on the H precovered rigid and mobile Ni(111) surfaces and the clean rigid and mobile Ni(111) surfaces, respectively.

In Figure 2, on the rigid lattice, we can see that the dissociation rates of H2 on the H precovered Ni(111) surface increase steadily with increasing temperature, and the rates increase by about 2 orders of magnitude from 200 to 1000 K. The comparisons with experimental and other theoretical results are not available because no data has been reported. It is also seen from Figure 2 that the Arrhenius plot has an obvious deviation from linearity at low temperatures, which demonstrates that the quantum tunneling effect becomes significant at low temperatures. By comparison of the dissociation rates of H2/H1−Ni(111) on the rigid lattice with those of H2/Ni(111), we can observe that the former is much smaller than the latter over the temperature range 200−800 K. For instance, on the rigid lattice, the dissociation rates ratio of H2/Ni(111) to H2/H1− Ni(111) is 5.22 at 300 K. The much smaller rates of H2/H1− Ni(111) should be caused by the repulsive effect and zeropoint energy. When H2 gets close to the H precovered Ni(111) D


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The Journal of Physical Chemistry C On the mobile lattice, the dissociation rates of H2/H1− Ni(111) still increase with increasing temperature. By comparison of these dissociation rates on the mobile lattice with those on the rigid lattice, it is apparent from Figure 2 that the former are always larger than the latter. This phenomenon demonstrates that the lattice motion promotes the dissociation of H2. To track down the reason, we investigate the effect of lattice motion from the free energy barrier. As seen in Figure 3, at 300 K, our calculated free energy barrier heights are 2.27 and 1.96 kcal/mol on the rigid and mobile lattices, respectively. It is clear that the lattice motion enhances the dissociation rate by lowering the dissociation free energy barrier. However, the difference of these two kinds of rates is not very large. For example, the ratio is only 1.29 at 300 K. This lattice motion effect is consistent with H2 dissociation on the clean Ni(111) surface,68 which reports a ratio of 1.30 at 300 K. This situation demonstrates that the lattice motion effect is not influenced by the surface coverage. The underlying mechanism is that the preadsorbed H atom interacts with H2 directly, and it cannot affect the H2 through the Ni atoms because of the large mass mismatch between H and Ni atoms. 3.2. The Arrangement Effect. When H2 dissociates at a bridge site, the preadsorbed H atom can locate at difference places. We have considered four possible arrangements of the preadsorbed H and the dissociated H2, that are H2/H1− Ni(111), H2/H2−Ni(111), H2/H3−Ni(111)), and H2/H4− Ni(111), as depicted in Figure 1. The dissociation rates corresponding to these four possible arrangements are calculated with the quantum instanton method on the rigid lattice, and the values are tabulated in Table S3 in the Supporting Information. Figure 4 displays the corresponding Arrhenius plots of these dissociation rates.

repulsive interaction between the preadsorbed H atom and H2, and zero-point energy. In Table S2, we can see that the zeropoint energy corrected potential energy barriers are 3.20, 2.01, 1.78, and 1.66 for H2/H1−Ni(111), H2/H2−Ni(111), H2/H3− Ni(111), and H2/H4−Ni(111), respectively. It is clear that, from H2/H1−Ni(111) to H2/H4−Ni(111), the distance between the preadsorbed H atom and H2 increases, and therefore, the repulsive interaction declines. This situation can also be illustrated by the free energy barriers, which further incorporate the quantum tunneling effect. As shown in Figure 5, the free energy barrier heights for H2/H1−Ni(111), H2/ H2−Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) are 2.27, 1.47, 1.27, and 1.10 kcal/mol at 300 K, respectively.

Figure 5. Free energy profiles along the reaction path for H2/H1− Ni(111), H2/H2−Ni(111), H2/H3−Ni(111), H2/H4−Ni(111), and H2/Ni(111) on the rigid lattice at 300 K.

A detailed comparison shows that the dissociation rates of H2/H1−Ni(111) are much smaller than those of H2/H2− Ni(111), but the rates of H2/H2−Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) are close to each other. For instance, the values of (H2/H2−Ni(111))/(H2/H1−Ni(111)), (H2/H3− Ni(111))/(H2/H2−Ni(111)), and (H2/H4−Ni(111))/(H2/ H3−Ni(111)) are 4.40, 1.31, and 1.08 at 300 K, respectively. This trend reveals that the repulsive interaction between the preadsorbed H atom and H2 is nearly negligible if the preadsorbed H is located further than the third-nearest neighbor site. As discussed in section 3.1, there is a remarkable quantum tunneling effect in the H2 dissociation reaction, which can be indicated by the Arrhenius plots of the rates that deviate from linearity at low temperatures. It is clear from Figure 4 that the quantum tunneling effects of H2/H2−Ni(111), H2/H3− Ni(111), and H2/H4−Ni(111) are much larger than that of H2/H1−Ni(111). This is because the free energy barriers of H2/H1−Ni(111) are much higher and wider than the others, as seen in Figure 5. Furthermore, the depth of the well between the reactant and transition state is increasing from H2/H1− Ni(111) to H2/H4−Ni(111), which makes the barrier thinner and easier to get through, and therefore, it also contributes a lot to the increase of the quantum tunneling. By comparison of the dissociation rates of H2/Hx−Ni(111) (x = 1, 2, 3, 4) with those of H2/Ni(111), we can see that the rates of H2/H1−Ni(111) are much smaller than those of H2/ Ni(111), which has been discussed in section 3.1, while the dissociation rates of H2/H2−Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) are close to the dissociation rates of H2/

Figure 4. Arrhenius plots of rate constants for H2/H1−Ni(111), H2/ H2−Ni(111), H2/H3−Ni(111), H2/H4−Ni(111), and H2/Ni(111) on the rigid lattice.

It can be seen from Figure 4 that all of the dissociation rates of H2/H1−Ni(111), H2/H2−Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) increase with increasing temperature at high temperatures, while the dissociation rates of H2/H2−Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) reach minima and keep stable at low temperatures. At a given temperature, the dissociation rate of H2/H1− Ni(111) is the smallest, while H2/H4−Ni(111) has the largest one. In general, the increasing dissociation rate order is H2/ H1−Ni(111) < H2/H2−Ni(111) < H2/H3−Ni(111) < H2/ H4−Ni(111). These differences are mainly caused by the E


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The Journal of Physical Chemistry C Ni(111). Detailed comparison shows that the rates of H2/H4− Ni(111) are always larger than those of H2/Ni(111) over the tested temperature range 200−800 K. This situation is in conflict with the zero-point energy corrected potential energy barriers. The zero-point energy corrected potential energy barrier of H2/Ni(111) is lower than that of H2/H4−Ni(111) by 0.09 kcal/mol. However, this phenomenon is consistent with the situation of the free energy barriers. In Figure 5, it is seen that the free energy barrier of H2/H4−Ni(111) is lower than that of H2/Ni(111) at 300 K. The underlying reason is that the existence of the preadsorbed H atom is beneficial for forming the physisorbed state of H2 even though the repulsive interaction plays an opposite role. This phenomenon is especially obvious if the repulsive interaction is weak. As seen in Figure 5, the free energy well between the reactant and transition state for H2/H4−Ni(111) is deeper than that for H2/ Ni(111). The situation is similar at 600 K, as displayed in Figuare S1 in the Supporting Information. The stable physisorbed state of H2 makes the free energy barrier thinner, and lowers the free energy barrier by the tunneling effect. Just as Mills et al.36 had discussed if the chain (with a path integral expression, the H atom is treated as a chain with P beads) was at a barrier, it would drape down on either side to sample a lower effective potential. Indeed, the thinner the barrier, the more the barrier will be lowered. 3.3. Kinetic Isotope Effect. We calculate the dissociation rates of D2 on D precovered Ni(111) surfaces and list the rates of D2/D1−Ni(111), D2/D2−Ni(111), D2/D3−Ni(111), and D2/D4−Ni(111) on the rigid lattice in Table S4 in the Supporting Information. In order to investigate the effect of lattice motion on the kinetic isotope effect, we also calculate the dissociation rates of D2/D1−Ni(111) on the mobile lattice. The corresponding Arrhenius plots of these rates are exhibited in Figure 6.

Figure 7. Free energy profiles along the reaction path for D2 on D precovered Ni(111) surfaces at 300 K.

D1−Ni(111) has the highest barrier, and therefore, its rate is the smallest. The underlying mechanism is that the repulsive interaction between the preadsorbed D atom and D2 and zeropoint energy changes the dissociation barrier of D2. Because the repulsive interaction strongly depends on the distance between the preadsorbed D atom and D2, it decreases from D2/D1−Ni(111) to D2/D4−Ni(111) with the increase of the distance. In Table S2, we can see that the zero-point energy corrected potential energy barriers are 3.25, 2.06, 1.84, and 1.73 for D2/D1−Ni(111), D2/D2−Ni(111), D2/D3−Ni(111), and D2/D4−Ni(111), respectively. As a result, the free energy barrier decreases and the dissociation rate increases from D2/ D1−Ni(111) to D2/D4−Ni(111). Detailed comparisons show that the rates differences between D2/D1−Ni(111), D2/D2−Ni(111), D2/D3−Ni(111), and D2/D4−Ni(111) increase with decreasing temperature. For example, the rate of D2/D2−Ni(111) is 4.07 times as large as that of D2/D1−Ni(111) at 300 K, while the former becomes 2.22 times larger than the latter at 800 K. This trend predicts that the activation energies are different for these four reactions. Indeed, our calculations show that the activation energies are 3.59, 3.23, 2.95, and 2.84 kcal/mol for D2/D1− Ni(111), D2/D2−Ni(111), D2/D3−Ni(111), and D2/D4− Ni(111), respectively (as seen in Table S2). According to Figure 6, the dissociation rates of D2/D2−Ni(111), D2/D3− Ni(111), and D2/D4−Ni(111) are close to each other at high temperatures. However, there are noticeable differences at low temperatures. For instance, the rates ratios of D2/D3−Ni(111) to D2/D2−Ni(111) and D2/D4−Ni(111) to D2/D3−Ni(111) are 1.42 and 1.23 at 250 K, respectively. This situation reveals that the repulsive interaction between the preadsorbed D atom and D2 still has an important impact on the dissociation rates; even the preadsorbed D is located at the fourth-nearest neighbor site. In Figure 6, we can also see that the Arrhenius plots of these rates exhibit obvious deviations from linearity at low temperatures, which reveals that the quantum tunneling effect is still significant for these reactions. According to the Arrhenius plots, we can infer that the quantum tunneling effect is increased from D2/D1−Ni(111) to D2/D4−Ni(111). This situation can be explained by the fact that the free energy barrier becomes thinner and thinner from D2/D1−Ni(111) to D2/D4−Ni(111), which makes the barrier easier to pass through, as illustrated in Figure 7.

Figure 6. Arrhenius plots of thermal rate constants for D2 on D precovered Ni(111) surfaces.

On the rigid lattice, from Figure 6, we can see that all of the dissociation rates increase with increasing temperature, and there is a general trend that the dissociation rates increase from D2/D1−Ni(111) to D2/D4−Ni(111). At a given temperature, D2/D4−Ni(111) possesses the largest value, while the rate of D2/D1−Ni(111) is the smallest. This phenomenon can be explained by the free energy barrier, as seen in Figure 7, at 300 K, the heights of free energy barriers for D2/D1−Ni(111), D2/ D2−Ni(111), D2/D3−Ni(111), and D2/D4−Ni(111) are 3.08, 2.18, 2.03, and 1.88 kcal/mol, respectively. It is clear that D2/ F


Article

The Journal of Physical Chemistry C Table 1. Kinetic Isotope Effects for H2 Dissociation on H Precovered Ni(111) Surfaces rigid lattice T (K)

mobile lattice

H2/Ni(111)/ D2/Ni(111)

H2/H1−Ni(111)/ D2/D1−Ni(111)

H2/H2−Ni(111)/ D2/D2−Ni(111)

H2/H3−Ni(111)/ D2/D3−Ni(111)

H2/H4−Ni(111)/ D2/D4−Ni(111)

H2/H1−Ni(111)/ D2/D1−Ni(111)

14.90a

12.25 6.40 4.42 3.96 2.57 2.41 1.90 1.73

12.68 6.27 4.77 3.09 2.90 2.04 1.81 1.76

12.17 5.53 5.14 3.43 2.43 2.31 1.82 1.75

7.20 4.99 3.37 3.34 3.02 2.21 1.89 1.80

5.69 5.14 3.78 2.79 2.18 1.85 1.44

200 250 300 400 500 600 800 1000

5.72 2.46 2.07

a

From ref 68.

As is shown in Figure 6, the rates of D2/D1−Ni(111) on the mobile lattice are larger than those of D2/D1−Ni(111) on the rigid lattice. This phenomenon can be explained by the fact that the lattice motion enhances the rates by lowering the free energy barrier. As depicted in Figure 7, the free energy barrier of D2/D1−Ni(111) on the mobile lattice is lower than that on the rigid lattice by 0.30 kcal/mol at 300 K. However, the rates of D2/D1−Ni(111) on the mobile lattice are only a little larger than those on the rigid lattice. For instance, the ratio is only 1.11 at 300 K. This case reveals that the lattice motion effect on the dissociation rate is not remarkable. We further obtain the kinetic isotope effects by calculating the rates ratios of H2/Hx−Ni(111) to D2/Dx−Ni(111) (x = 1, 2, 3, 4), so as to investigate whether the surface coverage, lattice motion, and arrangement effects would affect the kinetic isotope effect. The corresponding values have been tabulated in Table 1. On the rigid lattice, as shown in Table 1, all of the kinetic isotope effects for H2/Hx−Ni(111) (x = 1, 2, 3, 4) are much larger than 1, which demonstrates that the dissociation rates of H2 are always larger than those of D2. This phenomenon can be explained by the difference of free energy barriers. Our calculations show that the free energy barriers of D2/Dx− Ni(111) (x = 1, 2, 3, 4) are always higher than those of H2/ Hx−Ni(111) (x = 1, 2, 3, 4). For instance, the free energy barrier of D2/D1−Ni(111) is higher than that of H2/H1− Ni(111) by 0.81 kcal/mol at 300 K. The zero-point energy plays a minor role in the difference of the free energy barriers. Our normal-mode analysis shows that the zero-point energy corrected potential energy barrier of H2/H1−Ni(111) is lower than that of D2/D1−Ni(111) by only 0.05 kcal/mol. From Table 1, we can also see that all of the kinetic isotope effects for H2/Hx−Ni(111) (x = 1, 2, 3, 4) increase rapidly with decreasing temperature on the rigid lattice. For example, the kinetic isotope effect increases from 1.73 at 1000 K to 12.25 at 200 K for H2/H1−Ni(111). This trend is mainly caused by the quantum tunneling effect. The quantum tunneling effect becomes more and more significant with decreasing temperature, and it increases the dissociation rates of H2/H1−Ni(111) much faster than those of D2/D1− Ni(111). Detailed comparisons also show that the kinetic isotope effects of H2/H1−Ni(111), H2/H2−Ni(111), H2/H3− Ni(111), and H2/H4−Ni(111) are nearly the same at high temperatures, which indicates that the arrangement of the preadsorbed H atom and H2 gives little influence on the kinetic isotope effects at high temperatures. However, at low temperatures, the kinetic isotope effects of H2/H4−Ni(111) become noticeably smaller than the others. The underlying

mechanism is that, from H2/H3−Ni(111) to H2/H4−Ni(111), the quantum tunneling effect of H2 increases a little because it has reached its maximum at low temperatures where the rates are nearly constant, while the quantum tunneling effect of D2 still increases rapidly, which enhances the dissociation rates of D2. As a result, the kinetic isotope effects decrease from H2/ H3−Ni(111) to H2/H4−Ni(111). By comparison of the kinetic isotope effects of H2/H1− Ni(111) with those of H2/Ni(111), we find that the former is only a little smaller than the latter. After comparison of the kinetic isotope effects of H2/H1−Ni(111) on the mobile lattice with those on the rigid lattice, we notice that they are close to each other. For instance, the corresponding kinetic isotope effects for H2/Ni(111) on the rigid lattice and H2/H1− Ni(111) on the rigid and mobile lattices are 5.72, 4.42, and 5.14 at 300 K, respectively. These phenomena demonstrate that both surface coverage and lattice motion affect the kinetic isotope effect a little.

4. CONCLUSION We have calculated the dissociation rate constants of H2 on H precovered Ni(111) surfaces by using the quantum instanton method with a full-dimensional potential energy surface. Four possible arrangements of the preadsorbed H and the dissociated H2, in which the preadsorbed H is at the nearest (H2/H1−Ni(111)), second-nearest (H2/H2−Ni(111)), thirdnearest (H2/H3−Ni(111)), and fourth-nearest (H2/H4−Ni(111)) neighbor sites of the bridge site where the H2 is dissociated, have been investigated. By comparison of the dissociation rates of H2 on the clean Ni(111) surface (H2/Ni(111)) with those of H2/H1−Ni(111), we find that the former is much larger that the latter. For instance, the rate ratio of H2/Ni(111) to H2/H1−Ni(111) is 5.22 at 300 K. This situation is mainly due to the strong repulsive interaction between the preadsorbed H atom and H2 which hinders the dissociation of H2. The Arrhenius plot of H2/Ni(111) deviates from linearity much greater than that of H2/H1−Ni(111), which reveals that the quantum tunneling effect of H2/H1−Ni(111) is less than that of H2/Ni(111). Compared to the rigid lattice, the lattice motion plays a role in enhancing the dissociation rates of H2/H1−Ni(111) by lowering the free energy barrier. For instance, it promotes the dissociation rate by 29% at 300 K. This growth rate is nearly the same as that of H2/Ni(111), which reports an increase of 30% at 300 K. This phenomenon demonstrates that surface coverage has little influence on the lattice motion effect, which is due to the direct interaction between the preadsorbed H G


Article

The Journal of Physical Chemistry C

Interactions in Modeling the Dissociative Adsorption of H2 on Cu(100). J. Phys. Chem. C 2014, 118, 5374−5382. (5) Serrate, D.; Moro-Lagares, M.; Piantek, M.; Pascual, J. I.; Ibarra, M. R. Enhanced Hydrogen Dissociation by Individual Co Atoms Supported on Ag(111). J. Phys. Chem. C 2014, 118, 5827−5832. (6) Liu, T.; Fu, B.; Zhang, D. H. Validity of the Site-Averaging Approximation for Modeling the Dissociative Chemisorption of H2 on Cu(111) Surface: A Quantum Dynamics Study on Two Potential Energy Surfaces. J. Chem. Phys. 2014, 141, 194302. (7) Hu, X.; Jiang, B.; Xie, D.; Guo, H. Site-Specific Dissociation Dynamics of H2/D2 on Ag(111) and Co(0001) and the Validity of the Site-Averaging Model. J. Chem. Phys. 2015, 143, 114706. (8) Wijzenbroek, M.; Helstone, D.; Meyer, J.; Kroes, G. J. Dynamics of H2 Dissociation on the Close-Packed (111) Surface of the Noblest Metal: H2 + Au(111). J. Chem. Phys. 2016, 145, 144701. (9) Wijzenbroek, M.; Klein, D. M.; Smits, B.; Somers, M. F.; Kroes, G. J. Performance of a Non-Local van der Waals Density Functional on the Dissociation of H2 on Metal Surfaces. J. Phys. Chem. A 2015, 119, 12146−12158. (10) Seo, D. H.; Shin, H.; Kang, K.; Kim, H.; Han, S. S. FirstPrinciples Design of Hydrogen Dissociation Catalysts Based on Isoelectronic Metal Solid Solutions. J. Phys. Chem. Lett. 2014, 5, 1819−1824. (11) Kroes, G. J. Toward a Database of Chemically Accurate Barrier Heights for Reactions of Molecules with Metal Surfaces. J. Phys. Chem. Lett. 2015, 6, 4106−4114. (12) Jiang, B.; Hu, X.; Lin, S.; Xie, D.; Guo, H. Six-Dimensional Quantum Dynamics of Dissociative Chemisorption of H2 on Co (0001) on an Accurate Global Potential Energy Surface. Phys. Chem. Chem. Phys. 2015, 17, 23346−23355. (13) Á lvarez-Falcón, L.; Viñes, F.; Notario-Estévez, A.; Illas, F. On the Hydrogen Adsorption and Dissociation on Cu Surfaces and Nanorows. Surf. Sci. 2016, 646, 221−229. (14) Kroes, G. J.; Díaz, C. Quantum and Classical Dynamics of Reactive Scattering of H2 from Metal Surfaces. Chem. Soc. Rev. 2016, 45, 3658−3700. (15) Shen, X.; Li, Y.; Liu, X.; Zhang, D.; Gao, J.; Liang, T. Hydrogen Diffusion into the Subsurfaces of Model Metal Catalysts from First Principles. Phys. Chem. Chem. Phys. 2017, 19, 3557−3564. (16) Mondelo-Martell, M.; Huarte-Larranaga, F.; Manthe, U. Quantum Dynamics of H2 in a Carbon Nanotube: Separation of Time Scales and Resonance Enhanced Tunneling. J. Chem. Phys. 2017, 147, 084103. (17) Xu, C.-Q.; Xing, D.-H.; Xiao, H.; Li, J. Manipulating Stabilities and Catalytic Properties of Trinuclear Metal Clusters through Tuning the Chemical Bonding: H2 Adsorption and Activation. J. Phys. Chem. C 2017, 121, 10992−11001. (18) Mallikarjun Sharada, S.; Bligaard, T.; Luntz, A. C.; Kroes, G.-J.; Nørskov, J. K. SBH10: A Benchmark Database of Barrier Heights on Transition Metal Surfaces. J. Phys. Chem. C 2017, 121, 19807−19815. (19) Kroes, G. J.; Juaristi, J. I.; Alducin, M. Vibrational Excitation of H2 Scattering from Cu(111): Effects of Surface Temperature and of Allowing Energy Exchange with the Surface. J. Phys. Chem. C 2017, 121, 13617−13633. (20) Goldman, N.; Morales, M. A. A First-Principles Study of Hydrogen Diffusivity and Dissociation on δ-Pu (100) and (111) Surfaces. J. Phys. Chem. C 2017, 121, 17950−17957. (21) Lopez, N.; Lodziana, Z.; Illas, F.; Salmeron, M. When Langmuir Is Too Simple: H2 Dissociation on Pd(111) at High Coverage. Phys. Rev. Lett. 2004, 93, 146103. (22) Zhang, R.; Liu, F.; Zhao, X.; Wang, B.; Ling, L. First-Principles Study about the Effect of Coverage on H2 Adsorption and Dissociation over a Rh(100) Surface. J. Phys. Chem. C 2015, 119, 10355−10364. (23) Yang, K.; Zhang, M.; Yu, Y. Direct versus Hydrogen-Assisted CO Dissociation over Stepped Ni and Ni3Fe Surfaces: A Computational Investigation. Phys. Chem. Chem. Phys. 2015, 17, 29616−29627. (24) Amaya-Roncancio, S.; Linares, D. H.; Duarte, H. A.; Sapag, K. DFT Study of Hydrogen-Assisted Dissociation of CO by HCO,

atom and H2, and the large mass mismatch between H and Ni atoms. For the four possible arrangements of preadsorbed H atom and H2, the increasing dissociation rate order is H2/H1− Ni(111) < H2/H2−Ni(111) < H2/H3−Ni(111) < H2/H4− Ni(111). The dissociation rates of H2/H1−Ni(111) are much smaller than the others, while the dissociation rates of H2/H2− Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) are close to each other. This phenomenon is caused by the fact that the repulsive interaction between the preadsorbed H atom and H2 depends on the distance between them, and the repulsive interaction decreases quickly with increasing distance. In addition, the preadsorbed H atom has a role to stabilize the physisorbed state of H2. The calculated kinetic isotope effects are always larger than 1, which demonstrates that the dissociation rates of H2 are always larger than those of D2. The rapid increase of the kinetic isotope effects with decreasing temperature further indicates that the quantum tunneling effect is remarkable at low temperatures. Detailed comparisons show that the kinetic isotope effects of H2/Ni(111), H2/H1−Ni(111), H2/H2− Ni(111), H2/H3−Ni(111), and H2/H4−Ni(111) are close to each other, which reveals that surface coverage, lattice motion, and arrangement effects affect the kinetic isotope effect a little.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b10166. Details of the quantum instanton rate constants, potential energy barriers, zero-point energy corrections, activation energies, and free energy profiles along the reaction path (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yi Zhao: 0000-0003-1711-4250 Wenji Wang: 0000-0002-3607-1252 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant 21203151) and Chinese Universities Scientific Fund (Grants 2452015084 and 2452015432). This research used resources of the HPC of Northwest A&F University.

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REFERENCES

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H2 Dissociation on H Precovered Ni(111) Surfaces: Coverage

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