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C: Surfaces, Interfaces, Porous Materials, and Catalysis 2

H Dissociation on H Precovered Ni(100) Surface: Physisorbed State and Coverage Dependence Ying He, and Wenji Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10500 • Publication Date (Web): 13 Feb 2019 Downloaded from http://pubs.acs.org on February 19, 2019

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The Journal of Physical Chemistry

H2 Dissociation on H Precovered Ni(100) Surface: Physisorbed State and Coverage Dependence Ying He and Wenji Wang* College of Chemistry & Pharmacy, Northwest A&F University, Yangling, 712100, Shaanxi Province, P. R. China.

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ABSTRACT Hydrogen molecule dissociation on metal surfaces is a prototypical reaction to investigate the gas-surface interaction. In order to investigate the effect of lattice motion, the embedded cluster model is adopted to construct the quantum Ni(100) lattice, in which 11 Ni atoms are treated quantum mechanically. The direct and steady state dissociation rates of H2 on H precovered Ni(100) surface are calculated by quantum instanton method. Both the direct and steady state dissociation rates on H precovered Ni(100) are smaller than those on the clean Ni(100). This is because the repulsive interaction between H2 and the preadsorbed H raises the potential energy barrier. Moreover, this repulsive interaction is inversely proportional to the distance between H2 and the preadsorbed H. Owing to the classical relaxation and entropy effect of Ni atoms, the lattice motion promotes H2 dissociation by lowering the free energy barrier, but it hinders H2 recombination by raising the free energy barrier. There are remarkable kinetic isotope effects for the dissociation process, which is due to the entropy and quantum tunneling effects. However, no kinetic isotope effect is obtained for the recombination process.

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1. INTRODUCTION Adsorption, dissociation, diffusion and recombination of hydrogen molecule on metal surfaces have attracted the attention of scientists over the past decades. Hydrogen is widely used in heterogeneous catalysis, such as ammonia synthesis, hydrogenation of acetylene, and CO hydrogenation in Fischer-Tropsch synthesis. It is also considered as the energy source of the future with the advantages of abundant, renewable and non-polluting. In particular, hydrogen dissociation is the simplest prototypical reaction to explore the gas-solid interaction.1-6 Nickel is one of the commonly used catalysts in many industrial processes, and the dissociation of H2 on low-index nickel surfaces has been investigated extensively. With the molecular beam technique, Rendulic et al.7 measured the sticking coefficient for H2 on Ni(100). They speculated that the fall of the sticking probability with increasing beam energy at low temperatures was due to nonactivated adsorption via a precursor, and attributed the increase of the sticking probability with increasing beam energy at high temperatures to the activated adsorption. Zhu et al.8 further provided the evidence for the coexistence of direct and precursor dynamics. They found that the initial sticking coefficient of H2/Ni(100) decreased as the surface temperature increased from 100 to 200 K, and there was no temperature dependence above 200 K, which was consistent with the observation of Hamza and Madix.9 Christmann et al.10,11 studied the adsorption of hydrogen on Ni(100) by means of low energy electron diffraction, thermal desorption spectroscopy and work function measurements. They found that H2 chemisorption 3



occured in two atomic states β1 and β2, and the corresponding activation energies for desorption were 20±2 and 23±1 kcal/mol. Most recently, Kaufmann and co-workers12 measured quantum-state resolved angular and velocity distributions of H2/Cu(111). The results also showed that desorbing molecules had two channels. One was a “fast” channel, which was enhanced by both translational and vibrational energies, and the other was a “slow” channel, which was promoted by vibrational energy but inhibited by translational energy. The authors thought that this “slow” channel was probably caused by a physisorbed state. Nevertheless, Groβ et al.13 performed six-dimensional quantum dynamics calculations for H2/Pd(100), and predicted that the increase of the sticking probability with decreasing kinetic energy was caused by dynamical steering. Kresse14 confirmed this view by calculating the reaction channels of H2 dissociation on Ni(100), and showed that one of the dissociation channels was nearly barrierless which was beneficial for the steering effect with low beam energy. The calculations of Kresse with spin-polarized gradient corrected density functional theory indicated that there was no obvious potential energy curve corresponding to physisorbed state. However, Lee et al.15-16 showed that potential energy curve was deepened by including van der Waals17-18 forces for H2/Cu(100). Under this circumstance, we think that it is reasonable to assume that the physisorbed state of H2 on Ni(100) is existent. Indeed, several theoretical works have investigated the dynamics of H2/Ni(100) with a physisorbed state. Chakravarty and Metiu19 simulated the lifetime of physisorbed H2, and showed that there were a direct 4


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dissociation at high temperatures and a two-step process (first physisorbed and then dissociated) at low temperatures. Truong et al.20 calculated the dissociation rates of H2/Ni(100) with the canonical variational transition state theory under the steady state approximation. In our previous work,21 with the modified EM–LEPS (an Effective Medium modification on a London-Eyring-Polanyi-Sato four-body potential energy surface) potential energy surface,20 the quantum instanton method was used to investigate the role of the physisorbed state by calculating the direct and steady state dissociation rates of H2 on a clean Ni(100) surface. However, all of those theoretical works are based on a rigid clean Ni(100) surface, so the lattice motion effect on the dissociation rates of H2 from the gas phase state to chemisorbed state is not explored. The physisorbed state may be affected easily by the lattice motion22-27 and electron-hole pairs,28-30 especially if its lifetime is long. Recently, Shirhatti and co-workers31 detected the adsorption and subsequent desorption of vibrationally excited CO molecules on Au(111), and found that the vibrational lifetime of physisorbed CO(ν=1) was about 1.0 10-10 s. This is long enough for the energy transfer to occur and for the surface to corrugate. Although H2 is much lighter than CO, the lattice motion may also play an important role. Up to now, many approaches have been proposed to incorporate the effect of lattice motion. Sahoo et al.32-33 considered the surface phonon modes through a mean field approach for H2/Cu(100). Bonfanti et al.34 studied the effect of lattice displacement for H2/Cu(111) by using the Specific Reaction Parameter (SRP) approach to Density Functional Theory (DFT). Nattino et al.35 performed ab initio molecular 5



dynamics (AIMD) calculations for D2/Cu(111) to investigate effects of surface atom motions. Donald and Harrison36 explored the effect of surface temperature for H2/Cu(111) by using a dynamically biased precursor-mediated microcanonical trapping (d-PMMT) model. Kraus and Frank37 included the degrees of freedom of Pt atoms with Car–Parrinello molecular dynamics for H2/Pt(111). We also investigated the lattice motion effect on the dissociation rates of H2 from the physisorbed state to chemisorbed state on a clean Ni(100) surface38 with the quantum instanton method. All of the research reveals that the motion of the lattice modifies the reactivity. However, how the preadsorbed H influences the lattice motion effect of H2/Ni(100) is not clear yet. Surface coverage39-46 may have an important impact on the precursor mediated dynamics. Experimentally, Zhu et al.8 reported that the sticking coefficient of H2 on C precovered Ni(100) decreased much more than that on clean Ni(100) as the surface temperature raised from 100 to 200 K. Poelsema et al.47-48 observed a strong repulsive interaction between the adsorbed hydrogen atoms, and a strong decay of the sticking probability for H2/Pt(111) with the increase of the hydrogen coverage. Theoretically, Panczyk et al.49 designed a model for the dissociative adsorption of H2/Ni(100), and calculated the equilibrium adsorption isotherms with the grand canonical Monte Carlo method. This model successfully explained the experimentally observed phenomenon that the decreasing tendency of the slopes of the adsorption isotherms with increasing temperature. Xiao and Dong50 predicted that the sticking coefficient of H2/H-Pd(111) decreased with the increasing of surface coverage. Gudmundsdottir et al.51 revealed that 6


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the precovered H changed the binding energy and activation energy of H2 by changing the corrugation amplitude of Pt(110)-(1×2) surface. Yu et al.52 showed that the lateral repulsive interaction became more and more strong with the increase of H2 coverage, and low temperatures were beneficial for the stable coverage of H2 on Co(100). Groβ and co-workers53-55 showed that, with the same coverage, the different arrangements of the adsorbed atoms could lead to different coverage dependence of adsorption probability for H2/H-Pd(100), and the adsorption probability varied by a factor of five. German et al.56 demonstrated that different metal possessed different coverage dependence of dissociation adsorption probability. Our previous calculations of H2/H-Ni(111)57 revealed that the preadsorbed H atom not only affected the direct dissociation rates by raising the barrier but also changed the stability of the physisorbed state. However, what roles the preadsorbed H could play in the steady state and recombination rates are not investigated. In the present paper, we will calculate the direct, steady state and recombination rates of H2 on a H precovered Ni(100) surface (H-Ni(100)) with two objectives. One is to explore how the preadsorbed H affects the rates and physisorbed state of H2, and the other is to investigate how the preadsorbed H influences the effect of lattice motion. The direct and steady state rates are calculated by the quantum instanton method.58-60 The quantum instanton method is a short time approximation of the flux-flux correlation function, and it treats the Boltzmann operator quantum mechanically which includes delocalization, zero-point energy and tunneling effects. Together with path integral Monte Carlo technique,61 the quantum instanton method has been applied to complex 7



chemical reactions62-65 with large numbers of degrees of freedom, and has given accurate rate constants66-67 and kinetic isotope effects.68-71 This paper consists of four Sections. Section 2 describes the potential energy surface and the framework of direct and steady state rates with quantum instanton method, as well as computational details. Section 3 discusses the rate constants and kinetic isotope effects. Section 4 gives the conclusions. 2. THEORETICAL METHODS 2.1 Potential Energy Surface and Lattice Model Our quantum instanton calculations need a potential energy surface, which must meet following requirements. First, the interaction between Ni(100) lattice and at least three H atoms should be described accurately. Second, the Ni atoms have to be movable during H2 dissociation. Up to now, although many excellent approaches27,72-75 have been proposed to construct accurate potential energy surface for gas-surface reactions, the potential energy surface with movable metal atoms is still scarce. For H2 dissociation on clean and H precovered nickel surfaces, Truong et al.76-77 have constructed a full dimensional potential energy surface (the degrees of freedom of Ni atoms are included) with the embedded diatomics-in-molecules method. Although this potential energy surface is semi-empirical, the potential energy barriers are consistent with experimental measurements. For H2 dissociation on Ni(100), Truong et al. reported that all of the dissociation paths of H2 have a physisorbed state (with a classical potential energy well of 1.78 kcal/mol), and the most energetically favorable path is bridge-to-center (H2 is first dissociated over a bridge site, and then two H atoms are adsorbed at two adjacent fourfold hollow sites) with a classical potential energy barrier of 1.34 kcal/mol. They also 8


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showed that the dissociation over an atop site had a much higher potential energy barrier (about 6 kcal/mol). On the contrary, Kresse14 predicted that the most favorable channel for H2 dissociation on Ni(100) was over the top site (barrierless), and the dissociation over the bridge site possessed a relatively high barrier (3.46 kcal/mol). Considering that the reaction barrier height seriously depends on the electronic structure method78 and the potential energy surface of Truong et al. gives a reasonable barrier which is consistent with experimental observation9 (1.2 kcal/mol), we will use this potential energy surface in our following calculations. We further construct the rigid and quantum Ni(100) lattices for our calculations. In order to get insight into the surface coverage effect, we place one H atom on the Ni(100) surface before H2 dissociation. The embedded cluster model proposed by Truong and Truhlar79 is adopted to construct our lattices. We prepare four lattices, as shown in Figure S1 (in the Supporting Information), so as to test the convergence of H2 dissociation rates with respect to the lattice size, since Suleimanov80 reported that lattice model and the number of Ni atoms had an impact on the effect of lattice motion. In Table S1, we can see that the direct dissociation rates (as well as the steady state rates) of H2 on Lattice I and Lattice III are close to each other. We can also see from Figure S2 that the total free energy barrier on Lattice III is slightly higher than that on Lattice I by 0.04 kcal/mol at 600 K. These situations demonstrate that Lattice I is large enough to give converged rates on the rigid lattice. However, the direct dissociation rate of H2 on Lattice II is larger than that on Lattice IV by 11% at 600 K. It is also seen from Figure S2 that the total free 9



energy barrier on Lattice IV is higher than that on Lattice II by 0.11 kcal/mol at 600 K. Considering that Lattice IV does not improve the rates too much, and the computing time has a dramatic increase (details have been given in the Supporting Information), we finally chose Lattice II as the quantum lattice to calculate the rate constants. Lattice I and Lattice II will be called the rigid and quantum H1-Ni(100) lattices in the following paper. In order to investigate the arrangement effect, two arrangements of H2 and the preadsorbed H have been considered, as shown in Figure 1. In Figure 1(a), the preadsorbed H is located at the nearest hollow site along the bond axis of H2. In Figure 1(b), the preadsorbed H resides at the nearest hollow site perpendicular to the bond axis of H2.

Figure 1. The dissociation of H2 on H precovered Ni(100). Two arrangements ((a) and (b)) of H2 and preadsorbed H have been shown, in which H2 is located at the physisorbed state. 2.2 Reaction Mechanism 10


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There are two possible reaction paths19 for H2 dissociation on H precovered Ni(100) surface. At low temperatures, as described in the paper of Truong et al.,20 H2 could be first trapped in the physisorbed state, and then dissociated over the bridge site. k1

k2

H 2  gas  +H-Ni(100) == H 2 -H-Ni(100)  3H-Ni(100) k1

(1)

However, at high temperatures, H2 has enough energy to fly over the physisorbed state, and dissociates directly. kdirect

H 2  gas  +H-Ni(100) == 3H-Ni(100) krecom

(2)

Here, H-Ni(100) is H precovered Ni(100) surface, k1 is the physisorption rate constant, k-1 is the desorption rate constant of physisorbed H2, k2 is the dissociation rate constant of physisorbed H2, kdirect is the direct dissociation rate constant of gas phase H2, and krecom is the recombination rate constant of H2. If we assume that the concentration of the physisorbed H2 can reach a steady state20 during the reaction, we can obtain the steady state rate constant for the two-step reaction mechanism. ksteady 

k1k2 k1  k2

(3)

Considering that k1  k2 , the steady state rate constant can be approximated as ksteady 

k1  k2 =K  k2 k1

(4)

where K is the equilibrium constant. In the present paper, k2 and kdirect are calculated with the quantum instanton method, while the equilibrium constant K is obtained analytically. 11



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According to the approach proposed by Barber et al.,81 K can be written as K=

QPS exp  V QGS

(5)

where QPS and QGS are the partition functions of physisorbed state and gas phase state for H2/H-Ni(100), V is the potential energy difference between the gas phase state and the physisorbed state. The partition functions are calculated as a product of vibrational, rotational and translational partition functions. It should be noted that the rigid Ni(100) gives no contribution to the partition functions, but the vibrational partition function of the quantum Ni(100) lattice is important and included. 2.3 Quantum Instanton Rate Constant For H2 dissociation on H precovered Ni(100) surface, the rate constant can be calculated by the quantum instanton formula,58,59

kQI 

1 h C ff  0  Qr 4  H   

(6)

In the above formula, Qr is the reactant partition function per unit volume, Cff(0) is zero time value of the flux-flux correlation function, ˆ ˆ ˆ ˆ C ff  t   tr e   H /2 Fâ e   H /2 eiHt 2 / h Fˆb e  iHt 2 / h   

(7)

Here,  is the inverse temperature 1/ (k BT ) , Fâ and Fˆb are the flux operators, and Hˆ is the Hamiltonian operator of the H2/H-Ni(100) system, N pˆ 2 L Pˆ j2 Hˆ   i    Vˆ ( rˆ , Rˆ ) i j i 1 2 mi j 1 2 M j

(8)

where rî , mi , pˆ i and Rˆ j , M j , Pˆj denote the coordinates, masses and momenta of the ith H and jth Ni atoms, respectively, V(ri, Rj) is the potential energy, and N and L are the numbers of H and Ni atoms, respectively. 12


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Fâ and Fˆb are defined by, 2 i ˆ  H , h   rˆ    , (9) Fˆ   h  with  = a, b, h is the Heaviside function, r represents a collection of the Cartesian

coordinates of

H atoms, and  a (r ) and b (r ) stand for two separated dividing

surfaces. H (  ) , in Eq. (6), 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), H (  ) 

  0  Cdd 2Cdd  0 

h 2

(10)

with

Cdd  t   tr e   H /2 ˆ  a  rˆ   e   H /2 eiHt 2 / h ˆ b  rˆ   e  iHt 2 / h    ˆ

Here,

  a (rˆ) 

and

 b (rˆ) 

ˆ

ˆ

ˆ

(11)

are generalized delta-functions, which have the

following form,    rˆ       rˆ  

N

1  m     rˆ   ,   a, b  . i 1

2

i

(12)

i

where i   / ri . The dividing surfaces  a (r ) and b (r ) are defined as follows, in which there are adjustable parameters (  ，  a, b ) that shift the locations of the dividing surfaces.

 ( r ) 

sR (r )    0, (  a, b) sR (r )  s TS (r )

(13)

Here, sx 

Z x  H a   Z x  Hb  Z  H a   Z  Hb     Rx  H a -H b   R  H a -H b   (x=R, TS) 2 2

(14)

where Z  H a  and Z  H b  are the coordinates of the z-axis (normal to the Ni(100) 13



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surface) for the two hydrogen atoms ( H a and H b ) of the dissociated H2, respectively. R(X–Y) denotes the interatomic distance between atoms X and Y. The subscript R and TS represent the values at the reactant region and the transition state geometry, respectively. When calculating kdirect, the gas phase state that H2 is far away from the Ni(100) surface is considered as the reactant. When calculating k2, the physisorbed state is regarded as the reactant. With the above definition, if   0 , sR (r )  0 , the dividing surface is located at the reactant domain, if   1 , sTS (r )  0 , the dividing surface is fixed at the transition state region, and as  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

F  a , b   kBT log Cdd ( a , b )

(15)

and the free energy profile along the reaction path is given by

F    kBT log Cdd ( ,  )

(16)

with    a  b . The values of quantum instanton rate constants are calculated with path integral Monte Carlo technique61 and adaptive umbrella sampling approach.82 The details have been given in the previous papers.21,38,57,83 2.4 Computational Details In our path integral Monte Carlo simulation, the numbers of time slices for H atoms (P) and quantized nickel atoms (Pbath) are different, so as to obtain converged rate constants 14


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with relatively low cost of computation time. To be concrete, (P, Pbath) is set to (100, 10), (80, 8), (60, 6), (50, 5), (40, 4), and (20, 4) at 250, 300, 400, 500, 600, and 800 K, respectively. The number of the Monte Carlo cycle is (4-6) 106 for computing a single ensemble average. It converges most of the rate constants within 10% statistical errors. 3. RESULTS AND DISCUSSION 3. 1 Surface Coverage Effect We calculate the steady state and direct dissociation rates of H2 on H precovered rigid Ni(100) surface (H1-Ni(100), as seen in Figure 1) in the temperature range of 250-800 K. In order to explore the surface coverage effect, we further obtain the steady state and direct dissociation rates of H2 on a clean rigid Ni(100) surface. The calculated rates are listed in Table 1, and the corresponding Arrhenius plots are depicted in Figure 2. Table 1. The Equilibrium Constants K (cm3∙site-1), Rate Constants k2 (s-1), Steady State Dissociation Rates ksteady (cm3∙site-1∙s-1), and Direct Dissociation Rates kdirect (cm3∙site-1∙s-1) of H2 on Ni(100) and H1-Ni(100) T K 2.07(-24)a 2.44(-24) 3.23(-24) 4.17(-24) 5.26(-24) 7.97(-24)

250 300 400 500 600 800

H2/Ni(100) k2 ksteady b 7.61(11) 1.57(-12) 1.20(12) 2.92(-12) 1.66(12) 5.37(-12) 2.00(12) 8.33(-12) 3.00(12) 1.58(-11) 4.13(12) 3.29(-11)

kdirect 2.15(-12) 1.57(-12) 1.29(-12) 1.65(-12) 1.91(-12) 3.10(-12)

K 1.05(-24) 1.24(-24) 1.65(-24) 2.12(-24) 2.67(-24) 4.05(-24)

H2/H1-Ni(100) k2 ksteady 6.16(11) 6.49(-13) 8.32(11) 1.03(-12) 1.23(12) 2.02(-12) 1.71(12) 3.63(-12) 2.34(12) 6.26(-12) 3.62(12) 1.46(-11)

kdirect 6.49(-13) 5.98(-13) 7.11(-13) 1.04(-12) 1.35(-12) 1.84(-12)

a

Power of 10 in parentheses. b From ref 38. In Table 1, we can see that the steady state rates of H2 on H1-Ni(100) increase rapidly with increasing temperature. However, there is only a slow increase for the direct 15



rates of H2. The nearly temperature-independent direct rates at low temperatures on H1-Ni(100), as well as the negative temperature dependence84 of direct rates at low temperatures on Ni(100), demonstrate that the quantum tunneling dominates the direct dissociation rates of H2 at low temperatures.

-24.0

H2/Ni(100) steady state H2/Ni(100) direct 1

H2/H -Ni(100) steady state

-25.5

1

H2/H -Ni(100) direct

3

-1

-1

ln k (cm site s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-27.0

-28.5

1

2

3

1000/T(K)

4

Figure 2. Arrhenius plots of rate constants for H2/Ni(100) and H2/H1-Ni(100). The solid, dashed, dotted and dash-dotted lines stand for steady state and direct dissociation rates on the clean and H precovered rigid Ni(100) surfaces, respectively. On H1-Ni(100) surface, detailed comparisons show that steady state rates are much larger than direct rates at high temperatures, but it seems that the former would be smaller than the latter at low temperatures, as seen in Figure 2. These steady state and direct rates have an intersection point at about 250 K, at which these two kinds of rates are equal to 16


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each other. In Figure 2, it is also seen that the difference of steady state and direct rates increases with increasing temperature over the temperature range 250-800 K. To track down the underlying reasons, we analyze the equilibrium constant K and k2, which are two components of the steady state rate. We find that both the equilibrium constant K and k2 increase with increasing temperature, and they increase much faster than the direct rate. For instance, K, k2 and kdirect are increased by 3.86, 5.88 and 2.83 times from 250 to 800 K.

3 1

Free energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


250 K 300 K 400 K 500 K 600 K 800 K

2

1

H2/H -Ni(100)

0

-1 0.0

0.5

1.0

 Figure 3. Free energy profiles along the reaction path for H2/H1-Ni(100). The solid, dashed, dotted, dash-dotted, dash-dot-dotted and short-dash-dotted lines represent the free energy profiles at 250, 300, 400, 500, 600 and 800 K on the rigid lattice, respectively. We have also explored the temperature dependence of the free energy well, which corresponds to the physisorbed state. As seen in Figure 3, the free energy well between 17



the reactant and transition state becomes shallower and shallower with increasing temperature. For instance, the depth of the free energy well changes from -0.93 kcal/mol at 250 K to -0.65 kcal/mol at 800 K. This phenomenon reveals that the physisorbed state is stable at low temperatures, but it becomes more and more unstable with increasing temperature. This situation further confirms the reaction mechanism discussed in Section 2.2 that H2 is most probably dissociated through a two-step process at low temperatures, while it is ruptured directly at high temperatures.

300 K

1

0.96

H2/Ni(100)


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1

H2/H -Ni(100)

0.21

0

-0.90

-1 -1.16

0.0

0.5

1.0

 Figure 4. Free energy profiles along the reaction path for H2/Ni(100) and H2/H1-Ni(100) at 300 K. The solid and dashed lines represent the free energy profiles on the clean and H precovered rigid Ni(100) surfaces, respectively. In Table 1, we can also see that both the steady state and direct rates of H2 on the clean Ni(100) surface are much larger than those on H1-Ni(100). For instance, at 300 K, 18


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the steady state dissociation rate of H2 on the clean Ni(100) surface is 2.83 times larger than that on H1-Ni(100), and the corresponding ratio of direct rates is 2.63. These phenomena can be explained by the free energy profile along the reaction path. As illustrated in Figure 4, the preadsorbed H atom shallows the free energy well (the physisorbed state) and raises the dissociation free energy barrier. These situations reveal that there is a repulsive interaction between H2 and the preadsorbed H. Indeed, this repulsive interaction makes the classical potential energy barrier of H2 increased from 1.34 kcal/mol on Ni(100) to 1.51 on H1-Ni(100). If the zero-point energies are included, the potential energy barrier is raised from 1.15 to 1.36 kcal/mol. The steady state rate consists of equilibrium constant K and k2, it is seen from Table 1 that both K and k2 on Ni(100) are larger than those on H1-Ni(100). The larger equilibrium constant on Ni(100) is due to the fact that the free energy well on Ni(100) is deeper than that on H1-Ni(100), as seen in Figure 4. The deeper the well is, the larger the equilibrium constant will be. The larger k2 on Ni(100) is because the free energy barrier from the well to transition state on Ni(100) is lower than that on H1-Ni(100). The direct rate depends on the total free energy barrier from the reactant to transition state. It is seen that the total free energy barrier on H1-Ni(100) is higher than that on Ni(100) by 0.75 kcal/mol at 300 K, so the direct rate on Ni(100) is larger than that on H1-Ni(100). In order to get the activation energy and compare with experiment, we fit the rate constants to the Arrhenius form (Details have been given in the Supporting Information). The obtained preexponential factor (A) and activation energy (Ea) are listed in Table S2. From Table S2, we can see that the activation energy of direct process is always much lower than that of the steady state process. This is because the potential energy barrier 19



from the reactant (H2 is far away from Ni(100) surface) to transition state is much lower than that from the physisorbed state to transition state. For H2/Ni(100), the activation energy of direct process is 1.34 kcal/mol over the temperature range 400-800 K, which is in line with the experimental value9 (1.20 kcal/mol). We can also see that H2/H1-Ni(100) always possesses a higher activation energy than H2/Ni(100) regardless of the direct process or the steady state process. This is consistent with our aforementioned conclusion that there is a repulsive interaction between H2 and the preadsorbed H, which raises the potential energy barrier. The Arrhenius plot also has a role to reveal the quantum tunneling effect. If the Arrhenius plot deviates from linearity, it indicates that the quantum tunneling becomes significant. For instance, from Figure S3(c) (in the Supporting Information) we can infer that quantum tunneling dominates the direct dissociation of H2 on H1-Ni(100) below 390 K. 3. 2 Lattice Motion Effect We also calculate the steady state and direct dissociation rates of H2 on the quantum H1-Ni(100) surface, so as to reveal the lattice motion effect. In the simulation, 11 Ni atoms close to H2 and the preadsorbed H are treated quantum mechanically, 36 Ni atoms near to the quantum Ni atoms are movable and handled as classical particles, and the rest of Ni atoms are fixed. The obtained rates have been tabulated in Table 2. Figure 5 is the corresponding Arrhenius plots.

20


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Table 2. Steady State Dissociation Rates ksteady (cm3∙site-1∙s-1) and Direct Dissociation Rates kdirect (cm3∙site-1∙s-1) of H2 on the Rigid and Quantum H1-Ni(100) T

rigid lattice ksteady kdirect a 250 6.49(-13) 6.49(-13) 300 1.03(-12) 5.98(-13) 400 2.02(-12) 7.11(-13) 500 3.63(-12) 1.04(-12) 600 6.26(-12) 1.35(-12) 800 1.46(-11) 1.84(-12) a Power of 10 in parentheses.

quantum lattice ksteady kdirect 8.92(-13) 1.01(-12) 1.42(-12) 8.50(-13) 3.31(-12) 9.68(-13) 5.13(-12) 1.21(-12) 7.90(-12) 1.75(-12) 1.91(-11) 2.44(-12)

It is apparent from Figure 5 that both the steady state and direct rates on the quantum lattice are larger than those on the rigid lattice. For instance, at 300 K, the steady state rate on the quantum lattice is 1.24 times larger than that on the rigid lattice. Moreover, the direct rate on the quantum lattice exceeds the one on the rigid lattice by 1.42 times. These phenomena can be explained by the free energy profile along the reaction path. In Figure 6, we can see that the free energy well between the reactant and transition state on the quantum lattice is deeper than that on the rigid lattice, and the free energy barrier from the well to transition state on the quantum lattice is lower than that on the rigid lattice. The steady state rate relies on both the depth of the well and the height of the barrier. The deeper well on the quantum lattice means that the equilibrium constant on the quantum lattice is larger than that on the rigid lattice. Furthermore, the lower barrier on the quantum lattice also leads to a larger value of k2. These two factors make the steady state rate on the quantum lattice larger than that on the rigid lattice.

21



-24.0 steady state, rigid lattice direct, rigid lattice steady state, quantum lattice direct, quantum lattice

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3

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-1

ln k (cm site s )

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1

H2/H -Ni(100)

1

2

1000/T(K)

3

4

Figure 5. Arrhenius plots of rate constants for H2/H1-Ni(100). The solid, dashed, dotted, and dash-dotted lines stand for steady state and direct dissociation rates of H2 on the H precovered rigid and quantum Ni(100) surfaces, respectively.

22


Page 23 of 48

1

0.96

300 K 1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


H2/H -Ni(100), rigid lattice 1

0.62

H2/H -Ni(100), quantum lattice

0

-0.90

-1

-0.95

0.0

0.5

1.0

 Figure 6. Free energy profiles along the reaction path for H2/H1-Ni(100) at 300 K. The solid and dotted lines represent the free energy profiles on the H precovered rigid and quantum Ni(100) surfaces, respectively. The direct rate depends solely on the total free energy barrier from reactant to transition state. In Figure 6, we can see that the total free energy barriers from the reactant to transition state are 0.62 and 0.96 kcal/mol on the quantum and rigid lattices, respectively. It is clear that the lattice motion reduces the total free energy barrier by 0.34 kcal/mol at 300 K. To uncover the underlying reasons, we perform the normal mode analysis. Our calculations show that the zero-point energy of quantum lattice affects the potential energy barrier little. Under this circumstance, the large free energy barrier difference may come from the classical relaxation of the movable Ni atoms. The classical relaxation of the movable Ni atoms stabilizes the transition state more than the reactant, 23



and therefore the classical potential energy barrier declines from 1.51 to 1.36 kcal/mol. Moreover, the entropy effect may also contribute a lot to the decrease of the total free energy barrier on quantum lattice. The underlying mechanism is that the lattice motion increases the entropies of both reactant and transition state, but it increases the entropy of transition state more than that of reactant. The larger the entropy of transition state is, the lower the free energy barrier will be. 3.3 Arrangement Effect We have investigated the arrangement effect of H2 dissociation on a H precovered Ni(100). Two arrangements (H2/H1-Ni(100) and H2/H2-Ni(100), as seen in Figure 1.) of H2 and the preadsorbed H atom are considered. The steady state and direct dissociation rates corresponding to these two arrangements are calculated. The rates of H2/H2-Ni(100) are tabulated in Table 3. Figure 7 displays the Arrhenius plots of these rates. Table 3. Steady State Dissociation Rates ksteady (cm3∙site-1∙s-1) and Direct Dissociation Rates kdirect (cm3∙site-1∙s-1) of H2 on the Rigid H2-Ni(100) T ksteady kdirect 250 4.94(-13)a 4.09(-13) 300 7.71(-13) 4.33(-13) 400 1.52(-12) 5.01(-13) 500 2.89(-12) 7.79(-13) 600 4.85(-12) 1.12(-12) 800 1.15(-11) 1.41(-12) a Power of 10 in parentheses.

24


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Page 25 of 48

steady state

direct

1

H2/H -Ni(100)

1

2

H2/H -Ni(100)

H2/H -Ni(100)

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2

H2/H -Ni(100)

3

-1

-1

ln k (cm site s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-27.0

-28.5 1

2

3

1000/T(K)

4

Figure 7. Arrhenius plots of rate constants for H2/H1-Ni(100) and H2/H2-Ni(100). The solid, dashed, dotted and dash-dotted lines stand for steady state and direct dissociation rates of H2 on the rigid H1-Ni(100) and H2-Ni(100) surfaces, respectively. In Figure 7, we can see that both the steady state and direct rates of H2/H2-Ni(100) increase with increasing temperature, while the steady state rates grow much faster than those of direct rates. Detailed comparisons show that the steady state rates are much larger than the direct rates at high temperatures, but the direct rate becomes close to the steady state one at 250 K. This situation is similar to the case of H2/H1-Ni(100), and can be explained in the same way. It is the rapid increase of equilibrium constant and k2 that makes the steady state rates grow faster than the direct rates with increasing temperature.

25



1.05

300 K

1

0.96

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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H2/H -Ni(100) 2

H2/H -Ni(100)

0

-0.83

-1

-0.90

0.0

0.5

1.0

 Figure 8. Free energy profiles along the reaction path for H2/H1-Ni(100) and H2/H2-Ni(100) at 300 K. The solid and dashed lines denote the free energy profiles on the rigid H1-Ni(100) and H2-Ni(100) surfaces, respectively. In Table 1 and 3, it is seen that the direct rates of H2/H2-Ni(100) are smaller than those of H2/H1-Ni(100). For instance, the ratio of H2/H1-Ni(100) to H2/H2-Ni(100) is 1.38 at 300 K. This situation can be explained by the total free energy barrier from the reactant to transition state. As seen in Figure 8, the total free energy barriers for H2/H1-Ni(100) and H2/H2-Ni(100) are 0.96 and 1.05 kcal/mol, respectively. The lower the free energy barrier is, the faster the reaction will be. The higher free energy barrier on H2-Ni(100) is caused by the repulsive interaction between H2 and the preadsorbed H. Our studies show that the classical potential energy barriers for H2/H1-Ni(100) and H2/H2-Ni(100) are 1.51 and 1.68 kcal/mol, respectively. It is clear that the repulsive interaction on H2-Ni(100) is 26


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stronger than that on H1-Ni(100). Considering that the distance between H2 and the preadsorbed H on H2-Ni(100) is shorter than that on H1-Ni(100), our results demonstrate that the repulsive interaction is inversely proportional to the distance. The steady state rates are increased from H2/H2-Ni(100) to H2/H1-Ni(100) in the whole tested temperature range. For instance, the steady state rate on H1-Ni(100) is 1.34 times larger than that on H2-Ni(100) at 300 K. This phenomenon can also be explained by the free energy profile along the reaction path, as depicted in Figure 8. Compared the free energy profile of H2/H1-Ni(100) with that of H2/H2-Ni(100), we can see that the former has a deeper well and a lower barrier (from the well to transition state). The lower barrier of H2/H1-Ni(100) promotes the steady state rate by increasing k2, and the deeper well of H2/H1-Ni(100) enhances the steady state rate by increasing K. As a result, the steady state rates of H2/H1-Ni(100) are larger than those of H2/H2-Ni(100). 3.4 Kinetic Isotope Effect We have also calculated the steady state and direct rates of D2 on a D precovered Ni(100) surface (D2/D1-Ni(100)). In order to get insight into the lattice motion effect on the kinetic isotope effect, we further carry out the steady state and direct rates on the quantum lattice. The kinetic isotope effects are listed in Table 4. Table 4. Kinetic Isotope Effects for H2 Dissociation on H1-Ni(100) T

250 300 400 500

(H2/H1-Ni(100)) / (D2/D1-Ni(100)) rigid lattice quantum lattice steady state direct steady state direct 3.59 6.68 3.20 5.68 3.34 4.10 2.94 3.38 2.85 3.32 2.85 2.92 2.26 3.25 2.31 2.30 27



600 800

1.93 1.84

2.96 2.21

1.77 1.74

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2.02 1.81

From Table 4, it is seen that there are remarkable kinetic isotope effects for H2 dissociation on H precovered Ni(100) surface. All of the kinetic isotope effects are much larger than 1. This is because the free energy barriers of H2/H1-Ni(100) are always much lower than those of D2/D1-Ni(100) on both rigid and quantum lattices, as seen in Figure 9. For instance, the total free energy barriers of H2/H1-Ni(100) and D2/D1-Ni(100) are 0.96 and 1.78 kcal/mol on the rigid lattice at 300 K. Our normal mode analyses demonstrate that the zero-point energy corrected potential energy barrier of D2/D1-Ni(100) (1.39 kcal/mol) is only a little higher than that of H2/H1-Ni(100) (1.36 kcal/mol) on the rigid lattice, so the large difference of total free energy barriers should come mainly from the entropy effect. Due to the thin potential energy barrier, the chains of H atoms with P beads (one classical H atom is replaced by P images of itself in terms of path integral) at the transition state can delocalize and drape down to either side of the barrier to sample a lower potential,85 and therefore the chains of H atoms can distribute in larger areas and have more available configurations, which leads to a larger entropy at the transition state and lowers the free energy barrier. Due to relatively larger mass, the distribution areas of D atoms are smaller than those of H atoms, so the entropy decreases the free energy barrier of D2 less than that of H2. It is also seen that all of the kinetic isotope effects increase rapidly with decreasing temperature, which indicates that quantum tunneling is significant. Owing to relatively smaller mass, the quantum tunneling enhances the dissociation rates of H2 much more 28


Page 29 of 48

and faster than those of D2 with decreasing temperature.

2 1

H2/H -Ni(100) rigid lattice 1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


H2/H -Ni(100) quantum lattice

1

1

D2/D -Ni(100) rigid lattice 1

D2/D -Ni(100) quantum lattice

0

-1 0.0

0.5

1.0

 Figure 9. Free energy profiles along the reaction path for H2/H1-Ni(100) and D2/D1-Ni(100) on the rigid and quantum lattices at 300 K. Detailed comparisons show that the kinetic isotope effects of steady state process are smaller than those of the direct process. For instance, on the rigid lattice, the ratio of the direct and steady state kinetic isotope effects is 1.22 at 300 K. It is seen from Figure 9 that the depths of free energy wells for H2/H1-Ni(100) and D2/D1-Ni(100) are nearly the same, and therefore the difference of the steady state and direct kinetic isotope effects should be caused by the heights and widths of free energy barriers. The kinetic isotope effect is usually dominated by the zero-point energy and quantum tunneling. However, for the present reaction, the zero-point energy corrected potential energy barriers of D2/D1-Ni(100) (1.39 kcal/mol) and H2/H1-Ni(100) (1.36 kcal/mol) are close to each other. 29



So, quantum tunneling effect should be the main factor to affect the kinetic isotope effect. For the direct process, the gas phase H2 just needs to get through a low and thin barrier. However, for the steady state process, H2 is first trapped in the physisorbed state, and then dissociated from there with a high and thick barrier. These situations indicate that the quantum tunneling effect of the direct process is more remarkable than that of the steady state process. As a result, the kinetic isotope effects of the direct process are larger than those of the steady state process. This conclusion can be confirmed by the Arrhenius plots of the direct and steady state rates. In Figure S3(a-l) (in the Supporting Information), we can see that the Arrhenius plots of direct rates deviate from linearity much greater than those of steady state rates, which reveals that the direct process has a more remarkable quantum tunneling effect. In Table 4, we can also see that the kinetic isotope effects on the rigid and quantum lattices are close to each other, which reveals that the lattice motion affects the kinetic isotope effect little. Just as discussed in Section 3.2, the lattice motion influences the dissociation barrier by the classical relaxation and entropy of the Ni atoms. However, both the classical relaxation and entropy of Ni atoms lower the dissociation barrier of D2/D1-Ni(100) the same as that of H2/H1-Ni(100). Our calculated kinetic isotope effects are qualitatively consistent with the experimental observations of Hamza et al.9 and Zhu et al.,8 who reported that the initial dissociative sticking probability of D2 was lower than that of H2 on Ni(100). 3.5 Recombination Rates We calculate the recombination rate of H2 on a H precovered rigid Ni(100) surface. In our calculations, the preadsorbed H is located at the adjacent four-fold site along the bond 30


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axis of H2(H1-Ni(100)), as seen in Figure 1. During the reaction, the movement of the preadsorbed H atom is restrained in the four-fold hollow site, and the preadsorbed H atom acts as a spectator but gives an influence on the recombination of H2. We also calculate the recombination rate of H2 on the quantum lattice, so as to reveal the lattice motion effect. The obtained recombination rates of H2, together with those of D2, are tabulated in Table 5. Figure 10 is the corresponding Arrhenius plots. Table 5. Recombination Rate Constants (s-1) of H2/H1-Ni(100) and D2/D1-Ni(100) T 250 300 400 500 600 800 a

H2/Ni(100) rigid 3.89(-4)a 4.25(-1) 2.62(3) 3.36(5) 1.18(7) 8.39(8)

H2/H1-Ni(100) rigid quantum 2.59(-4) 1.39(-4) 3.06(-1) 1.49(-1) 1.43(3) 9.03(2) 2.67(5) 1.72(5) 8.41(6) 4.94(6) 6.16(8) 3.96(8)

D2/D1-Ni(100) rigid quantum 2.17(-4) 1.03(-4) 3.34(-1) 1.43(-1) 1.38(3) 8.40(2) 3.04(5) 1.60(5) 8.72(6) 5.57(6) 6.22(8) 4.16(8)

From ref 38, power of 10 in parentheses.

In Table 5, on the rigid lattice, we can see that the recombination rates of H2 on the clean Ni(100) surface are larger than those on H1-Ni(100). For instance, the ratio of these two kinds of rates is 1.39 at 300 K. The larger recombination rate on the clean Ni(100) surface is due to the relatively lower free energy barrier. As shown in Figure 11, the free energy barriers for H2 on rigid Ni(100) and H1-Ni(100) are 19.98 and 20.32 kcal/mol at 300 K. Our calculations demonstrate that the classical potential energy barriers for H2/Ni(100) and H2/H1-Ni(100) are 20.39 and 20.52 kcal/mol, respectively, and the zero-point energy corrections further raise the potential energy barriers by 0.50 and 0.52 kcal/mol, respectively. This situation reveals that the zero-point energy of the 31



preadsorbed H influences the potential energy barrier a little, but the repulsive interaction between the preadsorbed H and H2 raises the potential energy barrier a lot.

20.0

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H2/Ni(100), rigid lattice H2/H -Ni(100), rigid lattice

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5.0 0.0 -5.0

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1000/T(K)

Figure 10. Arrhenius plots of recombination rate constants for H2/Ni(100), H2/H1-Ni(100) and D2/D1-Ni(100). The solid line represents the recombination rates of H2 on the rigid Ni(100). The dashed, dotted, dash-dotted and dash-dot-dotted lines stand for recombination rates on the rigid and quantum H1-Ni(100) and D1-Ni(100) surfaces, respectively. Compared to the recombination rates of H2 on the rigid H1-Ni(100), the rates of H2 on the quantum lattice are much smaller. According to Table 5, the rate on the rigid lattice is 2.05 times larger than that on the quantum lattice at 300 K. This phenomenon can also be explained by the free energy barrier. As shown in Figure 11, the free energy 32


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barriers on the quantum and rigid lattices are 20.60 and 20.32 kcal/mol, respectively. It is clear that the former is 0.28 kcal/mol higher than the latter at 300 K. Our research shows that the classical potential energy barriers for H2/H1-Ni(100) on the quantum and rigid lattices are 20.44 (including the effect of classical relaxation of Ni atoms) and 20.52 kcal/mol, respectively, and zero-point energy corrections (0.49 and 0.52 kcal/mol on the quantum and rigid lattices, respectively, the zero-point energy of Ni atoms still contributes a little to the potential energy barrier.) increase these two potential energy barriers to 20.93 and 21.04 kcal/mol. It is clear that, although H2 has a lower zero-point energy corrected potential energy barrier on the quantum lattice, it possesses a higher free energy barrier on the quantum lattice. The underlying mechanism is that, compared to the rigid lattice, the quantum lattice enlarges the entropies of product (three H atoms are adsorbed at three adjacent four-fold hollow sites on Ni(100)) and transition state by including the entropy of Ni atoms, and it enhances the entropy of product more than that of transition state, which raises the free energy barrier. As shown in Figure 10, the recombination rates of H2/H1-Ni(100) and D2/D1-Ni(100) are nearly the same over the whole tested temperature range. This phenomenon can be explained by the fact that the zero-point energy correction raises the classical potential energy barrier for the recombination process, and it raises the barrier of H2/H1-Ni(100) more than that of D2/D1-Ni(100) by 0.16 kcal/mol. As a consequence, the free energy barrier of H2/H1-Ni(100) is higher than that of D2/D1-Ni(100). For instance, the former is higher than the latter by 0.22 kcal/mol at 300 K. Although the free energy barrier of H2/H1-Ni(100) is higher, which can hinder the recombination of H2, the quantum tunneling of H2/H1-Ni(100) is much more remarkable than that of D2/D1-Ni(100), which 33



can enhance the recombination rate. The overall effect is that the recombination rates of H2/H1-Ni(100) and D2/D1-Ni(100) are close to each other. This phenomenon indicates that there is no kinetic isotope effect for the recombination process.

quantum lattice

rigid lattice

20 Free energy (kcal/mol)

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H2/Ni(100) 1

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1 1

10 20

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18

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1.1

1.2

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 Figure 11. Free energy profiles along the reaction path for H2/Ni(100), H2/H1-Ni(100) and D2/D1-Ni(100) on the rigid and quantum lattices at 300 K. From Table 5, it is seen that the recombination rates of D2/D1-Ni(100) on the quantum lattice are much smaller than those on the rigid lattice. This case is due to the fact that the free energy barrier on the quantum lattice (20.46 kcal/mol) is higher than that on the rigid lattice (20.10 kcal/mol), as seen in Figure 11. This trend is similar to the case of H2/H1-Ni(100), and can be explained in the same way. Although the zero-point energy corrected potential energy barrier of D2/D1-Ni(100) on the quantum lattice is lower than that on the rigid lattice by 0.08 kcal/mol, the quantum lattice raises the free energy barrier 34


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by increasing the entropies of product and transition state, and the entropy of product is increased more than that of transition state. On the clean Ni(100) surface, our fitted activation energy of H2 recombination is 20.15 kcal/mol (Table S3 in the Supporting Information). On the H precovered Ni(100) surface, the activation energy is increased to 20.90 kcal/mol. These values are consistent with the experimental values of Christmann11 ( 20±2 and 23±1 kcal/mol). 4. CONCLUSIONS Hydrogen molecule can be dissociated on Ni(100) through two ways, one is the direct process, the other is the two-step process via the physisorbed state. We have calculated the direct and steady state dissociation rates of H2 with the quantum instanton method in full dimensionality, and investigated the surface coverage, lattice motion, arrangement and kinetic isotope effects. There is a repulsive interaction between H2 and the preadsorbed H, which can raise the potential energy barrier, and therefore both the direct and steady state dissociation rates of H2 on H precovered Ni(100) are much smaller than those on the clean Ni(100). Moreover, this repulsive interaction is inversely proportional to the distance between H2 and the preadsorbed H. For instance, the dissociation rates of H2/H1-Ni(100) are larger than those of H2/H2-Ni(100) which has a shorter distance. The stability of the physisorbed state is affected by temperature, repulsive interaction and lattice motion. The physisorbed state becomes more and more unstable with increasing temperature. The repulsive interaction between H2 and the preadsorbed H weakens the stability of the physisorbed state, while the lattice motion stabilizes the physisorbed state. 35



The lattice motion plays an import role in H2 dissociation and recombination. The zero-point energies of Ni atoms affect the potential energy barriers little, while the classical relaxation of Ni atoms reduces both the dissociation and recombination potential energy barriers. The entropy effect of the lattice lowers the free energy barrier for H2 dissociation, but it raises the free energy barrier for H2 recombination. The overall effect of lattice motion is that it enhances the dissociation rates, but hinders the recombination rates. It should be mentioned that the effect of lattice motion is affected by the lattice model and the number of Ni atoms. Due to the computing time issue, our calculations are based on the embedded cluster model with a few quantum Ni atoms, which could be improved by using the lattice with periodic boundary conditions. The calculated kinetic isotope effects of H2 dissociation are much larger than 1 and increase with decreasing temperatures. These situations are caused by the entropy and quantum tunneling effects, which enhance the dissociation rates of H2 more and faster than those of D2 with decreasing temperatures. However, no kinetic isotope effect is obtained for H2 recombination. The present surface coverage, lattice motion, arrangement, and kinetic isotope effects on H precovered Ni(100) are similar to our previous results on H precovered Ni(111). The lattice motion and kinetic isotope effects are nearly the same. However, the surface coverage and arrangement effects on Ni(111) are 2 times larger than those on Ni(100), which is because the repulsive interaction between H2 and the preadsorbed H atom is larger on Ni(111) due to the shorter distance. In addition, the preadsorbed H atom on Ni(111) affects the stability of the physisorbed state of H2 much more than that on Ni(100). 36


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ASSOCIATED CONTENT Supporting Information Details of the lattice size effect and fitting to Arrhenius form, as well as the obtained preexponential factors and activation energies, are given. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] ORCID Wenji Wang: 0000-0002-3607-1252 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. 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. REFERENCES (1) Alducin, M.; Díez Muiño, R.; Juaristi, J. I. Non-adiabatic Effects in Elementary Reaction Processes at Metal Surfaces. Prog. Surf. Sci. 2017, 92, 317-340.

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