Six-dimensional quantum dynamics study for the dissociative adsorption of HCl on Au(111) surface.

Six-dimensional quantum dynamics study for the dissociative adsorption of HCl on Au(111) surface Tianhui Liu, Bina Fu, and Dong H. Zhang Citation: The Journal of Chemical Physics 139, 184705 (2013); doi: 10.1063/1.4829508 View online: http://dx.doi.org/10.1063/1.4829508 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Six-dimensional quantum dynamics study for the dissociative adsorption of DCl on Au(111) surface J. Chem. Phys. 140, 144701 (2014); 10.1063/1.4870594 A six-dimensional wave packet study of the vibrational overtone induced decomposition of hydrogen peroxide J. Chem. Phys. 136, 164314 (2012); 10.1063/1.4705755 Quantum dynamics of dissociative chemisorption of CH 4 on Ni(111): Influence of the bending vibration J. Chem. Phys. 133, 144308 (2010); 10.1063/1.3491031 Six-dimensional quantum dynamics of H 2 dissociative adsorption on the Pt(211) stepped surface J. Chem. Phys. 128, 194715 (2008); 10.1063/1.2920488 The structure, energetics, and nature of the chemical bonding of phenylthiol adsorbed on the Au(111) surface: Implications for density-functional calculations of molecular-electronic conduction J. Chem. Phys. 122, 094708 (2005); 10.1063/1.1850455

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THE JOURNAL OF CHEMICAL PHYSICS 139, 184705 (2013)

Six-dimensional quantum dynamics study for the dissociative adsorption of HCl on Au(111) surface Tianhui Liu, Bina Fu, and Dong H. Zhanga) State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People’s Republic of China

(Received 25 September 2013; accepted 28 October 2013; published online 8 November 2013) The six-dimensional quantum dynamics calculations for the dissociative chemisorption of HCl on Au(111) are carried out using the time-dependent wave-packet approach, based on an accurate PES which was recently developed by neural network fitting to density functional theory energy points. The influence of vibrational excitation and rotational orientation of HCl on the reactivity is investigated by calculating the exact six-dimensional dissociation probabilities, as well as the four-dimensional fixed-site dissociation probabilities. The vibrational excitation of HCl enhances the reactivity and the helicopter orientation yields higher dissociation probability than the cartwheel orientation. A new interesting site-averaged effect is found for the title molecule-surface system that one can essentially reproduce the six-dimensional dissociation probability by averaging the four-dimensional dissociation probabilities over 25 fixed sites. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4829508] I. INTRODUCTION

The dissociative chemisorption of molecular species on transition-metal surfaces is of significant importance in heterogeneous catalytic reactions. It represents the rate-limiting step in heterogeneous catalytic processes; numerous efforts have been devoted to studying this dissociation process both experimentally and theoretically during the past several decades.1–15 Theoretically, it is therefore essential to investigate reaction mechanisms for dissociative adsorption processes at the quantum mechanical level. Starting from the reduced two-dimensional approach for the quantum mechanical calculations of dissociative adsorption of H2 on Ni(100),16 it is now possible to perform full-dimensional quantum dynamics calculations for the diatomic molecules dissociating on metals.17–25 However, due to the difficulties in constructing reliable potential energy surfaces (PESs) and developing quantum mechanical methodologies, very limited quantum dynamics calculations were carried out for dissociative adsorption reactions, mainly with the chemisorption of the simple H2 molecule on metal surfaces.17–32 A full-dimensional quantum mechanical description of polyatomic dissociative chemisorption is still extremely challenging. A total of 15 degrees of freedom should be considered on a rigid surface for the dissociative adsorption of CH4 on Ni surface, rendering it difficult to develop an accurate, global PES and to carry out quantum dynamical calculations. Hence, several quantum dynamical studies of CH4 on Ni surfaces resorted to employ low-dimensional models.33–36 Recently, Guo and coworkers investigated two polyatomic dissociative chemisorption reactions using reduced-dimensional approaches, i.e., a) Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-9606/2013/139(18)/184705/8/$30.00

six-dimensional quantum dynamics calculations of H2 O on Cu(111)37–39 and eight-dimensional calculations of CH4 on Ni(111).40 Accurate PESs were fit by the permutationally invariant polynomial approach of Bowman and co-workers41, 42 based on energy points from density functional theory (DFT) calculations. In this work we carried out full-dimensional (sixdimensional) quantum dynamics calculations of HCl dissociative chemisorption on Au(111), employing an accurate PES recently developed by neural network fitting to DFT energy points (LFZ PES).43 Experimentally, Lykke and Kay performed a molecule beam-surface scattering experiment of HCl scattered from Au(111) in 1990, indicating a direct inelastic scattering mechanism.44 Recently, Wodtke and coworkers investigated the energy transfer between gas and solid interfaces for this system, and a transition from an electronically adiabatic mechanical mechanism to an electronically nonadiabatic mechanism involving excited electron-hole pairs as the surface temperature increases was reported.45–48 To the best of our knowledge, none of theoretical investigations was reported for the title reaction except our study of the PES. Following our recent work for the construction of an accurate, six-dimensional PES of the title moleculesurface reaction,43 we present the detailed quantum dynamical results in this article. The motion of surface atoms and excited electron-hole pairs were ignored in the adiabatic PES we constructed, and all the calculations were based on the rigid surface approximation, thus the current theory is not able to directly describe the experimental quantities measured by Wodtke and co-workers.45–48 We utilize the time-dependent wave packet (TDWP) approach to carry out the full-dimensional (six-dimensional) and four-dimensional fixed-site calculations on the LFZ PES. The four-dimensional calculations are done with the center

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of mass (COM) of HCl fixed at the bridge, top, hollow, and fcc sites, respectively. The effect of vibrational excitation and rotational orientation of HCl on the reactivity is investigated in detail. Furthermore, we investigate the site-averaged effect for the title reaction, in contrast to the effect that was found in the H2 dissociative adsorption on Cu(111) by Dai and Light.18 In that work, they found the averaged dissociation probability of the four-dimensional calculations over the three symmetric impact sites (bridge, center, and top) for H2 initially in the ground rovibrational state (v = 0, j = 0) is similar in shape with the exact dissociation probability of the sixdimensional calculations, while the latter is shifted to higher energy by about 0.05 eV. They assumed this energy shift was caused by the zero point energy (ZPE) differences between the four-dimensional and six-dimensional calculations at the transition states, since the six-dimensional calculation incudes the ZPE for the two lateral coordinates x and y. However, as seen from results reported in that study, the dissociation probability of the six-dimensional calculations is obviously larger than the shifted four-dimensional site-averaged dissociation probability at high kinetic energy. Thus, in this work we aim to find out whether the exact dissociation probabilities of the six-dimensional calculations can be accurately reproduced in some way from the dissociation probability of the four-dimensional fixed-site calculations for the title reaction. The paper is organized as follows. In Sec. II we present the detailed TDWP methodologies used for the diatomic molecule-surface interactions. A brief description of the PES for the title reaction used in the current study is given too. The dissociation probabilities of four-dimensional fixed-site calculations and exact six-dimensional calculations are presented in Sec. III. The influences of initial vibrational excitations and rotational orientations on the reactivity, together with the site-averaged effect are discussed in detail in this section. A summary and conclusions are given in Sec. IV.

ez

Cl

r ey

Z θ

H

φ α =120

ex Au

FIG. 1. Molecular coordinates for the collision of HCl and Au(111), where (x, y, Z) are the center-of-mass coordinates of HCl, r is the internuclear distance of HCl, θ is the polar angle, and φ is the azimuthal angle. Here α is the skewing angle and equals 120◦ .

action potential energy. Here the skewing angle α equals 120◦ for Au(111) surface. The reference vibration eigenfunction φv (r) of HCl satisfies the equation ¯2 ∂ 2 − + V (r) φv (r) = εv φv (r), (2) 2μ ∂r 2 where V (r) is the 1D reference potential obtained from the total interaction potential V (x, y, Z, r, θ, φ) with other degrees of freedom fixed at specific values. The time-dependent wave function is expanded in terms of translational basis of R, φv (r), and angular momentum eigenfunctions Yjm (θ, φ) as (x, y, Z, r, θ, φ) = Fnvj m (t)uvn (Z)φv (r)Yjm (θ, φ). n,v,j,m

(3) II. THEORY A. The time-dependent wave packet approach

The exact dynamics calculations for dissociative adsorption of a diatomic molecule on a corrugated, rigid surface should include six degrees of freedom (6D). The 6D Hamiltonian for the title reaction is expressed in terms of molecule coordinates (x, y, Z, r, θ , φ) (shown in Fig. 1) as17, 18 1 ∂2 1 ∂2 j2 Hˆ = − − + 2M ∂Z 2 2μ ∂r 2 2μr 2 1 ∂2 1 ∂2 1 2cosα ∂ 2 + − − 2M sin2 α ∂x 2 sin2 α ∂x∂y sin2 α ∂y 2 + V (x, y, Z, r, θ, φ),

(1)

where M, m, and j are the mass, reduced mass, and rotational angular momentum of HCl, respectively. The x and y axes are parallel to the surface, Z is the perpendicular coordinate from COM of HCl to the plane of the surface, r is the internuclear distance of HCl, θ is the polar angle, and φ is the azimuthal angle. The last term V (Z, r, x, y, θ, φ) is the inter-

The translational basis function, uvn , which is dependent on v, is defined as ⎧

2 1) ⎨ Z −Z sin nπ(Z−Z , v ≤ vasy Z3 −Z1 3 1 v un =

(4) ⎩ 2 1) sin nπ(Z−Z , v > vasy , Z2 −Z1 Z2 −Z1 where Z2 and Z3 define, respectively, the interaction and asymptotic grid ranges, and vasy is chosen to be the number of energetically open vibrational channels plus a few closed vibrational channels of HCl. As we know, the spherical harmonic functions Yjm (θ, φ) which are the eigenfunctions of jˆ2 are non-direct product basis sets. The effort made to define the discrete variable representation (DVR) for the spherical harmonic functions was not successful.49 In order to circumvent this difficulty, Dai and Light decoupled the operator j2 so that the θ and φ coordinates can be separately represented by one-dimensional DVR basis functions, Legendre polynomials Pj0 (cos θ ), and eimφ ,50 i.e., φ dependency is separated from j2 as follows: jˆ2 = jˆ02 −

∂2 1 . 1 − cos2 θ ∂φ 2

(5)


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The differential operator in φ has eimφ (m as the integer) as eigenfunctions and the Legendre polynomials Pj0 (cos θ ) are eigenfunctions of jˆ02 , jˆ02 Pj0 (cos θ ) = j0 (j0 + 1)Pj0 (cos θ ).

(6)

hollow top

This direct product representations were proved to be stable and efficient, and are adequate to yield converged results for the quantum scattering calculations.50 The initial wave function(normal incidence) is chosen as (Z, r, x, y, θ, φ, t = 0) = G0 (Z)φv,j Yjm (θ, φ),

The wave function is propagated using the split-operator method51 and the time-dependent wave function is absorbed at the edges of the grid to avoid boundary reflections.52 The advantage using the direct-product DVR above is that computational time for a wave-packet propagation for a matrixvector product is reduced for split exponential propagators since a direct product representation is preserved for all the angles. The initial state-selected total dissociation probability is obtained by projecting out the energy dependent reactive flux. + denotes the time-independent (TI) full scattering wave If ψiE function, where i and E are, respectively, initial state and energy labels, the total reaction probability from an initial state i can be obtained by the formula (9)

In the above equation, Fˆ is the flux operator, defined as 1 (10) Fˆ = [δ(ˆs − s0 )vˆs + vˆs δ(ˆs − s0 )], 2 where s is the coordinate perpendicular to a surface located at s0 for flux evaluation, and vˆs is the velocity operator corresponding to the coordinate s. The full TI scattering wave + + | ψiE = 2π δ(E − E ). Using function is normalized as ψiE the expression in (10), Eq. (9) can be simplified to yield Pi (E) =

¯ + + Im(ψiE |ψiE )|s=s0 , μr

where + |ψiE

1 = ai (E)

fcc

(7)

where the wave packet G0 (Z) is chosen to be a standard Gaussian function (Z − Z0 )2 0 2 −1/4 exp(−ik0 Z). (8) G (Z) = (π δ ) exp − 2δ 2

+ + | Fˆ | ψiE . PiR = ψiE

bridge

(11)

FIG. 2. The irreducible triangle of Au(111) surface unit cell (shown in red triangle), the atoms in the first (second) layer are shown in golden (bronze) spheres.

for the title system.43 The resulting PES is accurate and smooth, based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations. All the energy points were calculated using the Vienna ab initio simulation package (VASP).53, 54 The interaction between ionic cores and electrons was described by fully nonlocal optimized projector augmented-wave (PAW) potentials,55 and the Kohn-Sham valence electronic states were expanded in a plane wave basis set.56 The electron exchange correlation effects were treated within the generalized gradient approximation (GGA),57 using the Perdew-Wang (PW91) functional.58 The Au(111) substrates consist of four layers with a 2 × 2 unit cell(1/4 ML coverage). A vacuum region between two repeated cells is 16 Å, the Monkhorst-Pack k-points grid mesh is 5 × 5 × 159 and the plane wave expansion is truncated at 400 eV. The optimized lattice constant for bulk Au is 4.1766 Å, which agrees well with the experimental value (4.0783 Å).60 The PES is very well converged with respect to the number of DFT energy points, as well as to the fitting process, examined by TDWP calculations. The resulting barrier heights on the fitted PES are 0.64 eV, 0.78 eV, 0.83 eV, and 0.8 eV for the bridge, hollow, top, and fcc sites, respectively. Interested readers can find more details of the PES in Ref. 43. III. RESULTS

∞

e

i(E−H )t/¯

|i (0)dt,

(12)

0

with ai (E) = φ iE | i (0) being the overlap between the initial wave packet i (0) and the energy-normalized asymptotic scattering function φ iE . The four-dimensional (4D) calculations are carried out with the COM of HCl (x and y) fixed at the top, bridge, hollow, and fcc sites, respectively, as shown in Fig. 2. B. The 6D PES

We used the neural network (NN) fitting to a total of 76393 DFT energy points to construct a six-dimensional PES

The numerical parameters used in the TDWP calculations are as follows: The two-dimensional unit cell formed by x and y is covered by a 25 × 25 evenly spaced grid. We used 511 and 40 sin-type DVR61, 62 points to describe Z and r coordinates, ranging from 3.2 to 17.0 bohr and 1.5 to 7.0 bohr, respectively. The orientation angle θ needs 41 Legendre DVR points and the azimuthal angle φ requires 61 evenly spaced Fourier grid points. The imaginary absorbing potentials are placed in the range of Z between 15.5 and 17.0 bohr and r between 5.0 and 7.0 bohr, respectively, and the dissociation flux is calculated on the dividing surface of r = 4.5 bohr. The time step for the propagation is 10 a.u. and we propagate the wave packets for 30 000 a.u. of time to converge the dissociation probabilities.


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(a)

v=0 v=1 v=2

Dissociation Probability

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0.4

0.2

0

0

0.4

0.8 Kinetic Energy (eV)

1.2

v=0 × 100 v=1 v=2

0.6

0.4

0.2

0

1.6

v=0 v=1 v=2

0.6


(b)


0.6

0.4

(a) top

(b) hollow

0.4

0.2

0.2

0

0

0.4

0.8 Total Energy (eV)

1.2

v=0 v=1 v=2

1.6

FIG. 3. (a) The six-dimensional dissociation probability as a function of kinetic energy for the ground rovibrational state of HCl, together with those for the first and second vibrational excited states. (b) Same as (a), except as a function of total energy.

A. Vibrational and rotational-orientation effect

The six-dimensional dissociation probability for HCl initially in the ground rovibrational state (v = 0, j = 0) as a function of the kinetic energy, together with those for the first vibrational excited state (v = 1, j = 0) and second vibrational excited state (v = 2, j = 0) are shown in Fig. 3(a), and those as a function of the total energy are shown in Fig. 3(b). The total energy is measured with respect to the energy of non-rotating HCl ground state, and thus it corresponds to the asymptotic incidence energy for the ground state. Overall, the dissociation probabilities for the three vibrational states increase steadily as the kinetic energy increases, presenting the thresholds of roughly 0.6 eV and 0.23 eV for v = 0 and v = 1 states, respectively, and no threshold for v = 2 state which results in several oscillatory structures at very low kinetic energy, as seen from Fig. 3(a). Obviously, the vibrational excitations of HCl enhance the reactivity substantially, resulting from the late barrier of the title molecule-surface reaction as shown in Ref. 43. When we see the results as a function of total energy in Fig. 3(b), the dissociation probabilities of v = 0 and v = 1 are larger than that of the ground state in the entire total energy region, implying the vibrational excitation of HCl


0

0.6

(c) bridge 0.4

0.2

0

0

0.4

0.8 Kinetic Energy (eV)

1.2

1.6

FIG. 4. (a) The four-dimensional dissociation probabilities of HCl initially in non-rotating v = 0, 1, and 2 states for the top site. (b) Same as (a), except for the hollow site. (c) Same as (a), except for the bridge site.

is more efficacious than the same amount of translational energy in promoting the reaction, and the Polanyi’s rules63 hold for this late-barrier gas-surface reaction. The dissociation probabilities for the fixed top, hollow, and bridge sites from four-dimensional calculations are illustrated in Figs. 4(a), 4(b), and 4(c), respectively, with HCl initially in the non-rotating v = 0, 1, and 2 states. As the dissociation probabilities for the fcc site are quite similar to the hollow site (see below), we will not discuss the results for the fcc site in this subsection. It is clearly seen that the enhancement from the vibrational excitations of HCl on the reactivity



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v=0, j=5

0.2

0 0.4

0.8 1.2 Kinetic Energy(eV)

1.6

FIG. 5. The six-dimensional dissociation probabilities with the same rovibrational state (v = 0, j = 5) but different orientations (m = 0-5).

for the fixed three sites is remarkable, in particular in the low energy region, for which the similar trend is also found in the 6D calculations. It is interesting that the dissociation probability for the fixed top site for HCl initially in the ground rovibrational state is rather small, which is roughly 100-200 times smaller than other probabilities, whereas those for the first and second vibrational excited states are in the same order of magnitude as the rest of 4D results and as the 6D results, implying that the initial vibrational excitation of HCl is much more effective at overcoming the barrier and thus at promoting the reaction for the top site than the other sites. The overall behavior of the 4D dissociation probabilities for different vibrational states resembles that of the 6D results, showing the dissociation probabilities rise steadily from the threshold with the increase of kinetic energy. The threshold of dissociation probability (v = 0) for the bridge site is roughly 0.15 eV lower than that for the hollow site, in corresponding to the slightly lower bare barrier height of the bridge site (0.64 eV) than the hollow site (0.78 eV);43 however, the threshold of v = 0 dissociation probability for the fixed top site is much higher, even though the barrier height is only 0.19 eV and 0.05 eV higher than the other two sites.43 It is also seen that as the kinetic energy increases, the enhancement of the reactivity from the vibrational excitations weakens for the three fixed sites, and the dissociation probability for the bridge site at v = 1 turns to be smaller than that at the ground state at the kinetic energy above 1.4 eV. Overall, the influence of the vibrational excitations on the dissociation probabilities from the four-dimensional fixed-site calculations is consistent with the exact probabilities from the six-dimensional calculation. The rotational-orientation effect in the dissociative adsorption of HCl on Au(111) is another important issue that we will consider. The six-dimensional dissociation probabilities for initial rovibrational states with the same rovibrational energy (v = 0, j = 5) but different orientations (m = 0-5) in the kinetic energy region of 0.4 eV and 1.6 eV are shown in Fig. 5. They are all smooth and monotonically increasing functions of the kinetic energy. We can see strong orientation

dependence of dissociation probabilities for the title reaction. Specifically, the dissociation probability increases as the rotation projection quantum number m increases except at energies around the threshold, with the largest dissociation probability of m = 5, and the smallest one of m = 0. It is shown that the dissociation probability of m = 5 is twice as large as that of m = 0 in the entire energy region. The dissociation probability of m = 4 is larger than that of m = 5 in the low kinetic energy region, presenting the slightly lower threshold for m = 4. Besides, the dissociation probability of m = 0 is slightly larger than those of m = 1 and m = 2 at energies just above the threshold. Therefore, the dissociation of HCl is most favored at the helicopter orientation (m = 5), but not at the cartwheel orientation (m = 0), seen from the exact 6D probabilities. We also present the four-dimensional dissociation probabilities of HCl (v = 0, j = 5, m) for the fixed top, hollow, and bridge sites in Figs. 6(a), 6(b), and 6(c), respectively. Different from the vibrational-excitation effect, it is found that the rotational-orientation effect of the four-dimensional fixed-site calculations is not completely consistent with the six-dimensional calculations. First, in contrast to the six-dimensional results, the dissociation probabilities of HCl (j = 5) for the fixed top site decrease as the rotation projection quantum number m increases, i.e., the dissociation process with the initial cartwheel orientation (j = 5, m = 0) gives rise to the largest dissociation probability, whereas that with the helicopter orientation (j = 5, m = 5) leads to the smallest dissociation probability, as shown in Fig. 6(a). Only at very high collision energy (>1.5 eV), the dissociation probability for initial HCl (j = 5, m = 0) turns to be smaller than that for HCl (j = 5, m = 1). Second, the dissociation probabilities for the fixed hollow site with various m show different trends, compared to the six-dimensional or four-dimensional top-site results, as shown in Fig. 6(b). Although the dissociation is always most favored at the helicopter orientation in the whole kinetic energy region of 0.4 eV and 1.6 eV, the cartwheel orientation gives medium dissociation probabilities. At high kinetic energy (>1.2 eV), the dissociation probability with m = 1 is smallest, but when the kinetic energy becomes lower than 1.2 eV, the orientation ( j = 5, m = 4) gives the smallest dissociation probability. Finally, we can see from Fig. 6(c) that the results of the fixed bridge site somehow resemble those of the six-dimensional calculations, showing the dissociation with the cartwheel orientation (j = 5, m = 0) results in the smallest probability and the helicopter orientation (j = 5, m = 5) gives the largest probability at kinetic energies higher than 1.0 eV. The dissociation probability does not fully increase as the rotation projection quantum number m increases, with the results of the orientation m = 1, m = 2, m = 3, and m = 4 coming quite close to each other at kinetic energies above 1.0 eV. The results for the fixed bridge site are similar to the 6D results at the low kinetic energy region. B. Site-averaged effect

Comparisons of the dissociation probability for HCl initially in the ground rovibrational state (v = 0, j = 0) calculated using the six-dimensional (6D) TDWP method and the


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0.1

m=0 m=1 m=2 m=3 m=4 m=5

v=0, j=5 Dissociation Probability


(a) top

0


0.6

(b) hollow

0.2

0.8 1.2 Kinetic Energy (eV)

1.6

FIG. 7. Comparisons of six-dimensional, four-dimensional, and siteaveraged dissociation probabilities for HCl initially in the ground rovibrational state. The site-averaged results are obtained by averaging the dissociation probabilities of four fixed sites (bridge, hollow, fcc, and top) with appropriate relative weights.

0.2

0

(c) bridge Dissociation Probability

0.4

0 0.4

0.4

0.6

0.4

0.2

0 0.4

0.6

4D bridge site 4D fcc site 4D hollow site 4D top site × 100 6D 4D site-averaged


1.6

FIG. 6. (a)The four-dimensional dissociation probabilities with the same rovibrational state (v = 0, j = 5) but different orientations (m = 0-5) for the fixed top site. (b) Same as (a), except for the hollow site. (c) Same as (a), except for the bridge site.

four-dimensional (4D) results for which HCl is fixed at the bridge, fcc, hollow, and top sites, in the kinetic energy region of 0.4 eV and 1.6 eV, are made and shown in Fig. 7. Overall, these dissociation probabilities are smooth and monotonically increasing functions of the kinetic energy. The 4D dissociation probability for the fixed bridge site is much larger than the rest of three 4D probabilities and 6D probability in the entire energy region, presenting the lowest threshold (roughly 0.56 eV) compared to other results. Significant differences between the 6D probability and the results calculated

by reduced-dimensional (4D) fixed-site approach are seen, indicating the importance of full-dimensional calculations. The overall behavior of 4D results for the fixed fcc site is very similar to that of the hollow site. More details and discussions can be found in Ref. 43. Then it is interesting to see whether we can reproduce the 6D probability using the site-averaged 4D results. Exploiting the C3v symmetry of the Au(111) surface, it is sufficient to map the PES only for the molecular configurations inside the irreducible triangle of the surface unit cell which is spanned by the top, hollow, and fcc sites, as shown in Fig. 2. Therefore, we averaged four symmetric sites (bridge, hollow, fcc, and top) with appropriate relative weights (3 for the bridge site, 1 for the hollow site, 1 for the fcc site, and 1 for the top site) to obtain the site-averaged dissociation probability, which is also shown in Fig. 7. The relative weights are determined by the number of the corresponding sites in the 2 × 2 unit cell, i.e., there are 12 bridge, 4 hollow, 4 fcc, and 4 top sites in the unit cell and thus the relative weights are 3, 1, 1, and 1, respectively. It is worth noting that we are currently doing in the slightly different way from that was done by Dai and Light for the H2 /Cu(111) system, where three symmetric sites (bridge, center, and top) were averaged to achieve the site-averaged dissociation probability with appropriate relative weights, as the Cu(111) surface was approximated to be of C6v symmetry by taking the potential at the hollow site to be the same as at the fcc site.18 We can still see large differences between the 6D dissociation probability and site-averaged results over four symmetric sites, though the shape and magnitude of the site-averaged dissociation probability become closer to the 6D probability, compared to any of the probability curve of the fixed-site 4D calculations. In the early work of Dai and Light18 for H2 dissociation on Cu(111), it was assumed that the differences in zero point energies between six-dimensional and four-dimensional calculations at


Liu, Fu, and Zhang

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top

J. Chem. Phys. 139, 184705 (2013)

hcp

bridge

fcc (b)


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4 site-averaged 9 site-averaged 25 site-averaged 6D 0.4

0.2

hcp 0 0.4

top

bridge

fcc FIG. 8. (a) The schematic of the distribution of 9 sites ( 4 red circles denote the bridge, hollow, fcc, and top sites, and 5 black circles denote the midpoints of the adjacent sites). (b) The schematic of the distribution of 25 sites (16 additional sites correspond to the midpoints of the adjacent sites of the 9 sites shown above).

the transition states give rise to the differences in dissociation probabilities. However, as we mentioned above, the 6D dissociation probability was obviously larger than the shifted site-averaged dissociation probability at high kinetic energies for the H2 /Cu(111) system in that work. As a result, the explanation that ZPE differences account for the four to six dimensional shift in energy is not convincing. To further investigate the site-averaged effect, we intended to calculate the 4D site-averaged dissociation probabilities over more sites. Specifically, the site-averaged probabilities over 9 sites and 25 sites were calculated, respectively. We can see from Fig. 8(a) that the current 9 sites consist of five midpoints of the top-hollow line, top-fcc line, top-bridge line, bridge-hollow line and bridge-fcc line, and the original four fixed sites (bridge, hollow, fcc, and top). Similarly, the 16 midpoints of the two adjacent sites of the 9 sites mentioned above and the 9 fixed sites constitute the 25 sites, as shown in Fig. 8(b). The averaged dissociation probability over the 9 sites was obtained from the 4D fixed-site calculations with appropriate relative weights (3 for the bridge site, 1 for the hollow site, 1 for the fcc site, 1 for the top site, 3 for the four sites on the boundary of the triangle, and 6 for the site inside the triangle). The 25 site-averaged dissociation probability was calculated using the similar relative weights as the 9 site-averaged probability. The 4 site, 9 site, and 25 site-averaged dissociation probabilities, together with the 6D dissociation probability are shown in Fig. 9 for HCl initially in the ground rovibrational state up to the kinetic energy of 1.6 eV. It is clearly seen that the similarity between the 9 site-averaged and 6D dissociation probabilities is significantly improved, compared to the 4 site-averaged and 6D results. The overall behavior of the


1.6

FIG. 9. Comparisons of six-dimensional dissociation probabilities and three site-averaged dissociation probabilities of HCl (v = 0, j = 0), obtained by averaging the 4D dissociation probabilities over 4 fixed sites, 9 sites, and 25 sites with appropriate relative weights.

9 site-averaged dissociation probability resembles that of the 6D dissociation probability, with the magnitude of the former larger than the latter at the kinetic energies less than 0.8 eV just above the threshold and smaller than the latter at kinetic energies above 0.8 eV. Furthermore, as we see from the green and blue curves, the agreement between the 25-site averaged probability and 6D probability is excellent and impressive. We can infer that the 6D results can be accurately reproduced from the higher site-averaged dissociation probabilities, i.e., 81 or higher site-averaged, as long as the site-selecting routine is maintained as mentioned above. It is quite interesting that one can eventually obtain the exact 6D dissociation probabilities from the site-averaged 4D results without doing six-dimensional calculations, which are much more computational time and memory consuming. However, further study is still necessary if this new site-averaged effect we observed exists in other molecule-surface interaction systems.

IV. CONCLUSIONS

To summarize, we have carried out six-dimensional quantum dynamics calculations for the dissociative adsorption of HCl on the rigid Au(111) surface using the TDWP approach. The four-dimensional fixed-site calculations for the top, hollow, bridge, and fcc sites are also performed in order to give a detailed comparison between the 6D and 4D dissociation probabilities. An accurate, six-dimensional PES which was constructed recently by the neural network fitting to DFT energy points was employed. The influence of the vibrational excitation and rotational-orientation of HCl on the reactivity is investigated in this study. The vibrational excitation of HCl enhances the reactivity of title reaction substantially, indicating the Polanyi’s rules hold for this late-barrier molecule-surface reaction. The dissociation is most favored for HCl molecules colliding with rotation in a plane parallel to the Au(111) surface (helicopter orientation) than for those colliding perpendicularly (cartwheel orientation). The


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effect of vibrational excitations from the 4D calculations is consistent with the 6D calculations, whereas the rotationalorientation effect between the two calculations is different. It is interesting that we can eventually reproduce the exact six-dimensional dissociation probability from the siteaveraged results over the 25 sites from the four-dimensional fixed-site calculations. Further study is expected to investigate whether one can observe this new site-averaged effect in other molecule-surface reactions.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant Nos. 91221301 and 90921014), the Chinese Academy of Sciences, and Ministry of Science and Technology of China. 1 R.

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