Six-dimensional quantum dynamics study for the dissociative adsorption of DCl on Au(111) surface Tianhui Liu, Bina Fu, and Dong H. Zhang Citation: The Journal of Chemical Physics 140, 144701 (2014); doi: 10.1063/1.4870594 View online: http://dx.doi.org/10.1063/1.4870594 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/14?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Six-dimensional quantum dynamics study for the dissociative adsorption of HCl on Au(111) surface J. Chem. Phys. 139, 184705 (2013); 10.1063/1.4829508 Six-dimensional quasiclassical and quantum dynamics of H2 dissociation on the c(2 × 2)-Ti/Al(100) surface J. Chem. Phys. 134, 114708 (2011); 10.1063/1.3567397 The reaction rate for dissociative adsorption of N 2 on stepped Ru(0001): Six-dimensional quantum calculations J. Chem. Phys. 122, 234702 (2005); 10.1063/1.1927513 Diffractive and reactive scattering of (v=0,j=0) HD from Pt(111): Six-dimensional quantum dynamics compared with experiment J. Chem. Phys. 118, 4190 (2003); 10.1063/1.1540981 Six dimensional quantum dynamics study for dissociative adsorption of H 2 on Cu(111) surface J. Chem. Phys. 107, 1676 (1997); 10.1063/1.474520
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THE JOURNAL OF CHEMICAL PHYSICS 140, 144701 (2014)
Six-dimensional quantum dynamics study for the dissociative adsorption of DCl on Au(111) surface Tianhui Liu, Bina Fu,a) 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 16 January 2014; accepted 26 March 2014; published online 8 April 2014) We carried out six-dimensional quantum dynamics calculations for the dissociative adsorption of deuterium chloride (DCl) on Au(111) surface using the initial state-selected time-dependent wave packet approach. The four-dimensional dissociation probabilities are also obtained with the center of mass of DCl fixed at various sites. These calculations were all performed based on an accurate potential energy surface recently constructed by neural network fitting to density function theory energy points. The origin of the extremely small dissociation probability for DCl/HCl (v = 0, j = 0) fixed at the top site compared to other fixed sites is elucidated in this study. The influence of vibrational excitation and rotational orientation of DCl on the reactivity was investigated by calculating six-dimensional dissociation probabilities. The vibrational excitation of DCl enhances the reactivity substantially and the helicopter orientation yields higher dissociation probability than the cartwheel orientation. The site-averaged dissociation probability over 25 fixed sites obtained from four-dimensional quantum dynamics calculations can accurately reproduce the six-dimensional dissociation probability. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4870594] I. INTRODUCTION
It is well known that the dissociative adsorption of molecular species on transition-metal surfaces is one of the significant reactions in heterogeneous catalysis. During the past several decades, the dissociative adsorption of molecules on various metal surfaces has been extensively studied both experimentally and theoretically,1–15 due to the fact that this dissociation process is often the rate-determining step in most of the chemical reactions. Theoretically, numerous efforts have been devoted to investigating the reaction mechanisms of these reactions at the quantum mechanical level. 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. The dissociative adsorption of H2 on metal surfaces is the most thoroughly studied dissociative chemisorption using the quantum dynamics calculations, ranging from the reduced two-dimensional model16 to the full-dimensional approach.17–25 Nonetheless, a full-dimensional quantum mechanical description of polyatomic dissociative chemisorption is still extremely challenging. Low-dimensional models were employed in recent quantum dynamics studies of CH4 on Ni surfaces,26–29 as a total of 15 degrees of freedom should be considered on a rigid surface for this reaction. Recently, Guo and co-workers carried out six-dimensional quantum dynamics calculations of H2 O on Cu(111)30–32 and eightdimensional calculations of CH4 on Ni(111).33 The PESs a) Authors to whom correspondence should be addressed. Electronic
addresses: [email protected] and [email protected]
0021-9606/2014/140(14)/144701/7/$30.00
employed were fit by the permutationally invariant polynomial approach of Bowman and co-workers34, 35 based on energy points from density functional theory (DFT) calculations. Jackson and Nave employed a fully quantum approach based on the Reaction Path Hamiltonian that includes all 15 molecular degrees of freedom and the effects of lattice motion to investigate the dissociative chemisorption of methane on a Ni(111) surface.36 In this work we carried out full-dimensional (sixdimensional) quantum dynamics calculations of deuterium chloride (DCl) dissociative chemisorption on Au(111) surface, employing an accurate PES recently developed by neural network fitting to roughly 70 000 DFT energy points (LFZ PES).37 Based on the small fitting errors and good agreement with the direct DFT calculations, this PES is sufficiently accurate to be used in the quantum dynamics calculations. In addition, time-dependent wave packet calculations show that the LFZ PES is very well converged with respect to the number of DFT data points, as well as to the fitting process.37 We note that the PES used describes the interaction of hydrogen chloride (HCl) with an idealised Au(111) surface, which cannot be realized in experiments due to surface reconstruction.38, 39 However, the results from quantum dynamics calculations on this ideal PES can be helpful for unraveling the dynamics of gas-surface reactions and understanding experimental results. Very recently, we reported the detailed dynamics results of hydrogen chloride dissociative chemisorption on Au(111) obtained from full-dimensional quantum wave packet calculations on the LFZ PES.40 The influence of vibrational excitation and rotational orientation of HCl on the reactivity was investigated by calculating the exact six-dimensional dissociation probabilities, as well as the
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Liu, Fu, and Zhang
four-dimensional (4D) fixed-site dissociation probabilities. The vibrational excitation of HCl enhances the reactivity and the helicopter orientation yields higher dissociation probability than the cartwheel orientation. Furthermore, an interesting site-averaged effect was found in that study that one can essentially reproduce the six-dimensional (6D) dissociation probability by averaging the four-dimensional dissociation probabilities over 25 fixed sites without zero-point energy (ZPE) corrections. Experimentally, Lykke and Kay carried out a molecule beam-surface scattering experiment of HCl scattered from Au(111) in 1990, and the rotationally inelastic scattering was investigated.41 In the past several years, Wodtke and coworkers investigated the energy transfer between HCl and Au(111) interfaces,42–45 where a transition from an electronically adiabatic mechanical mechanism to an electronically nonadiabatic mechanism involving excited electronhole pairs with the increase of surface temperature was reported. Theoretically, following our recent work for the construction of an accurate, six-dimensional PES and sixdimensional quantum dynamics study of the HCl/Au(111) system,37, 40 we present the detailed quantum dynamics results of DCl dissociative adsorption on Au(111) surface in this article. The motion of surface atoms and excited electronhole pairs were ignored in the current adiabatic PES, and the dynamics investigations were based on the rigid surface approximation, thus the current theory is not able to directly describe the experimental quantities measured by Wodtke et al.42–45 Our recent work37, 40 indicated 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 the rest of 4D results and the 6D results for the HCl/Au(111) system, though the bare barrier height for the top site is only 0.05 eV, 0.03 eV, and 0.19 eV higher than the hollow, fcc, and bridge sites, respectively. This is in strong contrast to the results found in other moleculemetal systems, e.g., H2 /Cu(111) and H2 /Cu(100), in which the dissociation probabilities for the fixed top site are in the same order of magnitude as the rest of 4D results and the 6D results.18, 46–48 Thus, it is still waiting to be answered whether the small dissociation probability for the top site exists for the isotopically substituted DCl/Au(111) reaction and what is the fundamental reason of this intriguing behavior? In addition, further study is still necessary to see whether our new finding for the HCl + Au(111) reaction, i.e., that the six-dimensional reaction probability can essentially be reproduced without any need for zero-point energy corrections by averaging the four-dimensional site-specific reaction probabilities over impact sites (as long as enough impact points are used in the averaging), holds also for the DCl + Au(111) reaction. As a result, we have carried out quantum wave packet calculations for DCl/Au(111) and present the detailed results below. The paper is structured as follows. In Sec. II we present the time-dependent wave packet method (TDWP) methodologies and brief description of PES used in dynamics calculation. Results and discussions are given in Sec. III. A summary and conclusions are given in Sec. IV.
J. Chem. Phys. 140, 144701 (2014)
II. THEORY A. The 6D time-dependent wave packet method
The accurate dynamics calculations for dissociative adsorption of a diatomic molecule on a corrugated, rigid surface should include six degrees of freedom. Since detailed descriptions of the general 6D initial state-selected wave packet approach to diatomic molecule-surface reactions have been presented before,17, 18, 40 we only give an outline of the methodology here. The six degrees of freedom of DCl/Au(111) include molecular coordinates, namely, X, Y, Z, r, θ , φ (as shown in Fig. 1), and the 6D Hamiltonian is expressed in terms of these coordinates as 1 ∂2 jˆ2 1 ∂2 − + Hˆ = − 2M ∂Z 2 2μ ∂r 2 2μr 2 1 ∂2 1 ∂2 1 2 cos α ∂ 2 + − − 2M sin2 α ∂x 2 sin2 α ∂x∂y sin2 α ∂y 2 + V (x, y, Z, r, θ, φ),
(1)
where M and μ are the total mass and reduced mass of DCl, respectively. The operator jˆ is the rotation operator. The x and y coordinate axes are parallel to the surface, Z is the perpendicular coordinate from the center of mass (COM) of HCl to the plane of surface, r is the interatomic distance of DCl, θ is the polar angle, and φ is the azimuthal angle. The last term V (Z, r, x, y, θ, φ) is the interaction potential energy. The skewing angle α is the angle between the x and y coordinate axes as indicated in Fig. 1. For Au(111), α = 120◦ . The time-dependent wave function is expanded in terms of translational basis of Z, 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)eikx x eiky y . (2) = n,v,j,m
Here, kx = 2π nx /Lx and ky = 2π ny /Ly , where Lx and Ly are the surface unit cell lattice constants. Because of the periodicity of the potential energy surface along x and y, we employed the superposition of periodic functions eikx x and eiky y
Cl
Z
r θ
D
y
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φ x α =120
Au FIG. 1. Molecular coordinates for the scattering of DCl from Au(111) surface, where (x, y, Z) are the center-of-mass coordinates of DCl, r is the internuclear distance of DCl, θ is the polar angle, and φ is the azimuthal angle. The skewing angle α = 120◦ for Au(111).
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to represent the wave functions of the x and y coordinates. The Z and r coordinates were efficiently represented by the sinDVR (discrete variable representation) basis functions,49, 50 while we used the direct product of Legendre polynomials Pn (cos (θ )) and eimφ as a good basis representation for the θ and φ coordinates by separating the φ-dependent term from jˆ2 .18, 51 We employed the split-operator method in which the exponential Schrödinger propagator is symmetrically split to propagate the wave packet.52 The initial state-selected total dissociation probability was obtained by projecting out the energy dependent reactive + denotes the time-independent full scattering wave flux. If ψiE function, where i and E are, respectively, initial state and energy labels, the total dissociation probability from an initial state i can be obtained by + ˆ + |F |ψiE . PiR = ψiE
(3)
Here, Fˆ is the flux operator, defined as 1 Fˆ = [δ(ˆs − s0 )vˆs + vˆs δ(ˆs − s0 )], (4) 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 time-independent + + |ψiE scattering wave function is normalized as ψiE = 2π δ(E − E ). Employing the expression (4), Eq. (3) can be simplified to yield ¯ + + Pi (E) = Im(ψiE |ψiE )|s=s0 , μr where + = |ψiE
1 ai (E)
∞
ei(E−H )t/¯ |i (0)dt,
(5)
(6)
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 4D calculations are carried out with the COM of DCl (x and y) fixed at the top, bridge, hollow, and fcc sites, respectively, as shown in Fig. 2. B. The 6D PES
The interaction potential energy V (X, Y, Z, r, θ, φ) of the DCl/Au(111) reaction is evaluated from the recent 6D PES, which was constructed by using the neural network fitting to a total of 76 393 DFT energy points.37 The resulting hollow top
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). The interaction between ionic cores and electrons was described by fully nonlocal optimized projector augmented-wave (PAW) potentials,53 and the Kohn-Sham valence electronic states were expanded in a plane wave basis set.54 The electron exchange correlation effects were treated within the generalized gradient approximation (GGA),55 using the PerdewWang (PW91) functional.56 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 MonkhorstPack k-points grid mesh is 5×5×157 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).58 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. Readers can refer to our recent work for the details of the PES.37 The potential energy of the DCl/Au(111) reaction with the coordinates (X, Y, Z, r, θ , φ) equals that of HCl/Au(111) with the coordinates (X , Y , Z , r, θ , φ), where they satisfy X = X − r
m D − mH sin(α − φ) mCl sin(θ ) , mH + mCl sin(α) mD + mCl
m D − mH sin(φ) mCl sin(θ ) , mH + mCl sin(α) mD + mCl mCl mD − mH Z = Z + r cos(θ ) , mH + mCl mD + mCl Y = Y − r
with mCl , mD , and mH representing the masses of Cl, D, and H, respectively. III. RESULTS
The relevant numerical parameters used in this TDWP calculations are similar with those used in the dynamics calculations of the HCl/Au(111) system.40 The dissociation flux is calculated on the dividing surface of r = 4.5 bohr. The number of grid points for the Z, x, and y coordinates remains the same because of the slight difference of the total mass of DCl and HCl. However, due to the fact that the reduced mass of DCl is nearly twice as large as that of HCl, we used 55 sintype DVR points to describe the r coordinate. The orientation angle θ needs 61 Legendre DVR points and the azimuthal angle φ requires 101 evenly spaced Fourier grid points. These parameters are all larger than the corresponding HCl parameters.
bridge
fcc
FIG. 2. The irreducible triangle of Au(111) surface unit cell (shown in black triangle), the atoms in the first, second, and third layers are shown in yellow, bronze, and black spheres, respectively. Note that the atoms in the third layer are right at the fcc site. Atoms in the fourth (fifth, sixth) layer are directly below the atoms in the first (second, third) layer.
A. 4D and 6D dissociation probabilities
The dissociation probability for DCl initially in the ground rovibrational state (v = 0, j = 0) calculated using the 6D TDWP method is shown in Fig. 3, together with the 4D results for which DCl is fixed at the bridge, fcc, hollow, and top sites, respectively, in the kinetic energy region of 0.4 eV and 1.6 eV. Overall, all the dissociation probabilities are smooth functions of the kinetic energy, and rise steadily as the kinetic
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other results, though the bare barrier height for the top site (0.83 eV) is only 0.03 eV, 0.05 eV, and 0.18 eV higher than the fcc site (0.80 eV), the hollow site (0.78 eV), and the bridge site (0.65 eV),37 respectively. The same behavior was also found in the HCl/Au(111) system recently.40 As shown in Fig. 2, the COM of the DCl/HCl molecule is right on the top of a single Au atom for DCl/HCl fixed at the top site. Because the COM of the DCl/HCl molecule is essentially on the Cl atom, implying that the Z coordinate is roughly the distance between the Cl and Au atoms. As shown in Fig. 4(a) representing the contour plot of the PES as a function of Z and r coordinates with θ and φ optimized for DCl fixed at the top site, the repulsion force between the Cl atom and Au atom increases very rapidly when Z decreases. Furthermore, we plot the evolution of the probability density on this contour plot and show them in Figs. 4(a)–4(f) at different propagation times, respectively. We can see from Figs. 4(a)–4(c) that the wave packet does not evolve along the minimum energy reaction path, but rushes to the potential energy wall along the Z coordinate. Obviously, the wave packet in the high kinetic energy region can reach the high potential energy region with very small Z coordinates without any change of r coordinates, implying the DCl molecule can get very close to the Au atom without the extension of its interatomic distance. Due to the steep PES with increasing Z, a large portion of the wave packet rebounds quickly to the DCl+Au(111) asymptote, but a very small portion of them leaks to the product region with large r, as shown in Figs. 4(d)–4(f), leading to the very small dissociation probability. Therefore, the kinetic energy in the translational motion (along Z coordinate) is not effective at all on promoting this type of late-barrier reactions with HCl/DCl fixed at the top site, while the vibrational excitation (kinetic energy along r coordinate) enhances the reactivity significantly, as has been indicated previously that the dissociation probabilities for the first and second vibrational states of HCl are in the same order of magnitude as the results for the other sites.40
Dissociation Probability
0.8
0.6
4D bridge site 4D fcc site 4D hollow site 4D top site × 100 6D
0.4
0.2
0 0.4
1.4
1.0 0.8 1.2 Kinetic Energy (eV)
0.6
1.6
FIG. 3. Comparison of dissociation probabilities for the scattering of DCl(v = 0, j = 0) from Au(111) between the six-dimensional and fourdimensional fixed-site calculations. As indicated, the dissociation probability for the top site is multiplied by a factor of 100.
energy increases. 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. The overall behavior of 4D results for the fixed fcc site is very similar to that of the hollow site, with the probability curves rise from the threshold of around 0.75 eV. The 6D probability is quite different from the results calculated by reduced dimensional (4D) fixed-site approach. The threshold of the 6D dissociation probability is about 0.02 eV higher than that of the 4D bridge site, in accord with the difference of their bare barrier heights,40 and the magnitude of the 6D probability is smaller than that of the bridge site in the entire energy region. It is interesting that the dissociation probability for DCl fixed at the top site is about 100–200 times smaller than the
(a) T=5400
(b) T=6000
(c) T=6900
4.5 0.8
0.9
0.8 0.9
0.9
0.8
0.9
0.8
0.9
0.8
3.5
0.9
r (bohr)
5.5
0.8
2.5 (f) T=10200
(e) T=8700
(d) T=7800
4.5 0.8
0.9
0.8 0.9
0.9
0.8
0.9
0.8
0.9
0.8
3.5
0.9
r (bohr)
1.5 5.5
0.8
2.5 1.5 3.5 4
4.5 5 5.5 6 Z (bohr)
6.5 3.5 4
4.5 5 5.5 6 Z (bohr)
6.5 3.5 4
4.5 5 5.5 6 Z (bohr)
6.5 7
FIG. 4. The evolution of the probability density of DCl(v = 0, j = 0) scattering from Au(111) at the fixed top site on the contour plot of the PES. The contours are relative to the DCl + Au(111) asymptote with an interval of 0.1 eV. The probability density is shown as a function of Z and r with the other coordinates integrated, and the contour plot is shown with other coordinates optimized. Different propagation times are indicated by the label “T” in panels (a), (b), (c), (d), (e), and (f), respectively.
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(a) v=0, j=0 v=1, j=0
Dissociation Probability
Dissociation Probability
0.4
0.5
0.3
0.2
0.1
0.0 0.0
m=0 m=1 m=2
v=0, j=2
0.4
0.3
0.2
0.1
0.2
0.4
0.6 1.0 0.8 Kinetic Energy(eV)
1.2
1.4
1.6
(b)
0.0 0.4
0.6
1.0 0.8 1.2 Kinetic Energy(eV)
1.4
1.6
FIG. 6. The six-dimensional dissociation probabilities with the same rovibrational state (v = 0, j = 2) but different orientations (m = 0–2).
Dissociation Probability
0.4
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6 1.0 0.8 Total Energy(eV)
1.2
1.4
1.6
FIG. 5. (a) The six-dimensional dissociation probability as a function of kinetic energy for the ground rovibrational state of DCl, together with that for the first vibrational excited state. (b) Same as (a), except as a function of total energy.
dimensional dissociation probabilities for initial rovibrational states with the same rovibrational energy (v = 0, j = 2) but different orientations (m = 0–2) in the kinetic energy region of 0.4 eV and 1.6 eV are shown in Fig. 6. 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, with the largest dissociation probability of m = 2, and the smallest one of m = 0. Therefore, the dissociation of DCl is most favored at the helicopter orientation (m = 2), but not at the cartwheel orientation (m = 0), seen from the exact 6D probabilities.
B. Site-averaged effect
The six-dimensional dissociation probabilities for DCl initially in the ground rovibrational state (v = 0, j = 0) and in the first vibrational excited state (v = 1, j = 0) as a function of the kinetic energy are illustrated in Fig. 5(a), together with those as a function of the total energy shown in Fig. 5(b). The total energy is measured with respect to the energy of non-rotating ground vibrational state of DCl. Overall, the dissociation probabilities for the two vibrational states increase steadily with increasing kinetic energy, presenting the thresholds of roughly 0.6 eV and 0.36 eV for v = 0 and v = 1 states, respectively, as seen from Fig. 4(a). Obviously, the vibrational excitations of DCl enhance the reactivity substantially, resulting from the late barrier of the title molecule-surface reaction as indicated in Ref. 37. When we see the results as a function of total energy in Fig. 5(b), the dissociation probability of v = 1 is larger than that of the ground state in the entire total energy region, implying that the vibrational excitation of DCl is more efficacious than the same amount of translational energy in promoting the reaction, and the Polanyi’s rules59 hold for this late-barrier gas-surface reaction. Next we consider the rotational-orientation effect in the dissociative adsorption of DCl on Au(111) surface. The six-
We recently improved the site-averaged effect for the dissociative adsorption of HCl on Au(111), demonstrating that the exact six-dimensional dissociation probability can be essentially reproduced by averaging the four-dimensional fixedsite dissociation probabilities over 25 sites40 without any need for ZPE corrections. It is still interesting to see whether this new finding exists in the scattering of DCl from Au(111) instead of HCl. To this end, we calculated the 4D site-averaged dissociation probabilities over 4, 9, and 25 sites, respectively, as has been done previously for HCl.40 The site-averaged effect for the molecule-surface interactions was first proposed by Dai and Light from the quantum dynamics studies for the H2 +Cu(111) reaction.18 In that work, three symmetric sites (bridge, center, and top) were averaged to achieve the siteaveraged dissociation probability, 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. However, the 6D dissociation probability was quite different from the shifted site-averaged dissociation probability at high kinetic energies and the explanation that ZPE differences account for the four to six dimensional shift in energy is not convincing in that study. It is worth noting that we are currently doing in the
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(a)
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hollow
top
bridge
fcc (b)
top
hollow
Dissociation Probability
0.5
4 site-averaged 9 site-averaged 25 site-averaged 6D
0.4
0.3
0.2
bridge 0.1
fcc FIG. 7. (a) The schematic of the distribution of 9 sites (4 black circles denote the bridge, hollow, fcc, and top sites, and 5 red 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).
slightly different way from that was done by Dai and Light for the H2 /Cu(111) system.18 Specifically, we averaged 4 symmetric sites (bridge, hollow, fcc, and top), as shown in Fig. 2, 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 4 site-averaged dissociation probability. 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. Figure 7(a) shows that five midpoints of the tophollow line, top-fcc line, top-bridge line, bridge-hollow line, and bridge-fcc line, and the original 4 fixed sites (bridge, hollow, fcc, and top) constitute the present 9 sites. Similarly, the 25 sites consist of 16 midpoints of the two adjacent sites of the 9 sites mentioned above and the 9 fixed sites, as shown in Fig. 7(b). We obtained the averaged dissociation probability over 9 sites 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 depicted in Fig. 8 for HCl initially in the ground rovibrational state up to the kinetic energy of 1.6 eV. Obviously, the 4 siteaveraged dissociation probability is remarkably larger than the 6D probability in the entire energy region. 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 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 energy lower than 0.8 eV just above the threshold, and smaller than the latter at the kinetic energy higher than 0.8 eV. Furthermore, the agreement between
0.0 0.4
0.6
0.8
1.0 1.2 Kinetic Energy(eV)
1.4
1.6
FIG. 8. Comparisons of six-dimensional dissociation probabilities and three site-averaged dissociation probabilities of DCl(v = 0, j = 0), obtained by averaging the 4D dissociation probabilities over 4 fixed sites, 9 sites, and 25 sites with appropriate relative weights.
the 25 site-averaged probability and 6D probability is excellent, seen from the green and blue curves. We anticipate that the 6D results can be completely reproduced from the higher site-averaged dissociation probabilities, i.e., 81 or higher, as long as the site-selecting routine is maintained as mentioned above. It is most gratifying that one can eventually obtain the exact 6D dissociation probabilities from the site-averaged 4D results without doing six-dimensional quantum dynamics calculations, which are rather computational time and memory consuming. We anticipate that this site-averaged effect we observed should generally exist in other molecule-surface interaction systems.
IV. CONCLUSIONS
In summary, the initial state-selected six-dimensional TDWP method has been employed to carry out the quantum dynamics calculations for the dissociative adsorption of DCl on the rigid Au(111) surface, based on an accurate, six-dimensional PES which was constructed recently by the neural network fitting to DFT energy points. The fourdimensional dissociation probabilities for DCl initially in the ground rovibrational state were also obtained by doing quantum dynamics calculations for the COM of DCl fixed at the bridge, fcc, hollow, and top sites, respectively. The dissociation probability with DCl fixed at the top site is 100–200 times smaller than the rest of 4D results and the 6D result, due to the fact that the repulsion force increases rapidly as the interatomic distance between the Cl atom of DCl and the Au atom of the first layer of Au(111) surface, with the Cl atom right on the top of the Au atom. The wave packet is able to rush to the high potential energy region with small Z coordinates without extension of the bond length of DCl molecule, quickly followed by the rebounce of the wave packet to the DCl+Au(111) asymptote, rather than to overcome the dissociation barrier for DCl dissociating on Au(111) surface. The increase of kinetic energy in the translational motion along
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the Z direction is not efficacious at all for this type of latebarrier reaction, but the vibrational excitation of DCl (kinetic energy along the r direction) is rather efficient in promoting the dissociation that it enhances the reactivity by 100–200 times with DCl(v = 1). The influence of the vibrational excitation and rotational-orientation of DCl on the reactivity is investigated in detail from six-dimensional calculations in this study. The vibrational excitation of DCl enhances the reactivity substantially, indicating that the Polanyi’s rules hold for this late-barrier molecule-surface reaction. The dissociation prefers to occur with DCl colliding with rotation in a plane parallel to the Au(111) surface (helicopter orientation), not with DCl colliding perpendicularly (cartwheel orientation). The new finding for the site-averaged effect in HCl/Au(111) holds also in the DCl/Au(111) system that one can eventually reproduce the exact six-dimensional dissociation probability from the site-averaged results over 25 sites from the four-dimensional fixed-site calculations. We anticipate that this site-averaged effect can be observed in many moleculesurface interactions. ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (Grant Nos. 91221301, 90921014, and 21303197), the Chinese Academy of Sciences, and Ministry of Science and Technology of China. 1 R.
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THE JOURNAL OF CHEMICAL PHYSICS 140, 144701 (2014)
Six-dimensional quantum dynamics study for the dissociative adsorption of DCl on Au(111) surface Tianhui Liu, Bina Fu,a) 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 16 January 2014; accepted 26 March 2014; published online 8 April 2014) We carried out six-dimensional quantum dynamics calculations for the dissociative adsorption of deuterium chloride (DCl) on Au(111) surface using the initial state-selected time-dependent wave packet approach. The four-dimensional dissociation probabilities are also obtained with the center of mass of DCl fixed at various sites. These calculations were all performed based on an accurate potential energy surface recently constructed by neural network fitting to density function theory energy points. The origin of the extremely small dissociation probability for DCl/HCl (v = 0, j = 0) fixed at the top site compared to other fixed sites is elucidated in this study. The influence of vibrational excitation and rotational orientation of DCl on the reactivity was investigated by calculating six-dimensional dissociation probabilities. The vibrational excitation of DCl enhances the reactivity substantially and the helicopter orientation yields higher dissociation probability than the cartwheel orientation. The site-averaged dissociation probability over 25 fixed sites obtained from four-dimensional quantum dynamics calculations can accurately reproduce the six-dimensional dissociation probability. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4870594] I. INTRODUCTION
It is well known that the dissociative adsorption of molecular species on transition-metal surfaces is one of the significant reactions in heterogeneous catalysis. During the past several decades, the dissociative adsorption of molecules on various metal surfaces has been extensively studied both experimentally and theoretically,1–15 due to the fact that this dissociation process is often the rate-determining step in most of the chemical reactions. Theoretically, numerous efforts have been devoted to investigating the reaction mechanisms of these reactions at the quantum mechanical level. 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. The dissociative adsorption of H2 on metal surfaces is the most thoroughly studied dissociative chemisorption using the quantum dynamics calculations, ranging from the reduced two-dimensional model16 to the full-dimensional approach.17–25 Nonetheless, a full-dimensional quantum mechanical description of polyatomic dissociative chemisorption is still extremely challenging. Low-dimensional models were employed in recent quantum dynamics studies of CH4 on Ni surfaces,26–29 as a total of 15 degrees of freedom should be considered on a rigid surface for this reaction. Recently, Guo and co-workers carried out six-dimensional quantum dynamics calculations of H2 O on Cu(111)30–32 and eightdimensional calculations of CH4 on Ni(111).33 The PESs a) Authors to whom correspondence should be addressed. Electronic
addresses: [email protected] and [email protected]
0021-9606/2014/140(14)/144701/7/$30.00
employed were fit by the permutationally invariant polynomial approach of Bowman and co-workers34, 35 based on energy points from density functional theory (DFT) calculations. Jackson and Nave employed a fully quantum approach based on the Reaction Path Hamiltonian that includes all 15 molecular degrees of freedom and the effects of lattice motion to investigate the dissociative chemisorption of methane on a Ni(111) surface.36 In this work we carried out full-dimensional (sixdimensional) quantum dynamics calculations of deuterium chloride (DCl) dissociative chemisorption on Au(111) surface, employing an accurate PES recently developed by neural network fitting to roughly 70 000 DFT energy points (LFZ PES).37 Based on the small fitting errors and good agreement with the direct DFT calculations, this PES is sufficiently accurate to be used in the quantum dynamics calculations. In addition, time-dependent wave packet calculations show that the LFZ PES is very well converged with respect to the number of DFT data points, as well as to the fitting process.37 We note that the PES used describes the interaction of hydrogen chloride (HCl) with an idealised Au(111) surface, which cannot be realized in experiments due to surface reconstruction.38, 39 However, the results from quantum dynamics calculations on this ideal PES can be helpful for unraveling the dynamics of gas-surface reactions and understanding experimental results. Very recently, we reported the detailed dynamics results of hydrogen chloride dissociative chemisorption on Au(111) obtained from full-dimensional quantum wave packet calculations on the LFZ PES.40 The influence of vibrational excitation and rotational orientation of HCl on the reactivity was investigated by calculating the exact six-dimensional dissociation probabilities, as well as the
140, 144701-1
© 2014 AIP Publishing LLC
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Liu, Fu, and Zhang
four-dimensional (4D) fixed-site dissociation probabilities. The vibrational excitation of HCl enhances the reactivity and the helicopter orientation yields higher dissociation probability than the cartwheel orientation. Furthermore, an interesting site-averaged effect was found in that study that one can essentially reproduce the six-dimensional (6D) dissociation probability by averaging the four-dimensional dissociation probabilities over 25 fixed sites without zero-point energy (ZPE) corrections. Experimentally, Lykke and Kay carried out a molecule beam-surface scattering experiment of HCl scattered from Au(111) in 1990, and the rotationally inelastic scattering was investigated.41 In the past several years, Wodtke and coworkers investigated the energy transfer between HCl and Au(111) interfaces,42–45 where a transition from an electronically adiabatic mechanical mechanism to an electronically nonadiabatic mechanism involving excited electronhole pairs with the increase of surface temperature was reported. Theoretically, following our recent work for the construction of an accurate, six-dimensional PES and sixdimensional quantum dynamics study of the HCl/Au(111) system,37, 40 we present the detailed quantum dynamics results of DCl dissociative adsorption on Au(111) surface in this article. The motion of surface atoms and excited electronhole pairs were ignored in the current adiabatic PES, and the dynamics investigations were based on the rigid surface approximation, thus the current theory is not able to directly describe the experimental quantities measured by Wodtke et al.42–45 Our recent work37, 40 indicated 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 the rest of 4D results and the 6D results for the HCl/Au(111) system, though the bare barrier height for the top site is only 0.05 eV, 0.03 eV, and 0.19 eV higher than the hollow, fcc, and bridge sites, respectively. This is in strong contrast to the results found in other moleculemetal systems, e.g., H2 /Cu(111) and H2 /Cu(100), in which the dissociation probabilities for the fixed top site are in the same order of magnitude as the rest of 4D results and the 6D results.18, 46–48 Thus, it is still waiting to be answered whether the small dissociation probability for the top site exists for the isotopically substituted DCl/Au(111) reaction and what is the fundamental reason of this intriguing behavior? In addition, further study is still necessary to see whether our new finding for the HCl + Au(111) reaction, i.e., that the six-dimensional reaction probability can essentially be reproduced without any need for zero-point energy corrections by averaging the four-dimensional site-specific reaction probabilities over impact sites (as long as enough impact points are used in the averaging), holds also for the DCl + Au(111) reaction. As a result, we have carried out quantum wave packet calculations for DCl/Au(111) and present the detailed results below. The paper is structured as follows. In Sec. II we present the time-dependent wave packet method (TDWP) methodologies and brief description of PES used in dynamics calculation. Results and discussions are given in Sec. III. A summary and conclusions are given in Sec. IV.
J. Chem. Phys. 140, 144701 (2014)
II. THEORY A. The 6D time-dependent wave packet method
The accurate dynamics calculations for dissociative adsorption of a diatomic molecule on a corrugated, rigid surface should include six degrees of freedom. Since detailed descriptions of the general 6D initial state-selected wave packet approach to diatomic molecule-surface reactions have been presented before,17, 18, 40 we only give an outline of the methodology here. The six degrees of freedom of DCl/Au(111) include molecular coordinates, namely, X, Y, Z, r, θ , φ (as shown in Fig. 1), and the 6D Hamiltonian is expressed in terms of these coordinates as 1 ∂2 jˆ2 1 ∂2 − + Hˆ = − 2M ∂Z 2 2μ ∂r 2 2μr 2 1 ∂2 1 ∂2 1 2 cos α ∂ 2 + − − 2M sin2 α ∂x 2 sin2 α ∂x∂y sin2 α ∂y 2 + V (x, y, Z, r, θ, φ),
(1)
where M and μ are the total mass and reduced mass of DCl, respectively. The operator jˆ is the rotation operator. The x and y coordinate axes are parallel to the surface, Z is the perpendicular coordinate from the center of mass (COM) of HCl to the plane of surface, r is the interatomic distance of DCl, θ is the polar angle, and φ is the azimuthal angle. The last term V (Z, r, x, y, θ, φ) is the interaction potential energy. The skewing angle α is the angle between the x and y coordinate axes as indicated in Fig. 1. For Au(111), α = 120◦ . The time-dependent wave function is expanded in terms of translational basis of Z, 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)eikx x eiky y . (2) = n,v,j,m
Here, kx = 2π nx /Lx and ky = 2π ny /Ly , where Lx and Ly are the surface unit cell lattice constants. Because of the periodicity of the potential energy surface along x and y, we employed the superposition of periodic functions eikx x and eiky y
Cl
Z
r θ
D
y
144701-2
φ x α =120
Au FIG. 1. Molecular coordinates for the scattering of DCl from Au(111) surface, where (x, y, Z) are the center-of-mass coordinates of DCl, r is the internuclear distance of DCl, θ is the polar angle, and φ is the azimuthal angle. The skewing angle α = 120◦ for Au(111).
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to represent the wave functions of the x and y coordinates. The Z and r coordinates were efficiently represented by the sinDVR (discrete variable representation) basis functions,49, 50 while we used the direct product of Legendre polynomials Pn (cos (θ )) and eimφ as a good basis representation for the θ and φ coordinates by separating the φ-dependent term from jˆ2 .18, 51 We employed the split-operator method in which the exponential Schrödinger propagator is symmetrically split to propagate the wave packet.52 The initial state-selected total dissociation probability was obtained by projecting out the energy dependent reactive + denotes the time-independent full scattering wave flux. If ψiE function, where i and E are, respectively, initial state and energy labels, the total dissociation probability from an initial state i can be obtained by + ˆ + |F |ψiE . PiR = ψiE
(3)
Here, Fˆ is the flux operator, defined as 1 Fˆ = [δ(ˆs − s0 )vˆs + vˆs δ(ˆs − s0 )], (4) 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 time-independent + + |ψiE scattering wave function is normalized as ψiE = 2π δ(E − E ). Employing the expression (4), Eq. (3) can be simplified to yield ¯ + + Pi (E) = Im(ψiE |ψiE )|s=s0 , μr where + = |ψiE
1 ai (E)
∞
ei(E−H )t/¯ |i (0)dt,
(5)
(6)
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 4D calculations are carried out with the COM of DCl (x and y) fixed at the top, bridge, hollow, and fcc sites, respectively, as shown in Fig. 2. B. The 6D PES
The interaction potential energy V (X, Y, Z, r, θ, φ) of the DCl/Au(111) reaction is evaluated from the recent 6D PES, which was constructed by using the neural network fitting to a total of 76 393 DFT energy points.37 The resulting hollow top
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). The interaction between ionic cores and electrons was described by fully nonlocal optimized projector augmented-wave (PAW) potentials,53 and the Kohn-Sham valence electronic states were expanded in a plane wave basis set.54 The electron exchange correlation effects were treated within the generalized gradient approximation (GGA),55 using the PerdewWang (PW91) functional.56 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 MonkhorstPack k-points grid mesh is 5×5×157 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).58 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. Readers can refer to our recent work for the details of the PES.37 The potential energy of the DCl/Au(111) reaction with the coordinates (X, Y, Z, r, θ , φ) equals that of HCl/Au(111) with the coordinates (X , Y , Z , r, θ , φ), where they satisfy X = X − r
m D − mH sin(α − φ) mCl sin(θ ) , mH + mCl sin(α) mD + mCl
m D − mH sin(φ) mCl sin(θ ) , mH + mCl sin(α) mD + mCl mCl mD − mH Z = Z + r cos(θ ) , mH + mCl mD + mCl Y = Y − r
with mCl , mD , and mH representing the masses of Cl, D, and H, respectively. III. RESULTS
The relevant numerical parameters used in this TDWP calculations are similar with those used in the dynamics calculations of the HCl/Au(111) system.40 The dissociation flux is calculated on the dividing surface of r = 4.5 bohr. The number of grid points for the Z, x, and y coordinates remains the same because of the slight difference of the total mass of DCl and HCl. However, due to the fact that the reduced mass of DCl is nearly twice as large as that of HCl, we used 55 sintype DVR points to describe the r coordinate. The orientation angle θ needs 61 Legendre DVR points and the azimuthal angle φ requires 101 evenly spaced Fourier grid points. These parameters are all larger than the corresponding HCl parameters.
bridge
fcc
FIG. 2. The irreducible triangle of Au(111) surface unit cell (shown in black triangle), the atoms in the first, second, and third layers are shown in yellow, bronze, and black spheres, respectively. Note that the atoms in the third layer are right at the fcc site. Atoms in the fourth (fifth, sixth) layer are directly below the atoms in the first (second, third) layer.
A. 4D and 6D dissociation probabilities
The dissociation probability for DCl initially in the ground rovibrational state (v = 0, j = 0) calculated using the 6D TDWP method is shown in Fig. 3, together with the 4D results for which DCl is fixed at the bridge, fcc, hollow, and top sites, respectively, in the kinetic energy region of 0.4 eV and 1.6 eV. Overall, all the dissociation probabilities are smooth functions of the kinetic energy, and rise steadily as the kinetic
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other results, though the bare barrier height for the top site (0.83 eV) is only 0.03 eV, 0.05 eV, and 0.18 eV higher than the fcc site (0.80 eV), the hollow site (0.78 eV), and the bridge site (0.65 eV),37 respectively. The same behavior was also found in the HCl/Au(111) system recently.40 As shown in Fig. 2, the COM of the DCl/HCl molecule is right on the top of a single Au atom for DCl/HCl fixed at the top site. Because the COM of the DCl/HCl molecule is essentially on the Cl atom, implying that the Z coordinate is roughly the distance between the Cl and Au atoms. As shown in Fig. 4(a) representing the contour plot of the PES as a function of Z and r coordinates with θ and φ optimized for DCl fixed at the top site, the repulsion force between the Cl atom and Au atom increases very rapidly when Z decreases. Furthermore, we plot the evolution of the probability density on this contour plot and show them in Figs. 4(a)–4(f) at different propagation times, respectively. We can see from Figs. 4(a)–4(c) that the wave packet does not evolve along the minimum energy reaction path, but rushes to the potential energy wall along the Z coordinate. Obviously, the wave packet in the high kinetic energy region can reach the high potential energy region with very small Z coordinates without any change of r coordinates, implying the DCl molecule can get very close to the Au atom without the extension of its interatomic distance. Due to the steep PES with increasing Z, a large portion of the wave packet rebounds quickly to the DCl+Au(111) asymptote, but a very small portion of them leaks to the product region with large r, as shown in Figs. 4(d)–4(f), leading to the very small dissociation probability. Therefore, the kinetic energy in the translational motion (along Z coordinate) is not effective at all on promoting this type of late-barrier reactions with HCl/DCl fixed at the top site, while the vibrational excitation (kinetic energy along r coordinate) enhances the reactivity significantly, as has been indicated previously that the dissociation probabilities for the first and second vibrational states of HCl are in the same order of magnitude as the results for the other sites.40
Dissociation Probability
0.8
0.6
4D bridge site 4D fcc site 4D hollow site 4D top site × 100 6D
0.4
0.2
0 0.4
1.4
1.0 0.8 1.2 Kinetic Energy (eV)
0.6
1.6
FIG. 3. Comparison of dissociation probabilities for the scattering of DCl(v = 0, j = 0) from Au(111) between the six-dimensional and fourdimensional fixed-site calculations. As indicated, the dissociation probability for the top site is multiplied by a factor of 100.
energy increases. 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. The overall behavior of 4D results for the fixed fcc site is very similar to that of the hollow site, with the probability curves rise from the threshold of around 0.75 eV. The 6D probability is quite different from the results calculated by reduced dimensional (4D) fixed-site approach. The threshold of the 6D dissociation probability is about 0.02 eV higher than that of the 4D bridge site, in accord with the difference of their bare barrier heights,40 and the magnitude of the 6D probability is smaller than that of the bridge site in the entire energy region. It is interesting that the dissociation probability for DCl fixed at the top site is about 100–200 times smaller than the
(a) T=5400
(b) T=6000
(c) T=6900
4.5 0.8
0.9
0.8 0.9
0.9
0.8
0.9
0.8
0.9
0.8
3.5
0.9
r (bohr)
5.5
0.8
2.5 (f) T=10200
(e) T=8700
(d) T=7800
4.5 0.8
0.9
0.8 0.9
0.9
0.8
0.9
0.8
0.9
0.8
3.5
0.9
r (bohr)
1.5 5.5
0.8
2.5 1.5 3.5 4
4.5 5 5.5 6 Z (bohr)
6.5 3.5 4
4.5 5 5.5 6 Z (bohr)
6.5 3.5 4
4.5 5 5.5 6 Z (bohr)
6.5 7
FIG. 4. The evolution of the probability density of DCl(v = 0, j = 0) scattering from Au(111) at the fixed top site on the contour plot of the PES. The contours are relative to the DCl + Au(111) asymptote with an interval of 0.1 eV. The probability density is shown as a function of Z and r with the other coordinates integrated, and the contour plot is shown with other coordinates optimized. Different propagation times are indicated by the label “T” in panels (a), (b), (c), (d), (e), and (f), respectively.
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J. Chem. Phys. 140, 144701 (2014)
(a) v=0, j=0 v=1, j=0
Dissociation Probability
Dissociation Probability
0.4
0.5
0.3
0.2
0.1
0.0 0.0
m=0 m=1 m=2
v=0, j=2
0.4
0.3
0.2
0.1
0.2
0.4
0.6 1.0 0.8 Kinetic Energy(eV)
1.2
1.4
1.6
(b)
0.0 0.4
0.6
1.0 0.8 1.2 Kinetic Energy(eV)
1.4
1.6
FIG. 6. The six-dimensional dissociation probabilities with the same rovibrational state (v = 0, j = 2) but different orientations (m = 0–2).
Dissociation Probability
0.4
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6 1.0 0.8 Total Energy(eV)
1.2
1.4
1.6
FIG. 5. (a) The six-dimensional dissociation probability as a function of kinetic energy for the ground rovibrational state of DCl, together with that for the first vibrational excited state. (b) Same as (a), except as a function of total energy.
dimensional dissociation probabilities for initial rovibrational states with the same rovibrational energy (v = 0, j = 2) but different orientations (m = 0–2) in the kinetic energy region of 0.4 eV and 1.6 eV are shown in Fig. 6. 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, with the largest dissociation probability of m = 2, and the smallest one of m = 0. Therefore, the dissociation of DCl is most favored at the helicopter orientation (m = 2), but not at the cartwheel orientation (m = 0), seen from the exact 6D probabilities.
B. Site-averaged effect
The six-dimensional dissociation probabilities for DCl initially in the ground rovibrational state (v = 0, j = 0) and in the first vibrational excited state (v = 1, j = 0) as a function of the kinetic energy are illustrated in Fig. 5(a), together with those as a function of the total energy shown in Fig. 5(b). The total energy is measured with respect to the energy of non-rotating ground vibrational state of DCl. Overall, the dissociation probabilities for the two vibrational states increase steadily with increasing kinetic energy, presenting the thresholds of roughly 0.6 eV and 0.36 eV for v = 0 and v = 1 states, respectively, as seen from Fig. 4(a). Obviously, the vibrational excitations of DCl enhance the reactivity substantially, resulting from the late barrier of the title molecule-surface reaction as indicated in Ref. 37. When we see the results as a function of total energy in Fig. 5(b), the dissociation probability of v = 1 is larger than that of the ground state in the entire total energy region, implying that the vibrational excitation of DCl is more efficacious than the same amount of translational energy in promoting the reaction, and the Polanyi’s rules59 hold for this late-barrier gas-surface reaction. Next we consider the rotational-orientation effect in the dissociative adsorption of DCl on Au(111) surface. The six-
We recently improved the site-averaged effect for the dissociative adsorption of HCl on Au(111), demonstrating that the exact six-dimensional dissociation probability can be essentially reproduced by averaging the four-dimensional fixedsite dissociation probabilities over 25 sites40 without any need for ZPE corrections. It is still interesting to see whether this new finding exists in the scattering of DCl from Au(111) instead of HCl. To this end, we calculated the 4D site-averaged dissociation probabilities over 4, 9, and 25 sites, respectively, as has been done previously for HCl.40 The site-averaged effect for the molecule-surface interactions was first proposed by Dai and Light from the quantum dynamics studies for the H2 +Cu(111) reaction.18 In that work, three symmetric sites (bridge, center, and top) were averaged to achieve the siteaveraged dissociation probability, 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. However, the 6D dissociation probability was quite different from the shifted site-averaged dissociation probability at high kinetic energies and the explanation that ZPE differences account for the four to six dimensional shift in energy is not convincing in that study. It is worth noting that we are currently doing in the
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(a)
J. Chem. Phys. 140, 144701 (2014)
hollow
top
bridge
fcc (b)
top
hollow
Dissociation Probability
0.5
4 site-averaged 9 site-averaged 25 site-averaged 6D
0.4
0.3
0.2
bridge 0.1
fcc FIG. 7. (a) The schematic of the distribution of 9 sites (4 black circles denote the bridge, hollow, fcc, and top sites, and 5 red 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).
slightly different way from that was done by Dai and Light for the H2 /Cu(111) system.18 Specifically, we averaged 4 symmetric sites (bridge, hollow, fcc, and top), as shown in Fig. 2, 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 4 site-averaged dissociation probability. 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. Figure 7(a) shows that five midpoints of the tophollow line, top-fcc line, top-bridge line, bridge-hollow line, and bridge-fcc line, and the original 4 fixed sites (bridge, hollow, fcc, and top) constitute the present 9 sites. Similarly, the 25 sites consist of 16 midpoints of the two adjacent sites of the 9 sites mentioned above and the 9 fixed sites, as shown in Fig. 7(b). We obtained the averaged dissociation probability over 9 sites 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 depicted in Fig. 8 for HCl initially in the ground rovibrational state up to the kinetic energy of 1.6 eV. Obviously, the 4 siteaveraged dissociation probability is remarkably larger than the 6D probability in the entire energy region. 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 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 energy lower than 0.8 eV just above the threshold, and smaller than the latter at the kinetic energy higher than 0.8 eV. Furthermore, the agreement between
0.0 0.4
0.6
0.8
1.0 1.2 Kinetic Energy(eV)
1.4
1.6
FIG. 8. Comparisons of six-dimensional dissociation probabilities and three site-averaged dissociation probabilities of DCl(v = 0, j = 0), obtained by averaging the 4D dissociation probabilities over 4 fixed sites, 9 sites, and 25 sites with appropriate relative weights.
the 25 site-averaged probability and 6D probability is excellent, seen from the green and blue curves. We anticipate that the 6D results can be completely reproduced from the higher site-averaged dissociation probabilities, i.e., 81 or higher, as long as the site-selecting routine is maintained as mentioned above. It is most gratifying that one can eventually obtain the exact 6D dissociation probabilities from the site-averaged 4D results without doing six-dimensional quantum dynamics calculations, which are rather computational time and memory consuming. We anticipate that this site-averaged effect we observed should generally exist in other molecule-surface interaction systems.
IV. CONCLUSIONS
In summary, the initial state-selected six-dimensional TDWP method has been employed to carry out the quantum dynamics calculations for the dissociative adsorption of DCl on the rigid Au(111) surface, based on an accurate, six-dimensional PES which was constructed recently by the neural network fitting to DFT energy points. The fourdimensional dissociation probabilities for DCl initially in the ground rovibrational state were also obtained by doing quantum dynamics calculations for the COM of DCl fixed at the bridge, fcc, hollow, and top sites, respectively. The dissociation probability with DCl fixed at the top site is 100–200 times smaller than the rest of 4D results and the 6D result, due to the fact that the repulsion force increases rapidly as the interatomic distance between the Cl atom of DCl and the Au atom of the first layer of Au(111) surface, with the Cl atom right on the top of the Au atom. The wave packet is able to rush to the high potential energy region with small Z coordinates without extension of the bond length of DCl molecule, quickly followed by the rebounce of the wave packet to the DCl+Au(111) asymptote, rather than to overcome the dissociation barrier for DCl dissociating on Au(111) surface. The increase of kinetic energy in the translational motion along
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the Z direction is not efficacious at all for this type of latebarrier reaction, but the vibrational excitation of DCl (kinetic energy along the r direction) is rather efficient in promoting the dissociation that it enhances the reactivity by 100–200 times with DCl(v = 1). The influence of the vibrational excitation and rotational-orientation of DCl on the reactivity is investigated in detail from six-dimensional calculations in this study. The vibrational excitation of DCl enhances the reactivity substantially, indicating that the Polanyi’s rules hold for this late-barrier molecule-surface reaction. The dissociation prefers to occur with DCl colliding with rotation in a plane parallel to the Au(111) surface (helicopter orientation), not with DCl colliding perpendicularly (cartwheel orientation). The new finding for the site-averaged effect in HCl/Au(111) holds also in the DCl/Au(111) system that one can eventually reproduce the exact six-dimensional dissociation probability from the site-averaged results over 25 sites from the four-dimensional fixed-site calculations. We anticipate that this site-averaged effect can be observed in many moleculesurface interactions. ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (Grant Nos. 91221301, 90921014, and 21303197), the Chinese Academy of Sciences, and Ministry of Science and Technology of China. 1 R.
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