Controlling Heterogeneous Catalysis of Water Dissociation Using Cu

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Controlling Heterogeneous Catalysis of Water Dissociation Using Cu-Ni Bimetallic Alloy Surfaces: A Quantum Dynamics Study Dhiman Ray, Smita Ghosh, and Ashwani Kumar Tiwari J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03237 • Publication Date (Web): 07 Jun 2018 Downloaded from http://pubs.acs.org on June 8, 2018

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The Journal of Physical Chemistry

Controlling Heterogeneous Catalysis of Water Dissociation using Cu-Ni Bimetallic Alloy Surfaces: A Quantum Dynamics Study Dhiman Ray, Smita Ghosh, and Ashwani K. Tiwari∗ Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur - 741246, West Bengal, India E-mail: [email protected]

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

Abstract Copper-Nickel bimetallic alloys are emerging heterogeneous catalysts for water dissociation which is the rate determining step of industrially important Water Gas Shift (WGS) reaction. Yet, the detailed quantum dynamics studies of water-surface scattering in literature are limited to pure metal surfaces. We present here, a three dimensional wave-packet dynamics study of water dissociation on Cu-Ni alloy surfaces, using a pseudo diatomic model of water on a London-Eyring-Polanyi-Sato (LEPS) potential energy surface in order to study the effect of initial vibration, rotation and orientation of water molecule on reactivity. For all the chosen surfaces reactivity increases significantly with vibrational excitation. In general, for lower vibrational states the reactivity increases with increasing rotational excitation but it decreases in higher vibrational states. Molecular orientation strongly affects reactivity by helping the molecule to align along the reaction path at higher vibrational states. For different alloys, the reaction probability follows the trend of barrier heights and the surfaces having all Ni atoms in the uppermost layer are much more reactive than the ones with Cu atoms. Hence the nature of the alloy surface and initial quantum state of the incoming molecule significantly influence the reactivity in surface catalyzed water dissociation.

Introduction The dissociative chemisorption of water on metal surfaces has recently drawn the attention of many theoretical and experimental scientists owing to its enormous importance in industrial processes. It is the rate determining step of water gas shift reaction (WGS) 1 which plays an essential role in the steam methane reformation 2 and hydrogen evolution in fuel cells. 3 Therefore a detailed understanding of metal catalyzed water dissociation has become necessary. 4 Theoretical and experimental studies have suggested that Cu and Ni are effective catalysts for water dissociation. 3,5,6 But the pure metallic Ni often catalyzes the decomposition of CO along with water leading to carbon deposition on the metal surface and the

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reduction of effective catalytic surface area. 3,7–9 Although metallic Cu has a higher barrier to dissociation of water, it does not suffer from the problem of carbon deposition. These observations inspired theoretical study of water dissociation on Copper-Nickel bimetallic alloy surfaces in search of a superior catalyst which can combine the effectiveness and overcome the problems of both the pure parent metals. 3,10 Ghosh et al. have studied water dissociation on Cu-Ni bimetallic catalysts of several different surface composition using Density Functional Theory. 3 They also employed Sudden Model 11,12 to incorporate the effect of lattice motion at finite temperature. They observed a wide variation of catalytic activity with the composition of the alloy surface. Interestingly, they predicted two particular compositions: one having higher and the other with lower reactivity compared to the both parent metal surfaces. 3 Certainly, these results call for further investigation, both theoretical and experimental, to get a detailed understanding of the dynamics of the reaction on alloy surfaces. In recent years, reactive scattering of H2 O molecule on metal surfaces has been studied extensively using Wave Packet propagation 2,13–24 or Quasi Classical Trajectory method 25 on high dimensional potential energy surfaces (PES). Jiang et al. have developed a permutationally invariant polynomial neural network (PIP-NN) method to fit the 9 dimensional potential energy surface of water on Cu(111) and Ni(111) taking into account all the degrees of freedom of the water molecule with respect to the metal surface. 26,27 They conducted classical as well as quantum dynamics calculation on these surfaces to study the effect of surface sites and various vibrational and rotational excitations of water molecule on reactivity. It has been observed previously that the water dissociation is a tunneling dominated reaction and the quantum effects play an important role on reactivity. 28,29 This necessitates the use of quantum mechanics in stead of QCT methods for studying the dynamics of the reaction. Indeed the quantum dynamical calculations of Jiang et. al. could reproduce the reactivity trends observed in experimental studies albeit qualitatively. 14–17 Their calculations showed that vibration of the molecule plays a significant role in the reaction for both Cu(111) and Ni(111) surfaces.

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There are two major difficulties associated with the approach of Jiang et al.. First the neural network based methods are black box fitting methods with poor extrapolation capability. 30,31 So a large number of ab-initio points (often in the range 104 − 106 ) spanning the entire reaction channel are required to produce a chemically accurate fit. 14,25 These large number of ab-initio calculations make the process computationally expensive. Secondly, the propagation of wave-packet in 9D is extremely challenging not only for the associated computational expense but also for the complexity in constructing the Hamiltonian and wave functions. The second problem was tackled by Zhang et al. and Liu et al. who performed a 9D fully coupled wave-packet dynamics calculation for water dissociation on Cu(111) surface 20 and Ni(100) surface 32 respectively. Prior to that Dai and Light proposed a site averaging approximation to take into account the effect of corrugation without explicitly treating the lateral coordinates in the wave-packet propagation. 33 This scheme has been improved and used extensively in studying water dissociation on Cu(111) surface 20–24 and other similar systems 34–36 by Zhang and coworkers. It allowed them to reduce the 9D Hamiltonian into 7D for quantum dynamics calculation while the results of the full dimensional calculations could be recovered by invoking the site averaging approximation. 20,32 Similar studies on water dissociation in Ni(111) surface were carried out by Jiang et al. 15 One approach to avoid these difficulties is the use of Reaction Path Hamiltonian method 37 which was applied to molecule surface scattering recently by different groups. 38–46 This method requires one to perform electronic structure calculations only on the reaction path and propagate a wave packet along a single coordinate. It also allows the incorporation of the effect of coupling between different vibrational modes. But this method is not suitable for studying the effect of rotation or orientation of the adsorbing molecule as it restricts the dynamics only in the reaction coordinate. Darling and Holloway have shown earlier that, apart from vibration, the rotation and the orientation of the incoming H2 molecule has significant impact on its dissociation probability on Cu(111) surface. 47–50 Recently, Mondal and co-workers have also reported that the reactivity of water on Cu(111) surface has

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strong orientation dependence. 29 To address vibrational, rotational and orientational effects altogether, multi dimensional dynamics is necessary. Another alternative approach is the use of a pseudo diatomic model on the conventional London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES) which has been traditionally used to study the dynamics of molecule-surface scattering. 11,12,29,51–53 The limitations of this method are that it cannot take into account all the degrees of freedom of water molecule and it is, in its primitive form, unable to differentiate between different surface sites. (However, the latter problem can be taken care of by using a corrugated LEPS PES where the PES parameters are allowed to vary across different surface sites.) 54,55 Yet, LEPS PES has certain advantages. First, the derivation of the potential energy function is inspired by the London Equation 56 which involves Coulomb and Exchange integral values of the current system. As a result the extrapolation capabilities are not as poor as generic fitting methods like neural network, which does not contain in itself any system specific information. 31 Second, the only variable parameters in the LEPS PES formula are the three Sato parameters which can be fitted or chosen to reproduce the ab initio or experimental results. So a comparatively less number of ab initio energy points are required to construct these PES’s. Moreover, an exact 3D quantum dynamics is much less computationally expensive than the 6D or 7D studies performed by Jiang et al. From the point of view of computational cost this method is preferable over high dimensional dynamics when a qualitative comparison of different systems is sought. Although the multidimensional quantum dynamics studies for water dissociation on pure metal surfaces are abundant in recent literature, such studies on alloy surfaces are rare. Ghosh et al. have studied dissociative chemisorption of water on Cu-Ni alloy surfaces only for the ground vibrational and rotational state. 3 It is interesting to know how the ro-vibrational excitation of the incident water molecule affects the reactivity. In the present work, we address this problem by performing detailed quantum dynamical calculation on LEPS form of PES to understand the influence of orientation, rotation and vibration of the water molecule

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on its dissociation on Cu(111), Ni(111) and two Cu-Ni bimetallic alloy surfaces of different composition.

Theory and Computational details Systems studied The following Cu-Ni alloy surfaces were chosen for the present study: Ni4-Cu(111) (Cu(111) host with all the atoms of uppermost layer replaced by Ni atoms) and Sub-Ni4-Cu(111) (Cu(111) host with all the atoms of subsurface layer replaced by Ni atoms). The naming convention of Ghosh et al. has been followed. 3 Previous DFT results show that the Ni4-Cu(111) surface has lower dissociation barrier height than both the parent metal surfaces (i.e. pure Cu(111) and pure Ni(111)) while the Sub-Ni4-Cu(111) surface has higher dissociation barrier than both the parent metal surfaces. 3 This makes these two alloy surfaces particularly interesting in terms of catalytic applications. In this work, we study these two alloys along with pure Cu(111) and Ni(111) in order to make a comparison between parent metals and alloys in terms of catalytic activity towards water dissociation in the ground and excited ro-vibrational states.

Potential Energy Surface (PES) The traditional London-Eyring-Polanyi-Sato (LEPS) PES for diatom-surface collision is used in this work. The modified version of the LEPS potential for diatom-surface scattering has been derived by McCreery and Wolken. 57 The water molecule has been modeled as a pseudodiatomic molecule R-H where R is the non-dissociating OH group. This model has been previously used to study H2 O dissociation dynamics on Cu(111) surface 29 and a similar model was used for CH4 dissociation on different metal surfaces. 11,12,51–53 Following the

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work of Mondal et al. 29 we have used the following form for the present study:

p V (Z, r, θ) = U1 (z1 )+U2 (z2 )+U3 (z3 )+ Q3 (r)2 + {Q1 (z1 ) + Q2 (z2 )}2 − Q3 (r){Q1 (z1 ) + Q2 (z2 )} (1) where

Ui (x) =

Di [(3 + ∆i )exp(−2αi (x − x0i )) − (2 + 6∆i )exp(−αi (x − x0i ))] 4 + 4∆i

(2)

Qi (x) =

Di [(1 + 3∆i )exp(−2αi (x − x0i )) − (6 + 2∆i )exp(−αi (x − x0i ))] 4 + 4∆i

(3)

and

where z1 = Z +

mOH rcosθ mw

and z2 = Z +

mH rcosθ. mw

They are the distance of the center

of mass of non-dissociating OH group and the dissociating H atom from the surface, respectively. The interactions H−surface, OH−surface and H−OH has been represented by the indices i=1,2 and 3 respectively. According to the LEPS potential model 57 D1 and D2 are, respectively, the adsorption energy of H and OH on the metal surface. D3 is the dissociation energy of the H-OH bond. Similarly x01 , x02 and x03 are the equilibrium distance between H−surface, OH−surface and H−OH respectively. The αi s are the corresponding Morse paq 2 µi ωi rameters given by αi = where the ωi is the bond stretching frequency. Following 2Di the work of Carré and Jackson the artificial alignment of the incident molecule far from the surface has been corrected by dampening out the θ dependence of the potential at large Z. 51 The values of D1 , D2 , D3 , x01 , x02 and x03 were calculated using DFT based Vienna abinitio simulation package (VASP). 58–61 Both H and OH were adsorbed separately on the fcc hollow sites which are the most stable adsorption sites for H and OH on the surfaces studied. Plane wave basis set and Perdew-Burke-Ernzerhof (PBE) 62,63 exchange-correlation functional within generalized gradient approximation was used to treat non local exchange correlation effects. Fully non local optimized projector augmented wave (PAW) potentials 64,65 are used

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to express the interaction between the ionic cores and electrons. Metal surface was modeled as slab super cell with periodic boundary conditions. The Ni(111), Cu(111) and the chosen bimetallic surfaces consist of four layers within 2 × 2 unit cell. Vacuum space of 11 Å is maintained between layers in the z-direction to avoid the interaction with surfaces of adjacent slabs. Equilibrium lattice constant 3.52 Å for Ni and 3.61 Å for Cu surfaces as found from the bulk geometry optimization in VASP is used for constructing the initial geometries for all surfaces. All the atoms of these surfaces are relaxed and optimized before using these surfaces for other calculations. For bimetallic surfaces we use the lattice constant of host metal surfaces. 5 × 5 × 1 gamma centered grid of k-points were used for structure optimization. Spin polarized calculations have been performed with plane wave expansion truncated at 400 eV. The convergence criterion is when all the forces are smaller than 0.01 eV/Å. The ωi ’s were calculated by normal mode analysis. The Sato parameters ∆i ’s were adjusted to reproduce the barrier height, adsorption energy, position of the transition state and the position of the adsorbed water from earlier study 3 as accurately as possible. The parameters used for the construction of the LEPS PES are provided in Table 1. Table 1: Parameters used in potential energy surface Cu(111)

Ni(111)

Ni4-Cu(111)

sub-Ni4-Cu(111)

D1 D2 D3 D1 D2 D3 D1 D2 D3 D1 D2 D3

= = = = = = = = = = = =

2.718 3.203 5.420 2.832 3.355 5.420 2.996 3.433 5.420 2.453 3.088 5.420

eV eV eV eV eV eV eV eV eV eV eV eV

α1 α2 α3 α1 α2 α3 α1 α2 α3 α1 α2 α3

8

= = = = = = = = = = = =

0.844 1.132 2.246 0.930 1.203 2.246 0.856 1.203 2.246 0.967 1.175 2.246

Å−1 Å−1 Å−1 Å−1 Å−1 Å−1 Å−1 Å−1 Å−1 Å−1 Å−1 Å−1


x01 x02 x03 x01 x02 x03 x01 x02 x03 x01 x02 x03

= = = = = = = = = = = =

0.924 1.418 0.964 0.917 1.359 0.964 0.816 1.270 0.964 0.918 1.398 0.964

Å Å Å Å Å Å Å Å Å Å Å Å

∆1 ∆2 ∆3 ∆1 ∆2 ∆3 ∆1 ∆2 ∆3 ∆1 ∆2 ∆3

= = = = = = = = = = = =

0.38 0.38 -0.48 0.39 0.38 -0.415 0.39 0.38 -0.43 0.41 0.40 -0.445

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Wave-packet propagation To study the effect of initial ro-vibrational and orientaional states (v0 , j0 , m0 ) of water on the reactivity, time dependent wave packet dynamics calculations were performed on the constructed LEPS potentials. It should be noted that (v0 , j0 , m0 ) are the quantum states of the pseudo-diatomic H-OH molecule and not the true eigenstates of asymmetric water molecule. So one should be careful not to overinterpret the influence of these states on reactivity. 29 Details of the wave-packet propagation methodology has been reported elsewhere. 29 A brief description of the procedure is provided below. Four coordinates of the dissociating water molecule has been included in our model. These are Z, the distance between the surface and the center of mass of the pseudo-diatomic HO-H, r, the distance between the center of mass of the non-dissociating OH group and the dissociating H atom, θ, the angle between the dissociating OH bond and the surface normal and φ, the azimuthal angle. The initial wave-packet which is propagated using time dependent wave-packet dynamics is as follows: exp(im0 φ) 1 0 Ψ(t = 0) = Gk0 (Z)ξvj00 (r)Θm j0 (θ) r (2π)1/2

(4)

where Gk0 (Z) is a Gaussian wave-packet corresponding to the incident translation of the molecule, given by Gk0 (Z) =

1 πδ 2

1/4

(Z − Z0 )2 exp − exp(−ik0 Z) 2δ 2

(5)

with width δ = 0.4 Å and situated at Z0 = 8 Å above surface and centered at k0 in the momentum space. The ξvj00 (r) is the v0 th Morse vibrational eigenfunction associated with exp(im0 φ) 29,51 0 the initial rotational state described by Θm The energy range available for j0 (θ) (2π)1/2 .

post-translational analysis is controlled by the width of the wave-packet δ. The initial wavefunction Ψ was re-scaled as Ψ = r−1/2 ψ and the ψ is propagated according to the Hamiltonian

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ˆ =K ˆ + Vˆ where K ˆ and Vˆ are the kinetic and potential energy operators respectively. The H kinetic energy operator is given by 2 2 2 2 2 ∂ ∂ 1 ∂ ∂ 1 ∂ h ¯ ∂ 1 h ¯ ˆ =− − × sinθ + 2 2 (6) − + + K 2mw ∂Z 2 2µw ∂r2 r∂r 4r2 r2 sinθ ∂θ ∂θ r sin θ ∂φ2 where mw and µw are the mass of the water molecule and the reduced mass between OH and H respectively. The finite basis representation was taken based on an eigenfunction of kinetic energy operator as :

0 Φα (Z)Rβj+1/2 (r)Θm j (θ)

exp(im0 φ) (2π)1/2

(7)

0 where Φα (Z) is a Fourier function, Rβj+1/2 (r) is a Bessel function and Θm j (θ) is an associated

Legendre function. Our potential energy function does not have φ dependence and therefore m0 is conserved in our calculations. So the kinetic energy part of the Hamiltonian becomes:

h ¯2 ∂2 h ¯2 ∂2 ∂ 1 1 ∂ ∂ m20 ˆ K=− − + − + × sinθ − 2 2 2mw ∂Z 2 2µw ∂r2 r∂r 4r2 r2 sinθ ∂θ ∂θ r sin θ

(8)

Split operator technique 66 was used to evolve the wave-packet in time. Translational Cartesian coordinate Z and the spherical coordinates r and θ were treated with Fourier transform, 67 Bessel transform 68,69 and Legendre transform 70–73 respectively. After the wavepacket is propagated for sufficiently long time, the dissociation probability for a given translational energy E is given by

Pdαj (E)

∂ψαj (r, E) 2π¯h2 ∗ = Im ψαj (rf , E) ∂r µw rf−1 r=rf

(9)

where rf is the point sufficiently far from the transition state towards the product region. 29 The product is supposed to form beyond r = rf . The energy dependent wave function

10


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ψαj (rf , E) was obtained as a Fourier transform of the time dependent wave function given by ψαj (rf , t) =

X

ψαβj (t)Nβj+1/2 Jj+1/2 (Kβj rf )

(10)

β 2 where Nβj+1/2 Jj+1/2 (Kβj rf ) is the normalized Bessel function with eigenvalues −Kβj . The

total dissociation probability is obtained from Pdαj (E) by summing over all α and j as P Pd (E) = αj Pdαj (E).

Results and discussion Potential Energy Surface The contour plots of the LEPS PES as a function of Z and r for the four systems are provided in Figure 1. In all the plots the value of θ was chosen to correspond to the minimum energy for all Z and r. During the construction of the LEPS potential more emphasis was given on reproducing the barrier height and and the adsorption energy with that in the ab-initio calculations of Ghosh et al. than the position of the barrier. The Z and r values of the transition state obtained by Ghosh et al.. was about 0.1 − 0.2 Å away from earlier studies by Jiang et al. 2,14 and Mondal et al. 29 . The position of the transition states in our LEPS PES’s for different systems are presented in Table 4. Table 2: Energy barrier in literature and current work Metal surface Cu(111) Ni(111) Ni4-Cu(111) sub-Ni4-Cu(111) a

Barrier height (eV) LEPSa Ghosh et. al. 3 1.15 1.14 0.71 0.72 0.62 0.61 1.21 1.20 current work b using PW91.

Jiang et. al. 2,14 Mondal et al. 29 1.49 0.97 0.67b -

The adsorption energy (Table 3) and barrier height (Table 2) values of the constructed 11



Cu(111)

4.5

4.5

4.0

4.0

3.5

3.5

3.0

3.0

2.5

2.5

2.0

2.0

1.5

1.5 1.0

1.5

2.0

2.5

3.0

r (Å)

3.5

4.0

4.5

5.0

1.0

Ni4-Cu(111)

5.0

4.0

4.0

3.5

3.5

Z (Å)

4.5

3.0

2.5

2.0

2.0

1.5

1.5 2.0

2.5

3.0

r (Å)

2.0

3.5

4.0

4.5

5.0

2.5

3.0

r (Å)

3.5

4.0

4.5

5.0

4.0

4.5

5.0

Sub-Ni4-Cu(111)

3.0

2.5

1.5

1.5

5.0

4.5

1.0

Ni(111)

5.0

Z (Å)

Z (Å)

5.0

Z (Å)

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

Page 12 of 32

1.0

1.5

2.0

2.5

3.0

r (Å)

3.5

Figure 1: LEPS potential energy surfaces for four different metal/alloy system. θ has been selected to give the minimum energy at each point (r,Z)

Table 3: Water adsorption energy in literature and current work Metal surface Cu(111) Ni(111) Ni4-Cu(111) sub-Ni4-Cu(111) a

Adsorption energy (eV) LEPSa Ghosh et al. 3 0.154 0.118 0.217 0.163 0.226 0.180 0.192 0.102 current work

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Table 4: Position of the Transition state in the LEPS potential energy surface LEPSa Z (Å) Cu(111) 1.81 Ni(111) 1.78 Ni4-Cu(111) 1.70 sub-Ni4-Cu(111) 1.80

r (Å) 1.47 1.41 1.39 1.52 a

θ (radian) 1.884 1.884 1.884 1.884 current work

Ghosh et. al. 3 Z (Å) r (Å) 1.94 1.68 1.92 1.56 1.88 1.53 1.92 1.69

θ (radian) 2.152 2.186 2.205 2.160

LEPS potential are in good agreement with the ab-initio calculations of Ghosh et al. and, therefore this LEPS potential can model the interaction between the dissociating water molecule and concerned metal surface adequately. The vibrational frequency of the diatomic adsorbate is 3847.26cm−1 when it is far from the metal surface. This value is quite close to the experimental gas phase symmetric stretching frequency of water molecule 74 i.e. 3832.2cm−1 . Previous study using RPH method has shown that the symmetric stretching mode has the biggest contribution in the reactivity of water molecule on Ni surfaces. 38

Effect of orientation of incoming water molecule To study the effect of the orientational quantum number m0 on the reactivity, the reaction probability values (Pd ) were plotted against the incident energy Ei for different orientational states for j0 = 3 for various vibrational states (Figure 2 and 3). For the catalyst surfaces used in the present study, the effect of m0 on the reactivity in the vibrational ground state is small. For Cu(111) Pd values for m0 = 3 is slightly lower than that of the m0 = 0, 1, 2 states which are almost same throughout the energy range. This result is consistent with the earlier study of Mondal et al. 29 For sub-Cu4-Ni(111) the following order is followed: m0 = 0 > m0 = 1, 2 > m0 = 3. For both Ni(111) and Ni4-Cu(111) surface m0 = 3 shows the lowest reactivity in the whole energy range. In the Ei range 0.2 to 0.4 eV Pd values for other orientations follow the order m0 = 1 > m0 = 0 > m0 = 2 while in the range Ei = 0.4-0.8 eV it becomes m0 = 1 > m0 = 2 > m0 = 0 and beyond 0.8 eV m0 = 2 > m0 = 1 > m0 = 0. For the v0 = 1 state, in case of Cu(111) surface for Ei = 0.2-0.6 eV the Pd values follow 13



the trend: m0 = 1 > m0 = 2 > m0 = 0 > m0 = 3. For Ei higher than 0.6 eV the trend changes to m0 = 2 > m0 = 1 > m0 = 0 ≈ m0 = 3. Similar trend is followed for sub-Ni4Cu(111) but Pd values for all the m0 states become same beyond 0.8 eV. For Ni(111) surface the reactivity for m0 = 0, 1, 2 states remain comparable in the concerned energy range. But the Pd value for m0 = 3 state is lowest at low Ei region and highest at high Ei region with a transition happening at around 0.4-0.5 eV. In case of Ni4-Cu(111) the reactivity follows the trend: m0 = 3 > m0 = 2 > m0 = 1 ≈ m0 = 0. For the vibrational second excited state the following order of Pd is followed: m0 = 3 > m0 = 2 > m0 = 1 > m0 = 0 for j0 = 3 for all the surfaces studied except for the subNi4-Cu(111). With increasing m0 value the dissociating O-H bond aligns more favorably along the reaction path which increases the reactivity. 29 For Ni4-Cu(111), almost same reactivity for m0 = 0, 1, 2 states is observed in the high incident energy region (Ei > 0.8 eV) although m0 = 3 state remains to be the most reactive one. For sub-Ni4-Cu(111) Pd value for m0 = 0, 1, 2 stays same throughout the energy range. For Ei < 0.6 eV m0 = 3 has the lowest reactivity while it becomes the highest reactive state beyond 0.8 eV with a transition happening in the intermediate region. Recently, the lowering of reactivity with higher m0 value in v0 = 0 state and the increase in reactivity with increasing m0 value in v0 = 2 state has been reported for Ni(111) surface from 7D time dependent wave-packet dynamics studies on a 9D PES 17 . Our results for v0 = 0 and v0 = 2 state of pseudo-diatomic water on Ni(111) surface are consistent with their findings.

Effect of initial Rotational and Vibrational states Rotational: To study the effect of rotational states, j0 , m0 averaged Pd values were plotted against incident energy for different vibrational states for all metal and alloy surfaces (Figure 4 and 5). Rotational excitation does not seem to affect the reactivity to a large extent. For all the surfaces in vibrational ground state i.e. v0 = 0, dissociation probability Pd increases 14


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10

3

Cu(111); v0 = 0

Ni(111); v0 = 0

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

10

1

10

2

10

3

10

4

10

5

10

6

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

Pd

4

Pd

10

10

10

5

6

0.2

0.4

0.6

Ei(eV)

0.8

1.0

1.2

0.2

0.4

Cu(111); v0 = 1

10

2

0.9 0.8

10

3

10

4

Ei(eV)

0.8

1.0

1.2

1.0

1.2

1.0

1.2

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

0.7

Pd

1

0.6

Ni(111); v0 = 1

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

Pd

10

0.6 0.5 0.4 0.3

0.2

0.4

0.6

Ei(eV)

0.8

1.0

1.2

0.2

0.6

Ei(eV)

0.8

Ni(111); v0 = 2 0.98

0.9

0.96

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

0.94

Pd

0.8 0.7 0.6

0.92 0.90 0.88

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

0.5 0.2

0.4

Cu(111); v0 = 2

1.0

Pd

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


0.4

0.6

Ei(eV)

0.8

1.0

0.86 0.84 1.2

0.2

0.4

0.6

Ei(eV)

0.8

Figure 2: Effect of initial orientational state m0 on reactivity for rotational state j0 = 3 for various vibrational states for the two pure metal surfaces

15



Ni4-Cu(111); v0 = 0

10

2

10

3

10

4

Pd

1

Pd

10

0.2

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3 0.4

0.6

Ei(eV)

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4

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Sub-Ni4-Cu(111); v0 = 0 j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

0.2

0.4

Ni4-Cu(111); v0 = 1 0.9

Pd

Pd 0.7 0.6 0.5 0.2

0.4

0.6

Ei(eV)

0.8

0.98

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1.2

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1.0

1.2

0.4

0.6

Ei(eV)

0.8

1.0

1.2

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Sub-Ni4-Cu(111); v0 = 2

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

0.8 0.7

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

0.6

0.97

Pd

0.96 0.95

0.5 0.4 0.3

0.94

0.2

0.93 0.2

Ei(eV)

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

Ni4-Cu(111); v0 = 2 0.99

0.6

Sub-Ni4-Cu(111); v0 = 1

j0=3; m0=0 j0=3; m0=1 j0=3; m0=2 j0=3; m0=3

0.8

Pd

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

Page 16 of 32

0.1 0.4

0.6

Ei(eV)

0.8

1.0

1.2

0.2

0.4

0.6

Ei(eV)

0.8

Figure 3: Effect of initial orientational state m0 on reactivity for rotational state j0 = 3 for various vibrational states for the two alloy surfaces

16


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


with increasing rotational excitation albeit in very small amount. The same trend is observed for v0 = 1 state for all the surfaces but the effect is too small to be detectable. Interesting deviations from this order is observed in v0 = 2 state. For Ni4-Cu(111) and Ni(111) surface at Ei in 0.2-0.4 eV region, the dissociation probability follows the order: j0 = 3 > j0 = 0 ≈ j0 = 1 > j0 = 2. For incident energy higher than 0.4 eV the Pd value for j0 = 0, 1 and 3 are the same but for j0 = 2 it is slightly lower. In case of Cu(111) for very small incident energy (Ei within 0.2-0.3 eV) the order of dissociation probability is: j0 = 3 > j0 = 2 > j0 = 1 > j0 = 0. Whereas, beyond 0.3 eV the order changes to: j0 = 0 > j0 = 1 > j0 = 3 > j0 = 2. Such a crossing behavior of reactivity plots for different initial rotational states has previously been reported for water 29 and H2 75,76 dissociation on Cu(111) and gas phase He, HD+ collisions. 77 Although the rotational states does not affect the reactivity significantly in the lower vibrational states (v0 = 0, 1) it has larger impact in the higher state (v0 = 2). Vibration at a particular mode of the reactant can facilitate the reaction if a significant component of the vibrational coordinate lies along the reaction path in the transition state region. 29 At higher j0 states, due to the high rotational motion of the molecule, the dissociating bond remains aligned along the reaction path for a lesser period of time and consequently reduces the reactivity. Our study could qualitatively reproduce the trends observed in previous high dimensional quantum dynamics studies of water dissociation on Cu(111) and Ni(111) surface. 17,18 But inclusion of multiple rotational modes was possible in those high dimensional studies which makes it difficult to directly compare our 3D results to the results obtained in their 7D studies. Vibrational: Irrespective of the catalyst surface, with vibrational excitation, dissociation probability increases significantly. For Ni(111) and Ni4-Cu(111) surface the reaction probability at v0 = 2 state almost reaches unity in the Ei range 0.2−1.2 eV. This behavior is expected from Polanyi’s Rules 78 as water dissociation on the concerned alloy and metal surfaces is a late barrier reaction. 29 Each quantum excitation of the vibrational mode corre-

17



sponds to 0.477 eV of energy which helps the wave-packet to cross the reaction barrier in the product channel. The observed increase in reactivity with vibrational excitation of incoming water molecule is consistent with the earlier full dimensional dynamics calculation of Jiang et al. on Cu(111) 19 and Ni(111) 15 surfaces.

Effect of catalyst surface Reaction probability for different metal and alloy surfaces has been shown in Figure 6. Reactivity plots only for the j0 = 0 state has been shown as the effect of rotation is not very large. For all the vibrational states of the incident water molecule the reactivity follows the trend of barrier height: lower the barrier height the higher the reaction probability. The present study qualitatively reproduces the trend of reactivity observed by Ghosh et al. 3 at the v0 = 0 state i.e. Ni4-Cu(111) > Ni(111) > Cu(111) > Sub-Ni4-Cu(111). The composition of the alloy causes orders of magnitude difference in the reactivity (Figure 4, 5, 6). For example in the ground vibrational and rotational state the m0 averaged reaction probability at Ei = 1.0 eV is 0.2 for the Ni4-Cu(111) surface while it is around 10−6 for the Sub-Ni4-Cu(111) surface (Figure 5). At v0 = 2 state, the reaction probability for Ni(111) and Ni4-Cu(111) gets close to unity. We have also investigated the effect of different impact sites on reactivity for the most reactive surface i.e. Ni4-Cu(111) surface. We observed that different sites have only minor effect in the PES structure and reactivity (see Supporting Info). One noticeable fact is that the reactivity plots for Cu(111) surface v0 = 1 are very close in magnitude to that for the Ni4-Cu(111) surface at ground vibrational state of incident water molecule (Figure 6). It suggests that replacing the uppermost layer of a Cu(111) host with Ni atoms can enhance the reactivity to an extent which can only be reached on pure Cu(111) surface by exciting the incident water molecule to its first vibrational excited state, which is prohibitively expensive for practical application.

18


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10

3

Cu(111); v0=0

Ni(111); v0=0

v0=0; j0=0 v0=0; j0=1 v0=0; j0=2 v0=0; j0=3

Pd

4

Pd

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6

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0.35 0.30

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v0=1; j0=0 v0=1; j0=1 v0=1; j0=2 v0=1; j0=3

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Ni(111); v0=2

v0=2; j0=0 v0=2; j0=1 v0=2; j0=2 v0=2; j0=3

0.98 0.96

v0=2; j0=0 v0=2; j0=1 v0=2; j0=2 v0=2; j0=3

0.94

Pd

0.7 0.6

0.92 0.90 0.88 0.86

0.5 0.2

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Ei(eV)

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Pd

Pd

0.25

0.00 0.2

v0=0; j0=0 v0=0; j0=1 v0=0; j0=2 v0=0; j0=3

0.2

Cu(111); v0=1

Pd

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


0.4

0.6

Ei(eV)

0.8

1.0

0.84 0.2

1.2

0.4

0.6

Ei(eV)

0.8

Figure 4: Effect of initial rotational state j0 on reactivity for various vibrational states for Ni(111) and Cu(111) surfaces

19



Ni4-Cu(111); v0 = 0 0.30 0.25

v0=0; j0=0 v0=0; j0=1 v0=0; j0=2 v0=0; j0=3

0.15

10

4

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5

10

6

Sub-Ni4-Cu(111); v0 = 0 v0=0; j0=0 v0=0; j0=1 v0=0; j0=2 v0=0; j0=3

Pd

Pd

0.20

0.10 0.05 0.00 0.2

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Ei(eV)

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Ni4-Cu(111); v0 = 2 0.98

Ei(eV)

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Pd

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v0=1; j0=0 v0=1; j0=1 v0=1; j0=2 v0=1; j0=3

0.6

Ei(eV)

0.8

Sub-Ni4-Cu(111); v0 = 2 0.8

v0=2; j0=0 v0=2; j0=1 v0=2; j0=2 v0=2; j0=3

0.7 0.6

0.96

v0=2; j0=0 v0=2; j0=1 v0=2; j0=2 v0=2; j0=3

Pd

0.5

Pd

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

Page 20 of 32

0.94

0.4 0.3 0.2

0.92

0.1 0.2

0.4

0.6

Ei(eV)

0.8

1.0

1.2

0.2

0.4

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Ei(eV)

0.8

Figure 5: Effect of initial rotational state j0 on reactivity for various vibrational states for the two alloy surfaces

20


Page 21 of 32

10

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10

6

v0 = 0; j0 = 0

0.2

v0 = 1; j0 = 0 100

Cu111 sub-Ni4-Cu111 Ni111 Ni4-Cu111

0.4

0.6

Ei(eV)

0.8

Pd

1

Pd

10

1.0

1.2

v0 = 2; j0 = 0

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Pd

0.6 0.4 Cu111 sub-Ni4-Cu111 Ni111 Ni4-Cu111

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1.0

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Cu111 (v0 = 1) sub-Ni4-Cu111 (v0 = 1) Ni111 (v0 = 0) Ni4-Cu111 (v0 = 0) 0.4

0.6

Ei(eV)

0.8

1.0

1.2

Figure 6: m0 averaged dissociation probability for j0 = 0 state for different vibrational states on various metal and alloy surfaces

21



Conclusion A reduced dimensional time dependent wave-packet dynamics has been performed to compute the dissociation probability of water on Cu(111), Ni(111) and two different Cu/Ni alloy surfaces. Our results show that the dissociation probability is influenced by the initial orientational, vibrational and rotational states of the incident water molecule. Although we model the water as a pseudo diatomic molecule our calculations qualitatively reproduce some of the results of earlier studies of water dissociation on pure Cu(111) 14,29 and Ni(111) surfaces 16,17 . This suggests that the reduced dimensional model is sufficiently accurate for the present study. For different catalytic surfaces the reactivity follows the trend of barrier heights (higher the barrier height lesser the reactivity) irrespective of the initial vibrational, rotational or orientational state. In general at lower vibrational states (v0 = 0, 1) rotational excitation increases reactivity while the opposite is true for higher vibrational state v0 = 2 with the exception of the subsurface alloy. For Sub-Ni4-Cu(111) rotational excitation increases reactivity for all vibrational states. Orientation of incoming molecule controls the reactivity to a significant extent. In general, with higher m0 values, water dissociation probability decreases in lower vibrational states and increases in higher vibrational states, although there are variations depending on the catalyst surface and incident energy. Vibrational excitation greatly enhances reactivity irrespective of all other factors. But in ground vibrational state, the dissociation probability of water on surfaces with the uppermost layer with Ni atoms (Ni4-Cu(111) and Ni(111)) is similar in magnitude with the reactivity in v0 = 1 state for surfaces with Cu atoms in uppermost layer (Cu(111) and Sub-Ni4-Cu(111)) (Figure 6). It suggests that the nature of the metal surface, specially the uppermost layer, plays a very important role in reactivity and a judicious choice of the catalyst surface composition can increase the catalytic efficiency enormously. We are hopeful that our results will encourage further studies, both theoretical and experimental, in the area of alloy based catalysts, especially in developing more accurate high dimensional potential energy surfaces. It will allow a more detailed understanding about 22


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how the dissociation of a polyatomic molecule like water is influenced by the excitation of different vibrational and rotational modes.

Acknowledgement D.R. thanks Kishore Vaigyanik Protsahan Yojana (KVPY) for fellowship. S.G. thanks IISER Kolkata for Senior Research Fellowship. A.K.T sincerely acknowledges Science and Engineering Research Board (SERB), New Delhi, India, for funding through Project No. EMR/2015/001337.

Supporting Information Available The following files are available free of charge. • supporting-info.pdf: PES parameters, reaction probability plots and discussion for the effect of impact sites on reactivity. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry

(v0,j0,m0)

Ni4-Cu(111)

Sub-Ni4-Cu(111)

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Controlling Heterogeneous Catalysis of Water Dissociation Using Cu

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