Bond Order Conservation Strategies in Catalysis Applied to the NH3

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Bond Order Conservation Strategies in Catalysis Applied to the NH Decomposition Reaction 3

Liang Yu, and Frank Abild-Pedersen ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.6b03129 • Publication Date (Web): 14 Dec 2016 Downloaded from http://pubs.acs.org on December 14, 2016

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Bond Order Conservation Strategies in Catalysis Applied to the NH3 Decomposition Reaction Liang Yu1,2, Frank Abild-Pedersen2* 1

SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA 2

SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA

ABSTRACT: Based on an extensive set of density functional theory calculations it is shown that a simple scheme exists that provide a fundamental understanding of variations in the transition state energies and structures of reaction intermediates on transition metal surfaces across the periodic table. The scheme is built on the bond order conservation principle and it requires a limited set of input data - still achieving transition state energies as a function of simple descriptors with less error compared to approaches based on linear fits to a set of calculated transition state energies. We have applied this approach together with linear scaling of adsorption energies to obtain the energetics of the NH3 decomposition reaction on a series of stepped fcc(211) transition metal surfaces. This information is used to establish a micro-kinetic model for the formation of N2 and H2 thus gaining insight into the components of the reaction that determines the activity.

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KEYWORDS: density functional theory, catalysis, transition state scaling relation, r-scaling, microkinetics, ammonia decomposition 1. Introduction

Reaction and activation energies of chemical processes in heterogeneous catalysis are necessary parameters to understand the activity and selectivity of catalysts. These energies serve as measures for scientists in the field seeking to optimize or develop new catalysts. The use of computational chemistry tools such as density functional theory (DFT) has given access to these measures and one can with a substantial effort obtain the full reaction pathway for a given catalytic reaction in a well-defined heterogeneous system and analyze the reactivity based on thermodynamic and kinetic theory. Progress in the field, requires dealing with larger and larger reaction networks, making the development of simplified schemes essential when computationally screening for new catalysts. The need is paramount in particular when it comes to the demanding task of calculating all elementary reaction barriers for a complicated process.

In an effort to identify a facile way of obtaining the kinetic information, the activation energy (E ) of an elementary reaction is usually approximated by a linear function of the reaction energy (ΔE ). E = α ΔE + β

(1)

This is known as the Brønsted-Evans-Polanyi (BEP) relation and the value of the constants, α and β determines the approximate bond order of a typical transition state and the reactivity of the surface, respectively.1 Recently it has been observed that these


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correlations are similar for many different classes of elementary reactions, including the dissociation of bonds formed between any two elements of C, N, or O or bonds between C, N, O and H.2 The BEP relation enables simple estimation of activation energies of catalytic reactions and provides an easy way of studying trends in reactivity among different transition metals. The construction of such universal relationships, however, requires a large number of time-consuming DFT calculations in order to get sufficient statistics. Usually the mean absolute error (MAE) of such correlations is more than 0.2 eV and thus it may limit their ability in giving accurate rates. In addition, the linear approximations of transition state energies in terms of reaction energies are only empirical and the underlying physical properties that give rise to these are still unveiled.

Another approach for predicting activation energy of reactions on transition metal surfaces was proposed by E. Shustorovich in the 1980’s, the so-called Bond-Order-ConservationMorse-Potential (BOC-MP) method, also known as the Unity Bond Index-Quadratic Exponential Potential (UBI-QEP) method.3 The method adopted a Morse potential formalism to describe the variation of bond order that atoms and molecules undergo during the reaction process. From that the activation energy is obtained assuming that the bond order in the transition state is 0. The method estimates the activation energy from linear combinations of the initial and final state energies, making it very similar to ordinary BEP relations. In all cases, the apparent structural effect of transition states is neglected and as for BEP relations this may lead to uncertainties in the accuracy of the predicted activation energies.

A different approach would be to try and build in the structural effects in the transition state


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energy vs. descriptor relations. Based on a principle of bond order conservation, we describe a new scheme called r-scaling (r denotes reaction coordinate) that establishes a non-linear scaling relation between transition state energies and simple descriptors - generally adsorption energies of the key species in the reaction steps. In this work we have chosen the NH3 decomposition reaction to apply the r-scaling scheme. NH3 decomposition has attracted attention as a potential solution for generating H2 for fuel cell application.4 We perform a systematic study of the reaction kinetics on pure metal surfaces, aiming to provide an understanding of the process limitations set by the catalyst properties, which can help in the development of novel catalysts for NH3 decomposition based on rational design.

The non-linear transition-state relations for the elementary steps in the NH3 decomposition described in this paper are calculated using two different r-scaling schemes. Firstly we introduce a more accurate global r-scaling scheme which is based on large data-sets, secondly the simplified r-scaling scheme which is based on a much smaller set of input data and therefore accessible with limited computational effort. This approach, which was first introduced for simple diatomic systems explicitly includes structural effects into the transition state energy search.5 Our results show that the transition state relations derived from the simplified r-scaling scheme have comparable MAEs with those from the global rscaling scheme, thus suggesting that reliable results can be obtained at a much lower computational cost. In addition, the transition state relations derived from the r-scaling schemes are all higher order functions of the energy descriptor and the MAEs are comparable to or smaller than the results derived from linear approaches like BEP or the UBI-QEP methods. The observed curvature of the transition state relations originate from variations in


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the geometric structure of transition states on different catalyst surfaces. These results provide new insights into the underlying origin of the BEP relations and it addresses the problem of non-negligible deviations between calculated points and the BEP relation.

Combining data obtained from intermediate energy scaling relations, transition state relations obtained from the simplified r-scaling scheme, and micro-kinetic modeling tools, we can effectively and more accurately map out the activity of the NH3 decomposition reaction.

2. Computational method

All electronic structure calculations are performed using the plane-wave based density functional theory program PWSCF (Quantum-ESPRESSO) as implemented in the Atomic Simulation Environment (ASE).6 The ultrasoft Vanderbilt pseudopotential method and the BEEF exchange-correlation functional are adopted.7 A cutoff energy of 500 eV for the wavefunctions and 5000 eV for the charge density are used. An excess of at least 20 electronic bands is used in each of our calculations. The Monkhorst-Pack scheme is used for sampling the Brillouin zone.8 Nine transition metal (TM) fcc(211) surfaces serve as the catalysts in this study (Figure 1). The slab models are built with 4 atomic layers in the [111] direction using rectangular 1×3 supercells with the bottom three [111] layers fixed during structural relaxations. A k-point grid of 4×2×1 and a vacuum thickness of 10 Å are used for all calculations. Dipole correction is applied to decouple the artificial interaction between slabs.

The potential energy curve (PEC) for the elementary reactions in NH3 dissociation is


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calculated on all nine TM surfaces using the Fixed Bond Length (FBL) method. The reactions considered are as follows: NH3* + * ⇌ NH2* + H*

(I)

NH2* + * ⇌ NH* + H*

(II)

NH* + * ⇌ N* + H*

(III)

N2(g) + 2* ⇌ 2N*

(IV)

H2(g) + 2* ⇌ 2H*

(V)

For reactions (I), (II), and (III), the PECs are calculated using the same range of fixed bond-lengths from 1.2 to 2.2 Å with increments of 0.1 Å. For reaction (IV), fixed bondlengths range from 1.25 to 2.60 Å with increments of 0.15 Å, and for reaction (V) from 1.0 to 1.6 Å with increments of 0.1 Å.

The un-catalyzed potential energy curve (UPEC) as will be used in the simplified r-scaling scheme, is calculated by stretching the dissociating bond of the species in the gas phase with the stretched bond-length being fixed during structural relaxations using the FBL method. In this process, spin-polarization is not considered since we need to restrict the dissociating species to have similar spin states as those adsorbed on the transition metal surfaces whose spin states are quenched. Similarly, the initial state and final state in the gas phase are also calculated without considering spin-polarization.

3. Results and Discussion


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3.1 Bond Order Conservation principle in the adsorption of reaction species on transition metal surfaces

The fundamental backbone of our r-scaling scheme is the bond order conservation (BOC) principle,3b which states that, if the central atom A of an adsorbate on a transition metal surface adsorbs covalently to the surface through ≤ bonds, where is the total number of bonds through A alone, then the normalized total bond order for atom A is conserved, such 9 that ∑ = 1, where Xi is the normalized bond order of single bond to A. Based on this

principle, for a fixed adsorbate structure bonding through a central atom A on transition metal surfaces, the adsorbate-surface bond strength can be described by a linear relation with the bond strength of the single atom A and the slope will be / , where is the normalized adsorbate-surface bond order of the given species and that of A. This concept has proven very effective in scaling the adsorption energies of a series of species including NHx, CHx, OHx, and SHx on TM surfaces, in which linear regressions of the DFT calculated points have slopes of approximately (N-x)/N when using the adsorption energies of the central atoms as the descriptors, where x is the total number of bonds terminated by hydrogen.10

According to the BOC principle, for a dissociation reaction (AB → A + B) on transition metal surfaces, where A and B can be individual atoms or molecular fragments, the adsorbate-surface bond order depends only on the geometric configuration of the adsorbate structure.

In the following we shall distinguish between relative, hybridization, and gas-phase-stretch energies, noted as E! , E"#$ , and E% , respectively. Relative energies are structural


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adsorption energies using the gas phase equilibrium structure as the fixed reference state, thus for a structure A−B with a fixed bond-length somewhere between the equilibrium structure AB(g) and its product species A and B along the reaction pathway we have for the relative energy: E! (A − B) = E)*+@%-. − E%-. − E)+(/)

(2)

Where E)*+@%-. is the total energy of A−B on the surface, E%-. the total energy of the surface, and E)+(/) the gas-phase energy of AB. The hybridization energy is the structural adsorption energy of the gas-phase A−B with a fixed bond-length between A and B: E"#$ (A − B) = E)*+@%-. − E%-. − E)*+(/)

(3)

Where E)*+(/) is the total energy of the gas-phase A−B. The gas-phase-stretch energy is the gas phase energy difference between A−B and AB: E% (A − B) = E)*+(/) − E)+(/)

(4)

From equations (2) - (4) we find that E! (A − B) = E"#$ (A − B) + E% (A − B)

(5)

Using the linear scaling principles outlined above, E"#$ (A − B) can be written as a linear combination of the adsorption energies (E0% ) of A and B: E"#$ (A − B) = γ) E0% (A) + γ+ E0%(B) + ξ"#$

(6)

So that for E! (A − B) we obtain:


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E! (A − B) = γ) E0% (A) + γ+ E0% (B) + ξ! Where ξ! = ξ"#$ + E% (A − B)

(7)

(8)

Only in cases where adsorbates bind entirely through A or B or where the bond strengths of A and B are linearly correlated can the equations (6) and (7) be reduced to a single parameter linear equation (see supporting information for details).

By explicitly assuming that the bond order conservation principle is valid throughout the A−B bond breaking process, we obtain the variation of γ and ξrel as a function of the reaction coordinate r. This is done through explicitly analyzing the scaling relations of the A-B structures with the bond-length between A and B fixed for a series of values along the reaction coordinate r. The functional form of γ(r) and ξrel(r) can be obtained via polynomial fitting of the data points, which enable us to derive the relative energy of the transition state (E% ) as a function of E0% (A) and E0% (B) through maximizing the potential energy curve E! (A − B) along the reaction coordinate r: E% 6E0% (A), E0% (B)8 = max; [γ) (r) ∗ E0% (A) + γ+ (r) ∗ E0% (B) + ξ! (r)]

(9)

In the following, we will apply this scheme in two ways, firstly, based on a large data-set including data from full PECs on all the nine transition metal surfaces considered (global rscaling scheme), and secondly, based on limited input data (simplified r-scaling scheme). We shall see that the two approaches give almost identical results and that a very accurate description of the reaction can be extracted from limited knowledge. We use the breaking of the N−H bond in NH2 and the dissociation of N2 to cooperatively elaborate the details of the


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two schemes.

Figure 1. Structure of fcc(211) surface of transition metals and the adsorption sites considered in this work. The dotted circles denote the step atoms.

3.2 Determining the descriptors

The fcc(211) surface adsorption sites considered in this study are shown in Figure 1. The adsorption energy of the key adsorbate on the most stable adsorption site is generally used as the descriptor for establishing the TSS relation. For the dissociation of N−H bond of NH3*, NH2*, and NH*, E0% (N) in the hollow1 site is used as the single descriptor in establishing the scaling relations based on equation (7). Here we use explicitly that E0% (N) and E0% (H) are linearly dependent on transition metal surfaces. In the case of N2 and H2 dissociation, E0% (N) in the hollow1 site and E0% (H) in the bridge site are used as the descriptors, respectively.

3.3 Global r-scaling scheme

The calculated PECs for N2 dissociation and NH2 activation using the FBL method are shown in Figure 2 for nine different transition metal surfaces. As can be seen from Figure 2 and Figure S2 in the supporting information, there exists a linear relation between E! (N −


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N) and E! (NH − H) and the descriptor E0% (N) for each fixed structure between the IS and FS. The variations of the slope γ and intercept ξrel of these linear relations with the reaction coordinate r (N−N and NH−H bond lengths for N2 dissociation and NH2 activation, respectively) are shown in Figure 3(a). The γ of both reactions increases monotonically with increasing r as implied by the BOC principle, in which γ approximately equals the ratio of surface-adsorbate bond order of the dissociating species to that of the descriptor species (* / or @* / ). As the bond-length of N−N and NH−H increases, more electrons from the metal surface are required to stabilize the structure and this leads to an increase in the adsorbate-surface bond order. Fitting the functional form of γ(r) and ξrel(r) enables us to establish a correlation between relative energies E! , the reaction coordinate r and the descriptor E0% (N) through equation (7). Knowing the PECs for all descriptor values allow us to derive a closed expression for the transition state energy E% as a function of E0% (N) using equation (9). The scheme is illustrated in Figure 3b, and the resulting transition state relations, E% 6E0% (N)8, for N2 dissociation and NH2 activation are shown and compared with actual calculations in Figure 3(c). A simple linear fitting to the points, which is custom for BEP relations leads to MAEs of 0.23 and 0.10 eV for N2 dissociation and NH2 activation, respectively, whereas the correlations based on bond order conservation leads to MAEs of 0.15 and 0.12 eV, respectively. The non-linear nature of E% 6E0% (N)8 is a result of the difference in the geometry of the transition state (ABC ) on different transition metal surfaces as can be seen from the PECs in


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Figure 2. If we assume that the bond order is conserved throughout the reactions it can be shown that: DEFG (EHIG (J)) DEHIG (J)

= γ(ABC )

(10)

Hence, E% 6E0% (N)8 is linear if and only if γ is a constant independent of ABC . In the global scaling scheme, E% 6E0% (N)8 was derived based on all calculated data for the full PECs on 9 transition metal surfaces. This is expected to be a highly accurate method but with significant computational cost, even more data than needed to establish linear BEP relations. In the following section, we propose another scheme for deriving the transition state relations, one that requires much less data than the global scheme but provides similar accuracy.

Figure 2. Potential energy curves for N2 dissociation (left) and NH2 activation (right) and the corresponding linear scaling relations for the relative energies (E! ) of N-N and NH-H structures with identical bond-lengths against the descriptor on 9 different fcc(211) transition metal surfaces.


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Figure 3. (a) Variation of the slope (γ) and intercept (ξrel) with the reaction coordinate r for the linear relations of E! vs. E0% (N) along the N2 dissociation (left) and NH2 activation (right) pathways. The solid lines show polynomial fitting to the points. (b) Scheme needed to extract E% for a given E0% (N) using the γ(r) and ξrel(r) functions. (c) Transition state


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relations (red curves) for N2 dissociation (left) and NH2 activation (right) derived from the global r-scaling scheme compared with calculated E% (black points) on the 9 transition metals surfaces.

3.4 Simplified r-scaling scheme As implied in the global scheme, the γ(r) and ξrel(r) functions are of key significance in determining the correlation between the transition state energies and the relevant descriptor(s). Thus establishing a method in which the functions γ(r) and ξrel(r) can be accurately determined is the most fundamental problem when applying the principle of bond order conservation.

In what follows, we assume that linear scaling relations have been established between all stable intermediates in the reaction, hence we have information about the energies of initial and final state structures for any given reaction step as a function of the relevant descriptor(s). The process of establishing the closed expressions for the functions γ(r) and ξrel(r) is easy and only requires a few simple steps:

(1) Two transition metal surfaces are chosen based on the scaling relations for the intermediates (initial and final state) in the considered reaction.

(2) Fixed Bond Length calculations of a reasonable number (2 or 3) of structures between the initial and final state of the reaction. This does not have to include the transition state on any of the surfaces.

(3) Calculation of the un-catalyzed potential energy curve (UPEC), which is the energy


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profile of the gas phase stretch (E% ) as a function of the reaction coordinate r for the reaction considered. (4) Fitting the γ(r) and ξrel(r) functions based on the calculations in (2) and (3), where γ(r) is constrained by the initial and final state scaling relations.

(5) Derive the transition state relation based on equation (9).

3.4.1 Selecting surfaces based on the scaling relations for the initial and final states

The two transition metal surfaces could in principle be chosen randomly, but by strictly choosing them so that they represent the initial and final state scaling relations the best and also span a reasonable range of descriptor space, more accurate results are achieved.

To evaluate the reliability of the two selected transition metal surfaces, we use the linear scaling relations for the relative energies E! of initial and final states.11 The root mean square error (σ) of the linear regressions of the initial and final state is used to partly describe the reliability of a transition metal surface: M M ⁄ σ = K(LC + LNC ) 2

(11)

Where RIS and RFS are the metal specific absolute residuals of the initial and final state linear regression, respectively. In order to avoid that only parts of the descriptor space is described sufficiently well, we need to ensure that the metals chosen reflect both the reactive and the noble part of the periodic table. Thus, we define an energy averaged root mean square error of the two metals combined:


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QRST =

V

UVW XUVY

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(12)

V

Y ()*E W ()| |EHIG HIG

Definition of the variables can be found in Figure S3 in the supporting information. We note that there are few particular cases where equation (11) and (12) will have difficulties providing a reasonable estimate of relevant surfaces. Firstly, when the initial state (reactant) or final state (product) is most stable in the gas-phase, then RIS or RFS are exactly zero and in this case one is forced to rely on one relation alone. Secondly, if the initial state is most stable in the gas-phase and the final state are the descriptors of the reaction, like N2 and H2 dissociation, then Q_ + Q_M is zero, and one will have to choose two metals that maximizes _

_

Y W the energy span |`Rab () − `Rab ()|, as shown in Figure 4 (a and c) for the case of N2

dissociation.

We have tested any combination of two transition metal surfaces to generate the final transition state relations for each elementary step in the reaction and we find that the combinations that minimizes equation (12) (NH3, NH2, and NH activations) or maximizes the descriptor energy span (N2 and H2 dissociations) always give reliable transition state relations with moderate MAEs. The schemes for N2 dissociation and NH2 activation are illustrated in Figure 4, where we find that the combinations [Re, Ag] and [Ru, Au] have the largest eT

cd |`Rab () − `Rab ()| and smallest QRST , respectively, and thus provide transition state

relations with relatively small MAEs.


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Figure 4. Linear scaling relations for the initial and final state of (a) N2 dissocaition and (b) NH2 activation. (c) Energy span of the descriptor (∆E0% (N)) and (d) energy averaged root mean square error (QRST ) for combination of any two metals for (c) N2 dissociation and (d) f fM NH2 activation, where ΔE0% (N) = |E0% (N) − E0% (N)|. Distribution of mean absolute errors

(MAEs) of the final transition state relations of simplified r-scaling scheme depending on (e) ∆E0% (N) for N2 dissociation and (f) QRST for NH2 activation, of the two selected metals.


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3.4.2 Generating the PEC from the hybridization curve and the UPEC

Unlike the global scaling scheme where a significant number of calculations are needed to establish PECs, we propose an efficient approach in which only a few constrained calculations are needed to generate the PECs on the two transition metal surfaces chosen in section 3.4.1.

The approach takes advantage of the UPEC (E% ) as defined in equation (4) and the hybridization energy curve (E"#$ ) as defined by equation (3). The UPEC can be easily calculated with many points at very limited computational cost. In Figure 5 the calculated E% points for N2 dissociation and NH2 activation in the gas phase are shown and the solid black curves are obtained as polynomial fits to the calculated points. The E"#$ is always a monotonically decreasing curve and due to its simple behavior, its approximate form can be fitted from very few constrained calculations. We find that 4 to 5 points including the initial and final state energies provides sufficient data points for an accurate fitting of E"#$ . In Figure 5 the fitted E"#$ potentials for N2 dissociation and NH2 activation based on 4 points on [Re, Ag] and [Ru, Au], respectively, are shown as solid red curves. The PEC (E! ) along the reaction coordinate r given by equation (2 and 5) can now be obtained by adding E"#$ (red curve) and E% (black curve). As shown in Figure 5, the derived PECs (blue curve) agree nicely with the calculated points (blue points), which verify the reliability of this approach of deriving the PECs.


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Figure 5. Energy profiles of un-catalyzed potential energy curve (E% ), hybridization energy curve (E"#$ ), and potential energy curve (E! ) on the two selected transition metal surfaces for (a) N2 dissociation and (b) NH2 activation. The black and red curves are the polynomial fitting of the black and red points, respectively. The blue curve is obtained as the sum of the black and red curves. The blue points show the calculated PECs. 3.4.3 Fitting the γ(r) and ξrel(r) functions and deriving the TSS relations. Unlike the global scaling scheme where the linear relations for deriving the γ(r) and ξrel(r) functions are bulit from 9 PECs, here the functions for N2 dissociation and NH2 activation are obtained from fitting the explicit linear relations set up by the two PECs generated in section 3.4.2. During the fitting, the function γ(r) is constrained to be monotonically increasing between the values explicitly set by the initial and final state scaling relations whereas the function ξrel(r) is required only to fulfill the boundary conditions set by the two scaling


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relations. The fitted curves of γ(r) and ξrel(r) for the two reactions are shown in Figure 6a, which all fits quite good with the full DFT calculated points. The final transition state relations derived from the fitted γ(r) and ξrel(r) using equation (9) matches well with the calculated transition state energies as shown in Figure 6b. For both reactions, the MAE is comparable to that obtained using the more accurate global scaling scheme.

Figure 6. (a) γ(r) and ξrel(r) curves obtained from fitting of two PECs compared with points from the global r-scaling scheme for N2 dissociation (left) and NH2 activation (right), respectively. (b) The transition state relations derived from the fitted γ(r) and ξrel(r) of the simplified r-scaling scheme compared with calculated Ets for N2 dissociation (left) and NH2


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activation (right), respectively.

Using both the global and simplified r-scaling schemes to obtain the transition state relations for the reactions (I), (III), and (V) (Figure S4 in the supporting information) we find that there are no significant difference in the accuracy between the two approaches, thus estalishing the simplified r-scaling method as a fast and accurate way to obtain relevant kinetic data for elementary reaction steps.

3.5 NH3 decomposition reaction kinetics

In the following, we have studied the decomposition of NH3 as given by reaction (I) to (V) on stepped fcc(211) transition metal surfaces applying the different schemes for transition states energies combined with linear scaling relations for reaction energies. The reaction micro-kinetics is simulated using the CatMap software.12 The free energies of adsorbates and transition states are calculated as Gi = Etot + ZPE + TSvib + RTlnθi, where Etot is the total energy of adsorbate obtained from linear scaling or the total energy of transition state obtained using one of the scaling schemes (linear, global, and simplified) described. ZPE is the zero point energy, Svib is the entropic part from vibrations derived in a harmonic approximation to the potential, and θi is the coverage of individual species. The free energies of the gas phase molecules is calculated as Gi = Etot + ZPE + Gshmt(T) + RTln(Pi/P0), where Gshmt(T) is the thermodynamic correction on the free energy using Shomate equations, Pi is the partial pressure of the molecule, and P0 is the total pressure (1 atm). The steady state approximation is adopted in solving the reaction rate equations set. The coverage effect is an important factor affecting the reaction kinetics and we have explicitly taken it into account to


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improve the precision of our results.12 We only considered the effect of nitrogen coverage θN* which is the dominant species on the surface throughout the reaction process. The differential formation energies of reaction intermediates as a function of θN* and Eads(N) are then calculated (see Figure S6 in the supporting information). The final θN* is determined using an iteration scheme in which θN* gradually increases based on the output θN* of the previous step, until the output θN* stops increasing and iteration is converged. Figure S7 shows the output θN* in the iteration process, reaching a maximum value of 0.55 in our descriptor space, which is used as the final θN* applied in the micro-kinetic simulations. Since Eads(H) and Eads(N) are linearly dependent, we can project the activity map onto a one-dimensional curve using Eads(N) as the only descriptor and this allows for an explicit comparison between the three different schemes. As shown in Figure 7, the activity volcanos for the consumption rate of NH3 are quite similar for the three different schemes. This indicates that the prediction of activity trends based on the microkinetics depends very little on achieving higher accuracy of the transition state scaling relations. However, it is important to note that the simplified r-scaling approach not only provides higher accuracy but also a significant reduction in computational time needed. We have found that the linear approach requiring explicit knowledge about the transition state, which is based on computationally demanding algorithms like NEB or CI-NEB, is a factor of 24 more costly in core hours for the NH3 decomposition reaction considered in this paper (details on the comparison can be found in the supporting information).

Using the simplified r-scaling scheme, we studied the rate of NH3 decomposition at 800K


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under different pressure ratio of the gas phase components ( w@x : w@Y : wY ), including 100:0:0, 99:0.75:0.25, 90:7.5:2.5, and 80:15:5 in percentage, to investigate the real-time activity distribution along the flow direction in a plug-flow reactor. The results are shown in Figure 8. The magnitude of reaction rate [log ({|}@x )] matches well with experimental values.4d, 13 With increasing conversion of NH3 along the tube, the top of the activity map moves towards stronger binding of N on the surface. The optimum catalyst changes from elemental Ni when the gas phase is pure NH3 to something more Ru like when w@x : w@Y : wY is 80:15:5, which agrees well with experimental findings that the best catalyst for NH3 decomposition is Ru under real conditions when the gas phase is a mixture of NH3, N2, and H2.4d, 13-14 This also justifies the experimental observation that an optimal NH3 decomposition catalyst is not the optimal catalyst for the opposite reaction.15 These results render our approach as a feasible and reliable strategy for designing catalyst.

Figure 7. The turnover frequency (TOF), based on the transition state relations derived from global r-scaling, simplified r-scaling, and linear scaling schemes for NH3 decomposition on


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stepped fcc(211) transition metal surfaces. Rates have been modeled at absolute temperature T = 800K and total pressure P = 1atm.

Figure 8. Variation in rate for the NH3 decomposition on stepped fcc(211) transition metals surfaces along the tube in a plug-flow reactor as obtained from microkinetic modeling using linear scaling of intermediate energies and the simplified r-scaling of transition state energies. Simulations have been performed at absolute temperature T = 800 K and total pressure P = 1 atm with varying pressure ratios for NH3, N2, and H2 in percentage.

4. Conclusion

Based on the bond order conservation principle we have established a simple scheme that effectively predicts transition state energies. The explicit inclusion of geometry dependence through the conservation of bonds provides a more accurate determination of the transition state energies as can be seen from the MAEs relative to the calculated energies. The observed


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non-linear nature of the relation between transition state energies and relevant descriptors is a consequence of the variation in the transition state structure and the associated change in the adsorbate-surface bond strength. In this work, we have investigated the pathway for NH3 decomposition using linear scaling relations for intermediate energies combined with linear as well as non-linear approaches to establish transition state energies. These relations enable us to describe the entire reaction path using at most two parameters, the hydrogen and nitrogen binding energies. The energetic information is used to construct a micro-kinetic model for the formation of N2 and H2 and to gain insight into the factors determining the NH3 decomposition activity on stepped transition metal surfaces. We find the increased accuracy of the transition state energies based on the descriptors to have very little influence on the shape and position of the activity volcano. Nevertheless, we suggest using our simplified method since it introduces significant reduction in computational cost compared to established linear approaches. Our analysis show that the optimal catalyst for NH3 decomposition differs as the pressure ratio of NH3, N2, and H2 in the gas phase varies during the reaction process, making a less reactive metal like Ni the choice of catalyst at low conversions (at reactor inlet) and moving towards more reactive metals like Ru and Fe as the conversion increases (at reactor outlet). This clearly suggests a way to maximize the conversion of NH3 by assembling the catalyst bed in a layered structure with each layer containing different active ingredients.

Supporting Information.

Reducible feature of γ parameters, algorithm of the fitting process, and evaluation of the


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efficiency of the simplified r-scaling scheme compared with the BEP scaling method.

Corresponding Author Frank Abild-Pedersen, E-mail: [email protected]

Acknowledgements

We acknowledge support from the Office of Basic Energy Sciences of the U.S. Department of Energy to the SUNCAT Center for Interface Science and Catalysis at SLAC/Stanford.

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Bond Order Conservation Strategies in Catalysis Applied to the NH3

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