Design of a promoter to enhance the stability of catalysts for hydrocarbon reactions 2

Nowadays, the combination of density functional theory DFT calculations, kinetic measurements, and experimental investigations is being used increasingly for the design of novel/improved

CHAPTER 1

INTRODUCTION

The continuous improvement of computational chemistry algorithms and the increasing computational resources have brought realistic first principles studies for industrially relevant catalytic reactions within reach Theory can be used to help provide

ever-a moleculever-ar level understever-anding of the mechever-anism of the cever-atever-alytic reever-action ever-and elucidever-ate the electronic origin of catalyst promotion Such understanding can lead to optimization

of the industrial process, i.e selection of improved process conditions, as well as the design of improved catalysts Nowadays, the combination of density functional theory (DFT) calculations, kinetic measurements, and experimental investigations is being used increasingly for the design of novel/improved catalysts, such as steam reforming and ammonia synthesis catalysts (Hinneman and Nørskov, 2003; Zhang and Hu, 2002)

Transition metal catalysts such as Fe, Co and Ni are widely used in hydrocarbon reactions because of the high activity and significantly lower cost in comparison with precious metal-based catalysts (Zonnevylleet al., 1990; Joyneret al., 1988) Especially

Ni based catalysts are commonly used in chemical processes of natural gas activation, such as steam reforming (SR) and catalytic partial oxidation (CPO) of natural gas (Twigg, 1996; Ponec and Bond, 1995) Natural gas is gaining importance as an energy source and as a raw material for the petrochemical industry The decreasing supplies of petroleum and more stringent environmental demands will further strengthen the

importance of natural gas In addition, natural gas conversion into hydrogen for the efficient production of electricity in fuel cells is attracting widespread research attention Its high hydrogen content makes methane a particularly interesting raw material Chemisorption and activation of methane on Ni catalysts is of considerable importance because SR and CPO of methane to produce syngas is the first step in several industrially important catalytic processes such as production of ammonia (Haber-Bosch), methanol and higher hydrocarbons (Fischer-Tropsch)

However, coke formation on Ni surfaces is an important technological problem Ni catalyzes SR and CPO of methane reactions, but it also catalyzes the formation of graphitic carbon deposits Carbon deposition on the catalyst might cause loss of activity, while growth of filamentous carbon nanotubes can lead to reactor blocking, leading to regular shutdowns and production losses (Trimm et al., 1981; Reyniers et al., 1994) Enhancing the stability of Ni based catalysts has therefore been an area of intensive research, and various promoters have been proposed One of the oldest proposals is to introduce trace amount (2 ppm) of H2S with the feed gas (Rostrup-Nielsen,1984) This method is industrially implemented in the Sulfur Passivated Reforming (SPARG) Process and was developed by Rostrup-Nielsen The sulfur selectively poisons the most active sites of the Ni catalyst, believed to be the step sites, leading to a small loss in the reforming activity However, trace amount of sulfur affects the deactivation rate much more than the reforming rate (Andersen et al., 1987) More recently, promoters such as

Au (Besenbacher et al, 1998; Bengaard et al., 2002), K (Rostrup-Nielsen, 1984), Sn (Nikolla et al., 2006) and B (Xu and Saeys, 2006) have been proposed and shown to

improve the stability of Ni catalysts

The objective of this thesis is to design a promoter to enhance the stability of Ni-based catalysts Thermodynamic and kinetic calculations were carried out to quantify the stability of different forms of chemisorbed carbon on a Ni catalyst, and to evaluate the diffusion of carbon atoms from the Ni surface to the first and second subsurface layer and to the Ni bulk Boron is found to show similar chemisorption characteristics with carbon and is proposed to selectively block sites that initiate catalyst deactivation Based on this molecular level understanding, boron is proposed as promoter to enhance the stability of Ni catalysts In this thesis, first principles DFT investigations are combined with experimental validation and optimization to design improved Ni catalysts.

This thesis is organized as follows In chapter 2, an overview is given of the the-art in first principles based design of metal catalysts In chapter 3, the theory and the computational methods used in this work are discussed In chapter 4, the stability of different forms of carbon that can exist on a Ni catalyst and the kinetics of carbon diffusion are addressed, and the effect of boron as a promoter to improve the coking resistance of Ni catalysts is proposed A more detailed analysis of the effect of carbon and boron on the activity of a Ni catalyst is presented in chapter 5 In chapter 6, an experimental validation of the proposed effect of boron on the stability of a Ni catalyst during steam methane reforming is presented Finally, the main conclusions of this work are summarized in Chapter 7

Hinneman, B., and Nørskov, J.K., J Am Chem Soc 125, pp 1466 2003

Joyner, R.W., Darling, G.R., and Pendry, J.B., Surf Sci 205, pp 513 1988

Nikolla, E., Holewinski, A., Schwank, J., and Linic, S., J Am Chem Sci 128, pp

11354 2006

Ponec, V., and Bond, G.C., Catalysis by Metals and Alloys, Elsevier, New York, 1995 Reyniers, G.C., Froment, G.F., Kopinke, F.D., and Zimmerman, G., Ind Eng Chem Res 33(11), pp 2584 1994

Rostrup-Nielsen, J.R., J Catal 85, pp 31 1984

Trimm, D.L., Holmen, A., and Lindvag, O., J Chem Technol Biotechnol 31(6), pp

311 1981

Twigg, M.V., Catalyst Handbook, 2nd Ed, Manson Pub., London, 1996

Xu, J., and Saeys, M., J Catal 242, pp 217 2006.

Zhang, C.J., and Hu, P., J Catal 116, pp 4281 2002

Zonnevylle, M.C., Geerlings, J.J.C., and van Santen, R.A., Surf Sci 240, pp 253 1990

CHAPTER 2

FIRST PRINCIPLES BASED DESIGN OF METAL

CATALYSTS

2.1 Introduction

Traditionally, heterogeneous catalysis has largely been an experimental field While this

is still true, the powerful computational resources available today and the continuous improvement of computational chemistry algorithms and software are providing new tools for the study and development of catalytic systems Using well-chosen and sufficiently accurate quantum chemical calculations, scientists have been able to provide new insights into reaction pathways, to predict properties of catalysts that have not been synthesized, and to bring information for a given system from many different experimental techniques into a coherent picture

Theory can be used to help provide a molecular level understanding of the reaction mechanism and elucidate the electronic origin of catalyst promotion Such understanding can lead to optimization of industrial processs, i.e selection of improved process conditions, as well as the design of improved catalysts It has been demonstrated how first principles calculations can provide a detailed understanding of the elementary steps of catalytic processes This molecular level insight was used to construct fundamental kinetic models from first principles for industrially important reactions (Saeys et al 2003; Neurock and van Santen, 2000; Neurock et al., 2000)

Recently, in particular the Nørskov group has demonstrated how collaboration between applied catalysis, surface science and theory can lead to the design from first principles

of improved catalyst for established processes such as steam reforming and ammonia synthesis (Besenbacher et al., 1998; Honkala et al., 2005)

In this chapter, we will review models using first principles computation to represent the surface of catalysts Here, results from first principles based computation for several notable processes which are metal catalyzed such as hydrogenation of olefins and aromatics, steam reforming, ammonia synthesis and selective catalytic oxidation will be presented

2.2 Models of catalytic surface

The choice of an appropriate model to represent a catalytic surface or active site is important as it can have significant effects on the accuracy of results Cluster calculations use a limited number of atoms to model the catalytic surface These models are computationally convenient because they employ atomic or molecular orbital basis sets to satisfy the boundary condition of zero electron density at infinite distance from the cluster It is also possible to study low coverage and calculate vibrational frequencies with cluster calculations Unfortunately, sufficiently large clusters need to

be used to obtain a reliable representation of the electronic band structure of a catalyst, especially in the case of a metal To partly overcome this problem, embedded cluster models have been proposed, where the central atoms (the active site) are treated with an

accurate computational method and the surrounding atoms are treated at a lower, often semi-empirical level

Figure 2.1 Three approaches and examples for modeling chemisorption and reactivity

on surfaces (Left) cluster approach, maleic anhydride on Pd; (center) embedding scheme: ammonia adsorption in a zeolite cage; (right) periodic slab model: maleic anhydride adsorption on Pd(111) (Neurock, 2003)

On the other hand, slab models use periodic boundary conditions to model extended surfaces In these models, the surface is represented by a unit cell which is repeated in 3 dimensions The slab models avoid the electronic structure artifacts that sometimes trouble cluster calculations Typically, the unit cell consists of a two-dimensional rectangular cluster of about 10 atoms and 3-5 atom layer thickness with a large vacuum layer on top of it, resulting in a model consisting of an infinite 2D slab of 3-5 layer thickness, separated from the next slab by a vacuum layer of 1-2 nanometer To study low coverage adsorption using periodic slabs, very large unit cells are required The slab models require the use of periodic basis sets to match the boundary conditions, and often plane waves are used The convergence can however be slow, depending on the

size of the plane wave basis set The three approaches are illustrated in Figure 2.1

2.3 Hydrogenation of olefins and aromatics

The adsorption of ethene (Fahmi and van Santen, 1996; Shen et al., 1999; Watwe et al., 1998), ethyne (Watwe et al., 1998; Clotet and Pacchioni, 1996; Medlin and Allendorf, 2003), propene (Valcarcel et al., 2002a), propyne (Valcarcel et al., 2002b), cyclohexene (Saeys, 2002), cyclohexadiene (Saeys, 2002; Saeys and Reyniers, 2002), and benzene (Mittendorfer and Hafner 2001; Saeys et al., 2002) on various transition metals (Ni, Pd, Pt) has been studied from first principles Reaction path studies have been carried out for gas phase hydrogenation of ethene (Pallassana et al., 1999; Pallassana and Neurock, 2000; Neurock and van Santen, 2000; Neurock et al., 2000), ethyne (Sheth et al., 2003), and benzene (Saeys, 2002; Saeys et al., 2003; Morin et al., 2003) Most of the results reported are based on the most thermodynamically stable (111) facet However, a few studies also employ the (100) and (110) facets These ideal surfaces are mostly studied with periodic slabs with a few employing cluster models

Ethene hydrogenation has been studied in the greatest detail, in particular by Neurock et al A series of DFT calculations was performed by Neurock et al to help elucidate the nature of the active sites, understand the kinetics and establish the source of the structure insensitivity The results indicate that the basic mechanism follows the ideas proposed by Horiuti and Polanyi (1934) At low or moderate coverages, hydrogen adds via a classical homogeneous catalyzed reductive-elimination step that involves

hydrogen insertion into a metal carbon bond to subsequently form an ethyl intermediate (Neurock and van Santen, 2000; Neurock et al., 2000) The three-center (Pd-C-H) transition state involves breaking of the metal-hydrogen and metal-carbon bonds The transition state is early along the reaction path whereby there is still a strong interaction between hydrogen and the metal as well as the carbon and the metal The C-H bond is still quite long The resulting transition state structure is consistent with results found for homogeneously catalyzed hydrogenation

The ethyl intermediate that forms reacts in a very similar way to yield ethane The transition state to ethane is remarkably similar to that for ethyl In fact, most of the hydrogenation reactions that have been examined in the literature are quite similar The important point is that the active surface complex involves only one or perhaps two metal atoms This is likely one of the reasons hydrogenation reactions are structure insensitive Subsequent calculations over the Pd(100) surfaces have been performed yielding barriers similar to that on Pd(111)

Ethene hydrogenation was examined on well-defined model Pd(111) surface At low coverage, the predicted intrinsic activation barriers for ethene and ethyl hydrogenation are quite similar at 72 and 71 kJ/mol, respectively The π-bound intermediate (ethene sits atop a single metal atom) is first converted to the di-σ-species (ethene binds parallel

to one of the bridge metal-metal forming two σ-metal-carbon bonds) before it reacts with hydrogen At higher surface coverages, the activation barriers for hydrogenation are reduced by the repulsive interactions between neighboring hydrocarbon and

hydrogen intermediates The higher coverages lead to the population of π-bound ethene states that provide a hydrogenation path which has a lower activation barrier at 36 kJ/mol (Neurock and van Santen, 2000; Neurock et al., 2000) The reaction from the π -bound state proceeds through a "slip-type" mechanism that was proposed in the homogeneous literature The only difference here is that the availability and participation of other surface metal atoms that can assist the reaction on the surface The transition state takes place over two metal atoms to form a more “five-center like” intermediate The classical homogeneous slip mechanism takes place over one metal atom to form a “four-center” transition state

Quantum chemical simulations can provide critical information on the nature of the active sites, the bonding, and the activation, reaction energy for individual steps This is only part of the picture with regard to catalytic performance A more complete analysis requires elucidating the formation and consumption of all reactants, intermediates, and products along with simulating the full set of possible reaction steps to establish what actual controls the outcome The Monte Carlo (MC) simulation enables to explicitly include the atomic surface structure and track the dynamics associated with atomic transformations in the adsorbate surface layer including surface diffusion A representative snapshot of the surface at some instant in time for ethene hydrogenation over Pd is shown in Figure 2.2 The simulation of ethene hydrogenation over Pd in a continuous flow reactor system nicely matches those found experimentally The apparent activation energy was calculated to be 40 kJ/mol which is within the range of 30-40 kJ/mol reported for fixed-bed experimental systems in the literature (Davis and

Boudart, 1991) In addition, by changing the partial pressures of ethene and hydrogen

we find partial reaction orders for hydrogen to be 0.65 to 0.85 and partial reaction orders of ethene to be –0.4 to 0.0 These are consistent with the experimental values of 0.7 to 0.9 for hydrogen and –0.2 to 0.0 for ethene

Heterogeneous catalytic reactions which take place over one- or two-metal-atom centers such as hydrogenation and dehydrogenation resemble analogous homogeneous systems and tend to be structure insensitive Alloys can be used in order to improve the selectivity of these reactions to specific products by shutting down unwanted paths that lead to byproduct formation The turn over frequency (TOF) for these reactions, however, does not change appreciably with changes in structure or surface composition For hydrogenation, this is due to a balance between lower hydrogen surface coverages which decrease the rate and more weakly bound hydrocarbon intermediates which increase the rate (Mei et al., 2003)

By calculating the adsorption energies, activation barriers and overall energies on model PdAu surfaces, Neurock and co-authors (Mei et al., 2003; Neurock and Mei, 2002) were able to simulate the kinetics over different PdAu alloys and surface ensembles The simulation results clearly demonstrate that the reaction is insensitive to the addition of gold regardless of the composition, and specific atomic arrangement of gold There is little change in the turnover frequency on a per palladium atom basis (Neurock and Mei, 2002) A more thorough analysis shows that gold reduces the number of sites to adsorb and activate hydrogen This decrease in the surface coverage of hydrogen will act to

lower the rate On the other hand, the presence of gold weakens the metal-hydrogen and metal-carbon bonds to increase the rate of reaction These two factors tend to compensate each other and the activity remains essentially the same (Mei et al., 2003) This is consistent with the experimental results by Davis and Boudart (1991), who show that the TOF for ethene hydrogenation was changed less than a factor of 2 by increasing

Au to 40% in the Pd/Au alloy The two important points in this system are that the reaction occurs over one to two metal atom centers and that the reaction environment near the active site is important

Benzene adsorption and hydrogenation was studied in detail by Saeys et al (2002; 2003) A fundamental kinetic model was constructed from first principles for the hydrogenation of benzene over a Pt catalyst by using theory to probe the elementary steps for this process over a Pt(111) surface Cluster density functional theory calculations were used to gain fundamental insight in the reaction mechanism and to obtain reasonable values for thermodynamic and kinetic parameters In combination with a limited number of laboratory scale experiments, a fundamental kinetic model was constructed, which can be implemented in mathematical reactor models for the simulation of industrial units

Figure 2.2 Representative kinetic Monte Carlo simulation snapshot for ethene

hydrogenation over Pd (Hansen and Neurock, 2000)

H H

H H

H

H H

H H

H

H

H

H H

H

H H H

H

H

H H

H

H H

H H H

H H

H H

Figure 2.3 Overview of the different reaction paths for benzene hydrogenation The

dominant reaction path is indicated in boldface The hydrogenation activation energies

for every step along the dominant reaction path are indicated The energy values are

given in kJ/mol (Saeys, 2002)

Benzene adsorption energies at the different sites of Pt(111) surface were calculated Benzene adsorbs at the hollow as well as the bridge sites on the Pt(111) surface (Saeys

et al 2002) Thermodynamics considerations and comparison of the calculated spectra with the experimental ones revealed that adsorption at the bridge site is preferred at low coverage, while adsorption at hollow site becomes more important at higher coverage Benzene hydrogenation follows a Horiuti-Polanyi type mechanism Several reaction paths can be suggested (Figure 2.3) A reaction path analysis based on DFT calculations indicates that there is a dominant reaction path, along which the activation energy of every elementary step is at least 15 kJ/mol lower than along an alternative path (Saeys, 2002; Saeys et al 2003) The dominant reaction path is shown in bold in Figure 2.3 Along the dominant reaction path, the addition of the fifth hydrogen to benzene to form the adsorbed cyclohexyl intermediate has the highest activation barrier at 104 kJ/mol and may likely be the rate determining step (Saeys, 2002)

A Langmuir-Hinshelwood-Hougen-Watson rate expression was constructed from the first principles based reaction path analysis with the addition of the fifth hydrogen atom

as the rate-determining step Only the coverage dependent hydrogen adsorption enthalpy was regressed to accurately model laboratory scale data for the hydrogenation

of toluene over a Pt catalyst The optimized hydrogen adsorption enthalpy of –62 kJ/mol is consistent with the value from experimental and theoretical studies of high coverage hydrogen adsorption

2.4 Ammonia synthesis

The synthesis of NH3 is probably the most studied reaction in heterogeneous catalysis The best elementary metal catalysts, such as Ru and Fe were discovered in large-scale screening experiments almost 100 years ago (Haber, 1966; Bosch, 1966; Mittasch, 1950) and the nature of the rate-determining step for Fe-based catalysts, N2 dissociation, was pinpointed as early as 1934 (Emmett and Brunauer, 1933; 1934) Since 1995, this process has been studied in great detail on Ru catalysts by Nørskov and co-workers using periodic DFT calculations His group's research, recently in collaboration with Haldor Topsøe A/S, has led to a detailed understanding of the elementary steps and the origin of catalyst promotion, as well as to the design of a new, improved catalyst

The starting point to the design of an ammonia catalyst is the volcano-shaped relation between the ammonia synthesis activity of different catalysts and their nitrogen adsorption energy shown in Figure 2.4 The transition state for N2 dissociation is late and resembles adsorbed atomic nitrogen (Jacobsen et al., 2002), and thus trends in the nitrogen dissociative chemisorption energy are strongly correlated with the reaction barrier and with the overall rate of reaction (Logadóttir et al., 2001) The volcano shape

of the plot in Figure 2.4 implies that there is an optimum for the nitrogen adsorption energy For metals on which nitrogen is relatively weakly bound, an increase in the endothermicity of nitrogen chemisorption and a lower coverage of adsorbed atomic nitrogen implies a high of the transition state energy and thus a lower rate of reaction For metals on which nitrogen is strongly bound, however, an increase in the strength of

Figure 2.4 Calculated turnover frequencies for ammonia synthesis as a function of the

adsorption energy of nitrogen for various transition metals and alloys (Jacobsen et al., 2002)

Figure 2.5 The calculated potential energy diagram for NH3 synthesis from N2 and H2

over Ru(0001) (dashed curve) and stepped Ru(0001) (solid curve) (Honkala et al., 2005)

the metal-nitrogen interaction leads to increased nitrogen surface coverage (site blocking) and thus to a decreased catalytic activity The net result of these two effects is

a volcano plot in which a maximum in the ammonia synthesis rate versus nitrogen chemisorption energy relationship is observed (Figure 2.4) The optimal catalyst thus has a low dissociation barrier, but does not bind nitrogen too strongly The optimal pure metals are Os, Ru and Fe However, Ru and Os are very expensive and thus commercially less attractive compared to the third, Fe Fe is sensitive to surface blocking (too strong nitrogen bonding), whereas Ru has a low sticking coefficient for

N2 (Egeberg et al., 2001) At higher conversions, Ru becomes a far better catalyst than

Fe, since it is less sensitive to self-poisoning by adsorbed N and NH (Logadóttir et al., 2001)

As indicated in Figure 2.4, a combination of Mo (which binds N too strongly) with Co (which binds N too weakly) should be close to optimum Jacobsen et al (2002) identified CoMo as a potential high-activity alloy catalyst by simple interpolation between the corresponding pure-metal components on the volcano curve (Figure 2.4) Then, they confirmed with first principles DFT calculations that nitrogen does, in fact, have the required intermediate chemisorption energy on CoMo surfaces They also calculated that the N2 dissociation energy on this alloy is intermediate between the dissociation energies on the pure metal components Finally, they used a Co3Mo3N catalyst to demonstrate experimentally that this alloy has an ammonia synthesis activity comparable to that of the best industrial catalysts (Jacobsen et al., 2002; Boisen et al., 2002)

The maximum of the volcano curve is also sensitive to the reaction conditions (Jacobsen et al., 2002) At higher NH3 partial pressures, a catalyst with a lower N-binding energy is preferred, to prevent site blocking As illustrated, the catalytic activity

is function only of the N-binding energy Since it is possible to design catalysts with the optimal binding energy it is possible to optimize the ammonia process In this way a link between DFT and catalyst selection and reactor design can be established (Jacobsen

et al., 2002)

Logadóttir and Nørskov (2003) provided a complete description of the reaction pathway

on both flat and stepped Ru(0001) (Figure 2.5) The calculations show that step sites on the surface are much more reactive than the terrace sites The intermediates in the reaction are bound stronger to the active sites located at steps than on flat terraces Based on these results, they suggested that the reaction mainly occurs at the step sites and N2 dissociation is the rate-determining step in the reaction over a Ru(0001) surface They calculated the activation barrier for N2 dissociation to be 183 kJ/mol on Ru(0001) and 39 kJ/mol on the stepped surface Note that the heat adsorption is incorporated This difference in activation energy (Dahl et a., 1999) leads to a 9 orders of magnitude difference in rate at 500 K This extreme surface sensitivity of N2 dissociation was also found in surface science experiments (Dahl et al., 2000) The active sites for N2

dissociation are therefore only the step site or the defects and have a relatively low surface concentration

2.5 Steam reforming

In the steam reforming process, hydrocarbons such as methane are converted to CO and

H2 over nickel catalysts The dissociative adsorption of methane and the adsorption and dehydrogenation of various CHx species on Ni(111) were studied in detail (Kratzer et al., 1996; Watwe et al., 2000; Yang and Whitten, 1992; Michaelides and Hu, 2000) using first principles DFT calculations The dissociative adsorption of CH4 is the rate-limiting step of the steam reforming process (Besenbacher et al., 1998) The breaking of the C-H bond in the adsorption of CH4 occurs on top of a Ni atom, with a barrier of about 100 kJ/mol Based on a combination of DFT calculations and experimental studies a very detailed mechanistic picture and a complete potential energy diagram of steam reforming including graphite formation on a Ni catalyst has been presented (Figure 2.6) (Bensgaard et al., 2002) Two types of active site were found: a more active one associated with step/defect sites and a less active one associated with closed-packed facets On closed-packed Ni terrace surface, a barrier of about 100 kJ/mol for methane activation was reported while a less 88 kJ/mol barrier was calculated for the Ni(211) surface (Abild-Pedersen et al., 2005) Graphite nucleation is however also initiated at step sites Promoters S, and Au preferentially bind to the step sites and block the sites where graphite formation is initiated, but also reduce the rate of the steam reforming process If 50% step sites are blocked by S, the barrier at the Ni(211) steps increase from 88 kJ/mol to 125 kJ/mol (Abild-Pedersen et al., 2005) An optimized catalyst will have enough amounts of promoters that graphite formation is effectively blocked, while

the fast reaction channel for methane activation is still open

Figure 2.6 Energies for the species on Ni(211) and Ni(111) All energies are relative to

CH4 and H2O in the gas phase and calculated using the results for the individual species.(Bengaard et al., 2002)

Figure 2.7 Conversion of n-butane as a function of time during steam reforming in a

3% n-butane-7% hydrogen-3% water in helium mixture at a space velocity of 1.2h-1 The dashed curve shows the n-butane conversion for the Ni and the solid curve is for

the Au/Ni supported catalyst (Besenbacher et al 1998)

Graphite formation is clearly a problem during steam reforming over nickel and leads to catalyst deactivation The Ni surface binds C too strongly, which leads to graphite formation (Besenbacher et al., 1998; Bengaard et al., 2002) As a possible solution to this problem, Besenbacher et al (1998) considered a gold-doped nickel catalyst Au was found to substantially improve stability of Ni catalysts under n-butane steam reforming (Figure 2.7) They also performed theoretical calculations for methane steam reforming They calculated the energy barriers of methane activation, when 0.25 ML of Au was substitutionally alloyed into the Ni surface layer The barrier increased by 38 kJ/mol (compared with pure Ni) for methane activation over Ni atoms with two Au neighbors Extensive surface characterization confirmed that a stable Au/Ni surface alloy could exist under in situ reaction conditions and that the catalyst could effectively catalyze the reforming reaction without substantial graphite formation

2.6 Selective catalytic oxidation

A microkinetic model for ethene epoxidation was derived by Linic and Barteau (2003a and 2003b) using surface science experiments and DFT calculations Theory was used

to study the various possible reaction paths It was found ethene adsorbs on top of an oxygen atom to form a surface oxametallacycle intermediate This intermediate reacts to form ethene oxide The surface oxametallacycle was also observed under UHV conditions using high-resolution electron energy loss spectroscopy (HREELS) and an intermediate with an almost identical vibrational fingerprint appeared during steady state catalytic experiments The activation energy of dissociative O2 adsorption and the

oxygen-silver bond strength are strongly coverage-dependent From the reaction path analysis a microkinetic model was constructed The activation energies and the pre-exponential factors were obtained from DFT The proposed kinetic model suggests that

in steady state catalytic process the dissociative adsorption of O2 and the reaction of weakly adsorbed ethene with oxygen-covered sites is the potential rate determining steps The resulting rate law is said to agree with experimental observations

The chemistry of the oxametallacycle intermediate was found to control the selectivity

of silver epoxidation catalysis (Linic and Barteau, 2003b) The selectivity of the epoxidation process is determined by the difference in the rate coefficients for the two reaction paths The difference in Gibbs free energy of activation is calculated to be 1.2 kJ/mol in favor of acetaldehyde formation This indicates that the selectivity to ethane oxide will predict selectivity of 40 % at 400-500 K

The calculations of Linic and Barteau correspond to a clean silver surface at rather low coverages, which is far from the catalytically relevant conditions Linic and Barteau argue that dissociatively adsorbed atomic oxygen is the reactive species, using experimental data Recently, Li at al (2003) and Gajdos et al (2003) have carried out detailed calculations for different oxygen adsorption states, including subsurface adsorption, and for varying coverages, taking into account temperature and pressure effects (Li et al., 2003), to provide a comprehensive picture of the behavior of oxygen

on silver and to obtain insight in the function of silver as an oxidation catalyst These studies have led to the identification of other possibly active oxygen species It seems

that at conditions typical for epoxidation, a thin silver-oxidelike structure is most stable (Li et al., 2003), in contrast to the dissociatively adsorbed oxygen atoms suggested by Linic and Barteau Such studies indicate the importance of understanding the surface structure under catalytically relevant conditions

Boisen, A., Dahl, S., and Jacobsen, C.J.H., J Catal 208, pp 180 2002

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Dahl, S., Tornqvist, E., and Chorkendorff, I., J Catal 192, pp 381 2000

Davis, R., and Boudart, M., Catal Sci., Technol 1, pp 129 1991

Egeberg, R.C., Dahl, S., Logadóttir, A., Larsen, J.H., and Nørskov, J.K., and Chorkendorff, I., Surf Sci 491, pp 183 2001

Emmett, P.H., and Brunauer, S., J Am Chem Soc 55, pp 1738 1933

Emmett, P.H., and Brunauer, S., J Am Chem Soc 56, pp 35 1934

Fahmi, A., and van Santen, R.A., J Phys Chem 100, pp 5676 1996

Gajdos, M., Eichler, A., and Hafner, J., Surf Sci 531, pp 272 2003

Haber, F., Nobel Price lecture 1918, in Nobel Lecture, Chemistry pp 1901-1921 Elsevier, Amsterdam, 1966

Hansen, E.W., and Neurock, M., J Catal 196, pp 241 2000

Honkala, K., Hellman, A., Remedeiakis, I.N., Logadóttir, A., Carlsson, A., Dahl, S., Christensen, C.H., and Norskov, J.K., Science, 307, pp 555 2005

Horiuti and M Polanyi, Trans Faraday Soc 30, pp 1164 1934

Kratzer, P., Hammer, B., and Nørskov, J.K., J Chem Phys 105, pp 5595 1996

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CHAPTER 3

COMPUTATIONAL METHODS

3.1 Quantum Chemistry: Theory and Methods

Ab initio, or first principles, methods solve the quantum mechanical equations which

govern the behaviour of a system The only information to be provided are the atomic numbers and positions of the atoms within the system In contrast, empirical or semi-empirical approaches require a model for the interactions between the atoms to be supplied The parameters of these models are usually derived by fitting the outcome of simulations to experimental data

3.1.1 Fundamentals

The ultimate goal in most quantum chemical calculations is to solve the multi-particle Schrödinger equation, which considers all ions and electrons in the system and their interactions The time-independent Schrödinger equation can be written as:

),()

,()]

,()

2

/

R x E R x R x V

3.1.2 Density functional theory (DFT)

In 1964, Hohenberg and Kohn put forward the density functional theory (DFT)

(Hohenberg and Kohn, 1964), which replaces the many body electronic wave functions,

)

,

( R x

ψ , with the electronic density, ρ(r), as the basic quantity DFT is a reformulation

of the Schrödinger equation, with a 3 dimensional electron density ρ(r)in place of the

4n dimensional electronic wave function This dramatically simplifies the quantum

chemical calculation as the electron density is now a function of only 3 variables, as

opposed to the n-electron wave function which is a function of 4n variables

The central quantity of DFT, the electron density, is defined as:

N S

x x x n

2 2

ρ determines the probability of finding any of the N electrons within the volume

element r d , but with arbitrary spin while other n-1 electrons have arbitrary positions

and spin in the state represented by

x

1

The major theoretical pillars on which all modern DFT methods are built are the two

Hohenberg-Kohn theorems (Hohenberg and Kohn, 1964) The first theorem of

Hohenberg and Kohn states that the ground state electron density uniquely determines

the external potential V ext (r) Thus, one writes the ground state energy E0[ρ0(r)] as a

functional of ground state electron density functional,ρ0(r):

)]

([)]

([)]

([)]

(

E ρ = ne ρ + ρ + ee ρ (3.3)

4444444

14

r

r d r d r r r

T r d r

V

r

r F r E

r

E

)]

([)

()(2

1)]

([)

([)]

(

[

0 12

2 1 2 0 1 0 0

0

0 0

0

0

ρρ

ρρ

ρ

ρρ

E is the nucleus-electron interaction energy (corresponding to the external potential of

the Hohenberg and Kohn theorem), T is the kinetic energy and the electron-electron

repulsion energy The electron-electron repulsion energy can be further split up in a

J ρ , the third term of eq (3.4), and a non-classical contribution, )]

(

[ 0 r

E ncl ρ , which contains the effect of exchange and correlation Exchange is a pure quantum mechanism effect and results from the anti-symmetry of the wave function required by the Pauli principle Correlation is a consequence of the charge of the electrons on the pair density

Further, the second Hohenberg and Kohn theorem proves that the ground state density minimizes the total electronic energy of the system

)]

(

~[)]

(

~[)]

(

~[)]

(

~[)]

The Hohenberg and Kohn theorems are merely proofs of existence, but do not provide a

way of finding the ground state density In eq (3.3), only J[ρ0(r)] is known The Kohn-Sham (Kohn and Sham, 1965) approach provides a route to bypass the construction of a major but unknown contribution to the Hohenberg and Kohn

functional, i.e kinetic energy functional T [ rρ( )] They introduce a non-interacting reference system, with the same electron density distribution as the real system Thus, the universal term of eq (3.4) can be written as

)]

([)]

([)]

([

3.1.3 Exchange-correlation functional

The major problem with DFT (eq 3.6) is that the exact form of the exchange and correlation functionals is not known The simplest form is given by the Local Density Approximation (LDA) It assumes that the shape of the exchange-correlation hole is derived for a hypothetical uniform electron gas This is a system in which electrons

move on a positive background charge distribution such that the total ensemble is electrically neutral The LDA is given by

r d r r

E XC LDA[ρ( )]=∫εxc(ρ)ρ( ) 3 (3.8) where εxcis the exchange-correlation energy per particle of the uniform electron gas LDA is the simplest and least accurate functional LDA often produces poor estimates

of binding energies (typical overbinding by 80-100 kJ/mol), though geometries might

be acceptable

As the LDA approximates the energy usinga local constant density, it fails in situations where the density undergoes rapid changes such as in molecules An improvement to this can be made by considering the gradient of the electron density, the so-called Generalized Gradient Approximation (GGA) It can be written as:

r d f

E GGA XC [ρα,ρβ]=∫ (ρα,ρβ,∇ρα,∇ρβ) (3.9) GGA includes the (spin) density gradient in a more general way and allows all powers

of ∇ρ to occur in the exchange-correlation energy

Using the GGA, very good results for molecular geometries and ground state energies have been achieved Many further incremental improvements have been made to DFT

by developing better representations of the functionals The particular GGA used in the

calculations in this work was introduced by Perdew and Wang (Perdew et al., 1992),

PW91

3.1.4 Plane-wave basis sets

To solve the Kohn-Sham equation numerically, the single particle density is expanded in terms of the basis set Typically, a finite number of plane wave functions are used, below a specific cutoff energy which is chosen for a certain calculation Plane wave basis sets are popular in calculations involving periodic boundary conditions Certain integrals and operations are much easier to code and carry out with plane wave basis functions than with their localized counterparts In practice, plane wave basis sets are often used in combination with a pseudopotential, so that the plane waves are only used

to describe the valence charge density This is because core electrons tend to be concentrated very close to the atomic nuclei, resulting in large wave function and density gradients near the nuclei which are not easily described by a plane wave basis set unless a very high energy cutoff is used

3.1.5 Pseudopotentials

In most materials the core electrons do not contribute to bond formation Only their absolute energies are affected by the average electrostatic potential in the vicinity of the nucleus Thus, a “frozen-core approximation” can be used The core electrons are calculated for a reference configuration (in general spherical) and kept fixed thereafter The wave functions for the valence electrons are “pseudized” to give the same energy levels as the all-electron wave-functions

The projector-augmented-wave (PAW) method is a frozen-core all-electron method that aims to make the advantages and accuracy of all-electron methods available to the

formally simpler (and computationally less demanding) pseudopotential approach It was established by Blöchl (Blöchl, 1994) The valence-only PAW method is implemented in the Vienna ab initio simulation package (VASP) Its results are almost identical to the most accurate density functional calculations presently available, which are based on the full-potential linearised augmented plane-wave-method (FLAPW) (Kresse and Joubert, 1999) FLAPW scheme describes all electrons essentially exact within DFT (with a much higher computational effort), even in the most difficult cases such as strong magnetic moments or large electronegativity differences (Teter et al., 1989)

3.1.6 The Vienna Ab initio Simulation Package

The Vienna Ab initio Simulation Package (VASP) (Kresse and Hafner, 1993; 1994) is a popular package for periodic DFT calculations VASP is characterized by a well parallelized architecture It includes an optimized set of ultrasoft and PAW pseudopotentials for all elements of the periodic system VASP solves the Kohn-Sham equations of local density or spin-density functional theory iteratively within a plane wave basis set The electronic ground state is determined either by a conjugate gradient algorithm as optimized by Teter et al (1989), by a blocked Davidson scheme proposed

by Davidson (Davidson 1983), or via an unconstrained band-by-band diagonalisation scheme based on a residual minimization method (RMM) (Kresse and Furthmüller, 1996a and 1996b; Wood and Zunger, 1985) At each iteration the charge density has to be recalculated To achieve numerical stability, the new density is mixed

matrix-with the input charge density of the previous cycle by an improved Pulay mixing scheme (Pulay, 1980)

Plane waves are used as the basis set and projector-augmented-wave pseudopotentials replace the core part of atoms This decreases computational time significantly Fast Fourier transformations (FFT) are used to switch from direct to reciprocal space and vice versa This decreases of the number of plane waves, which allows a partial diagonalization

Besides the pure local density approximation (LDA) for the exchange-correlation functional, the LM (Langreth and Mehl, 1983), the BP (Becke, 1988), the PW91 (Perdew et al., 1992), and the PBE functionals (Perdew et al., 1996) also are implemented in VASP

To calculate the energy band dispersion in the Brillouin-zone, sampling in reciprocal space is done at the points of the Monkhorst-Pack special grids (Monkhorst and Pack, 1976) The number of k-points to sample the irreducible part of the Brillouin zone is important for accurate integration of the properties computed in reciprocal space For the integration over the Brillouin zone, the tetrahedron method with Blöchl correction (Blöchl, 1994) and a generalized Gaussian smearing (Methfessel and Paxton, 1989) are available among other less involved methods

Ψ

trial-charge ρin and trial-wavevectors

Set up Hamiltonian H(ρin)

Iterative refinements of wavefunctions {Ψn}

new charge density ρout =∑n f n Ψn (r) 2

refinement of density ρin,ρout ⇒new ρin

Figure 3.1 Typical flow-chart of VASP for the self consistent determination of the

Kohn-Sham ground state (VASP guide, http://cms.mpi.univie.ac.at/vasp/vasp.html)

Calculate forces, update ions

Figure 3.1 shows a brief flow chart of VASP calculations The inner cycle is a self consistent energy calculation for a given structure, and the outer cycle is the geometry optimization After the determination of the electronic ground state for a given ionic configuration, the forces on the atoms are evaluated, as described below, leading to the local energetic minimum of a system

3.1.7 Nudged elastic band method (NEB)

The nudged elastic band (NEB) method (Jόnsson, 1998; Mills and Jόnsson, 1994), illustrated in Figure 3.2, is an efficient algorithm for finding the minimum energy path (MEP) between two given fixed states on the Potential Energy Surface (PES) Between the two states, often the reactant and product of a reaction, a set of intermediate states is

N-1 intermediate states are adjusted to converge to states on the MEP by an optimization method The typical number of states is between 4 and 20, depending on the complexity of the reaction path

NR R R R

i R

→

If the number of intermediate states in the NEB is too small as compared to the length

of the reaction path, none of the final states will eventually be close to the saddle point, and it becomes impossible to locate the TS through interpolation or through a second NEB with smaller steps

The term “nudged” indicates that the projection of the parallel component of true force acting on the images and the perpendicular component of the spring force are canceled

Figure 3.2 Schematic illustration of the nudged elastic band method Starting from an

initially guessed reaction path (dashed line) the chain converges to the nearest minimum path on the PES (full line) (Jόnsson 1998; Mills and Jόnsson, 1994)

3.2 Computational methodology

All calculations in this thesis have been performed using spin-polarized density functional theory (DFT) with the Perdew-Wang 91(Perdew et al., 1992) functional as

implemented in the Vienna ab initio simulation program VASP (Kresse and Hafner,

1993, 1994; Kresse and Furthmüller, 1996a, 1996b) VASP performs periodic boundary condition DFT calculations The calculations were performed using a plane wave basis, with a cut-off kinetic energy of 400 eV Projector-augmented-wave (PAW) (Blöchl, 1994; Kresse and Joubert, 1999) pseudopotentials were used to describe the inner shell electrons Terraces were modeled as a four-layered Ni(111) slab where the top two layers are allowed to relax while the remaining layers are fixed at their bulk positions Step sites were described by a nine-layer slab Ni(211) slab, equivalent to a three-layer Ni(111) surface To achieve numerical convergence, Methfessel-Paxton smearing is used with a smearing parameter σ of 0.2 eV The optimized Ni bulk lattice constant, 3.52 Å, is in good agreement with the experimental value, 3.524 Å (Lide, 1998) An interslab spacing of 12 Å was found to be sufficient to avoid interactions between repeated slabs

3.3 References

Becke, A.D., Phys Rev A, 38(6), pp 3098 1988

Blöchl, P.E., Phys Rev B 50(24), pp 17953 1994

Blöchl, P.E., Jepsen, O., and Andersen, O.K., Phys Rev B, 49(23), pp 16223 1994 Davidson, E.R., In Diercksen, G.H.F., and Wilson, S., eds., Methods in Computational molecular Physics, vol 113 of NATO Advanced Study Institute, Series C: Mathematical and Physical Science, pp 95 Plenum, New York 1983

Hohenberg, P., and Kohn, W., Phys Rev B 136, pp 864 1964

Henkelman, G., Uberuaga, B.P., and Jόnsson, H., J Chem Phys 113(22), pp 9901

2000

Jόnsson, H., Mills, G., and Jacobsen, K.W., ‘‘Nudged elastic band method for finding

minimum energy paths of transitions,’’ in Classical and Quantum Dynamics in

Condensed Phase Simulations, edited by B J Berne, G Ciccotti, and D F Coker

(World Scientific, Singapore, 1998), p 385

Kresse, G., and Hafner, J., Phys Rev B 47(1), pp 558 1993

Kresse, G., and Hafner, J., Phys Rev B 49 (20), pp.14251 1994

Kresse, G., and Furthmüller, J., Phys Rev B 54, pp 11169 1996a

Kresse, G., and Furthmüller, J., Comput Mater Sci 6, pp.15, 1996b

Kresse, G., and Joubert, D., Phys Rev B 59(3), pp 1758 1999

Kohn, W., and Sham, L.J., Phys Rev A, 140, pp 1133 1965

Langreth, D.C., and Mehl, M.J., Phys Rev B 38(4), pp 1809 1983

Lide, D.R (Ed.), CRC Handbook of Chemistry and Physics, 79th ed., CRC Press, Boca Raton, FL 1998

Methfessel, M., and Paxton, A.T., Phys Rev B, 40 (6), pp 3616 1989

Mills, G., and Jόnsson, H.,Phys Rev Lett., 72(7), pp 1124 1994

Monkhorst, H.J., and Pack, J.D., Phys Rev B 13(12), pp 5188 1976

Perdew, J.P., Chevary, J.A., Vosko, S.H., Jackson, K.A., Pedersen, M.R., Singh, D.J., Perdew, J.P., Burke, K., and Ernzerhof, M., Phys Rev Lett 77(18), pp 1996 1996 Pulay, P., Chem Phys Lett., 73, pp 393 1980

Teter, M.P., Payne, M.C., and Allan, D.C., Phys Rev B.40(18), pp 12255 1989

Wood, D.M., and Zunger, A., J Phys A 18, pp.1343 1985