Density-Functional Theory Study of NHx Oxidation and Reverse

J. Phys. Chem. C 2007, 111, 9839-9852

9839

Density-Functional Theory Study of NHx Oxidation and Reverse Reactions on the Rh(111) Surface C. Popa,* R. A. van Santen, and A. P. J. Jansen Molecular Materials and Nanosystems; Schuit Institute of Catalysis, ST/SKA, EindhoVen UniVersity of Technology, P.O. Box 513, NL-5600 MB EindhoVen, The Netherlands ReceiVed: February 7, 2007; In Final Form: May 10, 2007

The adsorption of NHx fragments and oxidation of them by O and OH on the Rh(111) crystal surface have been studied using first-principles density-functional calculations. The stability and configurations of OHx and NHx have been investigated and characterized using frequency analysis. Several paths of NHx (x ) 1-3) oxidation with O and OH and reverse elementary processes have been determined. The transition states have been determined and analyzed in detail. The activation barriers and thermodynamic and kinetic data have been calculated for all of the elementary steps. The calculations have shown that atomic oxygen does not promote ammonia decomposition. The elementary reactions with O are endothermic, and they have significant barriers, comparable with ammonia dehydrogenation barriers [Popa, C.; Offermans, W. K.; van Santen, R. A.; Jansen, A. P. J. Phys. ReV. B 2006, 74 (15), 155428-1-155428-10].1 The OH fragment does promote ammonia decomposition. The elementary reactions are exothermic or slightly endothermic, and the activation barriers are significantly lower. The activation entropies decrease the pre-exponential factors significantly. Nitrogen recombination on the Rh(111) surface has a high activation barrier, but it is comparable with the barriers on stepped surfaces of other metals. The first step of ammonia oxidation occurs late. The subsequent elementary steps are earlier and earlier from the geometrical point of view.

I. Introduction Single-crystal processes studied at the atomic level from theoretical and experimental point of view are of special importance in surface science. Ammonia oxidation is an important reaction for technological, economic, and environmental reasons. It can be used to convert ammonia to N2 directly, to reduce NOx in emissions by selective catalytic oxidation (SCO), and also as hydrogen source and storage in fuel cells.2-4 A widely applied process is the Ostwald process that converts ammonia to NOx. The adsorption and the reactivity of ammonia on transitionmetal surfaces have been the subject of numerous experimental and theoretical investigations. Experimental studies on the Rh(111) surface were performed using temperature programmed desorption (TPD), temperature programmed reaction spectroscopy (TPRS), static secondary ion mass spectrometry (SSIMS),3,5 and attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR).6 Also theoretical studies were dedicated to NH3 on several clean d-band metallic surfaces, as Rh,1,7,8 Ni, Pd,4 Ru,9,10 Pt,11,12 and Au.13 The stability of different fragments and the energetics of elementary processes for ammonia synthesis/decomposition on the Rh(111) surface were previously studied.1,8,14,15 The elementary steps of ammonia oxidation on Rh have not yet experimentally or theoretically been described in the literature. Nitrogen adsorption and recombination was previously studied as well on different metallic surfaces.3,4,16-20 The predicted activation barriers are rather large. Lower barriers are found for the processes that take place on the step edges.9,21 There remain many questions concerning the nature of the * E-mail address: [email protected].

transition state structure and the kinetic and thermodynamic characteristics of N2 decomposition on Rh(111) derived from ab initio data. The corresponding experimental data and the comparison with similar systems represent important sources of information for the study of ammonia oxidation on the Rh(111) surface. This process presents many interesting aspects from a scientific point of view as well for the potential applications. In the past decades, advances in electron density functional theory (DFT) based computational methods have enabled the modeling of a variety of physical systems based on an explicit treatment of the electronic structure. In a previous study, we presented a detailed ab initio density-functional investigation of the stability of the NHx species and corresponding transition states of the dehydrogenation on a Rh(111) surface.1 Kinetic and thermodynamic characteristics were derived from ab initio data. The present paper deals with self-consistent DFT-based electronic structure simulations of the NHx species coadsorbed with O, OH, and water and reactions between these fragments on the Rh(111) surface. The goal of this work is to give a detailed description of the interactions between the (co)adsorbed fragments NHx and HxO and the metal surface and to provide a theoretical description of the corresponding elementary processes. We analyze the role of adsorbed O and OH in the activation of NHx and key minimum energy paths leading to water, N2, and H2. Particularly interesting is also the nitrogen recombination reaction. First we discuss in detail the stability of adsorbed OHx and NHx fragments and their vibrations. The equilibrium species are characterized using vibrational analysis. Then we focus on the determination of different possible transition states for the dissociation/association reactions. Finally, the kinetic and

10.1021/jp071072g CCC: $37.00 © 2007 American Chemical Society Published on Web 06/16/2007

9840 J. Phys. Chem. C, Vol. 111, No. 27, 2007

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thermodynamic parameters of the rates of the elementary steps are determined via partition functions and discussed. Our paper is organized as follows. In section II, we briefly review the computational aspects of our study. We discuss the calculation of kinetic parameters using statistical thermodynamics and the method of finding transition states. Section III contains results and discussions. In section III.A, we discuss the adsorption and coadsorption of the NHx fragments on Rh(111) surface. In section III.B, the vibrational analysis is presented and a comparison with the available experimental data. Sections III.C-E present transition states of several reactions and the energetics of their elementary steps. Section III.G provides a discussion and comparison of the thermodynamic and kinetic parameters. Transition-state activation energies are given for the dehydrogenation and the reverse reactions of NHx hydrogenation. Section IV presents our conclusions. The Appendix deals with some details about coadsorption energies, lateral interactions, and frequency analysis. II. Computational Details The simulations were performed using DFT with the Vienna ab initio simulation package (VASP)22,23 code, with a plane wave basis set, ultrasoft Vanderbilt pseudopotentials,24 and the generalized gradient approximation (GGA)25 for the exchange and the correlation energy proposed by Perdew and Wang.26 Tests showed that the spin contribution to the total energy of the adsorbated systems is negligible and hence a spin-restricted approach was used27-29 except for the atoms and molecules in the gas phase. With the pseudopotentials considered, a cutoff energy of 400 eV for the plane wave basis ensures a good accuracy. For the Brillouin zone integration, a Monckhorst Pack 5 × 5 × 1 mesh was used for all structures. The employed models consisted of a p(2 × 2) supercell with five metal layers, which were allowed to fully relax, and an equivalent vacuum space (11.1 Å) in the z direction between successive slabs. The optimized bulk nearest-neighbor separation of 2.72 Å is in good agreement with the experimental value of 2.69 Å.30 The molecules were adsorbed on both sides of the metallic slab with a S2 symmetry center to avoid long-range dipole-dipole interactions between translational equivalent unit cells. Accuracy tests with different computational settings and configurations showed that the convergence of the total energy is within 5 × 10-2 eV. The conjugate-gradient algorithm was used to relax the ions into their equilibrium locations. Equilibrium is reached if the Hellmann-Feynman forces on the atoms are less than 0.02 eV Å-1 in each of the Cartesian directions. For the structures for which we have performed vibrational analysis, the forces were smaller than 10-3 eV Å-1 and the energy convergence smaller than 10-6 eV. The adsorption energy for all the high symmetry adsorption sites of the AHx (A ) N, O) fragments was calculated according to the equation

Eads ) [EAHx/Rh - ERh - nEAHx(gas)]/n

(1)

where EAHx/Rh is the total energy of the AHx system adsorbed on the Rh surface, ERh is the energy of the metallic slab, EAHx(gas) is the energy of the AHx fragment in gas phase, and n is the number of the AHx (co)adsorbates on the slab. Vibrational frequencies were computed for the initial and final states as well as for the transition states in the harmonic approximation as the method is incorporated in VASP. We applied a finite displacement in all directions, for the first layer Rh atoms and for the adsorbates. Tests showed that the phonons

of the inner metallic layers hardly do couple with the vibrations of the adsorbated fragments. This fact makes it possible to freeze the degrees of freedom of the inner metallic atoms in the frequency calculations. A reasonable value of the finite displacement is (0.02 Å, as a compromise between the accuracy of the force calculation and harmonic approximation. However, in the case of almost flat potential energy surfaces with respect to the degrees of freedom for adsorbates, 0.01 Å seems to be better to avoid anharmonicities. Despite the systematic error inherent in the GGA exchange-correlation and various numerical approximations, the computed frequencies are accurate to 2-3 %.31-33 All of the frequencies here were also calculated with the tremble program.34 We obtained an excellent agreement between the frequencies calculated using tremble and those obtained using VASP. The differences were only of maximum 5 cm-1 for the high-frequency modes and maximum 15 cm-1 for the low-frequency modes. Furthermore, these calculations were very important for checking the real stationary points on the PES by a fast estimate of the reliability of our calculations. The nudged elastic band method (NEB) implemented in the VASP program was used to determine the dissociation paths.35,36 The minimum energy path (MEP) relates the initial and the final states by a set of intermediate states connected by an elastic band and distributed along the reaction coordinate. All of the atomic coordinates were free to optimize during a NEB calculation. Each state is fully relaxed in the hyperspace perpendicular to the energy path. For difficult cases, we used the climbing image NEB or the variable NEB methods.37-39 Depending on the energy profile, we used 8-20 images for a NEB calculation. After the reaction, the fragments are coadsorbed on the surface. The adsorption energies were calculated according to eq 1. The barrier energy of the reaction is given by the difference between the energies of the transition state (TS) and of the reactants (R). The NEB calculation gives a configuration which is a good candidate for the transition state structure. After minimizing the residual forces, a vibrational analysis is used to check if indeed a transition state was found. If a molecule is in a real minimum of the potential energy surface, all frequency values are positive. Thus, a true transition state is a saddle point on the PES and must have one, and only one, imaginary frequency corresponding to the reaction path degree of freedom. For a single step reaction, the rate constant at temperature T can be written in an Arrhenius type expression E act

k ) ν*e-k BT

(2)

where ν* is the pre-exponential factor, Eact is the activation energy, and kB is the Boltzmann constant. If we assume the validity of harmonic transition state theory and use the partition functions for reactants and transition states (QR, QTS), it is possible to calculate also the activation energy and the pre-exponential factor of a reaction. In the harmonic transition state theory, the rate constant for a reaction can be calculated as

k)

kBT QTS -((ETS-ER)/kBT) e h QR

(3)

where ETS - ER ) Ebar is the difference between the energies of the transition state and of the reactants, i.e., the activation barrier.

NHx Oxidation and Reverse Reactions on Rh(111)

J. Phys. Chem. C, Vol. 111, No. 27, 2007 9841

TABLE 1: Adsorption Energies on the p(2 × 2)-Rh(111) Surface (eV Molecule-1)a system O O2 N2 OH tilted OH perp. H 2O

top

bridge

fcc

hcp

-3.35

-4.34b -4.87 (-4.80) -4.77 (-4.69) -0.50 -0.53 -0.45 -0.53 (-0.47) -0.07 -2.54 (-2.44) -2.85 (-2.73) -2.87 (-2.77) -0.33 (-0.27)

a The ZPE corrected adsorption energies are given in parenthesis. The values are given with respect to the fragments in the gas phase. The gas-phase energies were calculated in large unit cells, taking into account also the spin contribution (N2 - 16.52, O - 2.06, O2 - 9.86, OH - 7.76, H2O - 14.26, NO - 12.10). b Restricted geometry optimization.

The activation energy which includes also the zero-point energy (ZPE) correction is given by the following equation:

∂ ln k ) ∆H0# + kBT Eact,0 ) kBT 2 ∂T

(4)

where ∆H#0 is the activation enthalpy. For high activation # barriers kBT becomes negligible and Eact,0 ≈ ∆Hdiss,0 . Thte expression from harmonic transition state theory for the activation energy will give values very close to the experimental values obtained by fitting the Arrhenius expression (eq 2) to rate constants over a temperature range. The partition functions including the ZPE correction of the vibration modes and the free rotations of the adsorbates, the entropy of a system, and the pre-exponential factors are calculated according to the equations described in a previous paper.1 III. Results and Discussions A. Adsorption on the Rh(111) Surface. In a previous paper, we discussed the adsorption and coadsorption of the NHx species on the p(2 × 2)-Rh(111) surface.1 Here we briefly recall that the most stable positions and the adsorption energies (including ZPE) in eV are the following: NH3 on top -0.75 (-0.65), NH2 in bridge -2.75 (-2.56), NH in fcc -4.36 (-4.17) and hcp -4.35 (-4.17), N in hcp -5.07 (-4.98) and fcc -4.95 (-4.86), and H in fcc -2.84 (-2.68) and hcp -2.81 (-2.65). These selected positions will be used further to discuss the possible reaction paths. Some additional adsorption energies on the Rh(111) surface are presented in Table 1. For atomic oxygen, the previous DFT calculations16,40-43 give adsorption energies which vary with 0.5 eV, especially for O adsorbed in hollow sites, depending on the computational details (thickness of the metallic slab, relaxation, cutoff energy, k-points grid, and the employed functionals). Our findings are consistent with the results obtained by Mavrikakis et al.16 and reasonably close to the other results. For atomic oxygen, the fcc hollow site is preferred, with an adsorption energy of -4.87 eV; the hcp hollow site is slightly less stable (-4.77 eV). Taking into account the zero-point energy correction, the site preferences of atomic O do not change. The Rh-O distance is 2.009 Å for O fcc adsorbed and 1.996 Å for O hcp adsorbed, in good agreement with experimental LEED data (2.00 ( 0.06 Å). For O in fcc and hcp the Rh surface layer atoms are shifted upward from 2.242 Å (normal distance between the first two layers in a Rh slab) by 0.059 and 0.061 Å respectively, approximately 3%, in perfect agreement with the LEED experimental results44 (LEED: 2.24 ( 0.04 Å). The O2 molecule is not stable on the top position but adsorbs weakly in th ebridge position (-0.5 eV) as well in the hollow sites (-0.53 eV for fcc position and -0.45 eV for the hcp position).

N2 adsorption on rhodium was experimentally studied by Hendrickx et al.,45 and they found an adsorption energy of -0.35 eV. Hardeveld et al.3 concluded using TPD that N2 does not chemisorb dissociatively on the Rh(111) surface. Previous calculations16,18 showed that an N2 molecule adsorbs on the top position, with the N-N bond perpendicular to the metallic surface. Mavrikakis et al.,16 depending on the applied functional (PW91/RPBE), obtained a stable or unstable adsorption site for the bridge position. Our results are in good agreement with the previous calculations, using the same functional. The hollow sites are not stable configurations for the N2 molecule. For the bridge site, we obtained a weak physisorption (-0.07 eV). The top site is the most stable position, with a Rh-N distance of 1.945 Å and N-N of 1.133 Å. The Rh atom below the N2 on top is significantly shifted upward by 0.175 Å. The OH fragment adsorbs tilted in the bridge (-2.85 eV) and on top (-2.54 eV) positions. For the hollow sites we did not obtain stable tilted OH configurations. For OH adsorbed in bridge position the O-H bond has 0.976 Å length, with the H atom oriented above a fcc hollow site, and the Rh-O distance is 2.150 Å. In the z direction, the Rh-O distance is 1.708 Å, and the Rh atoms connected with the O atom are shifted upward by 0.064 Å. For OH adsorbed on the top position, the O-H bond is 0.982 Å long, the Rh-O distance is 1.977 Å, the Rh atom connected with the O is shifted upward by 0.062 Å, and the RhOH angle is 109 o. The OH also adsorbs in the upright position. This configuration is not stable on the top, bridge, and hcp hollow sites, but it adsorbs in the fcc hollow site, with adsorption energies comparable with those of the tilted OH. The stability of this hollow position might be an artifact, due to the local symmetry of the site. For this reason, we did not include it in further calculations searching transition states. Our results are close to those reported in previous calculations,16,42 although we could not find minima for the OH upright on the top, bridge, and hcp positions. H2O adsorbs weakly (-0.33 eV) in a p(2 × 2) unit cell on top position. The molecule is oriented parallel with the surface and the rotation around z axis is free. The Rh atom below the O atom is displaced in the z direction by 0.043 Å, the O-Rh bond length is 2.363 Å. The HOH angle is 105 o and the O-H bond length is 0.98 Å. Our results are in good agreement with the previous theoretically studies,42,46,47 although we did not find a second stable adsorption (on bridge) site at this coverage. We calculated the coadsorption energies for the combinations NHx + O, NHx + OH, and Nx + H2O as well (see the appendix for details). This is important for the selection of the initial and final states of the possible reactions. For some structures, we calculated different arrangements in a p(2 × 2) unit cell. The coadsorption energy of NHx with O, OH, or H2O increases while x is smaller. Coadsorption is stronger than adsorption of each separate fragment in the case of (NH3 + O or OH), (NH2 + OH or H2O), and (NH + H2O) systems. Therefore, the lateral interactions are attractive; between the adsorbed species, there are hydrogen bonds. These interactions can be large (0.06-1.23 eV) and they also affect the frequencies of the normal modes. For NH2 coadsorbed with O and NH coadsorbed with O and OH, the interactions are repulsive (0.31 - 0.43 eV). In this case, there are no hydrogen bonds involved. When two nitrogen atoms coadsorb, the repulsive lateral interactions are large, almost 1 eV. All of the studied systems are very stable on the Rh(111) surface, with coadsorption energies from -3.29 to -9.26 eV. The zero-point energy corrections are substantial too. When


Popa et al.

TABLE 2: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for O, OH, and H2O Adsorbed Systems on p(2 × 2)-Rh(111) Surface vibration mode νas νs δs Lw Lt T⊥ T|

O fcc

O hcp

OH top (tilted)

OH bridge (tilted)

OH fcc (perp.)

3687

3649

3715

798, 52

637, 613

507 516 525 415 360, 359 347, 345 211, 108 225, 163

H2O top

3687 3585 1526 456, 442 527 432 383 223 215, 120 116, 103

coadsorbed with O, they are 0.17-0.58 eV, to be compared with coadsorbed OH (0.18-0.76 eV), and of H2O (0.31-1.34 eV). These contributions are given by the high-frequency modes, as we will see in the next section. B. Frequency Analysis of NHx Adsorbates on the Rh(111) Surface. The frequencies of the vibration modes of atomic oxygen, OH, and H2O top adsorbed in the most stable adsorption sites on the Rh(111) surface are summarized in Table 2. All of the other individual fragments were discussed previously.1 Atomic oxygen adsorbed in fcc and hcp hollow sites gives similar values for the vibrations, and the differences are of the order of few cm-1. The highest frequency is given by the Rh-O stretching vibration perpendicular to the metallic surface (ν⊥ ) 507, 516 cm-1). The other two vibration modes are frustrated translations parallel with the surface (ν|). They are degenerate, and they have lower values of the frequencies (345-360 cm-1). The OH radical has an asymmetric O-H stretch vibration with values around 3700 cm-1, depending on the adsorption position. The rocking mode has a higher frequency for the top site (798 cm-1) and lower when adsorbed on bridge or in hollow (637 and 456 cm-1, respectively). The wagging modes have more differentiated values depending on the adsorption site, reflecting the strength of the adsorption: 613 cm-1 for the bridge site, 442 cm-1 for the fcc site, and only 52 cm-1 for the top position, where the H has a higher mobility and, thus, a higher entropy. The Rh-OH stretching mode (T⊥) follows the same tendency as the rocking modes. The lowest values of the frequencies are given by the frustrated translations parallel with the surface. It is important to notice that there are few vibration modes characteristic for the Rh surface atoms that couple with the low vibration modes of the adsorbates. This effect is always present especially in the OH containing systems. The water molecule adsorbed on the top position has highfrequency values for the (a)symmetric vibration modes (3687 and 3585 cm-1, respectively) and for the deformation (scissor) mode (1526 cm-1). The values are lower than those calculated for the gas phase (3879, 3763, and 1574 cm-1). The water molecule is physisorbed on the top site and actually is a free rotator on an axis perpendicular on the metallic surface. The weak adsorption energy is reflected by the small value of the Rh-H2O stretching frequency (223 cm-1). The other vibrational modes (wagging, twisting, and frustrated translations) have lower frequency values than the OH fragment. The calculated frequencies for NHx coadsorbed with O, OH, and H2O are described in detail in the Appendix. The low vibrational modes have in general higher values for the frequencies than those corresponding to individual adsorptions. The free rotation of the water molecule when adsorbed alone becomes a wagging mode (178-255 cm-1) when coadsorbed with a NHx fragment. It is very important to notice here that in systems with strong hydrogen bonds it is hard to assign a certain frequency to a vibration mode. The hydrogen bonds are very active in the low

range of the spectrum and it is difficult to say about a mode that it belongs to a certain group, NHx or OH. In the very low range of the frequencies spectra, there is some weak coupling with the metallic surface phonons. We noticed significant changes of the frequency values for certain adsorbed fragment from one coadsorption site to another one, and this fact is very useful when trying to identify an adsorbed fragment in a specific site. But one value of the frequency might correspond to a completely different frequency mode of another adsorbate. So one has to be careful assigning completely a frequency mode of a certain fragment. For instance, for the NH hcp + O hcp coadsorbed system, there is a frequency of 516.4 cm-1 which is clearly assigned to the frustrated translation in y direction mode (T| ,y) of the NH group. The (NH fcc + O hcp) coadsorbed system gives a frequency with a very close value (518.5 cm-1), which belongs completely to the frustrated translation in z direction mode (T⊥) of the O atom. The same value of 516 cm-1 is given by the O atom when adsorbed in a hcp site alone on the Rh(111) surface (see Table 2). The high-frequency modes of NHx do not couple with those of O, OH, or H2O, and for larger values of the frequencies the assignment is easier, although the values are slightly lower than those corresponding to single adsorbate fragments. C. Reaction Pathways for NHx Oxidation by O. 1. NH3 Oxidation by O. Starting from staggered ammonia on top coadsorbed with an oxygen atom in fcc/hcp hollow site the NEB method gives the following results (see Figure 1). Both MEPs lead to NH2 on bridge coadsorbed with an OH on top position. First a H-N bond from ammonia breaks and NH2 remains adsorbed on the top position, while an OH fragment is formed on the bridge position. The N-H bond breaking costs a lot of energy; therefore, the activation barriers are large, comparative with the activation barrier of ammonia dehydrogenation.1 Only after the transition states the fragments will move toward their minimum positions, i.e., NH2 on bridge and OH on top. We took into account also other routes for the MEPs, and we obtained the same shape for the MEP and structures for the transition states. Each oxidation step is followed by the diffusion of the fragments in which the energy increases because of the attractive interaction. 2. NH2 Oxidation by O. We next consider then a new oxygen atom coadsorbed in the unit cell with a NH2 fragment. For the reaction of NH2 on bridge with O in the fcc or hcp positions, more MEPs are possible. After the reaction, a NH adsorbed in the fcc or hcp hollow site and an OH fragment adsorbed on top or bridge position result. We studied two possible paths for the reaction of NH2 on bridge with the atomic O adsorbed in fcc position (see Figure 2). Depending on the trajectory of the transferred H atom, the final products are either (NH hcp + OH top) or (NH fcc + OH bridge). Both reactions occur early. The transition states are almost the same, with the transferred H atom situated between the N and O atoms. In the first case, after the transition state, the OH will move via the bridge to the top position and NH to the hcp hollow site. In the second case, after the transition state, the OH will move via the top to the bridge position and NH from the bridge to the fcc hollow site. The activation barriers are similar and slightly lower than the activation barriers for NH2 dissociation. If we consider the initial position of O in the hcp hollow site, the reaction has a different MEP. First the O atom moves to the bridge site, parallel with the NH2 on bridge. Then the transition state is reached, with the H atom situated between the N and O atoms. This transition state occurs later than in the



Figure 1. Ammonia oxidation on p(2 × 2)-Rh(111) surface (top view). For the transition states, the eigenvectors of the imaginary frequencies are shown. For the clarity of the atoms’ trajectories during a reaction, the atoms at the borders of the periodic unit cell may appear repetitively in the figures.

Figure 2. NH2 oxidation on p(2 × 2)-Rh(111) surface (top view). For the transition states, the eigenvectors of the imaginary frequencies are shown. For the clarity of the atoms’ trajectories during a reaction, the atoms at the borders of the periodic unit cell may appear repetitively in the figures.

previous cases. However, the transition state structures are similar, with NH2 and O aligned, cutting on diagonal a p (1 × 1) unit cell. Finally, the NH group moves toward a hcp hollow site and OH moves via the bridge toward a top site. The first displacement of the O atom to the bridge site decreases the activation barrier of this reaction in comparison with the previous cases. The (NH + OH) structures have repulsive lateral interactions. Therefore, at the desorption or diffusion of the OH fragment, the energy of the system will decrease. After that, we can consider the coadsorption of NH with a new O atom, when the energy increases again, due to the high repulsive lateral interactions. 3. NH Oxidation by O. Taking into account the most stable configurations for NH + O and N + OH systems, we found three transition states for these elementary processes (see Figure

3). They lead to an N atom adsorbed in the same hollow site as in the initial state and OH adsorbed in the bridge or top site. All of the transition states occur when the N-H bond breaks and a new O-H bond forms. The behavior of the H atom is essential for determining a certain MEP. The first case studied starts from NH and O in fcc hollow sites. The result is coadsorbed N in fcc with OH on the bridge site. The H atom is transferred from NH to the O half way over a bridge position. This process has a rather high activation barrier. If the reaction starts with NH in hcp and O in fcc hollow sites, the H atom is transferred at the transition state over a top site. This trajectory is highly unfavorable comparative with the previous case because the transfer of the H atom over the top requires more energy than over the bridge, and the initial state (honeycomb structure) is more stable than in the previous case


Popa et al.

Figure 3. NH oxidation on p(2 × 2)-Rh(111) surface (top view). For the transition states, the eigenvectors of the imaginary frequencies are shown.

Figure 4. NH3 oxidation by OH on p(2 × 2)-Rh(111) surface (top view). For the transition states, the eigenvector of the imaginary frequency is shown. For the clarity of the atoms’ trajectories during a reaction, the atoms at the borders of the periodic unit cell may appear repetitively in the figures.

(row structure). The difference between the adsorption energies of the H on top and on bridge is 0.33 eV and is the same as the difference in adsorption energy of the hydrogen atom. Starting with NH and O in hcp sites, the transfer of the H atom takes place over a bridge site. This reaction is comparable with the first discussed case in terms of the MEP and required activation barrier. After the transition state occurs, the N atom remains in its hcp adsorption site and the OH fragment ends on the top position. The possible N + OH structures that resulted in these elementary steps contain repulsive lateral interactions, and after the desorption or diffusion of the OH fragment, the system is more stable energetically. D. Reaction Pathways for NHx Oxidation by OH. 1. NH3 Oxidation by OH. NH3 and OH on the top positions can react together, leading to NH2 on the bridge and H2O on the top (see Figure 4). We also considered for the initial configuration NH3 on top coadsorbed with OH on the bridge position. This structure has a similar energy, but along the MEP, the first process is the diffusion of the OH fragment from the bridge to top positions. After diffusion, the reaction takes place identically with the previous considered case. First the breaking of a N-H bond occurs, and at the same time, the water molecule is formed. Then the transition state occurs, with small adjustments of the new adsorbates, i.e., NH2 to bridge and H2O to top. The eigenvector of the imaginary

frequency of the transition state is dominated by the H2O molecule. NH2 is already at its preffered site. After this point along the MEP, the two products will show small displacements and rotation until the minimum energy is reached. This reaction has a similar evolution as the NH3 oxidation by O atom, but the activation barrier is much lower due to the contribution of the hydrogen bonds in the initial configuration. The hydrogen bonds are present also in the final state, but their contribution at the total energy of the system is small. Thus, the energy of the adsorbed NH2 will increase only a little after the diffusion or desorption of the water molecule. 2. NH2 Oxidation by OH. For the reaction NH2 on the bridge coadsorbed with OH on the top position, we took into account two possibilities, depending on the final state, i.e., NH in fcc or hcp hollow site and H2O on the top position. The MEPs of these possible reactions are similar. NH2 and OH will tilt toward each other until the H atom is situated in between them, above a hollow site. The N-H bond breaks, and the remaining NH fragment moves then toward a neighboring hollow site. The water molecule is formed on the same top position as the initial OH. The activation barriers are lower than for the previously studied cases for NH2 dehydrogenation and oxidation due to the attractive hydrogen bonds between coadsorbated fragments. 3. NH Oxidation by OH. For the NH oxidation with OH, we considered as initial situations NH in a hollow site and OH on



Figure 5. NH2 oxidation by OH on p(2 × 2)-Rh(111) surface (top view). For the transition states, the eigenvectors of the imaginary frequencies are shown. For the clarity of the atoms’ trajectories during a reaction, the atoms at the borders of the periodic unit cell may appear repetitively in the figures.

Figure 6. NH oxidation by OH on p(2 × 2)-Rh(111) surface (top view). For the transition states, the eigenvectors of the imaginary frequencies are shown. For the clarity of the atoms’ trajectories during a reaction, the atoms at the borders of the periodic unit cell may appear repetitively in the figures.

the top or bridge site. After reaction, the N atom is in the same position as the initial NH fragment and H2O is on the top position (see Figure 6). The reactants do not contain anymore significant lateral interactions, except the NH fcc + OH bridge structure, which contains strong repulsive interactions between coadsorbated species. This repulsion will cause the OH fragment to move from the bridge to the top position, with a very small energy barrier. Further on, the reactions take place in the usual manner: NH and OH tilt toward each other until the H atom will be in between N and O atoms. The transition state is reached when the H atom is above a bridge position. In the final state, the coadsorbed N and H2O have attractive interactions, due to the new hydrogen bonds. Without considering the local minimum (i.e., NH fcc+ OH top), the activation barrier for the second reaction is much lower. The actual barrier for the OH displacement from bridge to top has to be taken into account as well, but even then the total activation barrier is still small and similar with the other discussed cases.

E. N Recombination. Nitrogen recombination on the Rh(111) surface is the last step in the process of NH3 decomposition (see Figure 7). We considered in the initial state two nitrogen atoms, one adsorbed in fcc and one in the hcp position, sharing one Rh atom. This honeycomb structure is very stable, although there are strong repulsive lateral interactions (-8.87 eV). However, the MEP does not lead to the molecular nitrogen. First the N atom adsorbed in fcc hops to the hcp position, crossing a bridge position. The diffusion barrier is significant. The N hcp + N hcp new minimum is even more stable than the initial arrangement, i.e., N fcc + N hcp (-9.07 eV). From this structure, the reaction occurs at once. At the transition state, one N atom is still in the hcp position and the other one is on a bridge site. Then the N2 molecule is formed above the fcc site and moves parallel with the bridge and finally on the top position. The activation barrier with respect to the pretransition state is high, 1.51 eV (including the ZPE correction) but comparable with the previous findings for N2 recombination on other metallic surfaces with steps.9,18-21 The opposite


Popa et al.

Figure 7. N recombination on p(2 × 2)-Rh(111) surface (top view). For the transition states, the eigenvectors of the imaginary frequencies are shown.

TABLE 3: N-H Distances (Å) for Reactants dN-H(R) (the Second Column) and Transition States dN-H(TS) (the Third Column); O-H Distances (Å) for Transition States dO-H(TS) (the Fourth Column) and Products dO-H(P) (the Fifth Column)a reaction

dN-H(R)

dN-H(TS)

δdN-H(%)

dO-H(P)

dO-H(TS)

δdO-H(%)

NH3 top + O fcc f NH2 bridge + OH top NH3 top + O hcp f NH2 bridge + OH top NH2 bridge + O fcc f NH fcc + OH bridge NH2 bridge + O fcc f NH hcp + OH top NH2 bridge + O hcp f NH hcp + OH top NH fcc + O fcc f N fcc + OH bridge NH hcp + O fcc f N hcp + OH bridge NH hcp + O hcp f N hcp + OH top NH3 top + OH top f NH2 bridge + H2O top NH2 bridge + OH top f NHfcc + H2O top NH2 bridge + OH top f NH hcp + H2O top NH fcc + OH top f N fcc + H2O top NH fcc + OH bridge f N fcc + H2O top NH hcp + OH top f N hcp + H2O top

1.024 1.016 1.024 1.023 1.018 1.026 1.027 1.026 1.033 1.050 1.031 1.022 1.039 1.023

2.312 2.134 1.365 1.342 1.341 1.267 1.360 1.209 2.653 1.343 1.352 1.179 1.179 1.172

126 110 33 31 32 23 32 18 157 28 31 15 13 15

0.979 0.978 0.983 0.983 0.985 0.985 0.973 0.982 0.975 0.982 0.984 0.983 0.984 0.983

0.988 0.991 1.158 1.183 1.183 1.292 1.293 1.357 0.988 1.167 1.154 1.426 1.426 1.452

1 1 18 20 20 31 33 38 1 19 17 45 45 48

a The fourth and the seventh columns represent the percentages of the N-H and O-H stretching at the transition state (δd N-H(%), δdO-H(%)) with respect to the initial and final state, respectively. They indicate if the transition state is late (high δdN-H and low δdO-H) or early (low δdN-H and high δdO-H).

reaction of N2 dissociation has a huge barrier, 2.41 eV (including the ZPE correction), which means that N2 will desorb rather than dissociate on the Rh(111) surface. F. Classification of the Transition States. We can classify the transition states as early or late, depending on the resemblance with the reactants and the final products. In the reactions discussed above, there are actually several processes that occur simultaneously or consecutively, the N-H bond breaking, the O-H bond formation, and the diffusion of the fragments on the surface. The reaction profiles along the MEP reveal that the activation barriers are determined either by the N-H bond breaking or by the rearrangement of the new fragments. The diffusion processes have practically no barrier. To describe this resemblance of structures and how early or late the transition states are, we discuss here the variation of the N-H and O-H distances for the bonds that will break or form during a reaction. Table 3 gives as a comparison the lengths of the N-H bond that will break in the initial and the transition states for the NHx reactions with O and OH. We also give the length of the O-H bonds that will be form in the final state and the transition states. For the transition states of the NH3 oxidation with O or OH, the N-H distance in the transition state is more than double the initial distance, and the O-H bond is only 1% elongated in comparison with the final state. At the transition states, the N-H bonds are practically broken and the O-H bonds are formed. We can say this oxidation reaction is rather late from a geometrical point of view. All of the following oxidation reactions can be considered from a geometrical point of view to occur early to halfway. The N-H distances increase by 13-33% with respect to the initial values. and the O-H distances are stretched with 1748% with respect to the final values. The transition states occur earlier as more H atoms are removed from NHx. This evolution of the system is identical with the elementary steps for ammonia

dehydrogenation, where the first step of NH3 dehydrogenation is late and all of the following steps are early to medium.1 The N-N initial distance in the N recombination process is 1.879 Å. At the transition state, the distance decreases to 1.810 Å, and in the N2 molecule, it is 1.133 Å. With respect to the final state (i.e., the N2 molecule), the N-N distance is only 4% larger at the transition state. It follows that geometrically this elementary step is late. G. Kinetics and Thermodynamics. The potential energy profile for all of the processes discussed for the NHx dehydrogenation1 and activation with O or OH over p(2 × 2)-Rh(111) surface is presented in Figure 8. Each elementary step of the NHx dissociation is slightly endothermic (the black profile), with overall reaction energies between 0.05 and 0.35 eV, prior to diffusion of hydrogen away from the N containing species. The activation barriers are high (0.84-1.1 eV). The same holds for the reverse reactions (0.73-1.06 eV). The nitrogen recombination has a high activation barrier, but the reaction is exothermic, with an overall reaction energy of -0.92 eV measured with respect to the coadsorbed state. Thus, nitrogen recombination is the overall determining step of ammonia decomposition. By adding oxygen to the system (the red profile), most of the elementary steps of NHx oxidation become more endothermic (and the reverse reactions more exothermic). We note that for the NH2 oxidation the transition states have the same energy, independent of the initial structures: the MEPs cross. The activation barriers remain high and are comparable to the ones for NHx dehydrogenation reactions. However, most of the opposite reactions (i.e., NHx-1 + OH f NHx + O) have activation barriers with values half that of recombinations reactions. This decrease might be due to the strong hydrogen bonds between the coadsorbated species. By adding oxygen to the system, the ammonia decomposition is enhanced. The reactions of NHx with OH (the blue profile) occur much easier. Their activation barriers are significantly lower (0.27-



Figure 8. Potential energy profile for the NHx dehydrogenation and activation with O or OH over the p(2 × 2)-Rh(111) surface. The energies (in eV) include ZPE corrections. The reference is given with respect to NH3 in gas phase, Rh slab, 3 O fcc/Rh, 3 OH bridge/Rh, and N hcp/Rh. Each step can be followed by the H atom diffusion far on the surface.

TABLE 4: Thermodynamic and Kinetic Parameters for NHx + O and Reverse Reactions on the p(2 × 2)-Rh(111) Surface(T ) 300 K)a

1a. 1b. 2a. 2b. 3a. 3b. 4a. 4b. 5a. 5b. 6a. 6b. 7a. 7b. 8a. 8b.

reaction/Rh(111)2 × 2

∆E (eV)

Ebar (eV)

ZPE (eV)

Eact,0 (eV)

Eact (eV)

∆S#0 (J/(mol K)

ν* (10+13 s-1)

NH3 top + O fcc f NH2 bridge + OH top NH2 bridge + OH top f NH3 top + O fcc NH3 top + O hcp f NH2 bridge + OH top NH2 bridge + OH top f NH3 top + O hcp NH2 bridge + O fcc f NH fcc + OH bridge NH fcc + OH bridge f NH2 bridge + O fcc NH2 bridge + O fcc f NH hcp + OH top NH hcp + OH top f NH2 bridge + O fcc NH2 bridge + O hcp f NH hcp + OH top NH hcp + OH top f NH2 bridge + O hcp NH fcc + O fcc f N fcc + OH bridge N fcc + OH bridge f NH fcc + O fcc NH hcp + O fcc f N hcp + OH bridge N hcp + OH bridge f NH hcp + O fcc NHhcp + O hcp f N hcp + OH top N hcp + OH top f NHhcp + O hcp

0.67 -0.67 0.52 -0.52 0.22 -0.22 0.12 -0.12 -0.06 0.06 0.41 -0.41 0.51 -0.51 0.08 -0.08

1.17 0.50 1.02 0.50 0.94 0.71 0.91 0.79 0.74 0.79 1.10 0.69 1.59 1.08 1.03 0.95

0.06 0.02 0.06 0.03 0.19 0.15 0.17 0.09 0.18 0.11 0.16 0.13 0.17 0.14 0.15 0.10

1.11 0.48 0.96 0.47 0.75 0.56 0.74 0.70 0.56 0.68 0.93 0.55 1.42 0.94 0.88 0.85

1.11 0.49 0.96 0.49 0.77 0.58 0.76 0.70 0.56 0.67 0.96 0.56 1.45 0.95 0.90 0.84

-19.87 -5.72 -19.10 -3.27 2.71 -0.80 -0.12 -24.22 -10.60 -28.94 2.88 -9.74 2.47 -9.91 2.18 -22.27

1.56 10-1 8.54 10-1 0.17 1.15 2.35 1.54 1.67 9.23 10-2 4.75 10-1 5.23 10-2 2.40 5.27 10-1 2.29 5.82 10-1 2.21 0.17

a ∆E is the heat of reaction (EP - ER), Ebar is the barrier height without zero-point contribution (ETS - ER), ZPE is the zero-point energy contribution, Eact,0 is the activation energy from eq 4, Eact is the activation energy from fitting the rate constants to an Arrhenius form (eq 2), ∆S#0 is the activation entropy, and ν* is the pre-exponential factor.

0.36 eV for the direct reactions and 0.44-0.72 eV for the reverse reactions). In the case of NH oxidation with OH, the transition state energies for all three possible reactions are practically the same. Except for the first oxidation step, all of the elementary steps are exothermic. By adding OH to the system, the oxidation becomes easier.

The kinetic and thermodynamic parameters for NHx + O and reverse reactions discussed above are summarized in Table 4. The stability of the (NHx + O) coadsorbed systems on the Rh surface increases when x decreases. Going from NHx + O to NHx-1 + OH, the difference in energy is rather small (see Figure 8). As a consequence, the oxidation reactions are endothermic


Popa et al.

TABLE 5: Thermodynamic and Kinetic Parameters for NHx + OH and Reverse Reactions on the p(2 × 2)-Rh(111) Surface (T ) 300 K)a

1a. 1b. 2a. 2b. 3a. 3b. 4a. 4b. 5a. 5b. 6a. 6b.

reaction/Rh(111)2 × 2

∆E (eV)

Ebar (eV)

ZPE (eV)

Eact,0 (eV)

Eact (eV)

∆S#0 (J/(mol K)

ν* (10+13 s-1)

NH3 top + OH top f NH2 bridge + H2O top NH2 bridge + H2O top f NH3 top + OH top NH2 bridge + OH top f NHfcc + H2O top NHfcc + H2O top f NH2 bridge + OH top NH2 bridge + OH top f NH hcp + H2O top NH hcp + H2O top f NH2 bridge + OH top NH fcc + OH top f N fcc + H2O top N fcc + H2O top f NH fcc + OH top NH fcc + OH bridge(top) f N fcc + H2O top N fcc + H2O top f NH fcc + OH bridge(top) NH hcp + OH top f N hcp + H2O top N hcp + H2O top f NH hcp + OH top

0.18 -0.18 -0.16 0.16 -0.18 0.18 -0.29 0.29 -0.29 0.29 -0.40 0.40

0.28 0.10 0.28 0.44 0.27 0.45 0.36 0.66 0.36 0.66 0.32 0.72

0.04 0 0.13 0.10 0.13 0.10 0.09 0.12 0.10 0.13 0.09 0.11

0.24 0.10 0.15 0.34 0.14 0.36 0.27 0.53 0.27 0.53 0.23 0.60

0.24 0.09 0.16 0.34 0.15 0.35 0.29 0.55 0.27 0.53 0.23 0.59

-18.08 -28.84 -7.61 -22.72 -12.07 -25.92 -0.15 -4.96 -17.79 -10.40 -22.06 -30.82

1.93 10-1 5.29 10-2 6.80 10-1 1.11 10-1 3.98 10-1 7.52 10-2 1.67 9.36 10-1 2.00 10-1 1.46 10-1 1.20 10-1 4.17 10-2

∆E is the heat of reaction (EP - ER), Ebar is the barrier height without zero-point contribution (ETS - ER), ZPE is the zero-point energy contribution, Eact,0 is the activation energy from eq 4, Eact is the activation energy from fitting the rate constants to an Arrhenius form (eq 2), ∆S#0 is the activation entropy, and ν* is the pre-exponential factor. a

TABLE 6: Thermodynamic and Kinetic Parameters for N Recombination and Reverse Reaction on the p(2 × 2)-Rh(111) Surface (T ) 300 K)a reaction/Rh(111)2 × 2

∆E (eV)

Ebar (eV)

ZPE (eV)

Eact,0 (eV)

Eact (eV)

∆S#0 (J/(mol K)

ν* (10+13 s-1)

N hcp + N hcp f N hcp + N fcc (hopping) N hcp + N fcc f N hcp + N hcp N hcp + N fcc f N2 top N2 top f N hcp + N fcc

-0.19 0.19 -0.92 0.92

0.71 0.90 1.57 2.48

0.03 0.02 0.06 0.07

0.68 0.88 1.51 2.41

0.70 0.90 1.53 2.41

-3.23 -4.88 8.06 -30.79

1.15 9.45 10-1 4.48 4.19 10-2

∆E is the heat of reaction (EP - ER), Ebar is the barrier height without zero-point contribution (ETS - ER), ZPE is the zero-point energy contribution, Eact,0 is the activation energy from eq 4, Eact is the activation energy from fitting the rate constants to an Arrhenius form (eq 2), ∆S#0 is the activation entropy, and ν* is the pre-exponential factor. a

or even slightly exothermic, with overall reaction energies between -0.06 and 0.67 eV, prior to diffusion of OH away from the N containing species. The barrier heights are large; the ammonia oxidation reaction has the highest barrier. The subsequent reactions of NH2 oxidation have in general slightly lower barriers. They are also smaller than those of the NH2 dehydrogenation reactions (0.84-0.95 eV). The last step of NH oxidation has high barriers, comparable with the barrier of NH dehydrogenation reaction (0.99 eV). If the transferred H atom follows at the transition state the route over the top, then the barrier is exceptionally high, 1.42 eV (see Figure 3). The ZPE corrections are substantial for all the initial and final states of the reactions (0.17-0.76 eV), but the ZPE corrections for the activation barriers have small values. As we showed in the frequency analysis, the contribution to the partition functions of low-frequency modes is important for entropic contributions. For low activation entropies, the pre-exponential factors are in the order of 10+13 s-1. We have negative activation entropies and the pre-exponential factors decrease to about 10+12 s-1. For the reactions, this means that the transition states are rather tight comparative with the initial configurations. The reverse reactions NHx-1 + OH f NHx + O are exothermic. They have low activation energies; approximately half of the activation energies corresponding to NHx-1 hydrogenation reactions. The activation entropies are negative, and therefore, the pre-exponential factors are decreasing by an order or two of magnitude from the classical value of 10+13 s-1. The rate-limiting step of ammonia oxidation is the first reaction, NH3 + O f NH2 + OH. All of the other oxidation reactions with O (excluding the unfavorable path for NH oxidation) have similar reaction rates. In total the NH3 dissociation in the presence of atomic oxygen is endothermic (the red profile in Figure 8). The NH3 dissociation alone is slightly exothermic, around -1 eV (the black profile in Figure 8).

Also the values for the activation energies obtained from Arrhenius eq 2 are listed in Table 4. We calculated the activation energies from a linear regression of ln(k) as a function on 1/T plots for temperatures between 100 and 1000 K. In this range, all of the reactions rates follow the linear dependence from the Arrhenius equation. The obtained values for activation energies are very close to the values of the ZPE corrected activation energies of eq 4 with a maximum of 0.03 eV. The kinetic and thermodynamic parameters for the NHx + OH and reverse reactions are summarized in Table 5. The stability of the NHx + OH coadsorbed systems on the Rh surface increases when x decreases. The difference in energy between NHx + OH and NHx-1 + H2O is rather small (see Figure 8). The reactions with OH are exothermic or slightly endothermic, with overall reaction energies between -0.40 and 0.18 eV, prior to diffusion of H2O away from the N containing species. The reactions of NH3 and NH2 with OH have the lowest activation barriers, due to the strong hydrogen bridges. The reactions of NH with OH have only slightly higher barriers, where the lateral interactions in the initial configurations are repulsive. The ZPE corrections for the activation barriers have small values, but they are important for the initial and final states of the reactions (0.18-1.34 eV). Therefore, the activation energies Eact,0 decrease, especially for the second and the third elementary step. However, the values of the activation energies are very little, and we cannot point out a limiting step. The values for the activation energies obtained from the Arrhenius eq 2 are very close to the values of the ZPE corrected activation energies of eq 4, with differences of 0.01-0.02 eV. The entropies of the reactants, products, and transition states are large, because of the contribution of low-frequency modes. They lead to negative activation entropies for the oxidation reactions, which means that the transition states are tight with respect to the initial configurations. The negative entropies

NHx Oxidation and Reverse Reactions on Rh(111) decrease the values of the pre-exponential factors to 10+12 s-1. Only one elementary step remains at the value of 10+13 s-1, the NH fcc + OH top reaction. The reverse reactions NHx-1 + H2O f NHx + OH are endothermic, except the first elementary step. The activation energies are higher than for the direct reactions. The activation entropies are negative, and the pre-exponential factors are lower. The kinetic and thermodynamic parameters for the nitrogen hopping and recombination and reverse reactions are summarized in Table 6. The first process of hopping of one nitrogen atom from the honeycomb structure to the zigzag structure is slightly exothermic (-0.19 eV), but the activation barrier is significant, 0.68 eV. The reverse process has a higher barrier (0.88 eV) and a smaller pre-exponential factor due to the decrease of the activation entropy. The real reaction of nitrogen recombination is exothermic (-0.92 eV) and the activation barrier is high, 1.51 eV. Nevertheless this value is surprisingly lower than the value predicted in literature for the reaction on Rh(111) or similar surfaces. It is comparable with values reported for stepped surfaces.17-20 The reverse reaction of nitrogen decomposition is exothermic and has a very large barrier, 2.41 eV. Due to the significant decrease of the entropy, this reaction has also a low pre-exponential factor and consequently a tight transition state. IV. Conclusions We have presented DFT results for the elementary steps of ammonia oxidation with O and OH and their respective reverse reactions on Rh(111). The calculations lead to a consistent image of the stability of N-, O- and H-containing fragments. The most stable species on the surface are NH, N, and O. Some species have more than one stable adsorption site; that is, they can be moved on the metallic surface. Therefore, they can lead to complicated reactions. The coadsorbed fragments in the p(2 × 2) unit cells have significant lateral interactions. We have described the normal vibrational modes for O, OH, and H2O species and for their coadsorption with NHx species. The frequency analysis showed a rather corrugated potential energy surface for the discussed species, providing a new insight in the MEPs. The nudged elastic band method was used to determine the transition states for the elementary reactions. Due to similar coadsorption energies for some NHx + O and OH systems, there are several possible MEPs. Using the vibrational analysis, we were able to determine the partition functions and the related thermodynamic and kinetic properties of the ammonia decomposition and reverse reactions. The reactions of NHx with O are endothermic, with reaction energies between 0.08 and 0.67 eV. The calculated activation barriers are quite high (0.56-1.11 eV). The first reaction, NH3 oxidation, is the rate-limiting step with an activation energy of 1.11 eV. The activation entropies are in general negative. For the reverse reactions, the pre-exponential factors are only 10+11 s-1. The presence of oxygen in the system does not have a significant influence over the activation barriers; atomic oxygen does not promote the ammonia decomposition. The oxidation reactions of NHx with OH are exothermic, with reaction energies between -0.40 and -0.16 eV, except the first step, which is slightly endothermic. The activation barriers are significantly smaller (0.14-0.27) than the barriers corresponding to ammonia dehydrogenation or oxidation with O. The activation entropies are negative and rather large, and they decrease the pre-exponential factors to 10+11 s-1. The presence of the OH

J. Phys. Chem. C, Vol. 111, No. 27, 2007 9849 group has a big impact on the thermodynamics and kinetics of ammonia decomposition. OH promotes the ammonia decomposition. The first step of ammonia oxidation with O or OH can be regarded as late with respect to the N-H and O-H bonds variation along the MEPs. All of the following elementary steps occur early to medium from geometrical perspective. Nitrogen recombination on the Rh(111) surface is an endothermic process (-0.92 eV) with a high activation barrier (1.51 eV). This elementary step is the overall determining step of ammonia decomposition. The reverse process, i.e., N2 dissociation, has an extremely high barrier (2.41 eV). The loss in entropy strongly influences the pre-exponential factor. Therefore, the nitrogen molecule will rather desorb than decompose on Rh(111) surface. Acknowledgment. This research was financially supported by the Foundation for Fundamental Research on Matter (FOM), The Netherlands, and the Dutch National Computing Facilities Foundation, SARA. C.P. thanks Joost de Greef for the visualization program and Dr. P. Vassilev and W. K. Offermans (from Eindhoven University of Technology) for the fruitful and nice discussions. Appendix: Coadsorption Energies, Lateral Interactions, and Frequency Calculations for NHx + O, NHx + OH, and NHx +H2O Systems The coadsorption energies for the combinations NHx + O, NHx + OH, Nx + H2O, and N + N are given in Tables 7-10. In the third column of each table, we list the sum of the separated adsorption energies, and in the last column are given the differences between sum of the separated adsorption energies and coadsorption energies. These differences between the two columns actually represent the lateral interactions. At 0.25 ML coverage, the lateral interactions contribute substantially to the activation barriers. For the NH3 + O fcc systems, we calculated two structures, where the N and O atoms are situated at different distances, sharing or not Rh atoms and the lateral interactions are repulsive or attractive. The calculated frequencies for NH3 on top coadsorbed with O in fcc or hcp hollow site are listed in Table 11. The characteristic frequencies of the ammonia molecule do not couple with those of the atomic oxygen. The frequency values are very similar for the two presented cases (coadsorbed O in fcc or hcp hollow site). Ammonia has the same vibration modes as when it is adsorbed alone on the surface, but the highfrequency modes (symmetric and asymmetric stretching) have slightly lower values and the low-frequency modes have higher values. There is a blue shift of the umbrella mode by 80-90 cm-1. The wagging libration modes are blue-shifted by almost 100 cm-1. The frustrated rotation of NH3 around the z axis has a higher frequency; from 53 cm-1, the value increases to 214 and 224 cm-1 respectively. The frustrated translations perpendicular on the surface for the oxygen atom (νRh-O) have lower values with 43-72 cm-1 and those parallel with the surface are lower by 49-74 cm-1. The frequency modes of NH2 bridge coadsorbed with O fcc or hcp have similar values and show the same behavior as NH3 (see Table 11). The high modes slightly increase their values (νas, νs, and δas) by only few cm-1. The libration and translation modes increase their values by 7-97 cm-1. The νRh-O and the frustrated translations parallel with the surface of the atomic oxygen are red-shifted.


Popa et al.

TABLE 7: Coadsorption Energies of (NHx + O) Fragments on p(2 × 2)-Rh(111) Surface, the Sum of Separate Adsorption Energies (eV Molecule-1), the Difference between Coadsorption Energies, and Separate Adsorption Energies and the Distances between the N Atom and the Coadsorbed O Atoma system NH3 top + O fcc NH3 top + O hcp NH2 bridge + O fcc NH2 bridge + O hcp NH fcc + O fcc NH fcc + O hcp NH hcp + O fcc NH hcp + O hcp a

dN-O (Å)

Ecoads (NHx + O)

Eads (NHx) + Eads (O)

[Ecoads (NHx + O) (Eads (NHx) + Eads (O)]

2.703 3.245 3.246 3.249 2.942 2.634 2.990 2.723 3.145 3.145 2.724

-5.24 -5.92 (-5.73) -5.76 (-5.48) -5.92 -7.31 (-7.02) -7.14 (-6.85) -7.09 -8.76 (-8.28) -8.71 (-8.42) -8.80 (-8.51) -8.61 (-8.33)

-5.62 -5.62 -5.51 -5.51 -7.62 -7.52 -7.52 -9.82 -9.72 -9.94 -9.84

0.38 -0.30 -0.25 -0.41 0.31 0.38 0.43 1.06 1.01 1.23 1.23

The ZPE corrected coadsorption energies are given in parenthesis.

TABLE 8: Coadsorption Energies of (NHx + OH) Fragments on the p(2 × 2)-Rh(111) Surface, the Sum of Separate Adsorption Energies (eV Molecule-1), and the Distances between the N Atom and the Coadsorbed O (from OH) Atoma system

dN-O (Å)

Ecoads (NHx + OH)

Eads (NHx) + Eads (OH)

[Ecoads (NHx + OH) (Eads (NHx) + Eads (OH)]

NH3 top + OH top NH3 top + OH bridge NH2 bridge + OH top

4.460 2.710 2.666 2.660 3.191 2.983 2.755 2.755 2.591 3.212 3.212 2.751 3.239 2.685 3.272 2.977

-3.79 (-3.56) -3.66 (-3.43) -5.58 (-5.25) -5.53 (-5.21) -6.90 (-6.60) -6.77 (-6.43) -6.81 (-6.05) -6.81 (-6.48) -6.72 (-6.39) -6.87 (-6.58) -6.87 (-6.57) -6.66 -7.41 (-7.19) -7.41 (-7.17) -7.58 (-7.37) -7.34 (-7.11)

-3.29 -3.60 -5.29 -5.29 -6.90 -7.21 -6.90 -7.21 -7.21 -6.90 -6.90 -7.21 -7.49 -7.80 -7.61 -7.92

-0.50 -0.06 -0.29 -0.24 0 0.44 0.09 0.40 0.49 0.03 0.03 0.55 0.08 0.39 0.03 0.58

NH fcc + OH top NH fcc + OH bridge

NH hcp + OH top NH hcp + OH bridge N fcc + OH top N fcc + OH bridge N hcp + OH top N hcp + OH bridge a


TABLE 9: Coadsorption Energies of (NHx + H2O) Fragments on p(2 × 2)-Rh(111) Surface, the Sum of Separate Adsorption Energies (eV Molecule-1), and the Distances between the N Atom and the Coadsorbed O (from H2O) Atoma system

dN-O (Å)

Ecoads (NHx + H2O)

Eads (NHx) + Eads (H2O)

[Ecoads (NHx + H2O) (Eads (NHx) + Eads (H2O)]

NH2 bridge + H2O top NH fcc + H2O top NH hcp + H2O top N fcc + H2O top

3.105 3.234 3.244 3.221 3.074 3.267

-3.29 (-1.95) -4.77 (-4.35) -4.75 (-4.33) -5.59 (-5.25) -5.26 (-4.95) -5.67 (-5.34)

-3.08 -4.69 -4.68 -5.28 -5.28 -5.40

-0.21 -0.08 -0.07 -0.31 0.02 -0.27

N hcp + H2O top a


TABLE 10: Coadsorption Energies of (N + N) Systems on the p(2 × 2)-Rh(111) Surface, the Sum of Separate Adsorption Energies (eV Molecule-1), the Difference between Coadsorption Energies, and Separate Adsorption Energies and the Distances between the N Atomsa system

dN-N (Å)

Ecoads (N + N)

N hcp + N fcc 3.142 -9.06 (-8.87) N hcp + N hcp 2.721 -9.26 (-9.07) a

Eads,1 (N) + Eads,2 (N)

[Ecoads (N + N) (Eads,1 (N) + Eads,2 (N)]

-10.02 -10.14

0.96 0.88


The frequencies for the coadsorbed NH and O in hollow sites (Table 12) have similar values for different combinations of the hollow sites fcc and hcp. The asymmetric stretch νas of the N-H bond is almost unchanged in comparison with NH alone in the unit cell. The twisting libration modes Lt of the NH

fragment have higher frequencies than NH adsorbed alone (685 cm-1). We note the same tendency for the frustrated translations T| and T⊥ for the NH group (originally 426-459 and 562-576 cm-1, respectively). Instead the frequencies of the T⊥ vibration modes of the O atom slightly decrease and T| of the O increase. The vibration modes of NH3 top + OH top or bridge coadsorbed systems are presented in Table 13. The highfrequency modes have in general lower values by approximately 50 cm-1 than the frequencies of ammonia adsorbed alone on the surface. The low-frequency modes increase significantly, sometimes spectacular by 170 cm-1. Many vibration modes contain actually contribution from both fragments, NH3 and OH. This is probably due to the hydrogen bridges. The vibration modes of coadsorbed NH2 with tilted OH on top or bridge positions (Table 14) have similar tendencies to the previous cases. The high-frequency modes of NH2 (νas, δs) have lower values than those corresponding to isolated adsorbate



TABLE 11: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (NH3 + O) and (NH2 + O) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

NH3 top + O fcc

NH3 top + O hcp

νas νs δas δs Lw Lt Lr T⊥ T| R (NH3) T⊥ (O) T| (O)

3508, 3505 3367 1575, 1574 1093

3511, 3508 3369 1575, 1574 1071

654, 653 379 99, 84 224 450 307, 287

640, 639 369 96, 84 214 444 298, 273

NH2 bridge + O fcc

NH2 bridge + O hcp

3502 3386

3512 3394

1469 747 733 697 503 337, 242

1465 743 730 697 494 335, 245

469 439, 359

468 419, 367

TABLE 12: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (NH + O) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

NH hcp + O hcp

NH hcp + O fcc

NH fcc + O hcp

NH fcc + O fcc

νas (NH) Lt (NH) T⊥ (NH) T| (NH) T⊥ (O) T| (O)

3435 773, 742 596 516, 466 501 436, 360

3411 806, 804 641 526, 464 464 359, 359

3413 802, 802 643 518, 461 461 391, 360

3435 757, 736 599 502, 465 496 434, 382

TABLE 13: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (NH3 + OH) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

NH3 top + OH top

NH3 top + OH bridge

νas (NH3) δas (NH3) δs (NH3) Lr (NH3) T| (NH3) T⊥ (NH3) R (NH3) νas (OH) Lr (OH) T⊥ (OH) T| (OH)

3468, 3250, 3154 1636, 1502 1136 846, 692 168, 65 425 220 3676 724, 585 391 365, 119

3534, 3475, 3233 1575, 1573 1128 720, 524 77, 66 368 220 3544 716, 595 317 265, 192

TABLE 14: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (NH2 + OH) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

NH2 bridge + OH top

NH2 bridge + H top(2)

NH2 + OH bridge

νas (NH2) δs (NH2) Lw (NH2) Lr (NH2) T⊥ (NH2) T| (NH2) νas (OH) Lw (OH) Lt (OH) T⊥ (OH) T| (OH)

3437, 3091 1464 893 789, 709 512 343, 321 3716 782 255 463 193, 154

3436, 3077 1453 897 792, 710 517 326, 303 3707 789 340 459 132, 130

3437, 3077 1453 899 791, 705 501 350, 326 3708 781 298 455 170, 165

fragments. The differences are substantial, 70-300 cm-1. However, the O-H stretching frequencies increase by 20-39 cm-1. All of the low-frequency modes increase their values, sometimes with hundreds of cm-1. The hydrogen bonds are very active in the low range of the spectrum. Some frequencies belong equally to two vibration modes, due to the hydrogen bonds.

TABLE 15: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (NH + OH) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

NH fcc + OH bridge

NH fcc + OH top

NH hcp + OH top

νas (NH) Lw (NH) T⊥ (NH) T| (NH) νas (OH) Lw (OH) T⊥ (OH) T| (OH)

3405 753, 633 553 483, 433 3463 724, 697 403 271, 179

3417 731, 664 556 457, 428 3687 821, 171 510 147, 140

3406 728, 664 572 462, 430 3685 812, 179 503 126, 75

TABLE 16: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (N + Oh) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

N fcc + OH top

N fcc + OH bridge

N hcp + OH top

N hcp + OH bridge

T⊥ (N) T| (N) νas (OH) Lw (OH) T⊥ (OH) T| (OH)

553 481, 478 3660 854, 242 537 150, 142

545 514, 453 3603 742, 674 426 206, 173

574 488, 483 3661 861, 201 556 160, 97

583 464, 458 3664 688, 650 415 274, 150

TABLE 17: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (NH2 + H2O) and (NH + H2O) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

NH2 bridge + H2O top

νas (NH2) δas (NH2) Lw (NH2)/NH T⊥ (NH2)/NH T| (NH2)/NH νas (OH) νs (OH) δas (H2O) Lw (H2O) T⊥ (H2O) T| (H2O)

3460, 3295 1513 693, 735, 829 498 208, 347 3795, 3425 1549 464, 285, 255 99 166, 72

NH fcc + H2O top

NH hcp + H2O top

3420

3410

717, 659 551 465, 411 3638 3551 1541 578, 439, 194 90 173, 166

727, 671 573 469, 406 3644 3556 1539 547, 426, 200 178 132, 88

At the coadsorption of NH with OH (Table 15), the high frequencies modes νas slightly decrease their values and the low ones increase significantly. It is still possible to distinguish between different adsorption sites if we analyze the high frequencies. OH adsorbed on the bridge has νas with 200 cm-1 lower than OH adsorbed on the top site. However, the difference between the frequencies given by NH adsorbed in fcc or hcp remains small, as for the individual adsorptions. Most of the low-frequency modes (librations, frustrated translations) have lower values, but there are also few with higher frequencies. It is remarkable that the wagging libration modes of NH and OH are strongly coupled, especially those with 697 and 633 cm-1. For the coadsorption of the N atom (fcc or hcp hollow site) with the OH group (on top or bridge site), we notice the same tendency of the frequencies as previously (Table 16). The highfrequency modes (stretchings) decrease, and the low-frequency modes (librations, frustrated translations) increase. For the same vibration mode, the difference can be important from one adsorption site to another. At the coadsorption of NH2 with water, the frequencies of the normal modes show large changes (Table 17). As for the coadsorption with O or OH, the high-frequency modes (stretchings) are lower by a few tens of cm-1. Starting with the deformation vibrations toward lower modes, the low-frequency modes generally increase their values. The free rotation of water becomes a libration wagging mode at 255 cm-1. Both N-H


Popa et al.

TABLE 18: Calculated Harmonic Frequencies (cm-1) of the Normal Modes for (N + H2O) Coadsorbed Systems on the p(2 × 2)-Rh(111) Surface vibration mode

N fcc + H2O top

νas (OH) νs (OH) δas (H2O) Lw (H2O) T⊥ (N) T| (N) T⊥ (H2O) T| (H2O)

3667 3569 1533 707, 610, 254 535 456, 412 235 164, 91

N fcc + H2O top (2) 3813, 3665 1565 482, 204, 178 549 449, 436 89 137, 42

N hcp + H2O top 3681 3580 1535 673, 590, 222 535 450, 431 248 95, 52

stretching frequencies become asymmetric due to the vicinity with OH, i.e., hydrogen bonds. At the coadsorption of NH in hollow sites with water on the top position (see Table 17), the frequencies show the same behavior as for the other discussed cases. The free rotation of water becomes a wagging mode around 200 cm-1. In the low range of the frequencies, we find some coupling with the surface. There is no coupling between the vibrational modes of NH and H2O because there are no hydrogen bonds have almost zero energy. Some coupling is found for the frequencies around 400 cm-1 (Lw (H2O) with T| (NH)). At the coadsorption of the N atom in a hollow site with H2O on top site, the normal-mode frequencies have the same behavior as in the previously discussed coadsorptions (Table 18). The high modes in general decrease their values, except in the second N fcc + H2O top structure, where one of the νas’s (OH) becomes higher with 150 cm-1 due to the close vicinity on the surface of H2O top with the N atom. Most of the low frequencies modes decrease their values and the free rotation of water becomes a libration mode (178-254 cm-1). References and Notes (1) Popa, C.; Offermans, W. K.; van Santen, R. A.; Jansen, A. P. J. Phys. ReV. B 2006, 74 (15), 155428-1-155428-10. (2) Busca, G.; Lietti, L.; Ramis, G.; Berti, F. Appl. Catal. B 1998, 18, 1-36. (3) van Hardeveld, R. M.; van Santen, R. A.; Niemantsverdriet, J. W. J. Vac. Sci. Technol. A 1997, 15, 1558-1562. (4) Stolbov, S.; Rahman, T. S. J. Chem. Phys. 2005, 123 (20), 2047161-204716-5. (5) Ganley, J. C.; Thomas, F. S.; Seebauer, E. G.; Masel, R. I. Catal. Lett. 2004, 96 (3-4), 117-122. (6) Leewis, C. M.; Kessels, W. M. M.; van de Sanden, M. C. M.; Niemantsverdriet, J. W. Appl. Surf. Sci. 2006, 253, 572-580. (7) Frechard, F.; van Santen, R. A.; Siokou, A.; Niemantsverdriet, J. W.; Hafner, J. J. Chem. Phys. 1999, 111 (17), 8124-8130. (8) Liu, Z.-P.; Hu, P.; Lee, M.-H. J. Chem. Phys. 2003, 119 (12), 62826289. (9) Logado´ttir, A.; Nørskov, J. K. J. Catal. 2003, 220, 273-279. (10) Zhang, C. J.; Lynch, M.; Hu, P. Surf. Sci. 2002, 496 (3), 221230. (11) Novell-Leruth, G.; Valcarcel, A.; Clotet, A.; Ricart, J.; PerezRamirez, J. J. Phys. Chem. B 2005, 109 (38), 18061-18069. (12) Offermans, W. K.; Jansen, A. P. J.; van Santen, R. A. Surf. Sci. 2006, 600, 1714-1734.

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