Computational Study of the Vibrational Structure of the Ammonia

Article pubs.acs.org/JPCC

Computational Study of the Vibrational Structure of the Ammonia Molecule Adsorbed on the fcc (111) Transition Metal Surfaces Elina Sal̈ li, Susanna Martiskainen, and Lauri Halonen* Laboratory of Physical Chemistry, Department of Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FI-00014 University of Helsinki, Finland S Supporting Information *

ABSTRACT: We have computationally studied adsorption and vibrational energy levels of the ammonia molecule adsorbed on the fcc (111) transition metal surfaces Ni(111), Cu(111), Rh(111), Pd(111), Ag(111), Ir(111), Pt(111), and Au(111). Vibrational Hamiltonians are obtained by combining an exact kinetic energy operator for the isolated ammonia molecule with plane-wave density functional theory (DFT) potential energy surfaces. The resulting eigenvalue problems are solved variationally. This procedure gives us the anharmonic vibrational energy levels of the adsorbed ammonia molecule. The local density of the states (LDOS) analysis reveals that ammonia adsorbs to all studied surfaces through its lone pair orbital. It makes the symmetric bending potential asymmetrical around the planar structure, quenches inversion splittings, and blue shifts the symmetric bend wavenumber, in agreement with experimental observations. In this work, it has been observed that the magnitude of this blue shift depends almost linearly on the adsorption energy. The asymmetric bend and the stretches red shift, which indicates loosening of the NH bonds upon adsorption.

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Ir surfaces.2−12 Interaction mechanism of ammonia with the metal surfaces has been studied experimentally with UPS on the Ir, Pt, and Ni (111) surfaces,6,11,12 with Penning spectroscopy on the Ni(111) surface,13 and with X-ray absorption2 on the Cu(110) surface. According to the experiments, the ammonia molecule adsorbs on the metal surface like an inverted umbrella with the C3 axis perpendicular to the metal surface. The lone pair electrons of the nitrogen atom bound the molecule to the surface. Most of the experimental papers suggest the atop adsorption site but the hollow adsorption site has been suggested on the Pt14 and Ir6 (111) surfaces. Vibrational energy levels of adsorbed ammonia have been measured with electron energy loss spectroscopy (EELS),1,9,12,16−30 infrared reflection absorption spectroscopy IRAS,14,31−33 and scanning tunnelling microscopy (STM).34 Upon adsorption, the wavenumber for the symmetric bend blue shifts whereas wavenumbers for asymmetric bend and for the stretches red shift. Relatively small shifts in the vibrational energy levels suggest that the internal structure of ammonia remains close to the gas phase geometry. The absence of asymmetric modes in some of these measurements confirms the upright adsorption geometry because the strict selection rules forbid these modes. In recent years, the adsorption geometry of the first layer ammonia has been studied extensively using plane-wave density functional

INTRODUCTION One principal objective of surface science is to understand the factors and periodic trends that influence the chemical reactivity of surfaces. In this paper, we investigate systematically how the different fcc (111) transition metal surfaces Ni(111), Cu(111), Rh(111), Pd(111), Ag(111), Ir(111), Pt(111), and Au(111) change the vibrational structure of chemisorbed ammonia molecule compared to the gas phase molecule using completely anharmonic vibrational calculations. The reactive transition metals Ni, Rh, Pd, Ir, and Pt catalyze industrially and economically important processes; decomposition of NH3 in fuel cells, production of HNO3 and HCN, and synthesis of ammonia from H2 and N2. The chemically inert Cu, Ag, and Au surfaces serve as comparison. Ammonia adsorbs molecularly on the fcc (111) transition metal surfaces. Thermal desorption spectroscopy experiments reveal the existence of three distinct molecular adsorption states: The first layer ammonia (α-ammonia) is directly chemisorbed to the surface. Molecules that are hydrogen bonded to the first layer molecules form the more weakly bound second layer (β-ammonia). The solid multilayer ammonia (γ-ammonia) desorbs at 115 K independent of the surface.1 The present study concentrates on the first layer ammonia molecules. It has been studied with X-ray and ultraviolet photoemission spectroscopies (XES and UPS), photoelectron diffraction, and electron stimulated desorption ion angular distributions (ESDIAD) techniques on the Ni, Ag, Cu, Pt, and © 2012 American Chemical Society

Received: April 24, 2012 Revised: June 5, 2012 Published: June 11, 2012 14960

dx.doi.org/10.1021/jp303955z | J. Phys. Chem. C 2012, 116, 14960−14969

The Journal of Physical Chemistry C

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theory methods on the Au(111),35−37 Rh(111),38−41 Ir(111),42 Cu(111),43 Ni(111),44,45 Pd(111),38,44 and Pt(111)38,46−49 surfaces. These calculations confirm the experimentally suggested adsorption geometry. Adsorption sites other than atop are repulsive or weakly bounding. Ammonia adsorbs upright with respect to the surface and it rotates almost freely along the surface normal. The harmonic energy levels of adsorbed ammonia have been calculated on the Pt, Ir, Pd, Rh, and Ni (111) surfaces.38,41,42,48−50 In this contribution, we calculate anharmonic vibrational energy levels.

C3v symmetry of ammonia is maintained, which facilitates the calculation of potential energy surfaces and interpretation of both vibrational and electronic states. This is strictly possible only on surfaces that possess the same symmetry as ammonia, like the (111) surfaces of fcc metals. To see how the ammonia molecules interact with different metal surfaces, we have performed local density of the states analysis using the program p4vasp.55 Vibrational Calculations. This part describes the calculations of the vibrational energy levels of the ammonia molecule adsorbed on Cu(111), Rh(111), Pd(111), Ir(111), Pt(111), and Au(111) surfaces. Computed vibrational energy levels for the isolated ammonia molecule and the ammonia molecule adsorbed on Ni(111) are taken from ref 45. Vibrational calculation for ammonia adsorbed on the Ag(111) surface differs insignificantly from the description in ref 45 and below. Adiabatic Approximation. In this work, we are interested in the high-frequency vibrations of the adsorbed ammonia molecule. We decided to model these by assuming that the ammonia molecule interacts with the surface only through the potential energy surfaces, which are calculated in the presence of the metal surface. It has been previously shown that this kind of adiabatic assumption works well for weakly bound adsorption systems45,56 and gas phase clusters.57−62 The assumption facilitates both the calculation of the potential energy surfaces and vibrational calculations as it reduces the number of vibrational coordinates from twelve to six assuming that the coordinates of the metal surface are fixed. The adiabatic approximation adopted means that we need to define an intermolecular equilibrium geometry around which the molecule vibrates. This geometry is defined by six coordinates that describe the place and orientation of the ammonia molecule with respect to the surface. We also fixed the structure of the metal surface. The translational coordinates that describe the place of the molecule on the surface were set by fixing the position of the nitrogen atom. The angular coordinates that describe the tilting of the molecule with respect to the surface were set by fixing the angles between the different N−H vectors and the normal of the metal surface equal to each other. Finally, the symmetry of the adsorption system was used to fix the rotational coordinate that describes spinning of ammonia around the C3-axis. Coordinates. After the adiabatic assumption, we can use the same coordinates for the isolated molecule and the adsorbed molecule. These are constructed from the bond lengths and bond angles of ammonia: r1, r2, r3, θ1 = ∠(r2,r3), θ2 = ∠(r1,r3), and θ3 = ∠(r1,r2). The bending part of the potential energy surface was expressed as a function of a symmetric bending coordinate63

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COMPUTATIONAL METHODS We optimized the structure of the adsorption systems and calculated the potential energy surfaces around the equilibrium geometries of the systems using standard plane-wave density functional theory (DFT) calculations. The anharmonic vibrational energy levels were computed with our own Fortran program that makes use of the variational method. Electronic Structure Calculations. Vienna ab initio simulation package (VASP) was used in all electronic structure calculations.51,52 The generalized gradient approximation (GGA) by Perdew and Wang (PW91) was employed to describe electron−electron exchange and correlation. Core electrons were described with projector augmented wave (PAW) potentials53 and the valence electrons with a planewave basis sets and a cut off energy 520 eV. The reciprocal space was sampled with a nonreduced gamma-centered Monkhorst−Pack k-point grid 5 × 5 × 1. The Fermi level was smeared by the second order Methfessel−Paxton method with the width of 0.2 eV. All calculations were non-spinpolarized. A test calculation on the Ni surface showed that this is adequate for the present purposes.54 The convergence criteria for the electronic problem was 10−4 eV. Adsorption systems, clean metal surfaces, and the isolated ammonia molecule were modeled with the periodic boundary condition. Lattice constants for the surface calculations were obtained by computing the total energy of a bulk metal super cell of 27 atoms and fitting the data to an analytic function. Adsorption systems and the surfaces were modeled with supercells containing five layers of metal atoms and nine atoms in each layer resulting in the coverage of 1/9. The layers were separated with a vacuum of 10 Å. The ammonia molecule was placed on one side of the metal surface. The isolated molecule was put inside a large cubic supercell with dimensions of 15 Å and only the gamma-point was used to sample the reciprocal space. The metal surface without ammonia, the isolated molecule, and the adsorption system were relaxed until the Hellmann−Feynman forces of all unconstrained atoms were less than 0.001 eV Å−1. In this procedure, the two uppermost layers were allowed to relax and the three bottom layers were kept fixed. Instead of performing extensive study of the possible adsorption sites and geometries, the geometry, where the ammonia molecule adsorbs on the top of a metal atom through the nitrogen atom with the C3 axis perpendicular to the metal surface, was used as a starting point in the geometry optimization. This geometry corresponds to experimental and computational findings about the first layer ammonia. The only coordinate that determines, whether the adsorption geometry is symmetrical is the rotational angle around the C3 axes. Two geometries that maintain the C3v symmetry were considered: an eclipsed structure where NHi (i = 1−3) vectors point to metal atoms and a staggered structure where NHi vectors point to empty space between the metal atoms. In these geometries, the

S2 = ±3−1/4 2π − θ1 − θ2 − θ3

(1)

for the isolated molecule, ΔS2 = S2 − S2eq

(2)

for the adsorbed molecule, and degenerate asymmetric bending coordinates S4a =

1 (2θ1 − θ2 − θ3) 6

(3)

and 14961



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Table 1. Optimized Geometry for the Ammonia Molecule Adsorbed on Metal Surfacesa metal

lattice constant (Å)

Ni Cu Rh Pd Ag Ir Pt Au without surface

3.515 3.637 3.844 3.956 4.158 3.881 3.986 4.174

eclipsed staggered eclipsed staggered staggered staggered staggered eclipsed

req (Å)

θeq (deg)

Δz (Å)

z (Å)

Eads (eV)

obs Eads (eV)b

1.023 1.023 1.021 1.021 1.021 1.022 1.022 1.020 1.021

108.7 108.2 109.2 109.4 108.3 109.3 109.8 109.1 106.6

0.21 0.20 0.14 0.11 0.13 0.11 0.10 0.08

1.99 2.12 2.15 2.15 2.45 2.15 2.12 2.40

−0.906 −0.559 −1.000 −0.849 −0.352 −1.162 −0.859 −0.412

from −0.97 to −0.74c −0.40d −0.88e −0.77f >−0.49g −0.83h from −1.00 to −0.86,i −1.1j −0.39k

The optimized bond lengths and bond angles are denoted req and θeq, respectively. The symbol Δz is the displacement of the atop metal atom, and z is the nitrogen−metal bond length. Adsorption energy is defined as Eads = ENH3+surface − ENH3 − Esurface, where ENH3+surface, ENH3, and Esurface are energies of the optimized adsorption system, isolated ammonia molecule, and the surface without ammonia, respectively. bObserved adsorption energies are obtained with the Redhead model. cTDS temperature 270−350 K.10−13,15,72 dTDS temperature 150 K.23 eTDS temperature 320 K.73,39 f TDS temperature 280 K on Pd on Mo(110).30 gAg(110) surface which should be more strongly bound than 111, TDS temperature 180 K.74,75 h TDS temperature 300 K.6 On Ir(100)76 and Ir(110)77 surfaces the desorption temperatures are 370 and 375 K. Therefore, we believe that this is a high-coverage TDS-temperature. iTDS temperature 310−360 K.12,22,29 jfrom a photo desorption experiment.78 kTDS temperature 145 K.79 a

S4b =

1 (θ2 − θ3) 2

vary from 79° to 120° when the hydrogen atoms point away from the surface, and on the other side of the planar reference structure the angles deviate as much as 20° from the planar structure. For the gas phase molecule, the symmetric bending potential is symmetric with respect to the origin. Therefore, data points corresponding to the negative values of the S2 coordinate were obtained from positive S2 points. The asymmetric bending grid for the S4a coordinate was determined from data points for which 2Δθ1 = −Δθ2 = −Δθ3 varies from −20 to 20°, with a step size of 2°. Displacements ±0.005 and ±0.100 Å or ±4 and ±8 were used for the two-dimensional parts of the potential. The C3v symmetry was used to derive other potential energy parameters for the surfaces that were not explicitly calculated. The potential energy surface was expanded as a power series with respect to the symmetrized bond length and bond angle coordinates, except for the one-dimensional S1 surfaces and the S1ΔS2 surfaces where the Morse coordinate y = 1 − e−aS1 was used instead of the S1 coordinate. Analytical representation of the potential energy surface was obtained with the nonlinear least-squares method using Mathematica program.64 The calculated potential energy surfaces are presented in the Supporting Information. Parameters that can be obtained from the given parameters using symmetry relations have been excluded. See ref 65 for more details. Kinetic Energy Operator. We use within the Born− Oppenheimer approximation an exact nonrelativistic kinetic energy operator for the isolated ammonia molecule. In the spirit of the adiabatic approximation, we also use the same operator for the adsorbed molecule. With a unit weight factor in the volume element of integration, it is66

(4)

for the isolated and adsorbed molecule. The equilibrium value of the S2 coordinate in eq 2 is obtained from eq 1 by using equilibrium bond angles and the positive sign. The kinetic energy operator and the basis functions were expressed in coordinates S2, S4a, and S4b. The ± signs in the S2 coordinate definition stand for the geometries on the different sides of the planar structure. The value S2 = 0 corresponds to the planar structure. For the adsorbed molecule, the positive value indicates that the hydrogen atoms point away from the metal surface whereas the negative value indicates that the hydrogen atoms point toward the metal surface. The stretching part of the potential energy surface was calculated as a function of symmetrized bond length coordinates 1 S1 = (Δr1 + Δr2 + Δr3) (5) 3 S3a =

1 (2r1 − r2 − r3) 6

(6)

1 (r2 − r3) 2

(7)

and

S3b =

where Δri = ri − ri(eq) are displacements from the equilibrium bond length. The kinetic energy operator and the basis functions were expressed in bond length coordinates r1, r2, and r3. The coordinates S1 describes the symmetric stretch. Coordinates S3a and S3b describe degenerate asymmetric stretches. Calculation of the Potential Energy Surfaces. Data points on the symmetric stretch S1 curve were calculated from Δr1 = Δr2 = Δr3 = −0.225 to 0.30 Å with the step size 0.025 Å. The asymmetric stretching grid for the S3a coordinate was determined in the data points for which 2Δr1 = −Δr2 = −Δr3 varies from −0.12 to 0.17 Å with a step size of 0.01 Å. The asymmetric stretching grid for the S3b coordinate was determined in the data points for which Δr2 = −Δr3 varies from 0.01 to 0.19 Å with a step size of 0.01 Å. The potential energy surface for the symmetric bending coordinate, ΔS2, was calculated with a 2° grid where bond angles θ1 = θ2 = θ3

T̂ = −

ℏ2 1/2 J 2

⎛ ∂ 1 ∂J ⎞⎟ (i , j) ∂ −1/2 + g J ∂qj ∂qi J ∂qi ⎟⎠ i,j=1 ⎝ 6

∑ ⎜⎜

(8)

where qi and qj coordinates are r1, r2, r3, S2, S4a, or S4b, the reciprocal metric tensor elements are given by 4

g(i , j) =

∑ α=1

1 ⃗ (∇α qi ·∇α⃗ qj) mα

(9)

and J is the Jacobian of the coordinate transformation. The summation index α runs through all atoms in the molecule and 14962



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mα is the mass of the αth nucleus. The g-tensor elements and the Jacobian of this work are in the Supporting Information of ref 45. Variational Calculations. The vibrational Hamiltonian was obtained by combining the calculated potential energy surface and the kinetic energy operator given in eq 8. The corresponding eigenvalue problem was solved variationally in a six-dimensional basis set that was constructed as products of one-dimensional Morse oscillator eigenfunctions for the stretches and one-dimensional harmonic oscillator eigenfunctions for the bends. Analytical formulas for Morse oscillator eigenfunctions were taken from ref 67. Basis set contraction was used to reduce the number of basis functions. See refs 45 and 62 for more details. All integrals were separated into stretching and bending parts. The stretching parts were computed with three-dimensional numerical Gauss−Laguerre integration and the bending parts with three-dimensional numerical Gauss−Hermite integration. The numbers of basis functions and integration points in each basis set contraction step are similar in refs 45 and 62. Finally, vibrational energy levels and wave functions were obtained by diagonalizing the Hamiltonian matrix.

surface without ammonia, respectively. The computed adsorption energies show periodic behavior when compared with the positions of the metals in the periodic table. Experimental counterparts for the adsorption energies in Table 1 are obtained from thermal desorption spectroscopy (TDS) experiments. According to ref 1, chemisorbed molecules that are directly bound to the surface desorb typically between 150 and 300 K. Desorption peaks are broad because strong lateral interactions between neighboring ammonia molecules saturate the first layer already at low coverage. Adsorption energy can be estimated from the TDS temperature profile by using the Redhead model68 ⎡ ⎛ νT ⎞ ⎤ E = kTmax ⎢ln⎜ max ⎟ − 3.64⎥ ⎣ ⎝ β ⎠ ⎦

where k is Bolzmann’s constant, Tmax is the maximum of the TDS peak, ν is called a frequency factor, and β is the heating rate. In principle, the Redhead model is applicable if desorption is a first order process and the peak maximum can be found. Estimates for the experimental adsorption energy in Table 1 have been obtained from the experimental TDS temperatures using the Redhead formula with a value 1013 K−1 for the quotient of the frequency factor and the heating rate. Experimental adsorption energies are in good agreement with our calculated values especially when it is taken into account that the zero-point energy correction (not included in our calculations) increases adsorption energy by about 0.1 eV.38,41 Molecular Orbital Calculations. We analyzed electronic structures of the adsorption systems by calculating the density of the states (DOS) for the isolated ammonia molecule, each of the adsorption systems and corresponding surfaces without the ammonia molecule. To explore this further, we performed the atomic local density of states (LDOS) analysis for NH3, N, and H atoms, and the metal atom right below the ammonia molecule. The DOS analysis shows that adsorption induces sharp and narrow peaks around −18 and −8 eV below the Fermi energy on all surfaces. The LDOS analysis reveals the existence of a third ammonia-related feature around −5 eV below Fermi energy on all surfaces and new adsorption induced features around between −3 and −1 eV below Fermi energy on the Cu, Ag, and Au surfaces. The LDOS analysis shows that the −18 and −8 eV features correspond to the 2a1 and degenerate 1e orbitals of the isolated ammonia molecule, respectively. These are the NH-bonding orbitals. The 2a1 orbital peaks are narrow and their energetic positions and heights are similar in all studied surfaces. On the basis of this, we conclude that the 2a1 orbital does not affect significantly the bonding with the surface. The 1e orbital does not seem to interact strongly with the surface either. The separation of the molecular orbital energies E(1e)−E(2a1) is 10 eV for the gas phase ammonia and only 0.2−0.3 eV smaller for the adsorbed ammonia. The 1e orbital peaks are also rather narrow. The feature around −5 eV below Fermi energy is hidden under the metal states. It is the 3a1 orbital of the ammonia molecule hybridized with the metal surface. In the gas phase ammonia, the lone pair electrons are located in the 3a1 orbital. It is ideal to form a bond with the dz2 electrons of the surface because it possesses the right symmetry and it is energetically close to the sd-band of the metal surface. In the gas phase, the 3a1 orbital is separated from the 1e orbital by 4.4 eV. On the

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RESULTS AND DISCUSSION First, we give the results of geometry optimizations together with corresponding experimental findings and report the results of molecular orbital calculations. Then, we report the calculated vibrational energy levels together with the experimental ones. Geometry Optimizations. Adsorption Geometries. The results of the geometry optimization are shown in Table 1. The computationally and experimentally confirmed fact that ammonia adsorbs on top of a metal atom through the nitrogen atom with the C3 axis parallel to the surface normal was the starting point for our geometry optimization. The references for the experimental work are listed in the Introduction. As the (111) surfaces of fcc metals are hexagonal, the only coordinate that determines whether the adsorption geometry is symmetrical is the rotational angle around the C3 axes. To maintain the C3v symmetry, we oriented NH vectors to point either along metal rows (eclipsed geometry) or to the hollow sites (staggered geometry). None of the optimized structures show any significant offset from the exact atop site, tilting of the molecule, or change in symmetry. In all studied surfaces, the distance between the nitrogen atom and the metal atom below it is about 2 Å. The metal atom right below the molecule shifts up by about 0.2 Å. The ammonia molecule maintains its gas phase symmetry, and its bond angles and bond lengths increase only a little. Both energetical and geometrical differences between azimuthal and staggered geometries are small, which indicates that the ammonia molecule rotates freely around the C3 axes. Our calculated geometry values are in good agreement with earlier computational results.35−49 The calculated distances 1.99 and 2.12 Å of the nitrogen atom from the nickel and copper atoms, respectively, agree well with values 1.97 and 2.09 Å determined from photoelectron diffraction measurements.3,71 Adsorption Energies. The computed adsorption energies in Table 1 are defined as Eads = E NH3+ surface − E NH3 − Esurface

(11)

(10)

where ENH3+surface, ENH3, and Esurface are energies of the optimized adsorption system, the isolated ammonia molecule, and the 14963



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surface. We found that the variational results are converged with respect to these parameters. Especially, the inclusion of higher-order potential energy terms changes the vibrational energy levels less than 1 cm−1. Comparison with Experiments. Experimental energy levels in Table 3 are obtained with electron energy less spectroscopy (EELS), reflection absorption infrared spectroscopy (RAIRS), and scanning tunnelling microscopy (STM) techniques. When results on the (111) surfaces have not been available, we give results on rougher surface planes (100), (110), and (311) or a metal layer on some support. Typically, these surface planes interact with the ammonia molecule more strongly than the (111) surface does. Therefore, it is likely that the adsorption induced shifts from these surfaces serve as an upper limit for the (111) surface plane shifts. Experimental results are obtained from low-coverage experiments unless stated otherwise. In our calculations, the coverage is 1/9. However, it is worth mentioning that the interpretation of the experimental spectra is not straightforward. A low-coverage surface seems no matter what to show features from all possible adsorption structures. Many desorption experiments listed in Table 3 show that the first layer ammonia saturates already at low coverages and the desorption temperatures are sensitive to the coverage of the surface. This indicates strong lateral interactions between the neighboring ammonia molecules. The vibrational energy level positions of the α-ammonia molecules also depend on the coverage. Additionally, the surface selection rule forbids the observation of the asymmetric modes of the upright lowcoverage ammonia layer. Symmetric bend and stretch on the other hand become more intense because of the surface selection rule. In typical experimental spectra, the symmetric bend is the strongest feature. It is visible already at low coverage but its position shifts up with decreasing coverage. Therefore, the experimental values in Table 3 are sometimes expressed with an interval. The larger wavenumber corresponds to the lowcoverage value, which may correspond to smaller or higher coverage than our computational coverage 1/9. Despite these inaccuracies in the experimental numbers, it seems that our model produces accurate estimates for the symmetric bend fundamental wavenumber. Unlike the symmetric bend, the asymmetric bend is often a very weak feature in the experimental spectra. In most experiments listed in Table 3, an accurate value for the asymmetric bend is missing in the low-coverage spectra. The asymmetric bend becomes visible when the coverage is increased, but then it is unclear whether the signal comes from single adsorbed molecules or a multilayer structure where ammonia molecules are likely to be tilted. Therefore, we believe that the observations for the asymmetric bend around 1600− 1640 cm−1 correspond to some sort of multilayer structures of ammonia. The value for the solid ammonia is 1650 cm−1.81 The distinct observations 1580 cm−1 on the Ni(111) and Ni(110) surfaces,12 1560 cm−1 on the Cu(100) surfaces,27 1600 cm−1 on the Cu(110) surfaces,25 1560 and 1600 cm−1 on the Ag(110) surface,1,75 and 1549 and 1580 cm−1 on the Pt(111) surfaces,19,33 which are in better agreement with our calculated values, probably correspond to the α-ammonia. Due to the resolution of the experimental methods and possible high-coverage samples, the stretches are often unresolved in experiments. Therefore, we calculated an average of the calculated stretching fundamentals and compare it with the experimental numbers.

metal surfaces, this separation is 2.7−3.6 eV. The heights of the 3a1 peaks are also decreased and the peaks are broadened with respect to the gas phase peaks. This indicates that this feature is the NH3−metal bonding orbital. On the basis of the LDOS analysis, we additionally interpreted that the adsorption induced features around between −3 and −1 eV present on the Cu, Ag, and Au surfaces are the occupied antibonding contributions of the NH3−metal bond. Vibrational Energy Levels. Gas phase NH3 Molecule. In Table 2, we show the vibrational energy levels of the gas phase Table 2. Calculated45 and Experimental69 Vibrational Energy Levels in cm−1 for the Isolated Ammonia Moleculea calculated

experimental

state

+

−

+

−

ν2 ν4 ν1 ν3

875 1573 3251 3351

919 1575 3253 3356

932 1626 3336 3444

968 1627 3337 3444

a The state labels ν1, ν2, ν3, and ν4 stand for the symmetric stretch and bend, and the degenerate asymmetric stretch and bend, respectively. The +/− signs are the inversion symmetrical (+) and antisymmetrical (−) states.

ammonia molecule from our previous contribution.45 The calculated values are obtained with the DFT potential energy surface. The experimental values are from ref 69. The standard normal mode quantum labels ν1, ν2, ν3, and ν4 stand for symmetric stretch and bend, and degenerate asymmetric stretch and bend, respectively.70 The assignments of the states are based on the wave function analysis. Comparison of the calculated and experimental energy levels shows that the calculated values are systematically smaller than the experimental ones. This kind of systematic deviation from the experimental values originates from the incorrectness of the DFT. Luckily, on the Ni(111) surface, we showed that these deviations are of similar magnitude for both the isolated ammonia molecule and the adsorbed ammonia molecule.45 Adsorbed NH3 Molecules. In Table 3, we give calculated and experimental vibrational energy levels for the adsorbed ammonia molecule. To correct the error induced by the DFT, we calculated shifts in the vibrational wavenumbers from the gas phase values to the adsorbed molecule Δνcalc − νgas,calc ̃ = νads,calc ̃ ̃

(12)

and used them to calculate vibrational energy levels from which the error induced by the DFT is partly corrected νcorr + Δνcalc ̃ = νgas,exp ̃ ̃

(13)

The wavenumber for the isolated molecule is calculated as an average of the ± levels. The corrected wavenumbers are also shown in Table 3. Due to the DFT error, the calculated energy levels in Table 3 are systematically smaller than the experimental numbers. The corrected energy levels, on the other hand, are in agreement with the experimental wavenumbers. Convergence Tests. Convergence of the calculated vibrational energy levels with respect to the sampling and representation of the potential energy surface, vibrational basis set, and integration grids in the variational calculation was tested for the ammonia molecule adsorbed on the Ag(111) 14964



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Table 3. Calculated and Experimental Vibrational Energy Levels in cm−1 for the Ammonia Molecule Adsorbed on fcc-Metal Surfacesh

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Table 3. continued

a

Result of variational calculation. bValue where the dft error is corrected. See text for more details. cAverage of the stretching wavenumbers. Frequency dependent on coverage of the surface. Larger wavenumber is the low coverage value. eProbably high-coverage value. Value for solid NH3 is 1650.81 fEstimate obtained from the published spectra. gStretches unresolved. hThe state labels ν1, ν2, ν3, and ν4 stand for the symmetric stretch and bend, and the degenerate asymmetric stretch and bend, respectively. Experimental energy levels are obtained from low-coverage experiments unless stated otherwise. Calculated energy levels for Ni(111) surface are from ref 45. d

Relation to the Adsorption Energy. The strength and quality of the interaction between ammonia and the surface are reflected not only in the adsorption energy but also in the vibrational energy levels. Typically, adsorption makes the internal structure of the adsorbed molecule looser because the occupied bonding molecular orbitals of the isolated molecule loose electron density and/or the unoccupied antibonding molecular orbitals gain electron density upon adsorption. Loosening of the internal structure of ammonia is manifested in the red-shifted stretching fundamentals. The symmetric bend of the ammonia molecule behaves differently. The C3v symmetry of the ammonia molecule results from the repulsion between the NH bonding orbitals and the lone pair orbital. However, the energy difference between the bent equilibrium geometry and the planar transition state is small. Therefore, ammonia undergoes easily the umbrella or inversion motion and the lone pair orbital adjusts to it. When an ammonia molecule adsorbs on a metal surface through its lone pair electrons, the adjustment of the free electron pair, which is required for the inversion, becomes infeasible. As a result, the molecule becomes confined to one side of the planar structure and the symmetric bending potential becomes unsymmetrical. Inversion splittings are quenched and the symmetric bend fundamental blue shifts. It is obvious that if adsorption induces changes in the vibrational energy levels, the adsorption induced shifts should depend on the adsorption energy in some systematic way. Therefore, we plotted the calculated vibrational energy levels of

the ammonia molecule adsorbed on the different metal surfaces as a function of the adsorption energy. These plots are shown in Figure 1. The relation between vibrational energy and the adsorption energy is almost linear for the symmetric stretch and bend. For the asymmetric stretch and bend, the shape of the curve resembles an exponential function.

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CONCLUSIONS We have computationally studied adsorption and vibrational energy levels of the ammonia molecule adsorbed on the fcc (111) transition metal surfaces Ni(111), Cu(111), Rh(111), Pd(111), Ag(111), Ir(111), Pt(111), and Au(111). In our vibrational model, the metal surface is a perturbing potential for the molecule. Therefore, we can use a nonrelativistic kinetic energy operator that is exact within the Born−Oppenheimer approximation for the isolated ammonia molecule. The potential energy surfaces are calculated with plane-wave density-functional theory method. Vibrational eigenvalues are solved variationally. Our calculations show that when an ammonia molecule attachs to the surface, it can no more invert. Therefore, the spectra show no inversion splittings. The wavenumber of the symmetric bending mode blue shifts from the calculated gas phase values. The wavenumbers for the asymmetric bend and for the stretches red shift. For the symmetric modes, the calculated adsorption-induced shifts show roughly linear behavior with the calculated adsorption energy. For the asymmetric modes, this behavior seems to be exponential. 14966



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Figure 1. Vibrational fundamental energy levels of the ammonia molecule adsorbed on fcc (111) transition metal surfaces as a function of adsorption energy.

Our computations combine accurate vibrational calculations with the DFT that produces systematic errors in the calculated potential energy surfaces. Our anharmonic vibrational model takes couplings between different modes into account. Especially, it enables us to calculate highly anharmonic energy levels of the gas phase ammonia molecule accurately. The error caused by DFT is partly canceled if adsorption-induced shifts are calculated. On the basis of this idea, we calculated DFTcorrected vibrational energy levels that should correspond to experimental values. These corrected energy levels are in good agreement with experiments. This indicates that DFT is able to describe rather well the interaction of ammonia molecules with the transition metal surfaces. It also proves that our adiabatic model that separates the motion of adsorbed molecule and the surface atoms works reasonably well. However, it is clear that the correlation effects not described in the DFT and the deficiencies of the adiabatic model produce an error interval for the calculated values. The only way to estimate the magnitude of the error bar is to compare calculated values with the experimental numbers. By doing so, we assume that our calculated numbers are reliable within some tens of cm−1. Most of the experimental surface spectra seem to show features from many adsorption structures. This makes the interpretation of the experimental spectra of adsorbed molecules difficult. One example is the asymmetric bend of ammonia molecule adsorbed on the fcc transition metal

surfaces. In some experiments it is seen between 1550 and 1600 cm−1 whereas in some other experiments it is seen between 1630 and 1640 cm−1. Our calculated values between 1570 and 1600 cm−1 support that the latter observations correspond to high-coverage ammonia. This example shows that our calculations provide a controllable way to explore periodic trends in the vibrational properties of adsorbed molecules.

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ASSOCIATED CONTENT

S Supporting Information *

Tables of calculated potential energy surfaces. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: lauri.halonen@helsinki.fi. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank CSC Scientific Computing Ltd for providing the computational time. E.S. is grateful to Magnus Ehrnrooth foundation for grants. The Academy of Finland is thanked for 14967



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(34) Bartels, L.; Wolf, M.; Klamroth, T.; Saalfrank, P.; Kühnle, A.; Meyer, G.; Rieder, K.-H. Chem. Phys. Lett. 1999, 313, 544−552. (35) Bilic̀, A.; Reimers, J. R.; Hush, N. S.; Hafner, J. J. Chem. Phys. 2002, 116, 8981−8987. (36) Liu, R.; Shen, W.; Zhang, J.; Li, M. Appl. Surf. Sci. 2008, 254, 5706−5710. (37) Hoft, R. C.; Ford, M. J.; McDonagh, A. M.; Cortie, M. B. J. Phys. Chem. C 2007, 111, 13886−13891. (38) Novell-Leruth, G.; Valcàrcel, A.; Pèrez-Ramírez, J.; Ricart, J. M. J. Phys. Chem. C 2007, 111, 860−868. (39) Frechard, F.; van Santen, R. A.; Siokou, A.; Niemantsverdriet, J. W.; Hafner, J. J. Chem. Phys. 1999, 111, 8124−8130. (40) Liu, Z.-P.; Hu, P.; Lee, M.-H. J. Chem. Phys. 2003, 119, 6282− 6289. (41) Popa, C.; Offermans, W. K.; van Santen, R. A.; Jansen, A. P. J. Phys. Rev. B 2006, 74, 155428. (42) Krekelberg, W. P.; Greeley, J.; Mavrikakis, M. J. Phys. Chem. B 2004, 108, 987−994. (43) Robinson, J.; Woodruff, D. P. Surf. Sci. 2002, 498, 203−211. (44) Stolbov, S.; Rahman, T. S. J. Chem. Phys. 2005, 123, 204716. (45) Sälli, E.; Hänninen, V.; Halonen, L. J. Phys. Chem. C 2010, 114, 4550−4556. (46) Novell-Leruth, G.; Valcàrcel, A.; Clotet, A.; Ricart, J. M.; PèrezRamirèz, J. J. Phys. Chem. B 2005, 109, 18061−18069. (47) Jennison, D. R.; Schultz, P. A.; Sears, M. P. Surf. Sci. 1996, 368, 253−257. (48) Offermans, W. K.; Jansen, A. P. J.; van Santen, R. A. Surf. Sci. 2006, 600, 1714−1734. (49) Ford, D. C.; Xu, Y.; Mavrikakis, M. Surf. Sci. 2005, 587, 159− 174. (50) Diawara, B.; Joubert, L.; Costa, D.; Marcus, P.; Adamo, C. Surf. Sci. 2009, 603, 3025−3034. (51) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15−50. (52) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169−11186. (53) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758−1775. (54) Kurtén, T.; Biczysko, M.; Rajamäki, T.; Laasonen, K.; Halonen, L. J. Phys. Chem. B 2005, 109, 8954−8960. (55) See http://p4vasp.at for details. (56) Sälli, E.; Jalkanen, J.-P.; Laasonen, K.; Halonen, L. Mol. Phys. 2007, 105, 1271−1282. (57) Low, G. R.; Kjaergaard, H. G. J. Chem. Phys. 1999, 110, 9104− 9115. (58) Salmi, T.; Hänninen, V.; Garden, A. L.; Kjaergaard, H. G.; Tennyson, J.; Halonen, L. J. Phys. Chem. A 2008, 112, 6305−6312. (59) Salmi, T.; Hänninen, V.; Garden, A. L.; Kjaergaard, H. G.; Tennyson, J.; Halonen, L. J. Phys. Chem. A 2012, 116, 796−797. (60) Salmi, T.; Kjaergaard, H. G.; Halonen, L. J. Phys. Chem. A 2009, 113, 9124−9132. (61) Salmi, T.; Runeberg, N.; Halonen, L.; Lane, J. R.; Kjaergaard, H. G. J. Phys. Chem. A 2010, 114, 4835−4842. (62) Sälli, E.; Salmi, T.; Halonen, L. J. Phys. Chem. A 2011, 115, 11594−11605. (63) Pesonen, J.; Miani, A.; Halonen, L. J. Chem. Phys. 2001, 115, 1243−1250. (64) Mathematica, version 8.0; Wolfram Research, Inc.: Champaign, IL, 2010. (65) Martin, J. M. L.; Lee, T. J.; Taylor, P. R. J. Chem. Phys. 1992, 97, 8361−8371. (66) Pesonen, J. Application of Geometric Algebra to Theoretical Molecular Spectroscopy; Ph.D. Thesis; Yliopistopaino: Helsinki, 2001. (67) Dahl, J. P.; Springborg, M. J. Chem. Phys. 1988, 88, 4535−4547. (68) Niemantsverdriet, J. W. Spectroscopy in Catalysis - An Introduction; Wiley-VCH Verlag GmbH&Co. KGaA: Weinheim, 2007. (69) Špirko, V. J. Mol. Spectrosc. 1983, 101, 30−47. (70) Herzberg, G. Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules; Krieger Publishing Co.: Malabar, FL, 1991.

funding the Finnish Centre of Excellence in Computational Molecular Science.

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REFERENCES

(1) Krasnopoler, A.; Kizhakevariam, N.; Stuve, E. M. J. Chem. Soc., Faraday Trans. 1996, 92, 2445−2452. (2) Hasselström, J.; Föhlisch, A.; Karis, O.; Wassdahl, N.; Weinelt, M.; Nilsson, A.; Nyberg, M.; Pettersson, L. G. M.; Stöhr, J. J. Chem. Phys. 1999, 110, 4880−4890. (3) Baumgärtel, P.; Lindsay, R.; Giessel, T.; Schaff, O.; Bradshaw, A. M.; Woodruff, D. P. J. Phys. Chem. B 1999, 104, 3044−3049. (4) Booth, N. A.; Davis, R.; Toomes, R.; Woodruff, D. P.; Hirschmugl, C.; Schindler, K. M.; Schaff, O.; Fernandez, V.; Theobald, A.; Hofmann, Ph.; Lindsay, R.; Giessel, T.; Baumgärtel, P.; Bradshaw, A. M. Surf. Sci. 1997, 387, 152−159. (5) Hirschmugl, C. J.; Schindler, K.-M.; Schaff, O.; Fernandez, V.; Theobald, A.; Hofmann, Ph.; Bradshaw, A. M.; Davis, R.; Booth, N. A.; Woodruff, D. P.; Fritzsche, V. Surf. Sci. 1996, 352, 232−237. (6) Purtell, R. J.; Merrill, R. P.; Seabury, C. W.; Rhodin, T. N. Phys. Rev. Lett. 1980, 44, 1279−1281. (7) Zheng, Y.; Moler, E.; Hudson, E.; Hussain, Z.; Shirley, D. A. Phys. Rev. B 1993, 48, 4760−4766. (8) Mocuta, D.; Ahner, D.; Yates, J. T., Jr. Surf. Sci. 1997, 383, 299− 307. (9) Ceyer, S. T.; Yates, J. T., Jr. Surf. Sci. 1985, 155, 584−595. (10) Netzer, F. P.; Madey, T. E. Surf. Sci. 1982, 119, 422−432. (11) Seabury, C. W.; Rhodin, T. N.; Purtell, R. J.; Merrill, R. P. Surf. Sci. 1980, 93, 117−126. (12) Fisher, G. B.; Mitchell, G. E. J. Electron Spectrosc. Relat. Phenom. 1983, 29, 253−259. (13) Bozso, F.; Arias, J. M.; Hanharan, C. P.; Yates, J. T., Jr.; Metiu, H.; Martin, R. M. Surf. Sci. 1984, 138, 488−504. (14) Villegas, I.; Weaver, M. J. Surf. Sci. 1996, 367, 162−176. (15) Dresser, M. J.; Lanzillotto, A. -M.; Alvey, M. D.; Yates, J. T., Jr. Surf. Sci. 1987, 191, 1−14. (16) Kang, W. M.; Li, C. H.; Tong, S. Y.; Seabury, C. W.; Jacobi, K.; Rhodin, T. N.; Purtell, R. J.; Merrill, R. P. Phys. Rev. Lett. 1981, 47, 931−934. (17) Madey, T. E.; Houston, J. E.; Seabury, C. W.; Rhodin, T. N. J. Vac. Sci. Technol. 1981, 18, 476−480. (18) Bassignana, I. C.; Wagemann, K.; Küppers, J.; Ertl, G. Surf. Sci. 1986, 175, 22−44. (19) Sexton, B. A.; Mitchell, G. E. Surf. Sci. 1980, 99, 523−538. (20) Mieher, W. D.; Ho, W. Surf. Sci. 1995, 322, 151−167. (21) Sun, Y.-M.; Sloan, D.; Ihm, H.; White, J. M. J. Vac. Sci. Technol. A 1996, 14, 1516−1521. (22) Gohndrone, J. M.; Olsen, C. W.; Backman, A. L.; Gow, T. R.; Yagasaki, E.; Masel, R. I. J. Vac. Sci. Technol. A 1988, 7, 1986−1990. (23) Sueyoshi, T.; Sasaki, T.; Iwasawa, Y. J. Phys. Chem. 1996, 100, 13646−13654. (24) Wu, K. J.; Kevan, S. D. J. Chem. Phys. 1991, 94, 7494−7498. (25) Lackey, D.; Surman, M.; King, D. A. Vacuum 1983, 33, 867− 869. (26) Afsin, B.; Davies, P. R.; Pashusky, A.; Roberts, M. W.; Vincent, D. Surf. Sci. 1993, 284, 109−120. (27) Davies, P. R.; Roberts, M. W. J. Chem. Soc., Faraday Trans. 1992, 22, 361−368. (28) Carley, A. F.; Davies, P. R.; Roberts, M. W.; Thomas, K. K. Langmuir 2010, 26, 16221−16225. (29) Gland, J. L.; Sexton, B. A.; Mitchell, G. E. Surf. Sci. 1982, 115, 623−632. (30) Xu, C.; Goodman, D. W. J. Phys. Chem. B 1998, 102, 4392− 4400. (31) Xu, Z.; Hanley, L.; Yates, J. T., Jr. J. Chem. Phys. 1992, 96, 1621−1627. (32) Pradier, C.-M.; Adamski, A.; Méthivier, C.; Louis-Rose, I. J. Mol. Catal. 2002, 186, 193−201. (33) Herceg, E.; Mudiyanselage, K.; Trenary, M. J. Phys. Chem. B 2005, 109, 2828−2835. 14968



Article

(71) Schindler, K.-M.; Fritzsche, V.; Asensio, M. C.; Gardner, P.; Ricken, D. E.; Robinson, A. W.; Bradshaw, A. M.; Woodruff, D. P.; Conesa, J. C.; Conzàlez-Elipe, A. R. Phys. Rev. B 1992, 46, 4836. (72) Chorkendorff, I.; Russell, J. N., Jr.; Yates, J. T., Jr. J. Chem. Phys. 1987, 86, 4692−4700. (73) van Hardeveld, R. M.; van Santen, R. A.; Niemantsverdriet, J. W. Surf. Sci. 1996, 369, 23−35. (74) Guo, X. C.; Madix, R. J. Surf. Sci. 2002, 501, 37−48. (75) Thornburg, D. M.; Madix, R. J. Surf. Sci. 1989, 220, 268−294. (76) Santra, A. K.; Min, B. K.; Yi, C. W.; Luo, K.; Choudhary, T. V.; Goodman, D. W. J. Phys. Chem. B 2001, 106, 340−344. (77) Westrate, C. J.; Bakker, J. W.; Rienks, E. D.; Lizzit, S.; Petaccia, L. J. Chem. Phys. 2005, 122, 184705. (78) Szulzevski, G.; Levis, R. J. J. Chem. Phys. 1995, 103, 10238− 10251. (79) Kay, B. D.; Lykke, K. R.; Creigthon, J. R.; Ward, S. J. J. Chem. Phys. 1989, 91, 5120−5121. (80) Dastoor, H. E.; Gardner, P.; King, D. A. Surf. Sci. 1993, 289, 279−289. (81) Nakamoto, K. Infrared and Raman spectra of Inorganic and Coordination Compounds; Wiley: New York, Brisbane, 1978.

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Computational Study of the Vibrational Structure of the Ammonia

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