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Theoretical study of the CO adsorption on the (100) surface of the face-centered cubic d-block transition metals
Surface Science 441 (1999) 344–350 www.elsevier.nl/locate/susc
Theoretical study of the CO adsorption on the (100) surface of the face-centered cubic d-block transition metals Yosslen Aray *, Jesus Rodriguez, Juan Rivero, David Vega 1 Centro de Quimica, IVIC, Apartado 21827, Caracas 1020 A, Venezuela Received 22 March 1999; accepted for publication 9 July 1999
Abstract The interaction of a CO molecule with the (100) surface of the fcc d-block transition metals is analyzed by the topology of the Laplacian of the electronic charge density −V2r. This analysis shows that the atomic graph for the top atoms is an octahedron that exposes, outside the (100) surface, a vertex V with a local maximum of charge, top and four faces F with a local minimum. The corresponding graph for the second-layer atoms is also an octahedron top that exhibits a vertex V outside the surface. Atomic graphs for the CO molecule show that the carbon atom has a sec non-bonded vertex C , and a torus C of charge depletion perpendicular to the CMO bond direction. Laplacian nb torus topology predicts CO perpendicular orientation in bridge- or top-sites. The bridge-site involves attractive interactions with two atoms of the surface: face (metal top atom)–vertex (C atom)–face (metal top atom). The top-site involves the attractive interaction vertex (C atom)–face (metal top atom). Attractive interaction between the surface and only one atom of the CO molecule rules out dissociation and predicts molecular adsorption. © 1999 Elsevier Science B.V. All rights reserved. Keywords: ADF-BAND; Atomic graphs; Carbon monoxide; d-block transition metals; Chemisorption; Density functional theory; Laplacian of the electronic charge density
1. Introduction The reactivity of molecules is reflected in the topology of the Laplacian of the charge density, V2r [1–4]. The key is a correlation between the critical points (CPs; maxima and minima) of −V2r in the valence shell and the location of the active sites in molecules. In general, a Lewis acid– base reaction corresponds to aligning a local charge concentration (a maximum on −V2r) of * Corresponding author. Fax: +58-3-504-1350. E-mail addresses: [email protected] ( Y. Aray), [email protected] (D. Vega) 1 Permanent address: FACYT, Universidad de Carabobo, Valencia, Venezuela.
the valence shell on the base with a local charge depletion (a minimum on −V2r) on the acid. This is a general phenomenon that is observed in many different kinds of interaction [5], examples being the formation of hydrogen bonds [6 ], the alignment of chlorine molecules in the solid [7], and the adsorption of molecules on a surface [8–12]. The topological approach has the advantage that the reactivity of molecules on surfaces is directly interpreted in terms of an observable, such as r(r), and is not linked to quantities of doubtful physical meaning such as the Mulliken populations or details of a specific set of molecular orbitals. The Laplacian of the electronic density provides a physical model that guides us in the determination of the sites of adsorption, the geometry of
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approach of the reactant relative to the surface site, and predicts whether the interaction will correspond to physi- or chemi-sorption [8]. CO adsorption on transition metals is an important process in a variety of catalytic reactions [13– 17]. It is well known [18] that the susceptibility of the CO molecule to dissociation upon chemisorption varies systematically depending on the position of the metal in the Periodic Table. Metals on the left-hand side of the Periodic Table (mostly bcc type) dissociatively chemisorb CO, but metals on the right-hand side (mostly fcc type) chemisorb non-dissociatively. The bond strength of the CO chemisorbed on fcc metals, measured as heats of adsorption, tends to decrease as we move rightwards along a row and upwards across a column of the Periodic Table [13]. In the present study, we have applied the topological approach to the study of CO adsorption on the (100) surface of the fcc d-block transition metals (Ni, Cu, Rh and Pd). Topological analysis of the isolated (100) surface shows why CO binds molecularly on that surface and predicts the correct trend of the interaction strength between the CO molecule and the surface studied.
2. Theory The topological properties of a scalar field such as V2r are summarized by its CPs [5]. These are points where the gradient vector field, V(V2r) vanishes, and they are classified according their type (m, n) by stating their rank m and signature n. The rank is equal to the number of non-zero eigenvalues of the Hessian matrix of V2r, whereas the signature is the algebraic sum of the signs of the eigenvalues of V2r. The Laplacian determines where the field is locally concentrated (V2r<0) and locally depleted (V2r>0) [5]. Since electron density is concentrated where V2r<0, the topology of the Laplacian is conveniently given in terms of −V2r. The atomic Laplacian exhibits alternating shells of charge concentration and charge depletion equal in number to the number of quantum shells. The outer valence shell of charge concentration ( VSCC ) contains a spherical surface over which r is maximally con-
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centrated. The distribution of −V2r over this surface in the free atom is uniform if one assumes that the nucleus has a negligible electric quadrupole moment. In general, this surface persists when the atom is in chemical combination, but the surface no longer has a uniform concentration. The formation of a bond produces changes in this distribution, and a number of local maxima, minima, and saddles appear in this surface of charge distribution [3]. The curvature of −V2r normal to this surface, i.e. the radial curvature, is negative, whereas the two tangential curvatures can assume either positive or negative values. If both of those curvatures are negative or positive then a local maximum, a (3, −3) CP, or local minimum, a (3, +1) CP, is formed on that surface respectively. When one of the tangential curvatures is negative and the other is positive a saddle, a (3, −1) CP, will be formed. Each maximum [3] is linked to another one by unique pairs of trajectories of the gradient of −V2r, which originates at the saddle points. The network of those trajectories partitions the surface of charge concentration into segments with curved faces. In the center of each face there is a local minimum in the surface of the VSCC. This structure is called an atomic graph (AG) [3,4] and succinctly summarizes the type and number of the CPs formed on the surface of charge concentration of an atom in a molecule. This graph provides the connectivity of the extremes of the −V2r in the corresponding surface of the VSCC distribution. The AG is most easily visualized in terms of the polyhedron whose vertices ( V ), edges ( E) and faces ( F ) satisfy Euler’s formula [4]: V−E+F=2. The (3, −3) CPs ( local maxima) define the vertices. The unique pair of trajectories that originate at the (3, −1) CPs define the edges, and the (3, +1) CPs ( local minumun) define the faces. A Lewis acid–base reaction corresponds to aligning a charge concentration of the VSCC on the base with a charge depletion on the acid, i.e. by directing a vertex of the graph on the base atom at a face of the polyhedron on the acid.
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Slater basis sets of triple-j quality contained in the ADF-BAND package were used. The topology of −V2r was analyzed using a local version of the BUBBLE program [29] contained in the NUMLAP [30] program and adapted to BAND code and Slater-type orbitals. For Cu we used a slab with three to five layers and the Laplacian topology is found to exhibit no significant dependence on slab depth, the values of −V2r at the CPs, in general, changing by only hundredths of an atomic unit or less. This locality of the VSSC CPs was also previously observed in an MgO topological analysis [8] of −V2r. Therefore, we used a slab of three layers for the other metals.
3. Method The lattice of bulk [19] transition metals considered in this work is described by the Fm3m space group with a=3.6147 (Cu), 3.5236 (Ni), 3.8907 ˚ (Rh). The required surface was (Pd) and 3.8044 A modeled by cleaving of the bulk in the specific plane. Thus, it is periodic in two dimensions, semiinfinite, and aperiodic in the direction perpendicular to the surface. The lack of translational symmetry perpendicular to that surface can be dealt with by approximating the semi-infinite crystal by a slab of finite depth. Experimental studies [20–24] have shown that the (100) surfaces of the metals studied do not reconstruct, with a probable multilayer relaxation of the outer layers of the metal crystals. Therefore, we have studied that surface using a slab model with the same geometrical parameters as the bulk. The electronic densities for the above slab models were calculated by means of the ADFBAND [25] program using the Kohn–Sham Hamiltonian with the gradient-corrected Becke exchange [26 ] potential together with the correlation potential of Perdew [27] and the unrestricted scheme to obtain spin-polarized wave functions. BAND contains a method [28] for calculations on periodic systems in which all aspects of numerical precision are efficiently controlled. The general precision parameter for numerical integration in real space, ACCINT, was taken as a value of four. A total of 15 points (k=5) over the Brillouin zone and the quadratic tetrahedron method were chosen for k-space numerical integration. Full electron
4. Results and discussion The (100) surface exposes alternating rows of up (top layer) and down atoms (second layer) to reacting molecules. We have located the CPs of −V2r on the VSCC of those atoms. The number, position with respect to the top layer, and the −V2r values at the CPs found for top atoms are displayed in Table 1. Those values agree with the corresponding maximum of the VSCC of the free atoms obtained by Shi and Boyd [31] using the Clementi and Roetti wave functions. The AG for the top- and second-layer atoms ( Fig. 1) is an octahedron with six vertices or local maxima of charge concentrations linked by 12 edges and eight faces joining those vertices. The graph of the top atoms exposes a local ‘‘peak’’ of charge, V , and top four minima, F , outside the surface. The graph top
Table 1 Data for CPs of −V2r(r) in the VSCC of (100) surface top atoms of the fcc transition metals (atomic units) CPs
Position with respect to top layer
Ni
Cu
Rh
Pd
One (3, −3) Four (3, −3) One (3, −3) Four (3, −1) Four (3, −1) Four (3, −1) Four (3, +1) Four (3, +1)
above in below above in below above below
59.708 55.815 57.074 47.238 48.744 48.185 44.638 45.919
66.938 67.182 65.976 65.175 64.568 65.111 65.161 64.411
7.966 6.981 7.782 6.182 6.238 6.273 5.856 5.981
10.250 10.165 10.139 9.024 8.257 9.174 8.335 8.505
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Fig. 1. AG for top- and second-layer atoms in the (100) surface of the fcc d-block transition metals. White and gray spheres denote the vertex (a local charge concentration) and the edges respectively. In the center of each face there is a minimum of charge concentration. The lines indicate the direction of the bond with the first nearest neighbors of the atom. In the case of the top atoms four outwardly directed bonds are missing.
of the second-layers atom also exhibits a vertex V outside the surface. The remaining five vertices sec point toward the second nearest neighbors of the atom. According to the Laplacian topology, the AGs found predict that the second-layer atoms prefer an interaction with an AG face on an atom of the adsorbate molecules. Top atoms can interact with faces or vertices on the incoming molecules by means of the V or F points respectively. top top The charge concentration distribution of the CO ground state [12] is shown in Fig. 2. The O atom shows two local maxima of charge concentrations located along the CMO directions. One is facing the carbon atom, O , whereas the other is V in the opposite side of the b shell forming a nonbonded vertex, O . A ring of degenerated CPs Vnb in a plane perpendicular to the CMO directions completes the O AG. The values of −V2r at O ,O and ring CPs reported in Ref. [12] are Vb Vnb 3.337 a.u., 3.744 a.u. and 1.418 a.u. respectively. The carbon atom exhibits only one local maximum (C ), which is located in the non-bonded region. Vnb
Fig. 2. Three-dimensional cross-section of the Laplacian distribution for carbon monoxide, showing the structure of CO VSSC. The contour values plotted are 0.0 and −2.5 a.u. The AGs of the C and O atoms are superposed. Small white spheres denote the vertex ( local maximum of charge concentration). Gray rings denote the torus of charge depletion and the degenerate minima of charge concentration in C and O atoms respectively. Only two edges are shown to keep the graphics uncluttered.
A torus of charge depletion (C ), around the torus internuclear axis with a ring of degenerated points is also present in the C AG. The values of −V2r and C CPs reported in Ref. [12] are at C torus Vnb 0.912 a.u. and −0.022 a.u. respectively. The negative value of −V2r at C is characteristic of the torus depletion zone of electronic charge density. The radial curvature of O , which measures the Vnb degree of contraction along the radial directions
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towards the nuclei, is much bigger than that of C [12]; therefore, the O atom should be able to V actnbas a hard base and the C atom as a soft base. Thus, according to the topological theory, the CO molecule can act as an electron donor by means point or as an electron acceptor of the C V through thenbC ring. torus From experiments [18] it is well known that CO adsorption tends, at room temperature, to be dissociative for transition metals on the left-hand side of the Periodic Table, but non-dissociative on the right-hand side. The bcc metals Fe, Mo and W give the borderline between molecular and dissociative adsorption [18]. The previously discussed AGs of the CO molecule and the (100) surface atoms explain why the CO adsorption is non-dissociative on the (100) surface of the fcc d-block transition metals. A previous analysis [12]
(a)
of the Laplacian topology of the Fe (100) surface showed that the AG of the top-layer Fe atoms is a cube that exposes a face, F , with a local top minimum of charge; the corresponding graph for the atoms of the second layer, however, is an octahedron that exhibits a vertex, V , or local sec ‘peak’ of charge to the incoming molecules. Thus, CO interacts with the Fe (100) surface in tilt orientation involving attractive interactions: C –(Fe)V and O –(Fe)F . Those attractorus sec V top tive interactions of thenbC and O atoms, towards two atoms of the surface, lead to bond breakage of the CO molecule. In contrast to the Fe case, in the fcc d-block transition metals, CO tilted on the (100) surface through the C –(Metal )V contorus top nection leads to a non-attractive vertex–vertex interaction of the V framework of the O atom nb with the V of the neighbor metals. Laplacian top
(b)
Fig. 3. CO orientation on fcc metals (100) surface predicted by the Laplacian topology. (a) Bridge site; (b) top site. White arrows show the attractive interactions: vertex (C atom)–face (top atoms). The arrows point to spheres with a cross representing the (3, +1) CPs that define the local minimum of charge in the face on the metal graph.
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topology predicts adsorption mechanisms such as those shown in Fig. 3, i.e. the adsorption pathway is initially determined by mutual alignment of the (3, −3) CP in the C atom with the (3, +1) CP on the top atoms of the surface. The bridge-site (Fig. 3a) involves attractive interactions with two atoms of the surface: face (metal top atom)–vertex (C atom)–face (metal top atom). The top-site (Fig. 3b) involves the attractive interaction vertex (C atom)–face (metal top atom). These results are in accord with experimental [32–38] and theoretical [39–44] findings. IR reflection absorption spectroscopy (IRAS ) [32], electron energy loss spectroscopy ( EELS ) [32], low energy electron diffraction (LEED) [33,36 ] and thermal desorption spectroscopy ( TDS ) [33] studies have shown that in Rh(100) and Pd(100) surfaces at coverage h<0.5 and low temperature (80–300 K ), the CO molecule is adsorbed in a bridged bond arrangement. A Fourier transformIRAS–TDS study [34] in the temperature range 125–350 K showed that at a coverage below h= 0.5 the CO adsorbs on the Ni(100) surface at top and bridge sites. The population of the sites is temperature dependent; bridge sites are favored over top sites at low temperature and vice versa. In the Cu (100) case, infrared spectroscopy–LEED [35] and dynamical LEED–EELS studies [37] have shown that at low coverage and low temperatures the CO molecules sit on top atoms forming a c(2×2)-CO structure. Ab initio [39–42] and semiempirical [43,44] CO adsorption studies on a cluster model of the Cu, Ni, Pd and Rh (100) surface have been reported. It is generally concluded that CO prefers to adsorb in the top site on Cu and Ni and in a bridge site on Pd and Rh, but the adsorption energy difference between the different coordination sites is small. In all cases, the optimized geometry of the clusters confirms that the CO molecule is perpendicularly linked to the (100) surface. In the present paper, binding of the CO molecule on the Cu, Ni and Pd (100) surface was explored using the powerful algorithms included in the CASTEP program [45]. In that program, a Car–Parinello approach [46 ], the conjugate gradients minimization scheme [47] is utilized to locate the electronic ground states directly [48]. Pseudopotentials in Kleinman–Bylander form [49]
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and the generalized gradient approximation of Perdew and Wang [50,51] are also utilized. Additionally, the geometry of the system studied can be optimized according to forces calculated by the Hellmann–Feynman theorem and total energies. We modeled the surface with a ˚ 3 super-cell of three atom 앀2a×앀2a×14.0 A layers fixed at bulk-terminated {100} positions. ˚ were used to Vacuum layers thicker than 10 A ensure that there was no interaction between adjacent slabs. One CO molecule was placed on the surface sites studied and the CMO, CMMetal distances and tilt angles relative to the surface plane were completely optimized. In all cases, CO remains perpendicularly adsorbed.2 We have found that the CO adsorption on the top site is 12.43 kcal/mol and 9.96 kcal/mol more stable than the bridging site for Cu and Ni respectively, whereas in Pd case the bridge site is 15.02 kcal/mol more stable than the top site. These results confirm the experimental and cluster inferences and also the Laplacian analysis predictions. In conclusion, attractive interaction between the surface and only one atom of the CO molecule rule out dissociation and predict molecular adsorption. Additionally, the topological theory also predicts that the attractive (C )V –(metal top atom)F nb interaction will be stronger as the value of the −V2r at the F (maxima local charge depletion) CP decrease. Therefore, as we can see from Table 1, the predicted order of decreasing C–Metal interaction strengths is Rh (5.856)>Pd (8.335)>Ni (44.638)>Cu (65.161). The experimental [52] trend of heats of adsorption, DH (a measure of ads bond strength) at room temperature of CO on the (100) surface is Pd (36.0 kcal/mol )>Ni (26.1 kcal/mol )>Cu (16.6 kcal/mol ). There are several difficulties in comparing the Laplacian and DH trends. Ab initio Laplacian determination ads has meaning at 0 K on ideal surfaces while DH are determined at room temperature. ads 2 The optimized geometrical parameters found are as follows. ˚ , R(CuMC )=1.814 A ˚ ; Ni, Top-site: Cu, R(CO)=1.170 A ˚ , R(NiMC )=1.810 A ˚ ; Pd, R(CO)=1.160 A ˚, R(CO)=1.165 A ˚ . Bridge-site: Cu, R(CO)=1.175 A ˚, R(PdMC )=1.863 A ˚ ; Ni, R(CO)=1.170 A ˚ , R(NiMC )= R(CuMC )=2.101 A ˚ ; Pd, R(CO)=1.177 A ˚ , R(PdMC )=2.030 A ˚. 2.070 A
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Additionally, DH changes as the experimental ads conditions (temperature, adsorbate concentration, structural defects, etc.) are varied. However, it is very gratifying to note a good match between both trends.
Acknowledgements The authors want to acknowledge CONICIT of Venezuela (Project S1-95001616) for providing funding for the SGI Origin 2000 and SGI O2 workstations used in this work.
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Theoretical study of the CO adsorption on the (100) surface of the face-centered cubic d-block transition metals Yosslen Aray *, Jesus Rodriguez, Juan Rivero, David Vega 1 Centro de Quimica, IVIC, Apartado 21827, Caracas 1020 A, Venezuela Received 22 March 1999; accepted for publication 9 July 1999
Abstract The interaction of a CO molecule with the (100) surface of the fcc d-block transition metals is analyzed by the topology of the Laplacian of the electronic charge density −V2r. This analysis shows that the atomic graph for the top atoms is an octahedron that exposes, outside the (100) surface, a vertex V with a local maximum of charge, top and four faces F with a local minimum. The corresponding graph for the second-layer atoms is also an octahedron top that exhibits a vertex V outside the surface. Atomic graphs for the CO molecule show that the carbon atom has a sec non-bonded vertex C , and a torus C of charge depletion perpendicular to the CMO bond direction. Laplacian nb torus topology predicts CO perpendicular orientation in bridge- or top-sites. The bridge-site involves attractive interactions with two atoms of the surface: face (metal top atom)–vertex (C atom)–face (metal top atom). The top-site involves the attractive interaction vertex (C atom)–face (metal top atom). Attractive interaction between the surface and only one atom of the CO molecule rules out dissociation and predicts molecular adsorption. © 1999 Elsevier Science B.V. All rights reserved. Keywords: ADF-BAND; Atomic graphs; Carbon monoxide; d-block transition metals; Chemisorption; Density functional theory; Laplacian of the electronic charge density
1. Introduction The reactivity of molecules is reflected in the topology of the Laplacian of the charge density, V2r [1–4]. The key is a correlation between the critical points (CPs; maxima and minima) of −V2r in the valence shell and the location of the active sites in molecules. In general, a Lewis acid– base reaction corresponds to aligning a local charge concentration (a maximum on −V2r) of * Corresponding author. Fax: +58-3-504-1350. E-mail addresses: [email protected] ( Y. Aray), [email protected] (D. Vega) 1 Permanent address: FACYT, Universidad de Carabobo, Valencia, Venezuela.
the valence shell on the base with a local charge depletion (a minimum on −V2r) on the acid. This is a general phenomenon that is observed in many different kinds of interaction [5], examples being the formation of hydrogen bonds [6 ], the alignment of chlorine molecules in the solid [7], and the adsorption of molecules on a surface [8–12]. The topological approach has the advantage that the reactivity of molecules on surfaces is directly interpreted in terms of an observable, such as r(r), and is not linked to quantities of doubtful physical meaning such as the Mulliken populations or details of a specific set of molecular orbitals. The Laplacian of the electronic density provides a physical model that guides us in the determination of the sites of adsorption, the geometry of
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Y. Aray et al. / Surface Science 441 (1999) 344–350
approach of the reactant relative to the surface site, and predicts whether the interaction will correspond to physi- or chemi-sorption [8]. CO adsorption on transition metals is an important process in a variety of catalytic reactions [13– 17]. It is well known [18] that the susceptibility of the CO molecule to dissociation upon chemisorption varies systematically depending on the position of the metal in the Periodic Table. Metals on the left-hand side of the Periodic Table (mostly bcc type) dissociatively chemisorb CO, but metals on the right-hand side (mostly fcc type) chemisorb non-dissociatively. The bond strength of the CO chemisorbed on fcc metals, measured as heats of adsorption, tends to decrease as we move rightwards along a row and upwards across a column of the Periodic Table [13]. In the present study, we have applied the topological approach to the study of CO adsorption on the (100) surface of the fcc d-block transition metals (Ni, Cu, Rh and Pd). Topological analysis of the isolated (100) surface shows why CO binds molecularly on that surface and predicts the correct trend of the interaction strength between the CO molecule and the surface studied.
2. Theory The topological properties of a scalar field such as V2r are summarized by its CPs [5]. These are points where the gradient vector field, V(V2r) vanishes, and they are classified according their type (m, n) by stating their rank m and signature n. The rank is equal to the number of non-zero eigenvalues of the Hessian matrix of V2r, whereas the signature is the algebraic sum of the signs of the eigenvalues of V2r. The Laplacian determines where the field is locally concentrated (V2r<0) and locally depleted (V2r>0) [5]. Since electron density is concentrated where V2r<0, the topology of the Laplacian is conveniently given in terms of −V2r. The atomic Laplacian exhibits alternating shells of charge concentration and charge depletion equal in number to the number of quantum shells. The outer valence shell of charge concentration ( VSCC ) contains a spherical surface over which r is maximally con-
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centrated. The distribution of −V2r over this surface in the free atom is uniform if one assumes that the nucleus has a negligible electric quadrupole moment. In general, this surface persists when the atom is in chemical combination, but the surface no longer has a uniform concentration. The formation of a bond produces changes in this distribution, and a number of local maxima, minima, and saddles appear in this surface of charge distribution [3]. The curvature of −V2r normal to this surface, i.e. the radial curvature, is negative, whereas the two tangential curvatures can assume either positive or negative values. If both of those curvatures are negative or positive then a local maximum, a (3, −3) CP, or local minimum, a (3, +1) CP, is formed on that surface respectively. When one of the tangential curvatures is negative and the other is positive a saddle, a (3, −1) CP, will be formed. Each maximum [3] is linked to another one by unique pairs of trajectories of the gradient of −V2r, which originates at the saddle points. The network of those trajectories partitions the surface of charge concentration into segments with curved faces. In the center of each face there is a local minimum in the surface of the VSCC. This structure is called an atomic graph (AG) [3,4] and succinctly summarizes the type and number of the CPs formed on the surface of charge concentration of an atom in a molecule. This graph provides the connectivity of the extremes of the −V2r in the corresponding surface of the VSCC distribution. The AG is most easily visualized in terms of the polyhedron whose vertices ( V ), edges ( E) and faces ( F ) satisfy Euler’s formula [4]: V−E+F=2. The (3, −3) CPs ( local maxima) define the vertices. The unique pair of trajectories that originate at the (3, −1) CPs define the edges, and the (3, +1) CPs ( local minumun) define the faces. A Lewis acid–base reaction corresponds to aligning a charge concentration of the VSCC on the base with a charge depletion on the acid, i.e. by directing a vertex of the graph on the base atom at a face of the polyhedron on the acid.
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Slater basis sets of triple-j quality contained in the ADF-BAND package were used. The topology of −V2r was analyzed using a local version of the BUBBLE program [29] contained in the NUMLAP [30] program and adapted to BAND code and Slater-type orbitals. For Cu we used a slab with three to five layers and the Laplacian topology is found to exhibit no significant dependence on slab depth, the values of −V2r at the CPs, in general, changing by only hundredths of an atomic unit or less. This locality of the VSSC CPs was also previously observed in an MgO topological analysis [8] of −V2r. Therefore, we used a slab of three layers for the other metals.
3. Method The lattice of bulk [19] transition metals considered in this work is described by the Fm3m space group with a=3.6147 (Cu), 3.5236 (Ni), 3.8907 ˚ (Rh). The required surface was (Pd) and 3.8044 A modeled by cleaving of the bulk in the specific plane. Thus, it is periodic in two dimensions, semiinfinite, and aperiodic in the direction perpendicular to the surface. The lack of translational symmetry perpendicular to that surface can be dealt with by approximating the semi-infinite crystal by a slab of finite depth. Experimental studies [20–24] have shown that the (100) surfaces of the metals studied do not reconstruct, with a probable multilayer relaxation of the outer layers of the metal crystals. Therefore, we have studied that surface using a slab model with the same geometrical parameters as the bulk. The electronic densities for the above slab models were calculated by means of the ADFBAND [25] program using the Kohn–Sham Hamiltonian with the gradient-corrected Becke exchange [26 ] potential together with the correlation potential of Perdew [27] and the unrestricted scheme to obtain spin-polarized wave functions. BAND contains a method [28] for calculations on periodic systems in which all aspects of numerical precision are efficiently controlled. The general precision parameter for numerical integration in real space, ACCINT, was taken as a value of four. A total of 15 points (k=5) over the Brillouin zone and the quadratic tetrahedron method were chosen for k-space numerical integration. Full electron
4. Results and discussion The (100) surface exposes alternating rows of up (top layer) and down atoms (second layer) to reacting molecules. We have located the CPs of −V2r on the VSCC of those atoms. The number, position with respect to the top layer, and the −V2r values at the CPs found for top atoms are displayed in Table 1. Those values agree with the corresponding maximum of the VSCC of the free atoms obtained by Shi and Boyd [31] using the Clementi and Roetti wave functions. The AG for the top- and second-layer atoms ( Fig. 1) is an octahedron with six vertices or local maxima of charge concentrations linked by 12 edges and eight faces joining those vertices. The graph of the top atoms exposes a local ‘‘peak’’ of charge, V , and top four minima, F , outside the surface. The graph top
Table 1 Data for CPs of −V2r(r) in the VSCC of (100) surface top atoms of the fcc transition metals (atomic units) CPs
Position with respect to top layer
Ni
Cu
Rh
Pd
One (3, −3) Four (3, −3) One (3, −3) Four (3, −1) Four (3, −1) Four (3, −1) Four (3, +1) Four (3, +1)
above in below above in below above below
59.708 55.815 57.074 47.238 48.744 48.185 44.638 45.919
66.938 67.182 65.976 65.175 64.568 65.111 65.161 64.411
7.966 6.981 7.782 6.182 6.238 6.273 5.856 5.981
10.250 10.165 10.139 9.024 8.257 9.174 8.335 8.505
Y. Aray et al. / Surface Science 441 (1999) 344–350
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Fig. 1. AG for top- and second-layer atoms in the (100) surface of the fcc d-block transition metals. White and gray spheres denote the vertex (a local charge concentration) and the edges respectively. In the center of each face there is a minimum of charge concentration. The lines indicate the direction of the bond with the first nearest neighbors of the atom. In the case of the top atoms four outwardly directed bonds are missing.
of the second-layers atom also exhibits a vertex V outside the surface. The remaining five vertices sec point toward the second nearest neighbors of the atom. According to the Laplacian topology, the AGs found predict that the second-layer atoms prefer an interaction with an AG face on an atom of the adsorbate molecules. Top atoms can interact with faces or vertices on the incoming molecules by means of the V or F points respectively. top top The charge concentration distribution of the CO ground state [12] is shown in Fig. 2. The O atom shows two local maxima of charge concentrations located along the CMO directions. One is facing the carbon atom, O , whereas the other is V in the opposite side of the b shell forming a nonbonded vertex, O . A ring of degenerated CPs Vnb in a plane perpendicular to the CMO directions completes the O AG. The values of −V2r at O ,O and ring CPs reported in Ref. [12] are Vb Vnb 3.337 a.u., 3.744 a.u. and 1.418 a.u. respectively. The carbon atom exhibits only one local maximum (C ), which is located in the non-bonded region. Vnb
Fig. 2. Three-dimensional cross-section of the Laplacian distribution for carbon monoxide, showing the structure of CO VSSC. The contour values plotted are 0.0 and −2.5 a.u. The AGs of the C and O atoms are superposed. Small white spheres denote the vertex ( local maximum of charge concentration). Gray rings denote the torus of charge depletion and the degenerate minima of charge concentration in C and O atoms respectively. Only two edges are shown to keep the graphics uncluttered.
A torus of charge depletion (C ), around the torus internuclear axis with a ring of degenerated points is also present in the C AG. The values of −V2r and C CPs reported in Ref. [12] are at C torus Vnb 0.912 a.u. and −0.022 a.u. respectively. The negative value of −V2r at C is characteristic of the torus depletion zone of electronic charge density. The radial curvature of O , which measures the Vnb degree of contraction along the radial directions
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towards the nuclei, is much bigger than that of C [12]; therefore, the O atom should be able to V actnbas a hard base and the C atom as a soft base. Thus, according to the topological theory, the CO molecule can act as an electron donor by means point or as an electron acceptor of the C V through thenbC ring. torus From experiments [18] it is well known that CO adsorption tends, at room temperature, to be dissociative for transition metals on the left-hand side of the Periodic Table, but non-dissociative on the right-hand side. The bcc metals Fe, Mo and W give the borderline between molecular and dissociative adsorption [18]. The previously discussed AGs of the CO molecule and the (100) surface atoms explain why the CO adsorption is non-dissociative on the (100) surface of the fcc d-block transition metals. A previous analysis [12]
(a)
of the Laplacian topology of the Fe (100) surface showed that the AG of the top-layer Fe atoms is a cube that exposes a face, F , with a local top minimum of charge; the corresponding graph for the atoms of the second layer, however, is an octahedron that exhibits a vertex, V , or local sec ‘peak’ of charge to the incoming molecules. Thus, CO interacts with the Fe (100) surface in tilt orientation involving attractive interactions: C –(Fe)V and O –(Fe)F . Those attractorus sec V top tive interactions of thenbC and O atoms, towards two atoms of the surface, lead to bond breakage of the CO molecule. In contrast to the Fe case, in the fcc d-block transition metals, CO tilted on the (100) surface through the C –(Metal )V contorus top nection leads to a non-attractive vertex–vertex interaction of the V framework of the O atom nb with the V of the neighbor metals. Laplacian top
(b)
Fig. 3. CO orientation on fcc metals (100) surface predicted by the Laplacian topology. (a) Bridge site; (b) top site. White arrows show the attractive interactions: vertex (C atom)–face (top atoms). The arrows point to spheres with a cross representing the (3, +1) CPs that define the local minimum of charge in the face on the metal graph.
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topology predicts adsorption mechanisms such as those shown in Fig. 3, i.e. the adsorption pathway is initially determined by mutual alignment of the (3, −3) CP in the C atom with the (3, +1) CP on the top atoms of the surface. The bridge-site (Fig. 3a) involves attractive interactions with two atoms of the surface: face (metal top atom)–vertex (C atom)–face (metal top atom). The top-site (Fig. 3b) involves the attractive interaction vertex (C atom)–face (metal top atom). These results are in accord with experimental [32–38] and theoretical [39–44] findings. IR reflection absorption spectroscopy (IRAS ) [32], electron energy loss spectroscopy ( EELS ) [32], low energy electron diffraction (LEED) [33,36 ] and thermal desorption spectroscopy ( TDS ) [33] studies have shown that in Rh(100) and Pd(100) surfaces at coverage h<0.5 and low temperature (80–300 K ), the CO molecule is adsorbed in a bridged bond arrangement. A Fourier transformIRAS–TDS study [34] in the temperature range 125–350 K showed that at a coverage below h= 0.5 the CO adsorbs on the Ni(100) surface at top and bridge sites. The population of the sites is temperature dependent; bridge sites are favored over top sites at low temperature and vice versa. In the Cu (100) case, infrared spectroscopy–LEED [35] and dynamical LEED–EELS studies [37] have shown that at low coverage and low temperatures the CO molecules sit on top atoms forming a c(2×2)-CO structure. Ab initio [39–42] and semiempirical [43,44] CO adsorption studies on a cluster model of the Cu, Ni, Pd and Rh (100) surface have been reported. It is generally concluded that CO prefers to adsorb in the top site on Cu and Ni and in a bridge site on Pd and Rh, but the adsorption energy difference between the different coordination sites is small. In all cases, the optimized geometry of the clusters confirms that the CO molecule is perpendicularly linked to the (100) surface. In the present paper, binding of the CO molecule on the Cu, Ni and Pd (100) surface was explored using the powerful algorithms included in the CASTEP program [45]. In that program, a Car–Parinello approach [46 ], the conjugate gradients minimization scheme [47] is utilized to locate the electronic ground states directly [48]. Pseudopotentials in Kleinman–Bylander form [49]
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and the generalized gradient approximation of Perdew and Wang [50,51] are also utilized. Additionally, the geometry of the system studied can be optimized according to forces calculated by the Hellmann–Feynman theorem and total energies. We modeled the surface with a ˚ 3 super-cell of three atom 앀2a×앀2a×14.0 A layers fixed at bulk-terminated {100} positions. ˚ were used to Vacuum layers thicker than 10 A ensure that there was no interaction between adjacent slabs. One CO molecule was placed on the surface sites studied and the CMO, CMMetal distances and tilt angles relative to the surface plane were completely optimized. In all cases, CO remains perpendicularly adsorbed.2 We have found that the CO adsorption on the top site is 12.43 kcal/mol and 9.96 kcal/mol more stable than the bridging site for Cu and Ni respectively, whereas in Pd case the bridge site is 15.02 kcal/mol more stable than the top site. These results confirm the experimental and cluster inferences and also the Laplacian analysis predictions. In conclusion, attractive interaction between the surface and only one atom of the CO molecule rule out dissociation and predict molecular adsorption. Additionally, the topological theory also predicts that the attractive (C )V –(metal top atom)F nb interaction will be stronger as the value of the −V2r at the F (maxima local charge depletion) CP decrease. Therefore, as we can see from Table 1, the predicted order of decreasing C–Metal interaction strengths is Rh (5.856)>Pd (8.335)>Ni (44.638)>Cu (65.161). The experimental [52] trend of heats of adsorption, DH (a measure of ads bond strength) at room temperature of CO on the (100) surface is Pd (36.0 kcal/mol )>Ni (26.1 kcal/mol )>Cu (16.6 kcal/mol ). There are several difficulties in comparing the Laplacian and DH trends. Ab initio Laplacian determination ads has meaning at 0 K on ideal surfaces while DH are determined at room temperature. ads 2 The optimized geometrical parameters found are as follows. ˚ , R(CuMC )=1.814 A ˚ ; Ni, Top-site: Cu, R(CO)=1.170 A ˚ , R(NiMC )=1.810 A ˚ ; Pd, R(CO)=1.160 A ˚, R(CO)=1.165 A ˚ . Bridge-site: Cu, R(CO)=1.175 A ˚, R(PdMC )=1.863 A ˚ ; Ni, R(CO)=1.170 A ˚ , R(NiMC )= R(CuMC )=2.101 A ˚ ; Pd, R(CO)=1.177 A ˚ , R(PdMC )=2.030 A ˚. 2.070 A
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Additionally, DH changes as the experimental ads conditions (temperature, adsorbate concentration, structural defects, etc.) are varied. However, it is very gratifying to note a good match between both trends.
Acknowledgements The authors want to acknowledge CONICIT of Venezuela (Project S1-95001616) for providing funding for the SGI Origin 2000 and SGI O2 workstations used in this work.
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