Requirements for activation of surface oxygen atoms in MgO using the Laplacian of the electron density

surface science ELSEVIER

Surface Science 351 (1996) 233-249

Requirements for activation of surface oxygen atoms in MgO using the Laplacian of the electron density Y. A r a y a, R . F . W . B a d e r b,, a Instituto Venezolano de Investigaciones Cientificas, IVIC, Centro de Quimica, Apartado 21827, Caracas 1020-.4, Venezuela b Department of Chemistry, McMaster University, Hamilton Ont. L7L2T1, Canada Received 9 August 1995; accepted for publication 28 November 1995

Abstract

This paper demonstrates that the Laplacian of the electron density, the quantity VZp(r), can be used to determine the conditions required for activation of a surface atom and thus guides one in determining surface adsorption sites. It also predicts the geometry of approach of the substrate relative to the surface site and whether the interaction will correspond to physi- or chemisorption. The topology of the electron density and its Laplacian distribution for bulk MgO, its (100), (110) and (140) surfaces, as well as of embedded clusters that model these and other structural features of the surface, are studied to determine the conditions required for chemisorption of carbon monoxide. The unreactive nature of five-coordinated oxygen in the (100) surface is retained when its coordination is decreased to four in a step or to three in a corner. It is shown that electronic excitation can activate a surface oxygen atom towards reaction with a Lewis base through the creation of a "hole" in its valence shell of charge concentration, as defined by the topology of the Laplacian distribution. The results determine the site responsible for the formation of the CO~ radical anion on the surface of thermally activated MgO in the presence of CO gas. It also shown how a neighbouring activated oxygen atom in a stepped surface can lead to the formation of carbonate ion.

Keywords: Ab initio quantum chemical methods and calculations; Adhesion; Magnesium oxides; Models of surface chemical reactions; Single crystal surfaces

1. Introduction

Surfaces of the MgO crystal are important in a wide variety of catalytic processes and their interaction with adsorbed molecules has been extensively studied, experimentally and theoretically [ 1]. The theoretical studies have in the past been hampered by the lack of a physical model that can be used as a guide in the understanding and interpretation of the calculations. Obtaining an energy of interaction for some particular approach * Corresponding author. Fax: + 1 905 522 2509. 0039-6028/96/$15.00 © 1996 Elsevier Science B.V. All riglats reserved PII 0 0 3 9 - 6 0 2 8 ( 9 5 ) 0 1 3 5 2 - 0

geometry of the adsorbent molecule towards some particular site on the surface falls short of providing an understanding of the process, and it has proven difficult to predict the conditions required to observe chemical, as opposed to physical binding of a substrate such as carbon monoxide to a magnesium oxide surface. An oxygen atom in the (100) surface of MgO can be activated towards the abstraction of hydrogen from methane by the formation of a vacancy or by doping with alkali metal ions. It was recently shown [2] that the laplacian of the electron density, the quantity V2p(r), accounts for the activation through the formation of a region

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of local charge depletion, a "hole", in the valence shell charge concentration (VSCC) of the surface oxygen atom. An earlier paper reported on the correlation of the depth of the hole on oxygen in MgO and LiO molecules with the decrease in activation barrier for their abstraction of hydrogen from methane [3]. In this paper, the topology of the electron density and its Laplacian for bulk MgO, its (100), (110) and stepped (140) surfaces, as well as of embedded cluster models of these and other structural features are studied to determine the conditions required for chemisorption of carbon monoxide. It is again found that activation requires the formation of an accessible hole in the VSCC of the oxygen atom, its appearance in this case being the result of electronic excitation. The (100) surface of MgO is the most stable in terms of its surface energy and is the preferred cleavage plane [4]. Several studies have shown there is virtually no "rumpling" or surface relaxation for a defect-free (100) surface and it can be considered to be a simple bulk termination [5]. The (110) surface is stepped, corresponding to a set of (100) terraces with a single step in each lattice parameter [6]. The adsorption of CO on MgO surfaces has been extensively studied because of its role in heterogeneous catalysis [7]. Spectroscopic studies [ 8 - 1 2 ] have suggested formation of radicals or polymers of the CO molecule. Infrared spectra of CO adsorbed on sintered polycrystalline MgO have indicated that the CO is vertically adsorbed to a Mg ion in the (100) plane of the crystal [8]. An adsorption heat of 3 kcal mol-1 was calculated from integrated intensities [-9]. On the basis of ultraviolet reflectance spectra it has been proposed that CO forms dimers and oligomers such as (CO)~- which arise from an electronic donor process from surface oxide ions to CO, thus forming the anionic clusters [10,11]. Thermal evolution of a small amount of CO2 from MgO at 9 7 0 K following its absorption at 373-473 K has been reported [123. Oxygen isotopic exchange between CO and a MgO surface as reported for thermal-desorption gas analysis in the temperature range 1 0 0 - 8 0 0 K indicates a chemisorptive dissociation of CO [13]. Transmission-electron microscope studies in this latter

case suggested the presence of surface defects consisting of ultrafine grains. Ab initio calculations of small MgO clusters embedded in an array of point charges to simulate the Madelung field of the surrounding lattice have been used to study CO adsorption on non-defective (100) surface and extended defects on this surface in the form of corners and steps [14-16]. Charges of __2.0e (where e denotes the proton charge throughout the paper) were assumed for both the bulk and (100) surface atom. The calculations predicted the adsorption of CO to occur only at a Mg atom site through the carbon, with binding energy of 9 kcal mo1-1 accompanied by only a small degree of charge transfer, as determined using Mulliken charges. The binding was found to be slightly stronger at corners and steps and to occur only at the cationic sites. These results were verified in more realistic calculations employing a periodic slab to model the adsorption of CO to a nondefect (100) surface [17] and the stepped (110) surface [18]. Adsorption, without charge transfer, was found to occur only at the Mg atoms on both the planar and stepped surfaces, a value of 4.3 kcal mo1-1 for the binding through the carbon atom was determined for the (100) surface. The energy for adsorption to a Mg atom on a step was found to be 50% larger than for the (100) surface. Unlike the cluster approach, the slab calculations also predict binding, with an energy of 3.3 kcal tool -~, through the oxygen of CO to a Mg atom on the (100) surface. The same optimized basis set was used for both the bulk and slab calculations which indicated that the bulk is essentially completely ionic in terms of a Mulliken population analysis, with a slight decrease in net charge noted in the slab calculations. The general conclusions of these calculations is that normal and stepped surfaces of MgO do not lead to the chemisorption of CO or to its subsequent oxidation or polymerization to form the observed paramagnetic species. Chemical reaction of CO with MgO is however, predicted to occur if one uses a model which reduces the ionicity of the atoms in the vicinity of the site of adsorption. Matsumura et al. [ 19] have used clusters to model a step site and found that if the cluster is embedded in a set of point ions with net charges of +_0.18e rather than the usual

I1. Aray, R F W. Bader/Surface Science 351 (1996) 2 3 3 ~ 4 9

values of _+2.0e, the carbon of a CO molecule interacts with two oxygen atoms in the surface and is subsequently oxidized to form a carbonate-like ion species. The Mulliken charges on the ions in the cluster are reduced to 1.36e in this reduced Madelung field. Similarly, the same authors [13] find that a Mg vacancy in the cluster model, embedded in the same reduced Madelung field, results in the trapping of CO as the CO2 molecule on the point defect. These calculations demonstrate the importance of the degree of ionicity of the ions in the vicinity of the defect in accounting for the experimental observations. It is well established that O - centres on oxide surfaces are the sites for cleaving C - H bonds, as summarized by Mehandru, Anderson and Brazdil [20]. These authors, in a molecular orbital based cluster model calculation of the oxide surface, have demonstrated a reduction, relative to the bulk, in the band gap between the top filled band, mostly 2p on O, and the vacant Mg 3s and 3p bands for the surface. The use of a Mg210 2+ cluster leads to the introduction of a hole in the 2p band of the surface and correspondingly, to the formation of an O - ion and zero activation barrier for H atom abstraction from methane. It is shown here that electronic excitation of the surface leads to the formation of an oxygen atom with a greatly reduced net charge and with a pronounced hole in its valence shell Laplacian distribution. Activation of oxygen atoms by doping a MgO cluster with an alkali metal ion has the same effect of reducing the net charge on the oxygen atom in the adjacent surface [2].

2. Calculations The Hartree-Fock SCF CRYSTAL 92 program [ 21] was used for the calculation of wave functions for crystalline MgO. This program has been used previously for the study of bulk and surface properties of MgO [22-24], and for bulk Li20 [25] and other ionic solids [26]. The choice of basis set is important in terms of accuracy of the computed electron density, relative to the required computer time [27]. This work used the same basis Causa et al. [24] employed in their study of MgO; a

235

(15s,6p/3s,2p) basis for Mg and a (14s,5p/3s,2p) for oxygen. The valence shell s and p functions were optimized for the bulk, including additional 3s and 3p functions for Mg. A 6-31G* basis set was used for the description of carbon monoxide. The topology of p(r) and VZp(r) were analyzed using a locally modified version of the program T O P O N D [28]. Small clusters of MgO embedded in a mesh of point charges were also studied to investigate the effect of electronic excitation of the solid on the adsorption process, studies not possible using the periodic code of CRYSTAL 92. Previous studies have shown that such embedded clusters of MgO reproduce the topologies of p(r) and VZp(r) and their critical point data found for the bulk to within a few per cent [2]. The embedded cluster methodology contained in GAUSSIAN 92 [29] was used in the cluster calculations using the same basis sets employed for the bulk. Excited states of the dusters were determined using the CI-singles procedure [30] implemented in GAUSSIAN 92. The topologies of p(r) and VZp(r) for the clusters were analyzed using the AIMPAC suite of programs [ 31].

2.1. Structure and reactivity and the topologies of p and V2p 2.1.1. Structure of bulk MgO and the topology of the electron density The gradient vector field of the electron density yields a definition of structure in a molecule or a crystal by associating a chemical bond with those pairs of atoms whose nuclei are linked by a line of maximum electron density, a bond path [32]. A bond path determines and characterizes all of the atomic interactions in a given system [33,34] and has proven useful in the analysis of physical properties of insulators, metals and alloys [33-36]. The topological definition of structure is illustrated for bulk MgO in Fig. 1 and the data for the parameters that characterize each interaction are given in Table 1. The Table identifies the critical points within a unit cell with the corresponding Wyckoff letter in the International Tables for Crystallography [37], which serve as an aid in determining the topology of the electron density of an extended system [33]. Each bond path is

236

0

Y. Aray, RF. W. Bader/Surface Science 351 (1996) 233-249

Mg 8

0

0 /

Mg b

0 <

S

e

el

Fig. 1. Trajectories traced out by gradient vectors of the electron density; trajectories of Vp(r), in the (100) (a) and (110) (b) planes of MgO. The region of space traversed by trajectories that terminate at a given nucleus where p(r) is a local maximum, defines the basin of the atom. Each atom is bounded by sets of trajectories that terminate at (3,-1) or bond critical points. Only one pair from such a set appears for each bond critical point (denoted by a dot) in the (100) or (110) planes, as indicated for an O-O interaction in (a). A unique pair of trajectories also originate at each bond critical point defining a line of maximum electron density linking bonded nuclei, the bond path, as also indicated in (a). The remaining critical points in the (100) plane are (3,+ 1) or ring critical points (denoted by a triangle) and in this plane they denote points where p(r) is a minimum. In the (110) plane there are (3, + 3) or cage critical points (denoted by a square) where p(r) is a local minimum in addition to the same set of ring critical points shown in (a). Field maps (c) and (d) are plots of p(r) in the (100) and (110) planes overlaid with interatomic surfaces and bond paths, as defined by the gradient vector fields in (a) and (b).

defined by the unique pair of trajectories that originate at a ( 3 , - 1 ) or b o n d critical point. The gradient m a p displayed in Fig. 1 shows each M g a t o m to be linked by b o n d paths to six neighbouring oxygens, while each oxygen is, in addition, linked to twelve neighbouring oxygen atoms. The

basins of neighbouring atoms are separated by an interatomic surface defined by the trajectories terminating at the b o n d critical point. Thus each a t o m is b o u n d e d by a set of such surfaces which comprise its atomic surface. The M g a t o m is cubical in shape, while the oxygen is eighteen sided. A n interatomic surface exhibits a zero flux in the gradient vector field of the electron density. A region of space b o u n d e d by such surfaces is a proper open system, one whose observables obey the equations of m o t i o n defined by the principle of stationary action and all properties of the topological a t o m are defined by q u a n t u m mechanics [32,38]. A p r o p e r t y of immediate interest is the average electron population obtained by an integration of p(r) over the basin of an atom. Atomic charges determined in this manner, since they are the expectation values of the n u m b e r operator, are determined by the distribution of electronic charge within the system, and, unlike Mulliken charges, exhibit minimal basis set dependence. The atomic charges obtained for the atoms in M g O bulk are __ 1.82e. The value of the electron density at an M g - O b o n d critical point, denoting the primary interaction, is twice that for a secondary O - O interaction. Such weaker secondary interactions also link anions in other crystals and are particularly i m p o r t a n t in understanding the structures of molecular crystals, by defining the intermolecular interactions found in the crystalline forms of COz and C12, for example [ 3 4 ] . The relatively small values of the density and the positive values for the sum of its curvatures 2i, as found at the b o n d critical points in bulk M g O , quantities denoted by Pb and Vgpb, are characteristic of interactions between closed-shell ions. Such interactions are d o m i n a t e d by the Pauli principle which leads to a depletion of electron density in the interatomic surface and hence to low values of Pb. The accompanying separate accumulation of electron density in the basin of each a t o m results in the value of V2pb being d o m i n a t e d by its single positive curvature parallel to the b o n d path.

2.1.2. Topology of the Laplacian of p 32 The Laplacian of any scalar field such as p(r), determines where the field is locally concentrated V2p(r) < O, or locally depleted V2p > O. The atomic

I7. Aray, I~F W. Bader/Surface Science 351 (1996) 233-249

237

Table 1 D a t a for critical points in p for bulk and slab M g O and for adsorption of C O in atomic units Bulk F m 3 m #225; atomic charges = -t- 1.82e Wyckoff letter"

e d h c

24 24 48 8

Critical point b

Curvatures of p(ro)

"~1

22

J'3

-0.047 -0.012 -0.012 0.011

-0.047 --0.011 0.030 0.011

0.354 0.070 0.051 0.011

Mg-Obond O-Obond ring cage

p(ro)

V2p(re)

0.035 0.017 0.015 0.007

0,259 0,047 0.071 0.034

p(rc)

V2p(ro)

0.035 0.017 0.015 0.015

0.256 0.047 0.068 0.034

p(rc)

V2p(ro)

0.037 0.050 0.020 0.019

0.252 0.380 0.056 0.081

(100) surface°; P 4 / n m m #129; atomic c h a r g e s = _+1.81e Wyckoff letter"

c 8 f4 i 8 a 2

Curvatures of p(ro)

Critical point

Mg-Obond d O-O bondd ring d cage

21

22

23

--0.048 -0.013 -0.013 0.011

-0.047 -0.010 0.030 0.011

0.351 0.070 0.052 0.011

(110) surface; P m m n #59; atomic c h a r g e s = -t-1.80e Wyckoff letter"

f4 e4 c4 g 8

Critical point

Mg-O bond e Mg-O bond e O - O bonds ring

Curvatures of p(r~) 21

22

23

--0.049 -0.073 -0.015 -0.016

-0.048 -0.073 -0.017 0.033

0349 0.525 0.083 0.063

C O adsorption on (100) surface Bond

Length (~k)

21

22

23

Pb

V2pb

C - O free C - O adsorbed C-Mg C - O surface Mg-O

1.127 1.127 2.447 3.234 2.105

- 1.698 - 1.685 -0.017 -0.007 -- 0.049

- 1.698 - 1.685 -0.017 -0.005 -- 0.048

4.938 4.862 .1.0.138 0.040 0.348

0.486 0.486 0.014 0.009 0.036

1.541 1.492 0.103 0.028 0.251

a Wyckoff letter a n d multiplicity from International Tables [36]. b Critical points are labelled by rank, n u m b e r of non-zero 2i, and signature, s u m of algebraic signs of 2~. A b o n d critical point is (3,--1), ring (3,+ 1) and cage (3,-t-3). o Results are for a double layer. d For critical points in surface. Same values are obtained for critical points between layers. Position f for b o n d in a row of atoms, position e for bond between rows.

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Y. Aray, R.F W. Bader/Surface Science351 (1996)233-249

laplacian exhibits alternating shells of charge concentration and charge depletion equal in number to the number of quantum shells. The outer shell of charge concentration of a bound atom exhibits localized concentrations of charge which mimic in number, relative position and size the pairs of electrons assumed in the Lewis model, topological features that are absent from the relatively simple topology exhibited by the density itself. Since electron density is concentrated where V2p < 0, the topology of the laplacian is given in terms of -VZp(r), a localized charge concentration then corresponding to a maxima or ( 3 , - 3) critical point in -V2p. The structure of the laplacian for an atom, its atomic graph, is most easily visualized in terms of the polyhedron defined by the maxima in -VZp, a polyhedron whose vertices (V), edges (E) and faces (F) satisfy Euler's formula, V--E+F=2.

The maxima define the vertices V, the unique pairs of trajectories that originate at (3,-1) critical points and terminate at neighbouring vertices define the edges E, and the (3,+ 1) critical points define the faces F. The face critical points define the centres of local depletions in the valence shell of charge concentration. The valence shell charge concentration or VSCC, of an oxygen atom in bulk MgO exhibits six local charge concentrations and its atomic graph is a hexagon. Because of the ionic nature of the crystal, the Mg atom does not possess a valence shell of charge concentration, but the shell associated with its outer core exhibits structure which yields the same atomic graph as found for oxygen. The alignment of the two sets of hexagons is such that the vertices in the atomic graph of oxygen are directed at the faces of the atomic graphs of the neighbouring magnesium atoms with the edges of the oxygen polyhedron being bisected by the O - O bond paths. Because of the high site-symmetry in the crystal, the outer shell of charge concentration of each ion is nearly spherical with the result that the maxima in these shells exceed intervening minima by only small amounts, the maxima in -V2p in oxygen and magnesium equaling 3.000 and 55.160 au respectively, and exceeding the minima by 0.002 au. The radii of the shells are characteristic of the atom

and the shell. The radii for the VSCC in oxygen being 0.69 au and for the outer core of magnesium being 0.41 au. A Lewis acid-base reaction corresponds to aligning a charge concentration on the base with a charge depletion on the acid, that is, by directing a vertex of the atomic graph on the base atom at a face of the polyhedron on the acid, as found in the MgO crystal. This is a general phenomenon that is observed in many different kinds of interactions [32], examples being the formation of hydrogen bonds [39] the alignment of chlorine molecules in the solid [38] and the adsorption of molecules on surfaces [-2,3]. In addition to defining the sites involved in a given interaction, the geometry of approach is defined approximately through the alignment of the relevant critical points. 2.2. Properties of the 100 surface

The lack of translational symmetry in the direction perpendicular to the surface of MgO can be dealt with by approximating the semi-infinite crystal by a finite slab. Causa et al. [23] have shown that the geometry of the layer is essentially unchanged from that in the bulk and that a single layer is sufficient to give many of the surface properties accurately. In this work the (100) surface was studied using one to four layers of MgO atoms parallel to the (100) plane. The topology of both p(r) and its Laplacian are found to exhibit no significant dependence on slab depth for any of the surfaces studied here, the values of the functions at the critical points in general, changing by only hundreths of an atomic unit or less. This is exemplified by the finding that the values for pb(r) and V2pb(r) for both the Mg-O and O-O interactions in the two layer case are essentially unchanged from their values in the bulk, Table 1. The MgO lattice in this bilayer is closely, but not completely, described by the plane group P4/nmm, space group 129 in the International Tables. There are four atoms per unit cell, with the coordinates of a pair of atoms, one in each of the two layers, given by the c positions. Each atom has five oppositely charged nearest neighbours and eight next nearest neighbours of the same charge. The structure, as determined by the gradient vector field map,

239

Y. Aray, R.F. W. Bader/Surface Science 351 (1996)233-249

Fig. 2a, is a truncated form of that f o u n d for the bulk with b o n d paths linking each surface M g to its five neighbouring oxygens and a second set linking next nearest oxygen a t o m s to one another. A m a g n e s i u m a t o m in the surface is linked to only five oxygen a t o m s leaving it with a "free valency". The gradient vector field m a p for the surface, Fig. 2a, shows a set of trajectories, b o u n d e d by two M g - O interatomic surfaces, which originate at infinity above the surface and terminate at the M g nucleus. It is this set that is distorted by the a p p r o a c h of an adsorbate a t o m with which it forms an interatomic surface and b o n d path. It thus represents the "free valency" of the surface magnesium atom. The atomic charges of _+ 1.80e for the surface are essentially u n c h a n g e d from their values in the bulk. However, unlike the bulk atoms, there are large m o m e n t s induced in the surface atoms [ 3 2 ] : the negative end of the dipole on oxygen, with m a g n i t u d e 0.209 au, is directed into the surface and the perpendicular c o m p o n e n t of its traceless q u a d r u p o l e tensor equal to - 0 . 6 3 4 au indicates a significant q u a d r u p o l a r polarization corresponding to an a c c u m u l a t i o n of electronic charge along the perpendicular axis and to its removal from the plane of the surface. The same polarizations are f o u n d for a surface m a g n e s i u m a t o m but, as anticipated for a cation, are m u c h

smaller, the dipolar and q u a d r u p o l a r m o m e n t s equaling 0.008 and - 0 . 0 2 6 au, respectively. The properties of the laplacian at its critical points for the (100) surface are given in Table 2. The atomic graphs for surface atoms, Fig. 3, differ from those f o u n d in the bulk. C o r r e s p o n d i n g to the q u a d r u p o l a r polarization noted above, a surface oxygen exhibits two local charge concentrations (referred to as CC's) lying along the axis perpendicular to the surface, one above and the other below the surface. These two vertices of the atomic g r a p h are joined by four faces with the O - M g axes bisecting the edges. The atomic g r a p h for the magnesium a t o m has four vertices linked by four edges lying approximately in the surface. Table 2 Data for critical points in the Laplacian of p in slab MgO in atomic units (100) surface oxygen atom

magnesium atom

Critical point a

Value

Critical point

Value

(3,-3) above surface (3,-3) below surface four (3,--1) in surface four (3,+1) in surface

-3.141

four (3,-3) in surface four (3,-1) in surface (3,+1) above surface (3,+1) below surface

-55.663

-3.053 --2.930 --2.923

-55.651 --53.620 --54.987

(110) surface

/

I

Fig. 2. Gradient vector field maps of p(r) for the (100) surface in (a) and for CO adsorbed to the surface (b). Bond critical points are denoted by dots, and stars denote ring critical points. The Mg atom binding the carbon, like a Mg atom in the bulk, is six-coordinated and they are strikingly similar in form and spatial extent.

oxygen atom

magnesium atom

Critical pointS

Value

Critical point

Value

two (3,-3) in surface (3,--1) above surface (3,-1) below surface two (3,+ 1) along MgO

-3.448

two (3,-3) along MgO (3,-1) below surface (3,+1) above surface

-56.477

-3.099 -2.700

-56.267 -52.823

-2.687

a Critical points of --VZp are labelled by rank, number of nonzero 21, and signature, sum of algebraic signs of 2i. A (3,-3) denotes a maximum or vertex, a (3,-1) an edge, and a (3,+ 1) a face or "hole" in the polyhedron defining the atomic graph.

Y. Aray, R.F. IV. Bader/Surface Science 351 (1996)233-249

240 y

We-4_~A--q~/o %

•

&

~ ~

xMg

~,

0 - - ~ - - 0

I "-f/

I "~x

(a)

Y

//

''""" ,, i Mg

Mg>__~ _C~._I~ z

\/

(b) Fig. 3. Atomic graphs for surface atoms in (100) surface in (a) and the (110) surface in (b). The y-axis is perpendicular to the surface in (a) and in (b), the x-axis lies along a row of atoms.

Y. Aray, R.F. IV. Bader/Surface Science 351 (1996) 233-249

There are two (3,+ 1) critical points lying along the perpendicular axis, one above and one below the surface plane, which define the two faces capping the atomic graph. The critical point exposed on the surface is less negative than the hole embedded beneath the surface. A (3,+1) critical point denotes the position where the laplacian attains its least negative value in the shell described by the atomic graph. They mark the "holes" in the shell of charge concentration which serve as sites for the attachment of atoms with exposed charge concentrations, exposed CC's. In the (100) surface of the MgO crystal, such holes occur only above the magnesium atoms and these are the only sites capable of binding carbon monoxide. Binding to oxygen would require that a CC on the adsorbate interact with a CC on the surface. We find that the properties of p and VZp and the atomic properties for the (100) surface are well modelled by the central fivecoordinated ion in one layer of a two-layered Mg909 or Mg~O~z cluster embedded in two corresponding planes of 1440 point charges. This is also a general result: the topology of a suitable cluster is able to model that of a surface and the result is independent of cluster size in this ionic system. The values of the (3,--3) critical point above the surface of an oxygen atom are 3.14 au for slabs consisting of 2, 3 or 4 layers and 3.15, 3.18 and 3.19 au for the same central surface ion in the MgsO~, Mg909 and Mg~2012 clusters, respectively. Corresponding results are obtained for the (110) surface and its cluster models. Experiment [8,9,40] finds that a carbon monoxide molecule is adsorbed vertically to a magnesium atom in the (100) surface with a binding energy of -___3.6 kcal tool -~. Theory finds binding through the carbon at a magnesium [ 14-17] with a binding energy [17] ~4.0 kcal mol -~ or through the oxygen with a binding energy [17] of ~ 3 kcal mol-~. The adsorption of CO through the carbon to the (100) surface was studied here using a twodimension periodic supercell with one-quarter coverage and also using the Mg909 embedded cluster model. Causa et al. [18] have previously shown that total coverage of the (100) surface leads to repulsive interactions between the adsorbed molecules.

241

The gradient vector field map in Fig. 2b demonstrates the formation of a bond path between the carbon of CO and a surface magnesium atom, a result of the interaction of the nonbonded CC on the carbon atom with the hole on Mg, Fig. 4. The magnesium atom is transformed so as to be topologically homeomorphic with a Mg atom in the bulk and similar to it in spatial form and extent. This is a consequence of the carbon forming secondary interactions with the four oxygen atoms that neighbour the magnesium, interactions that mimic the O - O secondary interactions in the bulk. The interactions are summarized in Table 1. The Mg-C bond length is 0.3 A longer than a Mg-O link and the characteristics of the Mg-C bond

\

l i [ [

, \

II I

: I

\

~v/:~k",

t t %~)1.,; \~\

\~

i /

\

~\"~/dt

k \~. : ~

II.

,/." 1/

/~-Z'~, \ \ \ \ \

i I

j

II

i [I

I

I 11~I~--/~-~

;,,,'.,tt,,,.~)/::,, ,, ttl\~.d~/ I

' ' ~ : : / /

\\....

\ \

:

i-i~//

Fig. 4. Laplacian distribution for carbon monoxide molecule adsorbed on the (100) surface of MgO. Solid contours denote negative values of VZp, that is, concentrations of electronic charge, dashed contours, regions of charge depletion. The form of the distribution is important, rather than the values of contours. For this and following diagrams values of V2p at relevant critical points are given in captions or in the text. The nonbonded charge concentration on carbon, of magnitude 1.55 au, is directed at the (3,+ 1) critical point or hole in the atomic graph of the outer core of Mg.

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Y. Aray, R.F IV. Bader/Surface Science 351 (1996) 233-249

path denote a weak closed-shell interaction, the value of Pb being less than half of that for a M g - O interaction in the bulk or surface, the same being true of the interactions between the carbon and the four surface oxygen atoms. While weak, the secondary interactions are important and contribute to the binding. Their presence explains the increase in binding of CO to a Mg atom that is found when a cluster that includes the neighbouring oxygen atoms is used in place of a single magnesium atom embedded in an array of point charges. The values of Pb and V2pb that characterize the relatively weak closed-shell C - M g interaction can be contrasted with the values for the C - O bond, Table 1. The value of Pb for the C - O interaction is nearly forty times larger and the magnitudes of the perpendicular curvatures of p at the critical point, 2a and 22 indicate a considerable accumulation of electronic charge in the internuclear region, as also evidenced by the concentration of charge in this region evident in the Laplacian map, Fig. 4. The interaction, while resulting from the sharing of density by both atoms, is also very polar, as evidenced by the large positive value of 23 and by the net charges of _+ 1.39e on the atoms. The weak nature of the C - M g interaction is reflected in the finding that the parameters characterizing the C - O bond in the adsorbed molecule, including its length, remain almost unchanged from their isolated molecule values. The atomic charges of the Mg, C and O atoms change by less than 0.01e and there is no significant charge transfer from the adsorbed molecule to the surface, the same conclusion being reached by Causa et al [18]. The small dipole on Mg is reduced to near zero by the adsorption of CO, while the large atomic dipole on carbon, directed away from oxygen in CO, is slightly reduced, from 1.71 to 1.68 au with an even greater reduction in its axial quadrupolar polarization from - 0 . 3 9 1 to - 0 . 2 1 0 au. These reductions in the dipolar and quadrupolar polarizations of the base atom are characteristic of such closed shell interactions, being found in hydrogen bonding as well, and correspond to the removal of electron density from the line of approach of the interacting atoms [39]. Similar results for the topological indices and atomic properties are obtained using

the Mg909 embedded cluster, but the adsorption energy is reduced from the extended slab value of 4 to 3 kcal m o l - ~. The very pronounced nonbonded CC on carbon that interacts with the region of charge depletion or "hole" in the outer shell of charge concentration on a surface Mg atom is evident in the Laplacian map, Fig. 4. The nonbonded CC on carbon, while of smaller magnitude than that on oxygen, 1.45 compared to 6.17 au, binds the more strongly of the two since it is less tightly bound and of greater spatial extent. The magnitude of the CC on carbon is increased to 1.55 au in the adduct.

2.3. Properties of the 110 surface Following Causa et al. E223 the (110) surface was modelled and its geometry optimized using a two-layer slab parallel to the (110) plane. The (110) surface consists of alternating rows of up and down atoms, Fig. 5a. A seven per cent compression of the surface plane is found [22] with the MgO distance of 3.978 au in a row of atoms reduced to 3.720 au between up and down rows. Each atom in an up row has four nearest neighbours that are of opposite charge, two located in the same row and two in down rows, and four second nearest neighbours of the same charge located in down rows. A contour map of the electron density of the top rows of atoms is shown in Fig. 5b. The bond paths indicated in the figure show that each magnesium atom in a given row is linked to two oxygens in the same row and to two more in neighbouring rows, down or up to the row in question. In addition, each oxygen atom in an up row is linked to four other oxygens in two neighbouring down rows. The six primary interactions in the bulk are reduced to five in the (100) surface and to four in the (110) surface, while the twelve secondary interactions in the bulk are reduced to eight in the (100) surface and to four in the (110) surface, the decrease in bond paths per structural unit paralleling the decrease in their relative stabilities. The values of Pb and of Vepb for the primary and secondary interactions in the (110) surface are very similar to the values for the (100) surface. The values of pb(r) for the (110) surface exhibit slight increases relative to the values for the bulk with

II. Aray, R.F W. Bader/Surface Science 351 (1996) 233--249

243

into the surface and it together with two charge concentrations lying along the M g - O axes in the row of atoms completes the atomic graph of a surface Mg. The atomic graph of oxygen consists of two holes opposed to the charge concentrations of the neighbouring magnesium atoms in the same row, two charge concentrations displaced towards the interior and directed towards the magnesium atoms in neighbouring rows, and two ( 3 , - 1 ) critical points along the axis perpendicular to the surface, one below and one above. The value at the exposed critical point is 0.04 au more negative than the exposed charge concentration for an oxygen in a (100) surface. Thus oxygen atoms in the (110) surface, like those in the (100) surface, expose only critical points where charge is concentrated rather than depleted and they do not serve as receptor sites for adsorbate bases.

\

/

2.4. Steps and corners

( \

Fig. 5. (a) Model of the 110 surface illustrating the alternating rows of up and down atoms; (b) contour m a p of the electron density for the top rows of atoms in the (110) surface. The bond paths and b o n d critical points are indicated for the central row of atoms by solid fines and dots. Bond paths directed to atoms in down rows from the central M g and its neighbouring oxygens are indicated by dashed lines, an open circle denoting an oxygen, an open square a M g atom in a down row.

the value for a row bond being greater than for one between adjacent rows. Similar to its behaviour in the (100) surface, the magnesium atom in the (110) surface exhibits an exposed (3,+ 1) critical point or hole in - V 2 p on an axis perpendicular to the surface which serves as the binding site for adsorption, Fig. 3b. Its value is more positive by 0.8 au than it is for the hole in the (100) surface and correspondingly, the binding of CO to the (110) surface is calculated to be ~ 2.5 kcal mo1-1 more stable than for the (100) surface, the same result obtained by Causa et al [18]. A ( 3 , - 1) critical point lies on the same axis directed

The (110) surface can be transformed into a surface with extended steps by increasing the number of rows of down atoms before stepping up. This is illustrated in Fig. 6a for a (104) surface, which consists of three rows of five-coordinated atoms. It is referred to as a (104) stepped surface and is approximated in its simplest form using a slab of five layers parallel to the (104) plane. The topologies of both p(r) and its laplacian in the three rows of atoms forming the terrace of a step are the same as those found for the corresponding

Fig. 6. (a) Section of the CRYSTAL model of a (104) stepped surface. The rows of atoms of atoms extend to infinity; (b) supercell for modelling of corner atoms.

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five-coordinated atoms in the (100) surface, while in the row forming the edge of the step they are the same as for the four-coordinated atoms in the (101) surface. In addition, there are no significant differences between the values of p(r) and V2p(r) at the corresponding critical points. Since the Laplacian distributions of the outer shells of the oxygen and magnesium atoms are unchanged, a stepped surface is no more reactive towards C O adsorption than are the corresponding atoms in the (100) or (101) surfaces. The same results regarding the unreactive nature of a four-coordinated oxygen a t o m in the edge of a step are obtained for a cluster calculation wherein an oxygen a t o m in the edge is modelled in the planar Mg404 cluster illustrated in Fig. 7a and embedded in a Madelung field consisting of sixtyfour point charges equal to __2.0e. The M g O separations were taken to be the bulk values. The atomic charges increase to _+ 1.90e but the atomic graphs for 05, the five-coordinated oxygen atom lying in the terrace of the step and for 0 4 the fourcoordinated a t o m at the edge as shown in Fig. 8a, are the same as for the corresponding atoms found in the (100) surface and the (104) or (101) step, respectively. An embedded Mg404 cubic cluster, Fig. 7b, serves to model three-coordinated oxygen and magnesium atoms in corner positions. The M g O separation of the two three-coordinated atoms in the edge of the cluster was found on optimization, to decrease from the bulk value of 2 . 1 0 4 ' to 2.014 A while the separations to their neighbours decreased by 0.2 A with the external charges fixed at +2.0e. The Mg and O atoms in the exposed edge have charges of __ 1.80e. The atomic graph for a corner or three-coordinated oxygen atom, Fig. 8b, exhibits an exposed ( 3 , - 3 ) charge concentration with V2p= - 3 . 9 3 au and a pair of (3,+ 1) critical points perpendicular to the indicated plane where V 2 p = - 2 . 6 9 au. Thus a three-coordinated oxygen a t o m is predicted to be unreactive towards C O adsorption. The atomic graph for the corner Mg a t o m exhibits a pronounced hole where VZp = - 51.4 au, these are the most positive values found for a Mg a t o m in any of the structures studied here. Correspondingly, the three-coordinated Mg a t o m

Fig. 7. (a) Diagram of the embedded Mg404cluster model of a single step containing a four-coordinated oxygen atom. The points denote the number and location of the point charges making up the embedding field. (b) The Mg404cubic cluster model of a three-coordinated oxygen atom (c) The Mg404 double-step cluster model. is predicted to bind C O most strongly, with an energy of 13.2 kcal/mol. Furthermore, the optimized angle of 135 ° that the adsorbed C O forms with the M g - O edge of the cube is only 5 degrees greater that the corresponding angle formed by the position of the (3,+ 1) critical point which is the initial predicted site of binding. These results are in agreement with the binding energy of 14.5 kcal/mol and an angle of 140 ° obtained by Colburn and M a c k r o d t [16] using a similar cluster model but a different basis set.

Y. Aray, R.F.W. Bader/Surface Science351 (1996) 233-249

O4

b

0 4 ~

¢

~

03

d

Fig. 8. Laplacian distributions for the ground states and triplet excited states of the single step and cubic cluster models. Critical points (cp's) in -VZp are denoted by squares for CC's or (3,-3)'s and by dots for (3,-1)'s. (a) Ground state of the single step model. The other oxygen shown is 05. The two CC's and a (3,-1) cp on 04 in this plane are of magnitude 3.7 au. Two equivalent (3, + 1) cp's along the axis perpendicular to this plane are of magnitude 1.8 au. (b) Ground state of the cubic cluster, in a diagonal plane. The exposed and interior CC's of the three-coordinated oxygen are of magnitude 3.8 and 3.2 au respectively. The two (3, + 1) cp's of magnitude 2.69 au lie on an axis perpendicular to the plane. The Mg has an exposed hole with the least negative value of V2p (equal to -51.4au) of all the structures. (c), (d) Triplet states of the single-step and cubic clusters, respectively. The curved arrows mark the positions of the exposed holes on 04 and on 03 whose presence activates these atoms towards CO adsorption. The reactivity of three-coordinated atoms can also be studied using the option in C R Y S T A L of constructing a supercell, in this case one consisting of 32 a t o m s in the (100) surface arranged in a 4 x 4 array with a M g 2 0 2 square of a t o m s forming an a d d e d layer in the middle of each supercell, Fig. 6b. This corresponds to a M g 4 0 4 cube with its b o t t o m layer e m b e d d e d in the (100) surface. Optimization of just the four added a t o m s results in a 9 % reduction in the M g O separations. Its laplacian distribution is identical in form to that illustrated in Fig. 8b for a cluster m o d e l of a three-coordinated oxygen discussed above. The a t o m is therefore, unreactive, as are four- and five-coordinated oxygens. The three-coordinated m a g n e s i u m a t o m exhibits the same Laplacian and increased reactivity, as does the c o r r e s p o n d i n g corner a t o m in the cubic cluster.

245

O n l y the V S C C of a M g a t o m in the (100) or (110) surfaces, or in a step or a corner exposes a hole in the surface that serves to bind the charge concentration on the c a r b o n of CO. The binding increases with the size of the hole, the size of the hote (increasing value of VZp) increasing with the decrease in the c o o r d i n a t i o n n u m b e r of the atom. The V S C C of an oxygen a t o m in the same surfaces or in an edge or a corner of a cluster exposes only a charge concentration and is unreactive. In all of these cases the charge on the oxygen is close to the bulk value of - 1 . 8 e . Thus the reactivity of a surface oxygen a t o m towards C O adsorption and subsequent reaction is not a consequence of just its geometry, as determined by the n u m b e r of nearest neighbours, from five in a surface to four in a step to three in a comer. It is shown next that the net charge of a surface oxygen can be substantially reduced and its atomic g r a p h radically altered to yield an exposed hole in its V S C C t h r o u g h electronic excitation.

2.5. Activation of oxygen through electronic excitation Excited states of b o t h the planar and cubic e m b e d d e d M g 4 0 4 clusters were obtained using the "CI-singles" p r o g r a m of G A U S S I A N 92 [ 2 9 ] . The C a u s a et al. [-24] basis set was used to facilitate c o m p a r i s o n with the results obtained for the bulk and surface calculations. The use of the 6 - 3 1 G * basis for the planar step model yields an excited triplet whose Laplacian distribution exhibits a t o p o l o g y identical to that discussed below for the smaller basis, only the critical values of V2p are f o u n d to change slightly. Three luminescent bands in the range 2.60 to 5.70 eV observed for p o w d e r e d M g O have been associated with electron-hole r e c o m b i n a t i o n at the surface [ 2 0 ] . I n the planar step cluster the first three triplet excited states were f o u n d at energies of 4.81, 5.01 and 5.25 eV while for the cubic cluster, the first three triplet excited states were f o u n d at 4.47, 4.50 and 4.75 eV. The four-coordinated oxygen a t o m in the third excited state of the step cluster and the three-coordinated oxygen in the second excited state of the cubic cluster exhibit exposed ( 3 , + 1 ) critical points in their Laplacian distributions and are reactive

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Y. Aray, R.F.W. Bader/Surface Science 351 (1996) 233-249

towards the adsorption of CO. The excitation corresponds to the transfer of an electron to the band comprised mostly of vacant M g 3s and 3p orbitals and one anticipates that the excitation in the clusters, if localized to a particular oxygen atom, will lead to a reduction in its net charge. This is found to be the case. In the step cluster, the charge on 04, the a t o m in the edge of the step, is reduced from - 1 . 9 0 e to -1.65e. The reduction is still greater in the second excited state of the cubic cluster where the charge on 0 3 , the corner oxygen atom, decreases from - 1 . 7 9 e to -0.99e. The first and second excited states of the step cluster have atomic graphs for 0 4 similar to that shown for the ground state in Fig. 8a and charges of --1.93e on 04. The net charge on 0 3 in the first excited state of the cubic cluster is also reduced, to - 1.1e. The atomic graph for 0 4 in the third excited state of the step cluster, Fig. 8c, exhibits an accessible (3, + 1) hole in the valence shell with a value for V2p equal to - 0 . 4 6 au, considerably less negative than the value of - 1 . 7 6 au at the inaccessible (3,+ 1) critical points in the ground state cluster. The hole becomes more pronounced with the use of the larger basis set, with a value of - 0 . 1 5 an. The charge concentrations on 0 4 now lie along the axis in the face of the step and with values of -- 6.39 au directed up and - 5.77 au directed down, are more negative than the values of - 3 . 7 4 au found in the a t o m in the ground state. This dramatic change in the atomic graph is sufficient to weakly activate the oxygen and it adsorbs C O with a binding energy of 5.0 kcal/mol. The final adduct is pictured in Fig. 9a where one sees the incipient formation of the C O 2 radical ion. Only the O C O portion of the complex has been optimized. A complete optimization of the adsorbed C O and the complex, which would lead to a further reduction in the energy, could not be carried out because of computational limitations. The geometry and Laplacian distribution for the isolated radical ion are illustrated in Fig. 9b for comparison. The charges on the atoms in the bound complex are - 1.32e on the terminal oxygen, - 1 . 5 7 e on 0 4 and + 1.85e on carbon (compared to q(O) = - 1.39e and q(C)-- + 1.64e in the isolated molecule), charges which sum to - 1 . 0 4 e for the

C b Fig. 9. Laplacian distributions (a) of CO adduct with 0 4 of single step model; (b) of isolated C O l radical ion; (c) of CO adduct with double step and (d) of triplet state of isolated MgCO3 molecule.

bound fragment. In the free ion the bond angle is 135.2 ° and the bond length is 1.224 ,~ compared to the optimized values for the bound ion where the angle is 130.0 ° and the bond lengths are 1.300 to 0 4 and 1.207 A to the second oxygen. The value of Pb for the bond between C and the external O is 0.41 au, a decrease from that in the isolated molecule, while that between C and 0 4 of the cube has a value of 0.33 au, signifying a significant interaction. The Laplacian distribution of the adsorbed radical ion, like its geometry and atomic charges, is also similar to that of the isolated species, Fig. 9b. In particular the binding of carbon to 0 4 causes the formation of a new nonbonded charge concentration on carbon with a value of - 0 . 9 5 au in the complex and - 0 . 8 8 au in the free radical ion. In addition, both oxygens exhibit two nonbonded charge concentrations, as opposed to the single nonbonded axial concentration present in free CO or CO adsorbed to Mg, Fig. 4. This pattern of nonbonded charge concentrations is typical of a carbonyl oxygen or a CO bridging group in metal carbonyls [41] and is indicative that the adsorption causes a substantial redistribution of electronic charge in the C O fragment. In the single step cluster the nonbonded CC created on carbon is directed away from the oxygen

Y. Aray, 1LF IV. Bader/Surface Science 351 (1996) 233-249

atom and its exposed charge concentration that lies in the step. However, in the triplet state of a double step cluster, which models the (110) surface, both 0 ( 4 ) and 0 ( 5 ) have outwardly directed holes in their VSCC's and the adsorbed CO is twisted relative to the single step case so that the nonbonded charge concentration on C is directed at the hole on 0 ( 5 ) , Fig. 9c with which it forms a bond path. This results in a considerable increase in the strength of binding, to 13.3 kcal/mol, a value that would increase still further if the whole cluster could be reoptimized. As a result of the binding of the carbon to the second oxygen of the step, the product in this case approaches a carbonate ion CO~-, bound to Mg 2÷ whose lowest energy triplet state is depicted an isolated cluster in Fig. 9d. The two equivalent C - O separations in the isolated cluster are 1.24 A compared to values of 1.38 and 2.24 A in the adsorbed species, with the corresponding values of the unique C - O distance equaling 1.31 A and 1.20 ?t, respectively. The oxygen atoms in the carbonate ion, in its ground state or in the triplet state bound to Mg +2, also exhibit the pattern of nonbonded charges typical of a carbonyl oxygen atom [41]. The nonbonded CC's on oxygen bonded just to carbon have magnitudes of - 6 . 5 au compared to - 7 . 0 au in the free molecule, while those on the remaining two oxygens range from - 5 . 0 to - 5 . 3 au compared to - 5 . 2 and - 4 . 9 au in the free molecule, the latter value being for the CC directed at the Mg. It is clear from Figs. 8 and 9, that one result of electronic excitation of a MgO cluster is to cause the atomic graph of an oxygen in an edge or a corner to change into one that has a pattern of nonbonded charge concentrations typical of a carbonyl oxygen as found in the product adducts CO~-, CO3z- or MgCO2, the adduct obtained from the cubic cluster. The corner oxygen, atom 03, in the second excited state of the cubic cluster is by far the most reactive of the oxygen sites investigated here. Fig. 8d shows the presence of two very marked holes in the VSCC of 0 3 lying along the threefold axis of the cube, the one outside of the cube being very accessible to an approaching charge concentration. The valence shell of charge concentration of 0 3 is now broken and the Laplacian at

247

the positions of these two holes is positive, with values of VZp = + 0.04 au and + 0.23 au for the outer and inner holes, respectively. The three-fold axis is encircled by a ring containing three alternating sets of ( 3 , - 3 ) and ( 3 , - 1 ) critical points, with V2p values lying between - 5 . 0 and - 5 . 8 au. Thus the belt of charge concentration is positioned to leave the exposed hole in the VSCC of 0 3 maximally accessible and resembles the pattern of charge concentrations of a carbonyl oxygen. The first excited state is less reactive, as the holes are less accessible, lying along an axis perpendicular to the three-fold axis of the cube and they are considerably more negative, with V2p = - 0 . 4 4 au, the same value as for the single step model. Carbon monoxide binds to the corner oxygen and magnesium atoms in the second exited triplet state of the cubic cluster with an energy of 107.4 kcal/mol to yield the complex pictured in Fig. 10a. Both CO bonds exhibit substantial values for p at their bond critical points, 0.34 au for the bond to 0 3 of the cluster and 0.40 au for the original CO bond. As with the other CO-bound clusters, only the geometry of the atoms external to the cluster have been optimized in minimizing the energy. The oxygen of CO forms a bond path to the corner Mg atom and the adduct has the form of the species COzMg which is illustrated in Fig. 10b. As for the step adducts, the geometry, atomic charges and Laplacian distribution of the adduct are quite similar to those found for the isolated species, as indicated by the diagram and its caption. Here, as in the binding of CO to a four-coordinated oxygen in the double step, the strength of binding is enhanced when the oxygen of CO as well as the carbon bonds with a surface atom.

3. Conclusions

The binding of a Lewis base such as carbon monoxide or methane to a surface oxygen of MgO requires that it have an exposed (3,+1) critical point or "hole" in its valence shell charge concentration. Such holes are not created on oxygen by the introduction of steps or corners. Thus the carbon atom of carbon monoxide binds only to magnesium and never to oxygen in any surface of

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b Fig. 10. Laplacian distributions for (a) CO adsorbed on 0 3 and Mg3 atoms forming the edge of cubic cluster in its triplet state and (b) triplet state of isolated MgCO3. The OCO bond angle and CO bond length of the isolated molecule are 124 ° and 1.232 A compared to 120° and bond lengths of 1.217 and 1.280 A for the bound species. The atomic charges and charge concentrations for the bound and isolated species, the latter in brackets, are q(C)=2.03 (2.06), q(O3)= -1.57 (-1.51), q(O)= - 1.42 ( - 1.51) and nonbonded CC on carbon = - 1.0 au ( - 1.0).

MgO regardless of the extent of coordination of the oxygen atom, from five in the (100) surface, to four in a (110) or a stepped surface to three in a corner position of a cube embedded in the surface, since only the magnesium and never the oxygen possesses an exposed hole in these structures. The same lack of binding to oxygen is found in cluster models of the same surfaces and defects. Surface accessible holes can be created within the VSCC's of oxygen atoms by the introduction of vacancies, by doping with ions of reduced charge [2,3] or by electronic excitation. The electronic excitation requires that the oxygen atom be three- or fourcoordinated, as found in a step or corner defect. It is found that only the oxygen atoms of those excited states which expose a surface accessible

hole also undergo a decrease in their net charge. The reactivity of such four- and three-coordinated oxygen atoms increases with the size of the hole and with the accompanying decrease in its negative charge. This observation explains the findings of Matsumara et al. [19] who found that CO binds to oxygen in a cluster model of a step, if the cluster is embedded in a field of charges equal to _+0.18e. If the single step cluster used in the present study is embedded in such a reduced field, the net charge on 0 4 becomes less negative, changing from - 1.90 to - 1 . 3 0 e and an accessible hole with VZp= - 0 . 5 9 au is formed within its VSCC. This value is only slightly more negative than the value of --0.46 au found for 0 4 in the reactive triplet excited state of the same cluster. This and earlier work [2,3,32] demonstrates the potential usefulness of the topology of the Laplacian of the electron density in determining the conditions governing the reactivity of surfaces and in locating the active centres for the adsorption of either Lewis bases or acids. Adsorption always involves the alignment of a local charge concentration with a local charge depletion or hole in the outer shell of charge concentration of the surface and adsorbent atoms, with either atom assuming either role.

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