J. Phys. Chem. 1995,99, 17010-17018
17010
Electronic Structure of F and V Centers on the MgO Surface Anna Maria Ferrari and Gianfranco Pacchioni* Dipartimento di Chimica Inorganica, Metallorganica e Analitica, Universith di Milano, via Venezian 21, 20133 Milano, Italy Received: June 13, 1995; In Final Form: August 30, I995@
The electronic structure of neutral and charged 0 and Mg vacancies at the surface of MgO (F, F+, FZf, V, V-, and V2- centers) has been investigated by means of cluster models and a b initio wave functions. For each center we have determined the formation energy and the local geometrical relaxation. The distribution of the electrons in the vacancy has been analyzed through the calculation of charge density plots and, for paramagnetic centers, isotropic hyperfine coupling constants. The latter are in good agreement with the EPR data. On F+ surface centers the unpaired electron is largely localized in the vacancy; the corresponding eigenstate is in the band gap. On V- centers, on the contrary, the unpaired electron is delocalized over the surface 0 neighbors and the eigenstate is in the valence band. For the first time we have considered also 0 vacancies at edge sites. The energetics of the formation of these sites and their electronic structure is not too different from that of the corresponding centers on the terraces of MgO, thus reinforcing the hypothesis that edge F centers can exist on the surface of thermally activated MgO.
1. Introduction Most of the chemistry at the surface of metal oxides is due to the presence of highly reactive defect sites.' These sites can be morphological defects such as edges, kinks, steps, and terraces, where the surface ions are low-coordinated, or they can correspond to cation or anion vacancies. In MgO these vacancies are classified as F centers, when an oxygen atom is missing, or V centers, when a Mg atom has been removed.2 F and V centers are naturally present in the bulk of MgO (like the Schottky defects, pairs of cation and anion vacancies), but their concentration can be considerably increased, for instance by y-rays or neutron irradiation of the ~ o l i d . ~In - ~ultrahighvacuum conditions (UHV) surface vacancies are created by impact with Ar+ ions with kinetic energy in the 500-2000 eV range.' In polycrystalline MgO surface vacancies can form by dehydroxylation at high temperatures; at the last stages of dehydroxylation proton migration can produce situations where two hydroxyls form near each other so that water is desorbed at the expense of a lattice oxygen ion:
Once the vacancies are formed, their electronic nature can be changed by adding or removing electrons. The most common techniques to do this refer to F centers. For instance, the use of y-rays causes the excitation of electrons from the valence band into the anion vacancy, thus leading to a "charged" d e f e ~ t . ~ Another common technique is the doping of the surface by metal vapor deposition.6-8 Metals with low ionization potentials, usually alkali and alkaline-earth metals, donate their valence electrons to the surface where they are trapped in the anionic vacancies in the form of F centers6-* Depending on their charge, F and V centers are classified as F2+,F+, F, V2-, V-, and V. The subscript s, F, or V,, usually indicates surface vacancies. The nature of the vacancy and the nomenclature used in this paper are specified in Table 1. Clearly, F,+ and V,- centers are paramagnetic, and their @
Abstract published in Advance ACS Abstracts, October 15, 1995.
0022-365419512099-17010$09.0010
electronic structure can be investigated by means of electron paramagnetic resonance (EPR). For the other, EPR silent, F and V centers the most commonly used techniques for a physical characterization are optical spectroscopies,W and visible, and photoemission, X P S or UPS. In this work we have studied the electronic structure of the F, and V, centers on the MgO surface by means of quantum chemical methods. Using finite clusters of atoms properly embedded in a Madelung field, we have determined the ab initio wave functions for neutral and charged 0 and Mg vacancies at the MgO surface. There are four questions that we would like to answer with this theoretical study. First, we want to compare 0 vacancies at the MgO terraces with similar vacancies at edges; the main difference is that the missing atom or ion is a five(surface) or a four- (edge) coordinated oxygen. The possible existence of paramagnetic vacancies at edge sites has been recently postulated on the basis of EPR data6 but not proved firmly. The second question is still related to EPR investigations and concerns the degree of localization of the open shell electron in F,+ and V,- centers. Third, we have considered the amount of local surface relaxation which follows the creation of the defect; the position of first and second nearest neighbors to the missing atom has been determined by means of analytical gradient techniques. Finally, the aim of this study is also to design cluster models of surface vacancies to be used in future investigations of the interaction with molecules, atoms, and metal clusters. The paper is organized as follows. We describe the details of the calculations in section 2. In section 3 we discuss the energetics of the formation of the F and V centers. In section 4 we report the geometrical data on the defect relaxation. Section 5 is dedicated to the electron distribution within the vacancies; we have examined the charge density plots as well as observable properties like the hyperfine isotropic constants of the paramagnetic centers. The conclusions are summarized in the last section.
2. Computational Method Two different types of clusters have been used to model the vacancy sites at the MgO (100) surface, stoichiometric clusters, 0 1995 American Chemical Society
F and V Centers on the MgO Surface
J. Phys. Chem., Vol. 99,No. 46, 1995 17011
TABLE 1: Clusters Used for the Study of Surface Defects in MgO (100) and Their Nomenclature (after Ref 2) cluster used description of the defect missing atom notation (100) surface site F?+ negative ion vacancy 02negative ion vacancy with 1 e0FS+ 0 negative ion vacancy with 2 eFS positive ion vacancy Mg2+ v,zpositive ion vacancy with 1 hole VSMg+ positive ion vacancy with 2 holes VS Mg
Figure 1. Structure of the 020Mg2~cluster used to model an oxygen vacancy on a terrace of the MgO surface. The cluster has been embedded in a large may of point charges to account for the Madelung potential of the ionic crystal.
Figure 2. Structure of the O13Mg14cluster used to model an oxygen vacancy at an edge site of the MgO surface (see also Figure 1). where the same number of cations and anions is present in the model of the ideal surface, and nonstoichiometric clusters where the number of cations and anions is different; see Table 1 and Figures 1 and 2. In the latter case extra electrons have been added or removed to account for the largely ionic nature of MgO, as indicated also by recent ab initio Hartree-Fock and configuration interaction calculations for cluster models9.I0and periodic systems.” All clusters are “embedded” in a (13 x 13 x 4) array of point charges, PC = f 2 , placed at the lattice positions. This array of PCs models the long-range Coulombic interactions and ensures that the effect of the Madelung potential in the cavity region is included.I2 A similar approach has been followed in other studies of bulk impurities in MgO.I3-l7 Differently from other works,I4 however, the positions of the PCs are not adjusted during the calculation. The entire system, cluster PCs, is neutral for the models of the perfect MgO surface. Neutral and charged defects have been considered; here the notion of “neutral” and “charged” is based on the atom leaving the surface. Thus, the extraction of a neutral 0 atom, which leaves on the surface the two extra electrons of the 02surface anion, leads to a “neutral” F, center; in a similar way, the extraction of a Mg atom gives a neutral V, center. Fs+, F?+, Vs-, and V?- correspond to the removal of 0-, 02-,Mg+, and Mg2+ ions, respectively, Table 1. We have determined all electron restricted Hartree-Fock, RHF, self-consistent field, SCF, wave functions. Unrestricted Hartree-Fock calculations, UHF, were performed only for the determination of the hyperfine coupling constants of the paramagnetic centers; the values of (p)= 0.75 f 0.01 indicate that the states correspond to pure doublets with no spin
+
edge site
contamination. Gaussian type orbital, GTO, basis sets were used to construct the molecular orbitals. Different basis sets were employed for the Mg ions depending on their position in the cluster; the five Mg ions at the vacancy site in F, centers have been treated with a larger basis, [13s8p/6s3p], which includes a good representation of the 3s and 3p Mg orbitals.I2 All the other Mg ions have been treated with single-g (SZ) basis, [8s4p/ 2slp].’* The 12 nearest neighbor 0 ions have been described with a double-5 (DZ) [8s4p/4s2p]basis;’*the rest, with the same basis contracted to SZ. Similarly, in the V, centers the 12 Mg and the 5 0 ions closest to the vacancy are treated with a DZ basis; the rest, with a SZ basis. For the cluster models of the F and V centers, Gaussian functions have been placed at the vacancy site. In particular, we used exactly the same basis of the missing atom, the [8s4p/4s2p] 0 basis for F, and the [13s8p/ 6s3pl Mg basis for V, centers. Thus, different sets of GTOs have been used to describe electrons at the F and V defect centers. However, the basis sets used are flexible enough to describe possible localized electronic states. Furthermore, this procedure removes the basis set superposition error, BSSE,I9 due to the incompleteness of the cluster basis set in the computation of the formation energies.I3 The BSSE for the isolated Mg or 0 atoms or ions is much smaller except for the 0- and 02-ions; in this case, however, other corrections have been introduced to account for the limitations of the theoretical treatment (see below). The relaxation of the ions around the vacancy site has been considered by performing a full geometry optimization by means of analytical gradient techniques. In the smaller clusters only the four top-layer ions around the vacancy were allowed to relax; in [02oMg21]and [Mg20021]relaxation of the second neighbors was also allowed. The remaining atoms of the cluster have been fixed at their lattice positions. The calculations have been performed with the program package Hondo 8 S 2 0 on IBM Risc 6000 workstations.
3. Formation Energies The extraction of an 0 or Mg atom or ion from a perfect MgO surface involves a high energy cost and has been the subject of several theoretical investigation^.'^^^'-^ With charged defects, the long-range polarization of the crystal becomes important and contributes to the decrease in the formation energies. Semiclassical techniques like the shell mode121%22 have proved very effective in taking account of both mechanical and electronic responses of the lattice. Other techniques treat these effects by a simple displacement of the surrounding PCsI4 or by addition of a corrective term.13 An accurate quantummechanical approach is that of ICECAP;23-26-35 here a quantum defect cluster is described in UHF with a self-consistent treatment of the polarization of the surroundings, described by a shell model. All approaches have been applied to the specific case of F centers in MgO. The relative importance of mechanical relaxation and electronic response, however, is not yet well understood; it has been ~ u g g e s t e d ~that ~ ~ ~lattice * relaxation plays a much less significant role in the formation energies of charge defects than do electronic structure effects. Another contribution which is usually neglected in the discussion
17012 J. Phys. Chem., Vol. 99, No. 46,1995
Ferrari and Pacchioni
TABLE 2: F, Centers on MgO: Total Energy for Relaxed eV;. Geometry (Et), au; Relaxation Energy (AEREL), eV; Ionization Potenhal (IP), Formation Energy (AEFoRM), eV . cluster site E, AEREL AEFORM' IP ~
10IN g s l 16[OIZM~S]I~[012Mgs]~~[0l2Mg5]l4[OiNg131 [OI2MgI31 [012Mg13]I+ [01zMg13]~+ KhiMg211 [020Mg211 [02oMgzil1+ [OzoMg21]*+
F,
Fs+ F+: F, Fs+ F?+ F, F,+ F?+
-2533.631 -2458.633 -2458.408 -2457.974 -4121.337 -4046.329 -4046.131 -4045.721 -6301.398 -6226.382 -6226.209 -6225.853
12 16 88 91 76 78 81 12 92 72 66 36
0.11 0.45 1.72 4.20 0.10 0.35 1.51 3.89
7.17 13.76 36.30
6.10 11.81
7.45 13.31 35.23
5.39 11.17
0.28 1.65 5.10
7.67 12.86 33.29
4.71 9.69
-4364.785 40 -4289.81308 -4289.673 07 -4289.308 53
0.10 0.20 0.92 2.49
6.48 10.76 31.42
3.81 9.92
edge site [014Mg141 [013Mg14] F, [013Mg14]I+ F,+ [013Mg14]~+ F>+ a
See text for definition. Reference energies: 0 = -74.734 24 au;
0- = -74.716 72 au; 02-= -74.322 04 au.
of formation energies is that of electronic correlation. In this paper neither correlation effects nor long-range lattice relaxation has been included. Therefore, the discussion of the formation energies must be considered as largely qualitative. We have determined the formation energy of the vacancy as the energy required to remove and bring to infinite distance a surface atom (or ion). For an F, center, this energy is defined as
hEFoRM = EIO,-,Mgm]'"-Y'-
+ E[@-] - EIO,Mgm]"- (1)
For a V, center AEFORM is
hEFoRM = EIMg,-,Om]'"-Y'+
+ E[M$+] - EIMgnOm]"+ (2)
One problem in this definition is that the 02-gas-phase ion does not exist, so that no reference can be made to this dissociation limit in reality. On the other hand, for a fixed set of GTOs there is an HF solution for 02-;we used this energy as a reference for the computation of the formation energies, Table 2. Of course, it must bome in mind that this dissociation limit is unphysical and must be corrected by the experimental double electron affinity, EA, of the 02-ion. Since this anion does not exist, we used for the double EA a recently reported estimated value of 7.7 eV.36 A similar correction has to be applied to 0-; in fact, EAs are poorly described in HF. For all clusters used, we found that the removal of a neutral 0 atom, forming an F, center, has the smallest ~ E F O R Table M , 2. This is reasonable since the presence of the two extra electrons in the vacancy gives rise to a strong Madelung stabilization. The removal of a neutral 0 atom costs about 7.2-7.7 eV depending on the cluster used. This value is not due to the use of an extemal field of PCs. In fact, we found a not too different energy, 6.1 eV, for the extraction of the central surface 0 atom from a [013Mg13] cluster without embedding PCs. For comparison, the energy required to remove a neutral 0 from the (100) surface of NiO, also an ionic crystal, was estimated to be 6.5 eV from complete active space SCF, CASSCF, calculations of clusters in PC fields3' For F, centers, the energy gain due to the cluster relaxation, ~ E R EisLrather , small, 0.3-0.4 eV, so that similar formation energies are obtained with relaxed and unrelaxed clusters, Table 2. The formation energy of an 0 vacancy in bulk MgO has been determined in additive coloring
experiments to be 1.53 eV above the experimental cohesive energy, 10.35 eV, for a total of 11.88 eV.38 A corresponding measure for the surface does not seem to exist, but it is logical to expect that the removal of an 0 atom from a surface site occurs at a lower energy cost. Gibson et aL2' found a formation energy of 1.82 eV for the bulk based on the stationary energy functional method and a slightly smaller value for the surface.28 Similar values for bulk MgO were recently reported by Wang and H~lzwarth.~' The removal of one electron from a neutral F, center to form an F,+ paramagnetic vacancy has a cost of 5-6 eV according to our calculations; see Table 2. Different ionization potentials, IPS, of the F, center are found depending on the clusters used. The differences can be explained with the polarization response of the cluster to the removal of the electron (the IP decreases as the cluster size increases) and not to a different amount of lattice relaxation. In fact, AERELis abut 1.5-1.7 eV for all clusters, Table 2. The formation energy of F,+ refers to the dissociation of an 0- ion. With the present basis set a considerable error arises from the fact that the EA of an isolated oxygen atom is positive, f0.48 eV, and not negative, as it should be. Correcting the 0- total energy by the experimental value of the EA, -1.41 eV, we obtain a reduced value, by 1.9 eV, for AEFORM.With this correction the F,+ formation energy is between 11 and 12 eV. This value should be further corrected by the polarization response of the crystal. The removal of one electron from the F,+ center to form an F?+ vacancy has a cost of 9.7 eV in [020Mg21],i.e. twice as large as the first IP, Table 2. This is due to the fact that the electron in the vacancy is strongly stabilized by the crystal Madelung potential. Thus, the order of stability of the defects is F, > F,+ > F?+, the same reported for the bulk F centers by means of supercell density functional calculation^.^^ The formation energy of a F?+ center must be corrected for at least two terms, the 02-EA and the lattice relaxation, which in this case is quite large. The second EA of 0 is 10.7 eV according to our calculations, while it is estimated to be 7.7 eV in the experiment; because of this error plus that of the first EA, our formation energies are too large by about 5 eV. A classical term which accounts for the continuum relaxation energy has been used by Grimes et aLI3 for the case of bulk MgO charged impurities. The relaxation energy, E(R), around a cavity of radius R is given by
E(R) = e 2 / 2 ~ ( 1- UE,J
(3)
where e is the effective charge of the defect site, and EO is the static dielectric c o n ~ t a n t . 'From ~ this formula the continuum relaxation energy was estimated to be more than 5 eV for an P+center, and the modified 02-formation energy, determined from ab initio cluster models, was found to be very close to that derived from a Mott-Littleton model, about 24 eV.I3 If we add these two corrective terms, the error in 02-EA, 5 eV, and the long-range polarization, 4 eV, to the best computed value, 33.3 eV, we obtain a crude estimate of the formation energy, 3123 eV, which is similar to that reported for the bulk based on quantum-mechanical calculation^^^ or interionic potentiak2',29,30 From an energetic point of view, the formation of an F center at an edge site, corresponding to the extraction of a fourcoordinated 0 atom, is not very different from that of a surface vacancy. All the formation energies, removal of O,O-, or 02-, are 1-2 eV lower than for the corresponding surface sites. Thus, a low-coordinated ion is slightly less strongly bound to the rest of the crystal than a surface atom. The relaxation energy due to the geometrical rearrangement is substantially smaller at the edge site, about half of the surface site; see Table 2 .
J. Phys. Chem., Vol. 99, No. 46, 1995 17013
F and V Centers on the MgO Surface TABLE 3: V, Centers on MgO: Total Energy for Relaxed eV; Geometry (Er),au; Relaxation Energy (AEREL), Formation Energy (AEFow), eV; Electron Amnity (EA), eV cluster
site
[Mg I 3 0 ~ 16+ 1 [Mg1205]~~+V, [Mg~zOs]'~+ V,[Mg1205]14+ V2[Mg I 3 0 I 31 [Mg12013] V, [Mg12013]~- V,- . [Mg12013]~- V?[Mgzi02 I 1 [Mg20021] V, [Mg20021]~- V,[Mg20021]*- V2-
ET -3526.953 -3326.720 -3326.934 -3326.933 -4120.403 -3920.171 -3920.426 -3920.473 -6300.543 -6100.307 -6100.586 -6100.686
&EL
54 96 28 08 44 61 09 42 16 72 18 19
0.03 0.21 1.17 2.70 0.14 0.24 1.18 2.70 0.29 0.54 1.98 4.70
AEFORM EA 17.37 18.11 32.85
-5.80 0.03
17.35 16.97 30.39
-6.92 -1.29
17.45 16.42 28.40
-7.58 -2.72
a See text for definition. Reference energies: Mg = -199.594 08 au; Mg+ = -199.353 52 au; Mg2+ = -198.813 23 au.
We come now to the V, centers, Table 3. The removal of a neutral Mg atom costs about 17 eV and is accompanied by a relatively small lattice relaxation, UREL = 0.54eV in Wg200211. A recently reported theoretical estimate for the same process in the bulk is 13.8 eV.27 The larger formation energy of the V, center than of the F, one is consistent with the low density of V defects on Mg0.39,40The V, center has a very high EA, about 6-7 eV, indicating that it is likely that neutral V, centers do not exist when alkali metals are deposited on the MgO surface. The cost of extracting a Mg+ ion from the surface, with formation of a V,- center, also involves high energies, on the order of 17-18 eV. The energy gained by relaxing the cluster is of about 1-2 eV. The results are basically the same for the different clusters used. However, different results are obtained when we consider the V,2- centers obtained by removing a Mg2+ ion. In fact, the [Mg1205]cluster gives a very small but positive EA for Vs-, indicating a similar stability for V,- and VS2-. On the contrary, with the [Mg120131and [Mg200211 clusters the V,2- center is considerably more stable than the V,- one, as shown by the negative values of the V,- EA. Clearly, the polarization is poorly described with the [Mg1205] cluster. Our best estimate of A&RM(V:-) is 28.5 eV, Table 3. As for the case of F centers, the formation energies must be taken with care. However, in V centers the description of the Mg"+ fragment is less problematic than that of the 0"- anion, and the largest source of error comes from the neglect of longrange lattice relaxation. In the doubly charged VS2-center this is expected to be larger than for the V,- vacancy. Thus, the larger stability of the VS2- center, due to the large gain in Madelung energy when the two electrons are placed in the cavity, is not going to be affected by this approximation. Several different theoretical approaches have been employed to estimate the Mg2+ vacancy formation energy in bulk MgO, from classical models29to supercell HF34and density functional calculation^,^^^^^.^^ from embedded-clu~ter~~ to first-principle molecular dynamics method^.^^.^^ The reported values go from a minimum of 22 eV to a maximum of 45 eV (see ref 34 for a partial summary of results). This gives an indication of the theoretical problems connected to the determination of formation energies of MgO vacancies.
4. Geometric Relaxation The surface rumpling for the regular (100) MgO surface is very small, and the atomic positions of the truncated bulk and of the relaxed (100) surface are very similar; see Tables 4-6. Also the neutral vacancies do not show a large relaxation. We analyze first the F, centers. Given the non-negligible relaxation of the second shell of neighboring ions, we discuss only the results from the larger clusters used. It should also be mentioned
that the use of two-layer clusters prevents us from relaxing the atoms in the second layer; in fact, the presence of the surrounding PCs would result in unphysical forces acting on the ions at the cluster border. In [020Mg21],F,, there is a 1.8% outward displacement of the four Mg ions around the vacancy and a -1.3% inward movement of the next shell of 0 ions; see Scheme 1, where the direction of the displacements is shown, and Table 4; this reduces the Mg-0 distance of the first neighbors by 1% to 2.08 8,. Substantial relaxation occurs on the charged vacancies. The largest displacements occur horizontally with the Mg or 0 atoms moving outward by 6.5% (F,+) and 11% (F?+)and the first shell of 0 ions moving inward by -4.5% (Fs+) and -9.1% (F:+), respectively; see Scheme 1. For comparison, an outward relaxation of the Mg nuclei of 4-8% was deduced from EPR experiments on a bulk F+ center.41 The changes in first-second-layer distance is much smaller (see the z coordinate in Tables 4 and 5). As a consequence of these displacements, the Mg-0 distance around the vacancy decreases to 2.02 8, in F,+ and 1.96 8, in F?+. The outwardinward relaxation of Mg and 0 nearest neighbors has been found also by Pandey and Vai125for bulk MgO. Large relaxation effects occur also for a charged 0 vacancy on an edge site; see Scheme 2 and Table 5. Here only the atoms along the edge are free to move; we denote these atoms as firstlayer atoms. While the only relaxation on a nondefective edge site is the inward movement by 0.04 8, of the four-coordinated 0 atom toward the second-layer Mg ions, a considerable expansion of the cavity accompanies the formation of the charged F,+ (edge) defect. The lower Madelung potential at this site42causes a larger geometrical rearrangement to increase the local electrostatic interaction. Similar results are found for the V, centers, Table 6. Also in this case, in fact, the relaxation of the 0 and Mg ions is relatively small for the neutral vacancies and increases for the charged V- and V2- centers; the displacements with respect to the unrelaxed lattice positions (see Scheme 1) are slightly less pronounced than for the case of the charged F, centers (see Tables 4 and 6). This may be connected to the different localization of the electronic charge in the two kinds of vacancies, as will be discussed in the following section. The relaxation of the second shell of neighboring ions in the doubly charged defects, FS2+and V>-, has important effects on the relaxation energy, which, for the larger clusters, is considerably larger than for the smaller ones; see Tables 2 and 3. This is due to the reduction of the Mg-0 distances around the cavity, which leads to a substantial gain in electrostatic energy.
5. Electron Distribution MgO is an excellent insulator, with a band gap of 7.8 eV.43 Band structure calculations predict some narrowing of the band gap at the surface. HF calculations fail in reproducing the gap because of the limits of applicability of Koopmans' theorem, in particular to empty states. In fact, the HOMO-LUMO energy gap in the largest cluster considered, [Mg21021],is about 14 eV. When a neutral 0 atom is removed, a doubly occupied electronic state appears in the fundamental gap of MgO, as shown schematically in Figure 3. This state is about midway between the top of the valence band, the 0 2p band, and the conduction band, basically formed by Mg 3s and 3p empty states. Band structure calculations28,44have found that in the bulk this state is significantly above the midgap, just below the conduction band. If one of the two electrons is promoted to the conduction band, it may move away from the defect leaving the surface 0 vacancy positively charged, F,+. In this case the impurity state is shifted toward the top of the valence band,
17014 J. Phys. Chem., Vol. 99,No. 46, 1995
Ferrari and Pacchioni
TABLE 4: Geometrical Parameters (in A) for Surface F. Center@ MV-Mgi) ideal lattice LO21Mg2 I 1 [02oMg211 [OzoMg21I I + [020Mgz112+ a
x(V-Mg I )
4Mgd
2.104 2.104 2.141 2.241 2.334
O.Oo0 0.058 0.098 0.080 0.103
(a) 0.0 1.8 6.5 11.0
V = center of the vacancy site; Mgl = nearest Mg ion;
0 2
Ar(V-02) x4V-02) 2.975 2.933 2.937 2.840 2.704
Z(O2)
(%)
O.Oo0
0.om 0.008 0.010 0.040
-1.4 -1.3 -4.5 -9.1
r(Mgi-02) 2.104 2.075 2.080 2.022 1.959
= nearest 0 ion.
TABLE 5: Geometrical Parameters (in A) for Edge F, Center@ AO-Mgl) ideal lattice [014Mg,4l [OI3Mg I 41 [013Mg141’+ [0i3Mgi4I2+ a
x(V-Mgi) 2.104 2.102 2.217 2.353 2.494
z(Mg1)
(%)
0.000 -0.039 0.000 -0.024 0.013
-0.1 5.4 11.8 18.5
V = center of the vacancy site; Mgl = nearest Mg ion;
0 2
Ar(V-02)
x(V-02) 4.208 4.207 4.241 4.25 1 4.298
Z(O2) 0.000 -0.082 -0.094 -0.100 -0.1 13
(a) 0.0 0.8 1.o 2.1
r(Mg1-02) 2.104 2.105 2.026 1.900 1.807
= nearest 0 ion.
TABLE 6: Geometrical Parameters (in di) for V, Center@ AdV-01) ideal lattice [Mgz1 0 2 11 [Mgzo021I [Mgm0211I [Mg2o0ziI2a
x(V-01)
Z(O1)
2.104 2.095 2.185 2.257 2.313
0.000 0.001 0.010 -0.022 -0.048
Ar(V-Mgz) xfi(V-Mgz)
-0.4 3.8 7.3 10.0
2.975 2.990 2.915 2.824 2.722
z(Mg2)
(%)
r(Oi-Mg2)
0.000 0.089 0.104 0.08 1 0.068
0.5 -2.0 -5.0 -8.5
2.104 2.117 2.068 2.016 1.967
V = center of the vacancy site; 01 = nearest 0 ion; Mg2 = nearest Mg ion,
SCHEME 1
ooa k2x(V-O*)
SCHEME 2
Figure 3. Also in the F,+ center the electron can be removed or promoted to the conduction band with formation of a doubly charged F?+ defect, and the resulting empty state is further stabilized. Thus, the eigenstates of F, centers appear to be in the band gap, irrespective of the formal charge of the vacancy. Things are different in V, centers. The removal of a neutral Mg atom leaves an empty state above the valence band with 0 2p character, Figure 3. The energy gained by adding one electron to this level corresponds to the EA of the V, center, about 7 eV; see Table 3. The singly occupied level then moves down into the valence band and becomes part of the 0 2p band. In the V?- case the 0 2p band is again full, as it is in the regular surface, and the impurity level is just above the top of the valence band, but almost indistinguishable from the rest of
the 0 2p levels. Thus, even a qualitative analysis of the cluster eigenstates provides a clear picture of the different nature of F and V surface defects in MgO: the electrons in the V, centers have largely valence band character with a spatial distribution similar to the other valence electrons, while electrons at F, centers have a distinct character, suggesting a high degree of localization. A very qualitative indication of the electronic structure and of the charge distribution at a defect site is provided by the Mulliken population analysis. However, the partition of the electronic charge between adjacent centers in this kind of analysis is not free from ambiguities, as it will be shown below. We consider first the simpler case of V, centers. In the neutral defect, V,, the electronic charge on the 0 atoms close to the vacancy is 9.5, indicating that about 0.5 electrons are missing from each of the formally 02-ions in the first layer. The electronic charge on the fifth axial 0 ion in the second layer remains close to 10. In V,- the extra electron is still delocalized over the four top-layer 0 atoms, which have now a electronic charge of 9.75. This is further confirmed by the plot of the open shell electron density, Figure 4: the localization of the unpaired electron on the four oxygens is apparent. No spin density is found in the center of the cavity. A similar situation occurs on V?-, where the two extra electrons are entirely localized on the 0 atoms, which now have their valence saturated; see Figure 5 . The data of population analysis and the charge density plots provide a consistent picture, and the localization of the negative charge on the oxygens is clearly established. Things are more complex for F, centers. Experimental studies on bulk MgO indicate a substantial degree of localization of the unpaired electron in the F+ vacancy:I The results of the Mulliken population analysis are very ambiguous and cannot be used to characterize the degree of localization of the unpaired electron. The reason is the very strong basis set dependence of the results. We give here an ,example. The spin population in [Ol ~Mgs]Is- has been determined with three different basis
J. Phys. Chem., Vol. 99, No. 46, 1995 17015
F and V Centers on the MgO Surface
conduction band
conductionband
tt-
+
I
valence band
valence band
FS+
Fs2"
FS
V$
VS-
VS
Figure 3. Schematic representation of electronic states in the band gap of MgO for F,, F,+, and F>+ centers and V, V,-, and VS2-centers. -7
-5
-3
-1
1
3
5
7
-7 Figure 4. Spin density plot of a V,- center. (top) Isocontours in the surface plane; (bottom) three-dimensional view. The lines are drawn in intervals of 0.005 e/A3.
sets; on each basis set we have simply varied the exponents of the most diffuse s function on the vacancy, &(V), and of the 3s and 3p Mg orbitals, a3s(Mg) and a3,(Mg). The first basis set, used for the structural determination (as(V> = 0.156,
-7
-5
-3
-1
1
3
-7
-5
-3
-1
1
3
5
7
7
Figure 5. Charge density difference plot V>--V,.
(top) Isocontours in the surface plane; (bottom) three-dimensional view. Solid lines indicate accumulation; dotted lines, depletion of charge density. The lines are drawn in intervals of 0.005 e/A3.
= 0.059, a3,(Mg) = 0.090), gives a spin population of 0.25 on the vacancy and the rest on the Mg ions. This would indicate very little localization. By using more contracted exponents for the 3s and 3p Mg orbitals ( a ( V ) = 0.156, a3,(Mg)
Ferrari and Pacchioni
17016 J. Phys. Chem., Vol. 99, No. 46, 1995
71--@-7r -1
-3
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Figure 7. Charge density difference plot F,-F,2+ (surface case). (top) Isocontours in a plane normal to the surface; (bottom) three-dimensional view. Solid lines indicate accumulation; dotted lines, deplFtion of charge density. The lines are drawn in intervals of 0.002 e/A3.
-7
Figure 6. Spin density plot of an F,+ center. (top) Isocontours in the surface plane; (bottom) three-dimensional view. The lines are drawn in intervals of 0.001 e/,&'.
= 0.09, a3,(Mg) = 0.25), the spin population on the vacancy goes to 0.46; using a more diffuse s orbital for the vacancy but keeping the original Mg basis (&(V) = 0.10, a3,(Mg) = 0.059, a3,(Mg) = 0.090), the electron is localized for more than 70% on the vacancy! Clearly, Mulliken population data are too basis set dependent. A more reliable description of the electronic structure is provided by the spin density plot, Figure 6: the plot clearly shows the localization of the unpaired electron on the center of the vacancy. Incidentally, very similar plots have been obtained for the bulk F+ by Wang and H~lzwarth.~' On a F, center the two electrons are distributed between the vacancy and the neighboring ions. The charge density difference map, F, - F?+, Figure 7, provides an indication of the electron distribution for the neutral defect; most of the electron density is on the vacancy, but a considerable fraction is delocalized over the Mg ions. A very similar picture is obtained for the corresponding edge site, F,(edge), Figure 8. As discussed previously, the Mulliken population is of little help in this case,
so that a more quantitative estimate of the degree of localization is not possible. Experimentally, the nature of the F+ and F,+ centers has been studied by means of the EPR spectros~opy,6~~~ also through the determination of the hyperfine isotropic coupling constant, Ao, of the electronic spin with the 5/2 nuclear spin of the 25Mg nuclide (natural abundance of 10.1%). A0 is related to the spin density at the nucleus (Fermi contact term) by the following equation (Table 7):
A, = ( 8 ~ ~ 3 ) g N P N g J l ~ v , ( 0 ) 1 2
(4)
where g N and g are the nuclear and electronic g-factors, and PN and /3 are the nuclear and Bohr magnetons. On bulk MgO the hyperfine spliaing constant is 3.94 G,"345-46 while on the surface A0 shows a temperature dependence and goes from 8.9 at 104 K to 11 G at 470 K,"7.48(the sign is not known); higher values have also been reported,2 but values around 10 G are more commonly observed.48 We have determined A0 for the various clusters and, for the [0,2Mg5]'5- case, also for different basis sets. We notice that, differently from the Mulliken population, the values of A0 are very moderately dependent on the basis set; they are in the range -4 to -7 G, in acceptable agreement with the experiment considering the small absolute values of the constants. An A0 constant of 9 G for the surface Mg ions"
"
~
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J. Phys. Chem., Vol. 99, No. 46, I995 17017
F and V Centers on the MgO Surface l
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Figure 8. Charge density difference plot F,-F:+ (edge case). (top) Isocontours in a plane normal to the edge; (bottom) three-dimensional view. Solid lines indicate accumulation; dotted lines, depletion of charge density. The lines are drawn in intervals of 0.002 e/A3.
TABLE 7: Spin Density at Nucleus and Hyperfine Coupling Constants for Paramagnetic F,+ and V,- Centers center cluster nucleus" spin density (au)b A0 (G) F,+ (surface) F,+ (surface) F,' (surface) ',F (edge) F,+ (exptl) V,- (surface)
[012Mgs]'~[OlzMgl# [0~0Mg21]+ [013Mg~]+ [Mg12013]-
25Mg 25Mg 25Mg 25Mg 25Mg I7O
0.053 (0.074) 0.056 (0.036) 0.043 (0.053) 0.077 (0.085) 0.09-0.11 0.162 (-0.OlO)c
-5.2 (-7.3) -5.5 (-3.5) -4.2 (-5.2) -7.6 (-8.3) 9-11 -35.2
a Isotope abundances: 2sMg 10.11%, I7O 0.04%; the following g N factors have been used: 25Mg = -0.342, 170 = -0.757. In parentheses is given the spin density on the second-layer atoms. The negative value is due to a small spin contamination in the UHF wave function.
corresponds to a spin density at the Mg nucleus of about 0.09 au; the computed value is about 50-60% of the experimental one. To estimate the degree of localization of the unpaired electron we have computed the Mg+ (3s)' isolated ion in the same basis used for the cluster calculations; the corresponding spin density is 2.08 au (1200 G ) . If we divide this value by the number of Mg ions around the vacancy, we obtain an average spin density of 0.42 au, assuming a delocalization of the unpaired electron in the Mg 3s-derived molecular orbitals. The computed spin density, 0.04-0.05 au, seems to indicate that the electron is distributed by only 10% over the Mg ions, the rest being trapped in the vacancy. This is in excellent
1
agreement with the experimental estimate of the electron being localized for only 5% on the Mg 3s orbital47 and is also consistent with the spin density plot, Figure 6. Tench and Nelsona have founnd that the five Mg ions on the F,+ centers are not equivalent and that the electron interacts more strongly with the Mg ion furthest from the surface and less strongly with the other four. Our data show a spin density on the Mg ion in the second layer which is about 25-35% larger than on the top-layer Mg ions, Table 7. However, in one case, [012Mg,3],the order is reversed, indicating a cluster dependence for this behavior, so that we are unable to firmly support this conclusion. To summarize, the analysis of the hyperfine coupling constants and of the spin density plots demonstrates unambiguously that the unpaired electron is largely localized on the vacancy. The hyperfine constants and the spin density at an edge F,+ center are similar to those of the surface F,+ sites, the only difference being an enhanced density and slightly larger constants, Table 7. The spin density on the Mg2+ ions along the edge, 0.077 au, is found to be slightly smaller than on the other two Mg2+ions in the second layer, 0.085 au. Considering that on high-area thermally activated MgO the amount of morphological defects sites (edges, kinks, steps, etc.) consist of about 25% of the total, this result helps explain the slight heterogeneity observed in the EPR spectra.6 Finally, we have determined the hyperfine constants for the V,- vacancy, Table 7. These sites are not observed in EPR because of the low natural abundance, O M % , of the I7Onuclide. However, using an I70-enriched MgO single crystal, it has been possible to determine the hyperfhe interaction parameter for VF centers, consisting of a Mg+ vacancy adjacent to an F+ impurity.48 The measured IAol, 22.8 G, is difficult to compare to our computed value, -35 G, given the rather different nature of the sites. This holds also for the experiment of Wong and Lunsford, who have measured the EPR spectrum of an 0trapped at an oxide anion F>+ center by reaction of MgO with I70-enriched N2OS5OHere the situation is similar to that of a regular MgO surface where one electron has been removed from the surface oxide anion. Thus, the comparison with experiment is quite difficult for V centers. Nevertheless, the computed coupling constants are of interest because they show once more that all the spin density is localized on the top-layer 0 atoms with no density at all at the vacancy or on the atom in the fifth coordinative position.
6. Conclusions The formation energy and the electronic structure of ion vacancies in bulk and surface MgO are subjects which have attracted considerable interest in the past decades. Many structural and electronic aspects of these defects have been clarified, but there are still several open questions. With the present theoretical study we have tried to describe the formation energies, the local relaxation, and the electronic properties of the entire series of 0 and Mg surface vacancies of MgO, F,, Fs+, F,2+, V,, Vs-, and VS2-. While many theoretical studies have been dedicated to one type of defect, very few have tied to address the nature of both 0 and Mg vacancies using the same level of theoretical description. Furthermore, most of the reported studies deal with bulk defects, and much less is known about surface defects. The order in stability of the F and V sites is F, > F,+ > F>+ and VS2- > V,- > V,. This result can be explained with the large stabilization arising from the Madelung energy which is gained by the presence of electronic charge in the vacancy. However, local geometrical relaxation is essential to properly describe the relative stabilities of the defects, in particular for
17018 J. Phys. Chem., Vol. 99, No. 46, 1995 V, centers. of course, even with the relatively large clusters used, the lattice relaxation was allowed only in a very small area: further work is needed to establish on a quantummechanical basis the extension of the perturbation produced by a vacancy on the lattice geometry. The low stability of the F?+ center is consistent with the fact that these species are not observed in bulk MgO and, when they form, are extremely shortlived.39 On the other hand, all three forms of V defects are known to be present in the bulk, although their concentration is found to be smaller than that of the dominant F defects.39A lot of discussion in the literature has concerned the more or less localized nature of the electron at the vacancy. We found that the electronic structure of surface F and V defects is distinct. In F, and F,+ the extra electrons are clearly localized on the vacancy; we also found a tendency for the Mg ions not to be equivalent, with preferential accumulation of charge on the apical Mg ion in the second layer. On the contrary, in V?and V,- sites the electrons are in the 0 2p band, localized over the neighboring 0 atoms. These results are supported by the charge and spin density plots and, for the paramagnetic centers, by the hyperfine isotropic constants. For the first time we have considered the electronic structure of 0 vacancies at the edges of the MgO (100) surface. We found that the energetics, the geometrical relaxation, and the electronic structure closely resemble those of the surface vacancies, which, in turn, are not dissimilar from those in the bulk. This is because the nature of the interaction at the lowcoordinated sites of MgO is still very ionic,51so that essentially the same mechanisms govern the defect formation in the bulk and on the surface. Finally, as we mentioned in the Introduction, our aim was also to define clusters which can be used for the modeling of adsorption processes. It has been suggested that the initial steps of the growth of metal clusters on the surface of ionic crystals like MgO occurs at the defect sites, mainly at the vacancies, the rest of the sites being weakly reactive or unreactive. The study of the electronic properties of the cluster models of the vacancy is an essential prerequisite for the investigation of adsorption phenomena. In this respect, the clusters and the basis sets used appear to be sufficiently extended to provide a reliable description of these sites. preliminary results on the adsorption of isolated atoms of Rb, Ag, and Pd on MgO vacancies show the essential role of these sites in the early stages of the metal cluster deposition on oxide surfaces.52 Acknowledgment. We thanks Prof. E. Giamello (Torino) for several useful discussions and for a critical reading of the manuscript. This work has been supported by the Italian Ministery of Scientific Research. Support from the European Community through the Cooperation Agreement INTAS-93, 1876 is also gratefully acknowledged. References and Notes (1) Henrich, V. E.; Cox, P. A. The Surface Science of Metal Oxides; Cambridge University Press: Cambridge, 1994. (2) Nelson, R. L.; Tench, R. L.; Harmsworth, B. J. Trans. Faraday Soc. 1967, 63, 1427. (3) Wertz, J. E.; Orton, J.; Auzins, P. Discuss. Faraday Soc. 1961, 31, 140. (4) Henderson, B.; Wertz, J. E. Adv. Phys. 1968, 17, 749. ( 5 ) Coluccia, S.; Lavagnino, S.; Marchese, L. Mater. Chem. Phys. 1988, 18, 445. (6) Giamello, E.; Ferrero, A.; Coluccia, S.; Zecchina, A. J . Phys. Chem. 1991, 95, 9385. (7) Zecchina, A.; Scarano, D.; Marchese, L.; Coluccia, S.; Giamello, E. Surf. Sci. 1988, 194, 531. (8) Murphy, D.; Giamello, E. J . Phys. Chem. 1994, 98, 7929. (9) Illas, F.; Lorda, A,; Rubio, J.; Torrance, J. B.; Bagus, P. S., J. Chem. Plzvs. 1993, 95, 389.
Ferrari and Pacchioni (10) Pacchioni, G.; Sousa, C.; Illas, F.; Parmigiani, F.; Bagus, P. S. Phys. Rev. B 1993, 48, 11573. (11) Causa’, M.: Dovesi, R.; Pisani, C.; Roetti, C. Phys. Rev. B 1986, 33, 1308. (12) Pacchioni, G.; Cogliandro, G.; Bagus, P. S. Int. J . Quantum Chem. 1992, 42, 1115. (13) Grimes, R. W.; Catlow, C. R. A.; Stoneham, A. M. J . Chem. SOC., Faraday Trans. 2 1989,85485; J . Phys.: Condens. Matter 1989, 1 , 7367. (14) Sharma, R. R.; Stoneham, A. M. J . Chem. SOC.,Faraday Trans. 2 1976, 72, 913. (15) Taurian, 0.E.; Tang Kai, A. H.; Lobatch, V. J . Phys. Chem. Solids 1986, 47, 59. (16) Tsukada, M.; Adachi, H.; Satoko, C. Prog. Sur$ Sci. 1983, 14, 113. (17) Kassim, H. A.; Matthew, J. A. D.; Green, B. Surf. Sci. 1978, 74, 109. (18) Huzinaga, S., Ed. Gaussian Basis Sets for Molecular Calculations; Physical Science Data, Vol. 16; Elsevier: Amsterdam, 1984. (19) Boys, S. F.; Bemardi, F. Mol. Phys. 1970, 19, 553. (20) Dupuis, M.; Johnston, F.; Marquez, A. HONDO 8.5 for CHEMStation IBM Co.: Kingston, 1994. (21) Catlow, C. R. A.; Faux, I. D.; Norgett, M. J. J . Phys. C.: Solid State Phys. 1976, 9, 419. (22) Catlow, C. R. A., Mackrodt, W. C., Eds. Computer Simulation of Solids; Lecture Notes in Physics, Vol. 166; Springer: Berlin, 1982. (23) Vail, J. M.; Harker, A. H.; Hading, J. H.; Saul, P. J . Phys. C.: Solid State Phys. 1994, 17, 3401. (24) Vail, J. M. J . Phys. Chem. Solids 1990, 51, 589. (25) Pandey, R.; Vail, J. M. J . Phys.: Condens. Matter 1989, 1, 2801. (26) Harker, A. H. J . Chem. SOC.,Faraday Trans. 2 1989, 85, 471. (27) Gibson, A.; Haydock, R.; LaFemina, J. P. Phys. Rev. B 1994, 50, 2582. (28) Gibson, A.; Haydock, R.: LaFemina, J. P. Appl. Surf. Sci. 1993, 72, 285. (29) Duffy, D. M.; Hoare, J. P.; Tasker, P. W. J . Phys. C.:Solid State Phys. 1984, 17, L195. (30) Mackrodt, W. C.; Stewart, R. F. J . Phys. C.: Solidstate Phys. 1979, 12, 431. (31) Wang, Q.S.; Holzwarth, N. A. W. Phys. Rev. B 1990, 41, 3211. (32) De Vita, A,; Gillan, M. J.; Lin, J. S.; Payne, M. C.; Stich, I.; Clarke, L. J. Phys. Rev. B 1992, 46, 12964. (33) Gillan, M. J.; Manassidis, I.; De Vita, A. Phil. Mag. B 1994, 69, 879. (34) Pisani, C.; Cor& F.; Dovesi, R.; Orlando, R. J . Electron Spectrosc. Relat. Phenom. 1994, 96, 1. (35) Meng, J.: Pandey, R.; Vail, J. M.; Kunz, A. B. Phys. Rev. B 1988, 38, 10083. (36) O’Keeffe, M. J . Solid State Chem. 1990, 85, 108. (37) Pettersson, L. G. M., Pacchioni, G. Chem. Phys. Lett. 1994, 219, 107. (38) Kappers, L. A.; Kroes, R. L.; Hensely, E. B. Phys. Rev. B 1970, 1, 4151. (39) Tench, A. J.; Duck, M. J. J . Phys. C.:Solid State Phys. 1973, 6, 1134. (40) Abraham, M. M.; Chen, Y.; Unruh, W. P. Phys. Rev. B 1974, 9, 1842. (41) Unruh, W. P.; Culvahouse, J. W. Phys. Rev. 1967, 154, 861. (42) Colboum, E. A. Su$ Sci. Rep. 1992, 15, 281. (43) Roessler, D. M.; Welker, W. C. Phys. Rev. 1967, 159, 733. (44) Klein, B. M.; Pickett, W. E.; Boyer, L. L.; Zeller, R. Phys. Rev. B 1987, 35, 5802. (45) Wertz, J. E.; Saville, G. S.; Hall, L.; Auzins, P. Proc. Br. Ceram. SOC. 1964, 1, 59. (46) Tench, A. J.; Nelson, R. L. J . Colloid Interface Sci. 1968,26, 364. (47) Tench, A. J. Surf. Sei. 1971, 25, 625. (48) Giamello, E.; Murphy, D.; Ravera, L.; Coluccia, S.; Zecchina, A. J. Chem. Soc., Faraday Trans. 1994, 90, 3167. (49) Schoenberg, A.; Suss, J. T.; Szapiro, S.; Luz,Z. Phys. Rev. Lett. 1971, 27, 1641. (50) Wong, H.-B.; Lunsford, J. H. J . Chem. Phys. 1971, 55, 3007. (51) Sousa, C.; Mejias, J. A,; Pacchioni, G.; Illas, F. Submitted. (52) Pacchioni, G.; Ferrari, A. To be published. Jp95 1623F
