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Theoretical studies of the bonding of oxygen to models of the (100) surface of nickel
Surface Science 75 (1978) 609-634 Q North-Holland Publishing Company
THEORETICAL STUDIES OF THE BONDING OF OXYGEN TO MODELS OF THE (100) SURFACE OF NICKEL * Stephen P. WALCH and W.A. GODDARD III ** Arthur Amos Noyes Laboratory of Chemical Physics, GzlifomiaInstitute of Technology, Pasadena, ~~ifor~~a 91125, WSA Received 11 March 1977; manuscript received in final form 27 February 1978
Electronic wavefunctions have been obtained as a function of geometry for an 0 atom bonded to Ni clusters (consisting of one to five atoms) designed to model bonding to the (100) surface of Ni. Electron correlation effects were included using the generalized valence bond and configuration interaction methods. For the (100) surface, we find that the charge distribution for the full 0 overlayer is consistent with taking a positively charged cluster. The four surface atoms in the surface unit cell and the atom beneath the surface are important in determining the geometry, leading to a Ni;O cluster as the model for the (100) surface. The optimum oxygen position with this model is 0.96 A above the surface (four-fold coordinate site) in good agreement with the value (0.90 f 0.10 A) from dynamic LEED intensity analysis. The atom beneath the surface allows important polarization effects for the positively charged cluster. The bonding to the surface involves bridging two diagonal surface Ni atoms, There is an O(2pn) pair which overlaps the other diagonal pair of Ni atoms leading to nonbonded repulsions which increase the distance above the surface. There are two equivalent such structures, the resonance leading to a c(2 X 2) structure for the 0 overlayer.
1. Introduction While there have been several theoretical studies of the chemisorption of 0 on the Ni( 100) surface using cluster methods [l], previous calculations have used the SCF-Xc&W method [Z] which leads to moderately good results for c~culated photoelectron spectra [ I] but for the usual muffin tin approximation does not yield reliable geometry information 13). After submission of this manuscript a paper appeared by Li and Connolly [4c] showing that use of the muffin tin approximation to SCF-Xc&W for N&O complexes leads to very poor geometries but that inclusion of muffin tin corrections leads to reasonable geometries. Experimentally geometry information for overlayers on metal surfaces is obtained from detailed
* Partially supported by a grant (DMR 74-04965) from the National Science Foundation, ** Partially supported by a grant (EX-76-C-03-1305) from the Energy Research and Development Administration.
610
S.P. Walch, W.A. Goddard III /Bonding
of oxygen to models of (I 00) Ni
analysis of low energy electron diffraction (LEED) intensities [5). However, because the theoretical analysis involves some severe approximations such geometries cannot be described as purely experimental and an independent theoretical determination for some well characterized systems would be useful. We report here accurate ab initio calculations for the bonding of 0 to Ni clusters designed to model the Ni(lOO) surface. A preliminary report of similar calculations for S on Ni has been presented elsewhere [6a]_ In this paper we concentrate principally on geometry predictions. (configuration interaction calculations based on similar wavefunctions also yield good results for the photoelectron spectra of CO [7a], &Hz [7b], and CzH4 [7b] on Ni; however, we have not carried out such calculations for 0 or S on Ni.) We find that the main differences between the 0 and S calculations have to do with fi) the smaller size of the oxygen atom, and (ii) the higher electronegativity of 0 (3.5 as compared with 2.5 for S [8a], The larger amount of ionic character in the 0 clusters requires that the atom beneath the surface be included in the cluster for the 0 case, whereas only the surface Ni atoms were important in the S case. In section 2, we describe the basis set and other calculational details. Section 3 describes the qualitative nature of the wavefunctions for the various Ni clusters and compares the calculated geometry for the (100) surface with results of dynamic LEED intensity c~culations [S]. Section 4 discusses the wavefun~tions for the clusters in somewhat more detail.
2. Calculational details We solved for the states of the finite clusters using the ab initio generalized valence bond (GVB) method 1131 which differs from the usual Hartree-Fock (HF) method in that it includes the dominant electron correlation effects necessary to describe bond formation. In these calculations we explicitly included all ten valence electrons of each Ni atom and all the electrons of the 0 atom; the 18electron Ar core of the Ni atom was replaced by an effective potential. The basis set and effective potential used for Ni have been reported previously [6b,21]. (The Ni basis is based on the set optimized for the third row atoms by Wachters [9]. The [3s,lp,2d] contraction of the Ni basis was used for the NiO and N&O calculations, while for the larger NiaO, N&O and N&O calculations the [2s, lp,ld] contraption was used [6b]. The basis for oxygen is the Dunning f3s,2p] contraction [lo] of the Huzinaga (9s,5p) set [ 111. This contraction is valence double zeta but uses a single Is-like contracted function and leads to energies within 0.0001 h of those obtained with the double zeta contraction [12]. For the NiO cluster a single set of d-functions (o = 1.04) was used on the 0, while for the N&O cluster the geometry was optimized without d-functions but d-functions were added at the opt~un~ geometry. ~-functions were omitted for the larger clusters.
3. Qualitative discussion Table 1 summarizes the results for bonding an 0 atom to the various Ni clusters. For the floO> surface, the surface unit cell contains four surface Ni atoms at the corners of a square (which we refer to as Nil, Ni2, Ni?, and Ni4) and one atom below the center of the square in the next layer down (which we refer to as NiS). For S on the Ni(100) surface, we found that only the faur surface Ni atoms (l-4) Table 1 Summary of results for bonding of oxygen to the Ni clusters Ciuster
Geometry
NiO
Ni-0
Model for
Ni20
Distance above plane (A)
RNiO (A)
D (eV)
1.65
1.65
3.95
(I IO) surface 0 on long edge
5.31
1.79
4.37
(115) surface 0 on long edge
5.08
1.76
3.32 a
5.56
1.85
9.22
Ni2
Ni30
/\
0
Ni5 \/ Ni4
NQO NiiO
(155) surface 0 at center of cell
(0.75)
b
-
-
0.65
I .88
1.93
(155) surface 0 at center of cell
5.96
2.51
3.59
a The NiO and Ni20 calculations used a [3s, lp, 2d/3s, 2p, fdf basis, while a f2s, lp, ld/3s, Zp] basis was used for the larger clusters, From comparisons of both types of calculations for Ni20 we estimate that this basis leads to an error in De of 5.24 eV, but does not have a significant effect on the geometry. Thus, we have added 5.24 eV to the D, vaiues for the NigO, N&O, and NisO clusters in order to compare with the NiO and X20 calculations, b This value is estimated from Koopmans’ theorem by assuming that the error in the geometry from Koopmans’ theorem for Nit0 (5.25 A) will also be the same in Ni$O.
612
S.P. Walch,
W.A. Goddard III /Bonding
of ox.gen
to models of (I 00) Ni
had to be included to describe the geometry. However, for the 0 case we find that Ni5 must be included to describe polarization effects in the direction perpendicular to the surface. In addition, the higher eIectronegati~ty of 0 requires a positive ion state of the NisO cluster in order to be consistent with the charge distribution expected for the full 0 overlayer when adsorbate-adsorbate interactions are considered (see section 3.2). Thus, we used a NiiO model for 0 on Ni(lOO). With this model we find that the 0 is a distance of 0.96 A above the surface, in excellent agreement with the value from dynamic LEED intensity analysis, 0.90 rt 0.10 A PI. A recent XCYcalculation [4c] using a NisO complex like ours and including nonmuffin tin corrections leads to a distance of 0.75 A. Without those corrections the Xa calculation leads to a geometry at least 0.45 A larger [4c]. In the following, we discuss qualitatively the essential features of the wavefunctions for the various clusters shown in table 1. For all the clusters considered here, we find that the Ni atom has the character of the 4s’ 3da con~guratio~~ and the bonding is dominated by the 4s orbital, while the orientation of the hole in the 3d shell leads to small energy effects. The simplest model which contains the qua~tative features of the bonding to the (100) surface is the Ni?O cluster. which corresponds to bridging across a pair of surface Ni atoms (say Ni2 and Ni4) along the diagonal of the square. 3.1. NiO and NizO Wavefunctions for numerous electronic states of NiO have been discussed in detail elsewhere [ 141. The bonding in NiO is dominated by the sigma bond which may be described qualitatively as a Ni(4s) orbital singlet paired with an O(2po) orbital. The orbitals of the bond pair are shown in fig. lc, d; as expected from the relative electronegativities (1.8 for Ni, 3.5 for 0 [8a]) there is a substantial amount of charge transfer [ 151 to the 0 atom (0.55 electrons). For the ground state of NiO, the 3d hole of the Ni 3d9 con~guration is 3dn, feading to a 3Zc- ground state which is quite analogous to the ground states of NiS (Sb) and of 02 1161. As indicated in fig. la, e, g, the Ni(3d) orbitals are only slightly affected by the bond. The major difference between NiO and NiS is the greater charge transfer (0.55 electrons for NiO as compared with 0.38 electrons for NiS [ 151). Bonding a second Ni atom to the singly occupied 0(2p,) orbital (fig. If) leads (after readjustment effects) to a structure with two equivalent sigma bonds (i.e., the NiaO cluster) 2 0
(1) j__ Nf4
NI
2
Y
S.P. Walch, W.A. Goddard III /Bonding
NiO
of oxygen to models of (100) Ni
613
X3x-
(b) 0 2s
(a) NI 342 r--
TWO
(e) NI 3d,,
(f) 0 2P” I
ONE
507
(g) Ni 3dxZ ~-~
(h)O2p, TWO I
X
Fig. 1. The GVB orbitals of X3x- ground state of NiO. Unless otherwise noted, all plots have uniformly spaced contours of 0.05 au. Solid lines indicate positive contours, short dashes indicate negative contours, and long dashes indicate nodal lines. The same conventions are used for other figures. [Note that because a Ni(4s) orbital is much more diffuse than a Ni(3d) orbital, even a relatively small amount of 3d character appears very pronounced in the contour plots. Thus, for example, the orbitals in fig. 3e, f, g, which appear to contain large amounts of 3do character, have -15% d character (from a Mulliken population analysis).] The same conventions are used for the other figures.
614
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
Solving for a wavefunction of the form (1) leads to a total charge transfer to the oxygen of 0.9 1 electrons, which is consistent with incorporating a substantial component of the ionic configuration (2j [ 171 Z
NY4
NI 2
Covalent bonding as in (1) favors 90” bond angles, whereas bonding to O- as in (2) favors 180” bond angles. Thus, incorporation of ionic character leads to large bond angles and small vertical displacements of the 0 atom (relative to the surface). For the NizO cluster, the optimum geometry is with the 0 atom 0.31 A above the surface, which is consistent with the overall charge transfer (0.91 electrons). The orbitals corresponding to (1) are shown in fig. 2. The bond pairs (fig. 2a, b, c, d) show a substantial amount of charge transfer to the oxygen. For one bond pair (fig. 2a, b), one component (fig. 2b) is essentially 0(2p)-like, while the other component (fig. 2a) corresponds approximately to a Ni(4s) orbital which contains a large amount of O(2p) character. (Thus, the covalent bond has an appropriate amount of ionic character.) The 0(2s)-like orbital (fig. 2e) has hybridized away from the bond pairs. We find that bridged bonding as in the NizO cluster is more favorable (D, = 4.37 eV) than bonding directly above a surface Ni atom as in NiO (D, = 3.95 eV). The small difference in bond energies here reflects the fact that the NizO cluster contains a large component of (2) which involves only a single sigma bond. 3.2. Ni40, Nit0 Including the nonbonded surface Ni atoms (Nil and Ni3) leads to the Ni40 cluster. Qualitatively the electronic configuration of the Nib0 cluster is Y Q
0
NI 2
I
a
(3)
S.P. Walch, W.A. Goddard III/Bonding
Ni,O
(0)
of oxygen to models
of (I 00) Ni
615
GVB C.?/PP)
UPPER NiO BOND (b)
0 2s PAIR (e) TWO
LOWER
NiO
BOND
_p
,.o!c.! ONE
’ “\A,,
ONE
Fig. 2. Selected orbitals of the NizO cfuster.
The bonding orbitals (shown in the yz plane) are analogous to the orbitals of (2). We find (as for N&S) that there are repulsive interactions between the doubly occupied O(2p.J orbital and the other two surface Ni atoms (Nil and Ni3) which lead to an optimum geometry with the 0 atom 0.56 A above the surface, 0.25 t\ higher than for the NizO calculation.
616
S.P. Walch, W.A. Goddard III / Bonding of oxygen to models of (I 00) Ni
For the full oxygen overlayer, Nil and Ni3 are involved in bonds to other 0 atoms. Considering the charge transfer involved in the bonds leads to a charge of -0.9 distributed between Nil and Ni3 (based on Ni*O). Thus, considering adsorbate-adsorbate interactions, the overall charge is more accurately represented within the limits of our cluster model by an ion state of the Niq cluster involving removal of one electron from among the orbitals corresponding to Nil and Ni3. It was anticipated that for the positively charged cluster polarization effects involving Ni.5 would be important, thus we used a Ni:O cluster as the model for 0 on Ni( 100). 3.3. Ni50, NifO
Here we consider first the neutral N&O cluster. For Ni50 we find that Ni5 is nonbonding and the remaining electronic configuration is similar to (3) for N&O. The orbitals of the neutral N&O cluster are shown in fig. 3. Looking first at the bond pair (fig. 3a, b), one sees that one component (fig. 3a) is essentially an 0(2p,) orbital, while the other component (fig. 3b) corresponds approximately to Ni2(4s))Ni4(4s) but contains a substantial amount of 0(2p,) character (indicating an ionic bond). The O(2pJ pair (fig. 3c) has delocalized somewhat onto the Ni, but the overall populations correspond most closely to an O- configuration for the 0 atom as in (3). The O(2s) pair (fig. 3d) is essentially atomic-like, but has built in a small amount of 3d character on the surface Ni atoms. The singly occupied orbitals (fig. 3e, f, g) are all derived from Ni(4s) orbitals (mainly on Nil, Ni3, and Ni5). The orbitals in fig. 3e, f correspond approximately to Nil(4s) + Ni3(4s) and Nil(4s) Ni3(4s), respectively; note however, that the symmetric combination (fig. 3e) has delocalized onto Ni5, leading to bonding character on all three centers. The other singly occupied orbital (fig. 3g) corresponds to a 4’s orbital on Ni5 and is antibonding in character. The optimum geometry for this cluster is with the 0 at 0.65 A above the surface, only 0.09 A higher than for the Ni40 cluster. Thus Ni5 has only a small effect on the geometry of the neutral cluster (as was predicted for bonding S to this cluster [6a]). Now we consider the Nil0 cluster. The lowest ion state of the N&O cluster involves ionizing the singly occupied orbital in fig. 3g. At the equilibrium geometry for N&O neutral, the orbitals of Ni;O are very similar to the corresponding Ni50 orbitals shown in fig. 3. However, the Nii cluster has a higher effective electronegativity than the NiS cluster which leads to more covalent bonding in Ni;O and an equilibrium geometry with the 0 atom further from the surface. Moving the 0 atom away from the surface, the doubly occupied O(2pJ orbital delocalizes more onto the Ni while the singly occupied Ni-Ni bonding orbital (fig. 3e) localizes on the 0 atom; leading (at the equilibrium geometry for Ni;O) to a singly occupied 0(2p,) orbital and a doubly occupied Ni-Ni bonding orbital (i.e., an electron has been transferred from 0 back to the metal).
S.P. W&h, hJ.A. Goddard HI /Bonding of oxygen to models of ~~~~~Ni Ni,O TOP
GVB (I/W’)
VIEW
XZ
PLANE
YZ
PLANE
N,‘4
THE BOND PAIR (b)
Cd) 0 2s
NI 4s ORBITALS (f)
(e)
5 *
es) _..
..oi?
:’- ,i lGd ;,*‘:‘h
:,,..,, :,*:
X
.._.
.j ._..’
/,
.’
‘\
/
//
-s.o;,o
/
/
0
2
‘1
‘7~ I 8.0
Fig. 3. Selected orbital5 of the NiSO cluster.
617
618
S.P. Waleh, W.A. Goddard III/Bonding
N15+0 TOP VIEW
of oxygen to models of (IOO) Ni
GVB(I/PP)
XL
PLANE
YZ
PLANE
ONE
(d) 0 2s
X
NI 4s ORBITALS (fi
-\ ONE
TWO
-8.0
i
-80
Z
SO-
Z
Fig. 4. Selected orbitals of the NiiO cluster.
. !ik
S.P. Walch, W.A. Goddard III/Bonding
The overall electronic
configuration
of oxygen to models of (I 00) Ni
619
is
. . ‘\ \
,
+i-,
.
.
: :/
+ /
(3 ’
(4)
I
i
I
0. I
We show the orbitals corresponding to (4) in fig. 4. The bond pair (fig. 4a, b) is very similar to the bond pair for NisO neutral (fig. 3a, b). The 0(2p,) orbital (fig. 4c) is now singly occupied and localized, while the orbital corresponding to the bonding combination of the Ni(4s) orbitals (fig. 4e) is doubly occupied. The remaining singly occupied orbital (fig. 4f) corresponds to Nil(4s) - Ni3(4s) and has not changed significantly from the corresponding orbital for NisO neutral (fig. 3f). Thus, the overall configuration for the NiSO cluster corresponds to a neutral oxygen atom configuration [but with about 0.5 electrons transferred in the bond pair (fig. 4a, b) leading to a total charge on the oxygen of 0.61 electrons as compared to 0.82 electrons for N&O neutral]. The net effect of the more covalent bonding is an equilibrium geometry with the 0 atom 0.96 A above the surface, 0.31 A higher than for N&O neutral. This value is in good agreement with the results of dynamic LEED intensity analysis, 0.90 ?r 0.10 A [5]. From table 1 we see that the NiiO cluster leads to a substantially larger bond energy 3.09 eV than for NisO neutral (1.93 eV). This effect derives largely from the antibonding character of the ionized orbital (fig. 3g). Thus, withdrawal of charge by adjacent 0 atoms on the surface leads to stronger bonding of 0 to the surface. This effect should lead to island formation at low coverages and formation of ordered overlayers at higher coverages. Fig. Sa shows the bonding expected for c(2 X 2) overlayers on the Ni(lOO) surface. The localized bonds shown in fig. 5a suggest a p(2 X 2) structure with the center and corner Ni atoms connected by a glide plane. However, there is a degenerate structure rotated by 90’ and these two structures are expected to have a strong interaction (resonance) leading to all the 0 atoms being equivalent. This leads to ~$2 X 2) as is observed [ 51. As shown in fig. 5a, bonding the 4s orbital of each Ni to one 0 leads to an 0 atom in only half the four-fold sites. Thus, this bonding picture suggests that the c(2 X 2) overlayer is particularly stable. The Van der Waals radius of the 0 atom is
620
S.P. Walch, W.A. Goddard III / Bonding of oxygen to models of (I 00) Ni (100)
SURFACE
( I IO)
SURFACE
Fig. 5. The c(2 X 2) structure for the 0 on (a) Ni(lOO) and (b) Ni(llO), respectively. Circles represent surface Ni atoms, crosses represent 0 atoms, heavy lines represent Ni-0 bonds, and dashed lines outline the unit cell. [Note that for the (110) surface recent LEED results [18] suggest that the 0 atoms are bonded across the short edge of the (110) surface unit cell. Since some of our clusters for the (100) surface constitute models for bonding to the long edge of the (110) surface unit cells, we illustrate this alternative registry here.]
1.40 i% [8b] considerably smaller than half the O-O distance for the c(2 X 2) structure (1.76 i%) but somewhat larger than half the O-O distance if an 0 atom were in each four-fold site (1.25 A). Thus, it seems that nonbonded repulsions between the 0 atoms alone would not account for the c(2 X 2) structure, while the bonding picture in fig. 5a does.
(a)
NI (100)
/-
(b) NICIIO)
TOP VIEW
SIDE VIEW
Fig. 6. The geometry of the 0 atom and nearest neighbor Ni atoms for the Ni(lOO) and Ni(ll0) surfaces. Ni atoms in the plane of the paper are illustrated by light circles, while those below the paper are illustrated by dashed circles and the 0 atom is illustrated by a somewhat larger heavy circle. [See note relative to the (110) surface in caption to fig. 5.1
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
621
3.5. The (1 IO) surface The simplest model for bonding of 0 along the Zongedge of the unit cell for the (110) surface is the Ni20 cluster. As shown in table 1, this model leads to a distance above the surface of 0.31 8. However, for the 0 this close to the surface, there should be interactions with the two Ni atoms in the next layer down. Fig. 6b shows the locations of these atoms relative to the surface atoms and the 0 atom. While we have not solved for the Nib0 cluster which includes the effects of these second layer atoms, we have solved for a NiaO cluster which includes the two surface Ni atoms and one of the atoms in the second layer. As indicated in table 1, the third Ni atom has an attractive interaction with the 0 atom leading to a decrease by 0.23 A in the distance between the 0 and the third Ni atom (this distance is not normal to the (110) surface). Thus, for this registry with the surface we predict that the 0 atom will be very close to the surface and might penetrate it. LEED studies [ 181, suggest that the 0 atoms are bonded along the short edge of the unit cell, a geometry which we have not investigated.
4. Further discussion of the wavefunctions Before discussing the bonding of an 0 atom to the various Ni clusters, we first consider the bonding in NiH and Niz, since these simple cases illustrate the basic characteristics of the bonding between Ni atoms and the bonding to an 0 atom. The Ni atom has two low-lying states 4s13dy(3D) and 4s23d8(3F). Ignoring spinorbit coupling effects, the ground state is 3D with the 3F state only 0.03 eV higher [19]. Thus, both states could play a role in the bonding. However, the Ni(4s) orbital is -2; times as large as the Ni(3d) orbitals (see fig. 7); thus, the 4s orbital dominates the bonding. Bringing up an H atom to the 4s23d* state of Ni leads to repulsive interactions much as for the case of HeH. The 4s’ 3d9 state of Ni, on the other hand, leads to a sigma bond between the Ni(4s) and H( 1s) orbitals and, hence, an attractive potential curve as for Hz. The remaining 3d9 configuration on the Ni then leads to ‘C+, 2TI, and 2A states depending on whether the singly occupied 3d orbital is taken as a 3do, 3dn, or 3d6 orbital respectively. As discussed elsewhere [21], while the Ni configuration is basically 4s13d9 there is some mixing in of components of 4s33d8 character, the energy of which varies over a range of several eV depending on whether the 4s’3dy configuration has a singly occupied 3da, 3dn, or 3dS orbital. The net effect (referred to as the interatomic coupling effect) leads to the ordering 2A < 2fI < 2Z’ with 2A 0.346 eV below *fI which in turn is 0.095 eV below 2Z+ (at R, for the X2A state) [22]. We find that these results are quite general for sigma bonds to the Ni(4s) orbital leading to an increased stability associated with having a 3d hole which is &like with respect to the bond axis. From the discussion of NiH, it is not surprising that the bonding in Ni2 [23]
622
S.P. Walch, W.A. Goddard III/Bonding
0.0
0.625
1.250
i 6375
of oxygen to models of (I 00) Ni
2.500
ilSTAPJCE
3.125
3.750
u .375
S.mO
(BOHR)
Fig. 7. Comparison of the 4s and 3d orbital sizes of the Ni atom. These orbitals are for the s2d8(3F) state, the orbitals for the s’~~(~D) state are quite similar. The 3d orbital shown is 3z2 -r2.
involves a 4s’ 3dY configuration on each Ni leading to a sigma bond between the 4s orbitals, and the lowest 3d occupation has both 3d holes taken in 3d6 orbitals (other 3d orbital occupancies lead to numerous low-lying excited states). As a generalization of these cases, we find that the bonding in the various Ni clusters involves the 4s’3d9 Ni configuration and is dominated by the Ni(4s) electrons, while the most favorable 3d9 configuration has the hole in the 3d shell taken to be delta-like with respect to the bond axis (axes). (See the discussion in ref.
i6bl.I 4.1. Ni20 From the above discussion, given (1) we expect the lowest 3d orbital occupancy to correspond to taking the 3d holes to be h-like with respect to the NiS bond axes u41. In these calculations we fixed the Ni-Ni distance at fi (where a is the nearest neighbor distance 2.49 A in Ni metal), as appropriate for next nearest neighbors on the Ni( 100) and Ni(ll0) surfaces. We then varied the NiO distance (retaining CZv symmetry). The resulting potential curve is shown in fig. 8, while the energies used
SP. W&h, W.A. Goddard III/Bonding af oxygen to models of (I&?/ Ni -0.0
623
-
-O.l-
-o.z-
3
hJ
-0.3-
s zl El
-O.u-
Fig. 8. Ni?O geometry optimization.
The calculated points are indicated.
to construct the curve are given in table 2. The optimum geometry from the potential curve corresponds to a distance above the surface of 0.31 A which leads to a NiO bond length of 1.79 A and a NiONi angle of 160.0’. Including only the two bond pairs (in the following discussion we include only the 4s electrons of each Ni atom), the GVB wavefunction corresponding to (1) is Table 2 Ni20 geometry variation da
1.5 1.2 1 .o 0.8 0.6 0.4
Energy CVB(2ipp) b
GVBWPPI c
-155.91732 -155.92398 -155.92644 -155.92197 -155.92842 -155.92818
-155.90678 -155.90909 -155.91034
a d is the perpendicular distance (in au) from the 0 to a line between the two Ni atoms. b This corresponds to wavefunction (5). The optimum geometry corresponds to a d value of 0.31 A which gives a NiO distance of 1.79 A and a NiONi angle of 160.0”. The De values are 3.87 eV and 4.37 eV for GVB and CI wavefunctions respectively. c This corresponds to wavefunction (8).
624
S.P. Watch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
written in terms of natural orbitals as (& - ~@;‘>(cl: - hG2) .
(9
where the two GVB pairs correspond to the localized bond pairs shown in fig. 2. An alternative way to correlate this wavefunction using symmetry orbitals is (la; - h2a:)flb:
- X!b:),
where
One may imagine (6) to correspond tion
to bonding the 0 atom in the following orienta-
0
~ NI 2
0
Y
(7)
* Nt 5
The bond pairs may then be qualitatively described as (1) an aI pair with one component essentially 0(2p&like and the other component corresponding to Ni2(4s) + Ni4(4s); (2) a bz pair with one component essentially 0(2p,)-like and the other component corresponding to Ni2(4s) - Ni4(4s). However, because of the ionic character of Ni20, we find that the at pair corresponds essentially to an 0(2p& doubly occupied orbital, leading to a wavefunction of the form la:(lb:
- h2bz),
(8)
which corresponds to the ionic configuration (2). For NizO (5) is lower in energy than (8) (see table 2). Thus, we optimized the geometry based on (5). However, from the populations it is clear that there is a large ionic col~ponent corresponding to (8). For larger clusters, we find that the presence of nearby Ni atoms restricts the correlation effects leading to a wavefunction of the form (8) being lower. We show the orbitals of (8) in fig. 9. From fig. 9 one sees that the Ia1 orbital (fig. SC) is essentially an O(2pJ orbital, while the bz pair has one component (fig. 9a) which is essentially 0(2p,)Jike, while the other component (fig. 9b) corre-
S.P. Walch, W.A. Goddard III/Bonding
NI*O
GVB(I/pp),
THE (a)
of oxygen to models of (100) Ni
C2v
BOND
625
S’fMMETRY
PAIR
(b)
024 ~-
ONE
I I
i
ONE
Cc) 02p,
6.0
Y
60
Fig. 9. The GVB orbitals for NizO using the wavefunction (8).
sponds to Ni2(4s) - Ni4(4s) but has built in a substantial amount of 0(2p,) character (indicating an ionic bond). To calculate the D, for the NizO cluster, we carried out a small configuration interaction (CI) calculation using the orbitals of (5). Here, we projected these orbitals onto (6), leading to basis functions which have the C,, symmetry of the molecule. In addition to these four orbitals, all the remaining occupied orbitals were included in the CI, leading to 17 basis functions (including the O(ls)-like orbital which was kept doubly occupied in all configurations). The configurations were generated by allowing all single excitations from the set of generating configurations in table 3.
a These orbit& correspor~d to the bond orbitofs 01‘ Nil 0 pmjccted PII ” The parenthesis indicate that WC take products of tlrc conl‘igurntion~ with those in the right pnrenthcscs, resulting in f’ocir ~~oni’ipuratlom.
( ‘2b“4rnmctr~ in the Ict’t parentheses
The resulting D, value is 4.37 eV as compared with a D, of 3.95 eV for a comparable Cl treatment for NiO (see reference [ 161) indicating that 0 prefers bridged sites on the Ni(lOO) surface as compared with bonding positions directly above a surface Ni atom.
Adding Ni atoms I and 3 leads to the Ni40 cluster. The electronic
configuration
is
---
0
Nl 1 x
(‘1)
where the bond orbitals (shown in the _r*zplane) correspond to the orbitals of(g). Adding to (8) the doubly-occupied 0 7px rxbital ( 1bf) and the 4s orbitals of Ni 1 and Ni3 which are triplet-tousled (3a, 1 2b: ,I leads to the overall ~OrlfigLlrati~~n [Xi]. la:(lbz
~- X2bi) lb: 21; 2bl .
(10)
Repulsive nonbonded interactions between the 0(7px) pair and Ni atoms 1 and 3 lead to an equilibrium geometry with the 0 0.56 A above the surface, 0.25 ‘4 higher than for Ni20. The resulting potential curve is slwwn in fig. 10, while the energies are given in table 4. In table 5, we show Mull&en populations for the various clusters. For NizO and Ni40 we see that Ni atoms 7I and 4 have populations corresponding to charges of -+0.5 electrons. Considering adsorbate ~aclsorbate interactions due to the other
S.P. Walch, W.A. Goddard III / Bonding of oxygen to models of (I 00) Ni
621
-o.o-
-O.l-
; w
-0.2-
z (3 E z
-0.3-
I
Fig. 10. Ni40 geometry
variation.
The calculated
points
are indicated.
oxygen atoms in the overlayer, we see from fig. 5 that, the overall charge distribution in our five Ni atom cluster is approximately described by an ion state where one 4s electron has been ionized from among the 4s orbitals of Nil and Ni3 [i.e., ionizing an electron from the 2ar or 2b 1 orbital of (lo)]. For the positively charged clusters, we anticipated that polarization effects in a direction perpendicular to the surface would be important. Therefore, we added the Ni atom beneath the surface, leading to the NiiO cluster as the model for 0 on Ni( 100).
Table 4 Ni40 geometry
variation
da
Energy
1.5 1.1 0.7
-237.02681 -237.03187 -237.02857
b
a d is the perpendicular distance (in au) from the 0 to the plane containing the four Ni atoms. b For a GVB(l/pp) wavefunction. The optimum geometry corresponds to ad of 0.56 A which corresponds to a NiO distance of 1.85 A and a NiONi angle of 144.7”. The De value is 2.98 eV for a GVB(l/pp) wavefunction. The basis set used here is [2s, lp, ld/3s, 2p] which we estimate to lead to an error in the energy of 0.239 eV (from comparison of NisO calculations using these basis sets) as compared with the [3s, lp, 2d/3s, 2p, Id] basis used for the NiO and NiaO calculations. Thus, this correction should be added to the De value to compare with the NiO and NisO calculations, leading to 3.22 eV as our best estimate for De.
628
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (I 00) Ni
Table 5 Mulliken populations for the N&O clusters a*b Niz 0
NisO
N&O
NisO
Nil0
10.00 9.55 10.00 9.55 10.08 8.82
9.15 9.52 9.75 9.52 9.85 8.61
._ Nil ’ Ni2 Ni3 Ni4 Ni5 0
_ 9.55 9.55 8.91
10.02 9.54 10.02 9.54 _ 8.88
9.57 _ 9.51 9.99 8.87
a Near the optimum geometry in each case, which corresponds to vertical displacements 0.1, 1.1, 1.2, and 1.8 au for NizO, NiaO, Ni40, NisO and NilO, respectively. b See ref. [ 151 in the text. c The numbering of the Ni atoms is as shown in fig. 6a [Ni(lOO)].
of 0.6,
4.3. Ni5 0, Ni: 0 We find for the neutral function [26] la:(lbz
NisO cluster that Ni5 is nonbonding,
- X2b:) lb: 2a] 3a] 2b; .
leading to a wave-
01)
We show the orbitals corresponding to (11) in fig. 3. The orbitals of the GVB pair (1 bi - h2bi) are shown in fig. 3ab, where one sees that they are similar to the corresponding orbitals of (8) (fig. 9a, b). The la; pair (fig. 3c) is essentially a doubly occupied 0(2p,) orbital. The 2ar orbital (fig. 3e) has bonding character on all three Ni atoms, while the 3ar orbital (fig. 3g) is essentially a 4s orbital on Ni5 and is antibonding in character. The 2br orbital (fig. 3f) corresponds approximately to Nil(4s)-Ni3(4s). The lowest ion state of the N&O cluster corresponds to ionizing the 3ar orbital leading to the wavefunction la:(lb:
- h2bz) lb: 2a: 2bf
(12.1
Near the equilibrium geometry for the neutral NisO cluster, the orbitals of (12) are very similar to the corresponding orbitals of (11) (as assumed in using Koopmans’ theorem). However, the Ni’, cluster has a larger effective electronegativity than the Nis neutral cluster, which leads to more covalent bonding for Ni;O than for NisO neutral. As expected from the discussion in section 4.1, this leads to an equilibrium geometry with the 0 further from the surface than for the Ni;O cluster. As the 0 atom moves from the equilibrium geometry for Ni50 neutral toward the equilibrium geometry for the Ni;O cluster, an electron is transferred from 0 back to the metal leading to the la: pair being mainly on the Ni (bonding orbital) while the 2ar orbital becomes a singly occupied 0(2p,) orbital. The resulting orbitals for the Nil0 cluster near its equilibrium geometry are
S.P. Walch, W.A. Goddard Ill/Bonding
of oxygen to models of (100) Ni
629
shown in fig. 4. Here one sees that the orbitals of the GVB pair (fig. 4a, b) are very similar to the corresponding orbitals of the N&O neutral cluster (fig. 3a, b). The doubly occupied la1 orbital (fig. 4e) has bonding character on all three Ni atoms and also shows NiO bonding character. The singly occupied 2aI orbital (fig. 4c) is
-0.0
-
-0.1
-
NljO
GEOMETRY
OPTIMIZRTION
N150
GEOMETRY
OPTIMIZRTIBN
ZI -o.z;: B Y
lLA -0.3-
Fig. 11. Ni50, NiiO geometry variation. The calculated points are indicated.
630
S.P.
Walch,
W.A.
Goddard III /Bonding of oxygen to models of (I OO}Ni
Table 6 N&O and Ni;O geometry variation Energy da Nis 0 ‘~ GVB
2.1 1.8 1.S 1.2 0.9 0.6
-
Ni;O -._..GVB c
“- --.- --.--~_-__I---~.. Koopmans theorem
-277.5567
-277.4016 -277.4044 -277.4023
-277.3854
-2ll.S588 -277.5564 -277.5517
-277.3988 -277.3932 -277.3853
-217.3851 --217.3794 -
d
a d in the perpendicular distance (in au) from the 0 to the plane containing the four surface Ni atoms. b For a GVB(l/ppf wavefunction. The optimum geometry corresponds to a d value of 0.65 A which leads to NiO distance of 1.88 A and a NiONi angle af 139.5”. The De value is 1.69 eV (see footnote b of table 4). c For a GVB(l/pp) wavefunction. The optimum geometry corresponds to a d value of 0.06 A which Ieads to a NiO distance of 2.01 A and a NiONi angle of 122.8”. The D, value is 2.85 eV (see footnote b of table 4). d The Koopmans” theorem energies Iead to an optimum geometry with the 0 atom 0.71 A above the surface.
essentially an 0(2p,) orbital and the 2bl orbital (fig. 4f) is similar to the corresponding orbital of (11) The ~ulliken populations (table 5) indicate that the Ni atoms involved in NiO bonds (Ni2 and Ni4) have Mulliken populations consistent with charges of -+0.5 electrons. From table 5 we see that the Ni:O cluster has a positive charge of -0.5 electron distributed between Nil and Ni3 as compared with -1.0 electron expected for Ni;O. Thus, we expect larger nonbonded repulsions between the 0(2p,) pair and the surface Ni atoms (1 and 3) for NiiO than for Ni;O. This effect, which derives from polarization effects involving Ni5, leads to an equilibrium geometry for Nil0 with the 0 atom 0.23 L%further from the surface than for NiiO. In fig. 11 we show the potential curves for the NisO and Ni:O clusters, whiIe the energies are given in table 6. As indicated in table 1r the NiiO cluster leads to a distance above the surface of 0.96 .A which is in excellent agreement with the results of dynamic LEED intensity analysis, 0.90 zi:0.10 A [S]. 4.4, NiJO Starting with the wavefunction (8) for NizO and adding the atom beneath the surface (Ni5) leads to the NiaO cluster. We find that NiS is nonbonding, leading to
631
Y L
--.-~____ -._I
-I-tiE BOND
(Cl)
.l_l.__._ “^___
T-""-"
PAIR
(b)
Fig. 12. Selected orbitals of the Ni30 cluster. Table 7 NW geometry variation da
Energy b
1.0 0.7 0.4 0.1 -0.2
-196.46073 -196.47057 -196.47960 -i96.48297 -196.47092
a d is the perpendicular distance (in au) from the 0 to a lime connecting Ni2 and Ni4. b For a GV~(~/pp) ~avefunct~on. The optimum geometry corresponds to a d value of 0.08 A which gives a NiO distance of 1.76 A and a NiONi angle of 174.8’. The De value is 3.08 eV (see footnote b of table 4).
S.P. Walch, W.A. Goddard I/I 1 Bonding of oxygen to models of (I 00) Ni
632 OS-
-0.2 -
-o.uL ;r g
-0.5-
6
I
I
-0.2
-0.1
I
-0.0
I DISTi&~
Fig. 13. Ni30 geometry
the qualitative
description
variation.
I
RNG;~AclN
la: 2a](lbi
I
0.5
I
0.6
are indicated.
L_-----+Y Nt2
l
to the GVB wavefunction
~ h2bi).
points
I
0.u
for NiaO:
0
which corresponds
I 0.3
The calculated
NI 4
0
1
NI 5
[27] (13)
We show the orbitals of (13) in fig. 12. Here one sees that the b, bond pair (fig. 12a, b) is qualitatively similar to the corresponding pair in NizO (fig. 9a, b), N&O (fig. 3a, b), and NiSO (fig. 4a, b). The 2ar orbital (fig. 12d) corresponds approximately to a 4s orbital on Ni5 but has hybridized away from the 0 atom. This leaves a partially exposed 3d9 core on Ni.5 which we expect to have an attractive interaction with the doubly occupied 0(2p,) orbital (as for the 50 orbital of CO upon bonding to Ni [21]). It is apparently this effect that leads to an equilibrium geometry for the NisO cluster with the 0 atom only 0.08 a above the surface, 0.23 i$ closer than for the NizO cluster [28]. The resulting potential curve is shown in fig. 13, while the energies used to construct fig. 13 are given in table 7.
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
633
In the case where the 0 bonds at the long edge of the (100) surface unit cell (fig. 6b), there are two Ni atoms below the surface (atoms 3 and 4 for geometry A), which can interact in the manner that Ni5 did for the Ni30 cluster. This leads to the expectation that for an 0 bridging Ni atoms 1 and 2 of fig. 6b there will be attractive interactions between the two doubly occupied p orbitals of the 0 atom and Ni atoms 3 and 4.
NI 3
N14
‘0
(14)
NI 1
Thus, for this registry with the surface, the oxygen would be expected to lie approximately in the plane of the surface (not more than 0.1 A above the surface).
References [ 11 (a) I.P. Batra and 0. Robaux, Surface Sci. 49 (1975) 653; (b) D.E. Ellis, H. Adacki, and F.W. Averill, Surface Sci. 58 (1976) 497. [2] See e.g. J.W.D. Connolly, in: Modern Theoretical Chemistry, Vol. 7, Ed. G.A. Segal (Plenum, New York, 1977) pp. 105-132. [3] The principal difficulty with the Xcz method for determining geometries is that usually only the muffin-tin approximation to the energy is evaluated. Errors in this approximation lead to very poor geometries (e.g. water is predicted to be linear [4a]). It is possible to make corrections to the muffin-tin energy leading to much better results [4b]. However, these corrections are often not carried out. [4] (a) J.W.D. Connolly and J.R. Sabin, J. Chem. Phys. 56 (1972) 5529. (b) J.B. Danese, Chem. Phys. Letters 45 (1977) 150. (c) C.H. Li and J.W.D. Connolly, Surface Sci. 65 (1977) 700. [S] J.E. Demuth, D.W. Jepsen and P.M. Marcus, Phys. Rev. Letters 31 (8) (1973) 540. [h] (a) S.P. Walch and W.A. Goddard III, Solid State Commun. 22 (1977) 907. (b) S.P. Walch and W.A. Goddard III, Surface Sci. 72 (1978) 645; see also ref. [21]. [7] (a) S.P. Walch and W.A. Goddard III, Surface Sci., submitted. (b) T.H. Upton and W.A. Goddard III, to be published. [8] (a) L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell University Press, New York, 1972) p. 93; (b) ibid, p. 260. [9] A.J.H. Wachters, J. Chem. Phys. 52 (1970) 1033. [lo] T.H. Dunning, Jr. and P.J. Hay, Gaussian Basis Sets for Molecular Calculations, in: Modern Theoretical Chemistry, Methods of Electronic Structure Theory, Vol. 3, Ed. H.F. Schaefer III (Plenum, New York, 1977) pp. l-27. The p functions are the same as in ref. [ 121, the tightest seven s functions are contracted into a single s function based on the 1s HF orbital, the second and third most diffuse are contracted into a basis function based on the 2s HF orbital; the most diffuse function is uncontracted.
634 [ 111
S.P. Walch, W.A. Goddard III/Bonding
S. Huzinaga,
unpublished. Jr., J. Chem. Phys.53 (1970) 2823. W.A. Goddard III. T.H. Dunning, Jr., W.J. Hunt and P.J. Hay, Accts. Chem. Res. 6 (1973) 368, S.P. Walch and W.A. Goddard III, J. Am. Chem. Sot. 100 (1978) 1338. This is from Mulliken populations. Generally, these populations indicate a greater charge transfer than would be indicated, for example, by the dipole moment. Thus, the populations although indicative of charge transfer should not be taken too literally. (a) B.J. Moss and W.A. Goddard III, J. Chem. Phys. 63 (1975) 3523: (b) B.J. MOSS, F.W. Bobrowicz and W.A. Goddard III, J. Chcm. Phys. 63 (1975) 4632. A wavefunction of the form (1) leads to an energy -0.5 eV below a wavefunction of the form (2). However, the qualitative description is like (2). J.E. Demuth, J. Colloid Interface Sci. 58 (1977) 185. The quoted atomic separations are obtained by taking a weighted average over the spectral levels corresponding to a given f, and S (spinorbit interactions are not included in our calculations). The values are from ref. [ 201. C.E. Moore, Atomic Energy Levels, Vol. II (National Bureau of Standards, 1952). S.P. Walch and W.A. Goddard III, J. Am. Chcm. Sot. 98 (1976) 7908. M.J. Sollenberger, M.S. thesis, California Institute of Technology (1975). T.H. Upton, W.A. Goddard III and C.F. Melius, J. Am. Chem. Sot., to be submitted. Them are two possible choices for the delta-like orbitals on each Ni. Their cncrgics arc within -0.04 eV and we chose to solve self-consistently for the case where each Ni 3d6 hole is asymmetric with rcspcct to the molecular plane, since this choice srmplifies the SCF calculations. The Ni(3d) holes for Ni atoms 2 and 4 (involved in Ni-0 bonds) were taken to be dcltalike with respect to the NiS bond axis and asymmetric with respect to the 1%: plane (containing Ni2, Ni4, and the S) which is the same orientation as for the NiaO calculation. The Ni(3d) holes for Nil and Ni3 were taken in 3d,, orbitals which are delta-like with respect to the x axis, which passes through Nil and Ni3. The Ni(3d) holes for Ni atoms l-4 are the same as for the Ni,O cluster (see ref. (251). The 3d hole for Ni5 is taken in a 3d,, orbital which is thus delta-like with respect to the z axis (regarded as the bond axis for bonding Ni5 to the surface Ni atoms). The Ni(3d) holes for Ni atoms 2 and 4 are the same as for the Ni,O calculation (see ref. [24]). The 3d hole for Ni5 is the same as for the NisO calculation (see ref. [26]). l:or the N&O cluster repulsive effects between the nonbonded Ni atoms (1 and 3) and the O(2pn) pair lead to a geometry with the 0 atom further above the surface than for Ni,O. Apparently, at larger distances stabilization of the 0(2p,) pair is less significant than nonbonded repulsion due to the Ni5(4s) orbital, leading to a slightly repulsive effect due to Ni5.
[12] T.H. Dunning, [13] [14]
[ 151
1161 [17] [18] [19]
[20] [21] [ 221 (231 [24]
(251
[ 261
[27] [28]
of oxygento models of (100) Ni
THEORETICAL STUDIES OF THE BONDING OF OXYGEN TO MODELS OF THE (100) SURFACE OF NICKEL * Stephen P. WALCH and W.A. GODDARD III ** Arthur Amos Noyes Laboratory of Chemical Physics, GzlifomiaInstitute of Technology, Pasadena, ~~ifor~~a 91125, WSA Received 11 March 1977; manuscript received in final form 27 February 1978
Electronic wavefunctions have been obtained as a function of geometry for an 0 atom bonded to Ni clusters (consisting of one to five atoms) designed to model bonding to the (100) surface of Ni. Electron correlation effects were included using the generalized valence bond and configuration interaction methods. For the (100) surface, we find that the charge distribution for the full 0 overlayer is consistent with taking a positively charged cluster. The four surface atoms in the surface unit cell and the atom beneath the surface are important in determining the geometry, leading to a Ni;O cluster as the model for the (100) surface. The optimum oxygen position with this model is 0.96 A above the surface (four-fold coordinate site) in good agreement with the value (0.90 f 0.10 A) from dynamic LEED intensity analysis. The atom beneath the surface allows important polarization effects for the positively charged cluster. The bonding to the surface involves bridging two diagonal surface Ni atoms, There is an O(2pn) pair which overlaps the other diagonal pair of Ni atoms leading to nonbonded repulsions which increase the distance above the surface. There are two equivalent such structures, the resonance leading to a c(2 X 2) structure for the 0 overlayer.
1. Introduction While there have been several theoretical studies of the chemisorption of 0 on the Ni( 100) surface using cluster methods [l], previous calculations have used the SCF-Xc&W method [Z] which leads to moderately good results for c~culated photoelectron spectra [ I] but for the usual muffin tin approximation does not yield reliable geometry information 13). After submission of this manuscript a paper appeared by Li and Connolly [4c] showing that use of the muffin tin approximation to SCF-Xc&W for N&O complexes leads to very poor geometries but that inclusion of muffin tin corrections leads to reasonable geometries. Experimentally geometry information for overlayers on metal surfaces is obtained from detailed
* Partially supported by a grant (DMR 74-04965) from the National Science Foundation, ** Partially supported by a grant (EX-76-C-03-1305) from the Energy Research and Development Administration.
610
S.P. Walch, W.A. Goddard III /Bonding
of oxygen to models of (I 00) Ni
analysis of low energy electron diffraction (LEED) intensities [5). However, because the theoretical analysis involves some severe approximations such geometries cannot be described as purely experimental and an independent theoretical determination for some well characterized systems would be useful. We report here accurate ab initio calculations for the bonding of 0 to Ni clusters designed to model the Ni(lOO) surface. A preliminary report of similar calculations for S on Ni has been presented elsewhere [6a]_ In this paper we concentrate principally on geometry predictions. (configuration interaction calculations based on similar wavefunctions also yield good results for the photoelectron spectra of CO [7a], &Hz [7b], and CzH4 [7b] on Ni; however, we have not carried out such calculations for 0 or S on Ni.) We find that the main differences between the 0 and S calculations have to do with fi) the smaller size of the oxygen atom, and (ii) the higher electronegativity of 0 (3.5 as compared with 2.5 for S [8a], The larger amount of ionic character in the 0 clusters requires that the atom beneath the surface be included in the cluster for the 0 case, whereas only the surface Ni atoms were important in the S case. In section 2, we describe the basis set and other calculational details. Section 3 describes the qualitative nature of the wavefunctions for the various Ni clusters and compares the calculated geometry for the (100) surface with results of dynamic LEED intensity c~culations [S]. Section 4 discusses the wavefun~tions for the clusters in somewhat more detail.
2. Calculational details We solved for the states of the finite clusters using the ab initio generalized valence bond (GVB) method 1131 which differs from the usual Hartree-Fock (HF) method in that it includes the dominant electron correlation effects necessary to describe bond formation. In these calculations we explicitly included all ten valence electrons of each Ni atom and all the electrons of the 0 atom; the 18electron Ar core of the Ni atom was replaced by an effective potential. The basis set and effective potential used for Ni have been reported previously [6b,21]. (The Ni basis is based on the set optimized for the third row atoms by Wachters [9]. The [3s,lp,2d] contraction of the Ni basis was used for the NiO and N&O calculations, while for the larger NiaO, N&O and N&O calculations the [2s, lp,ld] contraption was used [6b]. The basis for oxygen is the Dunning f3s,2p] contraction [lo] of the Huzinaga (9s,5p) set [ 111. This contraction is valence double zeta but uses a single Is-like contracted function and leads to energies within 0.0001 h of those obtained with the double zeta contraction [12]. For the NiO cluster a single set of d-functions (o = 1.04) was used on the 0, while for the N&O cluster the geometry was optimized without d-functions but d-functions were added at the opt~un~ geometry. ~-functions were omitted for the larger clusters.
3. Qualitative discussion Table 1 summarizes the results for bonding an 0 atom to the various Ni clusters. For the floO> surface, the surface unit cell contains four surface Ni atoms at the corners of a square (which we refer to as Nil, Ni2, Ni?, and Ni4) and one atom below the center of the square in the next layer down (which we refer to as NiS). For S on the Ni(100) surface, we found that only the faur surface Ni atoms (l-4) Table 1 Summary of results for bonding of oxygen to the Ni clusters Ciuster
Geometry
NiO
Ni-0
Model for
Ni20
Distance above plane (A)
RNiO (A)
D (eV)
1.65
1.65
3.95
(I IO) surface 0 on long edge
5.31
1.79
4.37
(115) surface 0 on long edge
5.08
1.76
3.32 a
5.56
1.85
9.22
Ni2
Ni30
/\
0
Ni5 \/ Ni4
NQO NiiO
(155) surface 0 at center of cell
(0.75)
b
-
-
0.65
I .88
1.93
(155) surface 0 at center of cell
5.96
2.51
3.59
a The NiO and Ni20 calculations used a [3s, lp, 2d/3s, 2p, fdf basis, while a f2s, lp, ld/3s, Zp] basis was used for the larger clusters, From comparisons of both types of calculations for Ni20 we estimate that this basis leads to an error in De of 5.24 eV, but does not have a significant effect on the geometry. Thus, we have added 5.24 eV to the D, vaiues for the NigO, N&O, and NisO clusters in order to compare with the NiO and X20 calculations, b This value is estimated from Koopmans’ theorem by assuming that the error in the geometry from Koopmans’ theorem for Nit0 (5.25 A) will also be the same in Ni$O.
612
S.P. Walch,
W.A. Goddard III /Bonding
of ox.gen
to models of (I 00) Ni
had to be included to describe the geometry. However, for the 0 case we find that Ni5 must be included to describe polarization effects in the direction perpendicular to the surface. In addition, the higher eIectronegati~ty of 0 requires a positive ion state of the NisO cluster in order to be consistent with the charge distribution expected for the full 0 overlayer when adsorbate-adsorbate interactions are considered (see section 3.2). Thus, we used a NiiO model for 0 on Ni(lOO). With this model we find that the 0 is a distance of 0.96 A above the surface, in excellent agreement with the value from dynamic LEED intensity analysis, 0.90 rt 0.10 A PI. A recent XCYcalculation [4c] using a NisO complex like ours and including nonmuffin tin corrections leads to a distance of 0.75 A. Without those corrections the Xa calculation leads to a geometry at least 0.45 A larger [4c]. In the following, we discuss qualitatively the essential features of the wavefunctions for the various clusters shown in table 1. For all the clusters considered here, we find that the Ni atom has the character of the 4s’ 3da con~guratio~~ and the bonding is dominated by the 4s orbital, while the orientation of the hole in the 3d shell leads to small energy effects. The simplest model which contains the qua~tative features of the bonding to the (100) surface is the Ni?O cluster. which corresponds to bridging across a pair of surface Ni atoms (say Ni2 and Ni4) along the diagonal of the square. 3.1. NiO and NizO Wavefunctions for numerous electronic states of NiO have been discussed in detail elsewhere [ 141. The bonding in NiO is dominated by the sigma bond which may be described qualitatively as a Ni(4s) orbital singlet paired with an O(2po) orbital. The orbitals of the bond pair are shown in fig. lc, d; as expected from the relative electronegativities (1.8 for Ni, 3.5 for 0 [8a]) there is a substantial amount of charge transfer [ 151 to the 0 atom (0.55 electrons). For the ground state of NiO, the 3d hole of the Ni 3d9 con~guration is 3dn, feading to a 3Zc- ground state which is quite analogous to the ground states of NiS (Sb) and of 02 1161. As indicated in fig. la, e, g, the Ni(3d) orbitals are only slightly affected by the bond. The major difference between NiO and NiS is the greater charge transfer (0.55 electrons for NiO as compared with 0.38 electrons for NiS [ 151). Bonding a second Ni atom to the singly occupied 0(2p,) orbital (fig. If) leads (after readjustment effects) to a structure with two equivalent sigma bonds (i.e., the NiaO cluster) 2 0
(1) j__ Nf4
NI
2
Y
S.P. Walch, W.A. Goddard III /Bonding
NiO
of oxygen to models of (100) Ni
613
X3x-
(b) 0 2s
(a) NI 342 r--
TWO
(e) NI 3d,,
(f) 0 2P” I
ONE
507
(g) Ni 3dxZ ~-~
(h)O2p, TWO I
X
Fig. 1. The GVB orbitals of X3x- ground state of NiO. Unless otherwise noted, all plots have uniformly spaced contours of 0.05 au. Solid lines indicate positive contours, short dashes indicate negative contours, and long dashes indicate nodal lines. The same conventions are used for other figures. [Note that because a Ni(4s) orbital is much more diffuse than a Ni(3d) orbital, even a relatively small amount of 3d character appears very pronounced in the contour plots. Thus, for example, the orbitals in fig. 3e, f, g, which appear to contain large amounts of 3do character, have -15% d character (from a Mulliken population analysis).] The same conventions are used for the other figures.
614
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
Solving for a wavefunction of the form (1) leads to a total charge transfer to the oxygen of 0.9 1 electrons, which is consistent with incorporating a substantial component of the ionic configuration (2j [ 171 Z
NY4
NI 2
Covalent bonding as in (1) favors 90” bond angles, whereas bonding to O- as in (2) favors 180” bond angles. Thus, incorporation of ionic character leads to large bond angles and small vertical displacements of the 0 atom (relative to the surface). For the NizO cluster, the optimum geometry is with the 0 atom 0.31 A above the surface, which is consistent with the overall charge transfer (0.91 electrons). The orbitals corresponding to (1) are shown in fig. 2. The bond pairs (fig. 2a, b, c, d) show a substantial amount of charge transfer to the oxygen. For one bond pair (fig. 2a, b), one component (fig. 2b) is essentially 0(2p)-like, while the other component (fig. 2a) corresponds approximately to a Ni(4s) orbital which contains a large amount of O(2p) character. (Thus, the covalent bond has an appropriate amount of ionic character.) The 0(2s)-like orbital (fig. 2e) has hybridized away from the bond pairs. We find that bridged bonding as in the NizO cluster is more favorable (D, = 4.37 eV) than bonding directly above a surface Ni atom as in NiO (D, = 3.95 eV). The small difference in bond energies here reflects the fact that the NizO cluster contains a large component of (2) which involves only a single sigma bond. 3.2. Ni40, Nit0 Including the nonbonded surface Ni atoms (Nil and Ni3) leads to the Ni40 cluster. Qualitatively the electronic configuration of the Nib0 cluster is Y Q
0
NI 2
I
a
(3)
S.P. Walch, W.A. Goddard III/Bonding
Ni,O
(0)
of oxygen to models
of (I 00) Ni
615
GVB C.?/PP)
UPPER NiO BOND (b)
0 2s PAIR (e) TWO
LOWER
NiO
BOND
_p
,.o!c.! ONE
’ “\A,,
ONE
Fig. 2. Selected orbitals of the NizO cfuster.
The bonding orbitals (shown in the yz plane) are analogous to the orbitals of (2). We find (as for N&S) that there are repulsive interactions between the doubly occupied O(2p.J orbital and the other two surface Ni atoms (Nil and Ni3) which lead to an optimum geometry with the 0 atom 0.56 A above the surface, 0.25 t\ higher than for the NizO calculation.
616
S.P. Walch, W.A. Goddard III / Bonding of oxygen to models of (I 00) Ni
For the full oxygen overlayer, Nil and Ni3 are involved in bonds to other 0 atoms. Considering the charge transfer involved in the bonds leads to a charge of -0.9 distributed between Nil and Ni3 (based on Ni*O). Thus, considering adsorbate-adsorbate interactions, the overall charge is more accurately represented within the limits of our cluster model by an ion state of the Niq cluster involving removal of one electron from among the orbitals corresponding to Nil and Ni3. It was anticipated that for the positively charged cluster polarization effects involving Ni.5 would be important, thus we used a Ni:O cluster as the model for 0 on Ni( 100). 3.3. Ni50, NifO
Here we consider first the neutral N&O cluster. For Ni50 we find that Ni5 is nonbonding and the remaining electronic configuration is similar to (3) for N&O. The orbitals of the neutral N&O cluster are shown in fig. 3. Looking first at the bond pair (fig. 3a, b), one sees that one component (fig. 3a) is essentially an 0(2p,) orbital, while the other component (fig. 3b) corresponds approximately to Ni2(4s))Ni4(4s) but contains a substantial amount of 0(2p,) character (indicating an ionic bond). The O(2pJ pair (fig. 3c) has delocalized somewhat onto the Ni, but the overall populations correspond most closely to an O- configuration for the 0 atom as in (3). The O(2s) pair (fig. 3d) is essentially atomic-like, but has built in a small amount of 3d character on the surface Ni atoms. The singly occupied orbitals (fig. 3e, f, g) are all derived from Ni(4s) orbitals (mainly on Nil, Ni3, and Ni5). The orbitals in fig. 3e, f correspond approximately to Nil(4s) + Ni3(4s) and Nil(4s) Ni3(4s), respectively; note however, that the symmetric combination (fig. 3e) has delocalized onto Ni5, leading to bonding character on all three centers. The other singly occupied orbital (fig. 3g) corresponds to a 4’s orbital on Ni5 and is antibonding in character. The optimum geometry for this cluster is with the 0 at 0.65 A above the surface, only 0.09 A higher than for the Ni40 cluster. Thus Ni5 has only a small effect on the geometry of the neutral cluster (as was predicted for bonding S to this cluster [6a]). Now we consider the Nil0 cluster. The lowest ion state of the N&O cluster involves ionizing the singly occupied orbital in fig. 3g. At the equilibrium geometry for N&O neutral, the orbitals of Ni;O are very similar to the corresponding Ni50 orbitals shown in fig. 3. However, the Nii cluster has a higher effective electronegativity than the NiS cluster which leads to more covalent bonding in Ni;O and an equilibrium geometry with the 0 atom further from the surface. Moving the 0 atom away from the surface, the doubly occupied O(2pJ orbital delocalizes more onto the Ni while the singly occupied Ni-Ni bonding orbital (fig. 3e) localizes on the 0 atom; leading (at the equilibrium geometry for Ni;O) to a singly occupied 0(2p,) orbital and a doubly occupied Ni-Ni bonding orbital (i.e., an electron has been transferred from 0 back to the metal).
S.P. W&h, hJ.A. Goddard HI /Bonding of oxygen to models of ~~~~~Ni Ni,O TOP
GVB (I/W’)
VIEW
XZ
PLANE
YZ
PLANE
N,‘4
THE BOND PAIR (b)
Cd) 0 2s
NI 4s ORBITALS (f)
(e)
5 *
es) _..
..oi?
:’- ,i lGd ;,*‘:‘h
:,,..,, :,*:
X
.._.
.j ._..’
/,
.’
‘\
/
//
-s.o;,o
/
/
0
2
‘1
‘7~ I 8.0
Fig. 3. Selected orbital5 of the NiSO cluster.
617
618
S.P. Waleh, W.A. Goddard III/Bonding
N15+0 TOP VIEW
of oxygen to models of (IOO) Ni
GVB(I/PP)
XL
PLANE
YZ
PLANE
ONE
(d) 0 2s
X
NI 4s ORBITALS (fi
-\ ONE
TWO
-8.0
i
-80
Z
SO-
Z
Fig. 4. Selected orbitals of the NiiO cluster.
. !ik
S.P. Walch, W.A. Goddard III/Bonding
The overall electronic
configuration
of oxygen to models of (I 00) Ni
619
is
. . ‘\ \
,
+i-,
.
.
: :/
+ /
(3 ’
(4)
I
i
I
0. I
We show the orbitals corresponding to (4) in fig. 4. The bond pair (fig. 4a, b) is very similar to the bond pair for NisO neutral (fig. 3a, b). The 0(2p,) orbital (fig. 4c) is now singly occupied and localized, while the orbital corresponding to the bonding combination of the Ni(4s) orbitals (fig. 4e) is doubly occupied. The remaining singly occupied orbital (fig. 4f) corresponds to Nil(4s) - Ni3(4s) and has not changed significantly from the corresponding orbital for NisO neutral (fig. 3f). Thus, the overall configuration for the NiSO cluster corresponds to a neutral oxygen atom configuration [but with about 0.5 electrons transferred in the bond pair (fig. 4a, b) leading to a total charge on the oxygen of 0.61 electrons as compared to 0.82 electrons for N&O neutral]. The net effect of the more covalent bonding is an equilibrium geometry with the 0 atom 0.96 A above the surface, 0.31 A higher than for N&O neutral. This value is in good agreement with the results of dynamic LEED intensity analysis, 0.90 ?r 0.10 A [5]. From table 1 we see that the NiiO cluster leads to a substantially larger bond energy 3.09 eV than for NisO neutral (1.93 eV). This effect derives largely from the antibonding character of the ionized orbital (fig. 3g). Thus, withdrawal of charge by adjacent 0 atoms on the surface leads to stronger bonding of 0 to the surface. This effect should lead to island formation at low coverages and formation of ordered overlayers at higher coverages. Fig. Sa shows the bonding expected for c(2 X 2) overlayers on the Ni(lOO) surface. The localized bonds shown in fig. 5a suggest a p(2 X 2) structure with the center and corner Ni atoms connected by a glide plane. However, there is a degenerate structure rotated by 90’ and these two structures are expected to have a strong interaction (resonance) leading to all the 0 atoms being equivalent. This leads to ~$2 X 2) as is observed [ 51. As shown in fig. 5a, bonding the 4s orbital of each Ni to one 0 leads to an 0 atom in only half the four-fold sites. Thus, this bonding picture suggests that the c(2 X 2) overlayer is particularly stable. The Van der Waals radius of the 0 atom is
620
S.P. Walch, W.A. Goddard III / Bonding of oxygen to models of (I 00) Ni (100)
SURFACE
( I IO)
SURFACE
Fig. 5. The c(2 X 2) structure for the 0 on (a) Ni(lOO) and (b) Ni(llO), respectively. Circles represent surface Ni atoms, crosses represent 0 atoms, heavy lines represent Ni-0 bonds, and dashed lines outline the unit cell. [Note that for the (110) surface recent LEED results [18] suggest that the 0 atoms are bonded across the short edge of the (110) surface unit cell. Since some of our clusters for the (100) surface constitute models for bonding to the long edge of the (110) surface unit cells, we illustrate this alternative registry here.]
1.40 i% [8b] considerably smaller than half the O-O distance for the c(2 X 2) structure (1.76 i%) but somewhat larger than half the O-O distance if an 0 atom were in each four-fold site (1.25 A). Thus, it seems that nonbonded repulsions between the 0 atoms alone would not account for the c(2 X 2) structure, while the bonding picture in fig. 5a does.
(a)
NI (100)
/-
(b) NICIIO)
TOP VIEW
SIDE VIEW
Fig. 6. The geometry of the 0 atom and nearest neighbor Ni atoms for the Ni(lOO) and Ni(ll0) surfaces. Ni atoms in the plane of the paper are illustrated by light circles, while those below the paper are illustrated by dashed circles and the 0 atom is illustrated by a somewhat larger heavy circle. [See note relative to the (110) surface in caption to fig. 5.1
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
621
3.5. The (1 IO) surface The simplest model for bonding of 0 along the Zongedge of the unit cell for the (110) surface is the Ni20 cluster. As shown in table 1, this model leads to a distance above the surface of 0.31 8. However, for the 0 this close to the surface, there should be interactions with the two Ni atoms in the next layer down. Fig. 6b shows the locations of these atoms relative to the surface atoms and the 0 atom. While we have not solved for the Nib0 cluster which includes the effects of these second layer atoms, we have solved for a NiaO cluster which includes the two surface Ni atoms and one of the atoms in the second layer. As indicated in table 1, the third Ni atom has an attractive interaction with the 0 atom leading to a decrease by 0.23 A in the distance between the 0 and the third Ni atom (this distance is not normal to the (110) surface). Thus, for this registry with the surface we predict that the 0 atom will be very close to the surface and might penetrate it. LEED studies [ 181, suggest that the 0 atoms are bonded along the short edge of the unit cell, a geometry which we have not investigated.
4. Further discussion of the wavefunctions Before discussing the bonding of an 0 atom to the various Ni clusters, we first consider the bonding in NiH and Niz, since these simple cases illustrate the basic characteristics of the bonding between Ni atoms and the bonding to an 0 atom. The Ni atom has two low-lying states 4s13dy(3D) and 4s23d8(3F). Ignoring spinorbit coupling effects, the ground state is 3D with the 3F state only 0.03 eV higher [19]. Thus, both states could play a role in the bonding. However, the Ni(4s) orbital is -2; times as large as the Ni(3d) orbitals (see fig. 7); thus, the 4s orbital dominates the bonding. Bringing up an H atom to the 4s23d* state of Ni leads to repulsive interactions much as for the case of HeH. The 4s’ 3d9 state of Ni, on the other hand, leads to a sigma bond between the Ni(4s) and H( 1s) orbitals and, hence, an attractive potential curve as for Hz. The remaining 3d9 configuration on the Ni then leads to ‘C+, 2TI, and 2A states depending on whether the singly occupied 3d orbital is taken as a 3do, 3dn, or 3d6 orbital respectively. As discussed elsewhere [21], while the Ni configuration is basically 4s13d9 there is some mixing in of components of 4s33d8 character, the energy of which varies over a range of several eV depending on whether the 4s’3dy configuration has a singly occupied 3da, 3dn, or 3dS orbital. The net effect (referred to as the interatomic coupling effect) leads to the ordering 2A < 2fI < 2Z’ with 2A 0.346 eV below *fI which in turn is 0.095 eV below 2Z+ (at R, for the X2A state) [22]. We find that these results are quite general for sigma bonds to the Ni(4s) orbital leading to an increased stability associated with having a 3d hole which is &like with respect to the bond axis. From the discussion of NiH, it is not surprising that the bonding in Ni2 [23]
622
S.P. Walch, W.A. Goddard III/Bonding
0.0
0.625
1.250
i 6375
of oxygen to models of (I 00) Ni
2.500
ilSTAPJCE
3.125
3.750
u .375
S.mO
(BOHR)
Fig. 7. Comparison of the 4s and 3d orbital sizes of the Ni atom. These orbitals are for the s2d8(3F) state, the orbitals for the s’~~(~D) state are quite similar. The 3d orbital shown is 3z2 -r2.
involves a 4s’ 3dY configuration on each Ni leading to a sigma bond between the 4s orbitals, and the lowest 3d occupation has both 3d holes taken in 3d6 orbitals (other 3d orbital occupancies lead to numerous low-lying excited states). As a generalization of these cases, we find that the bonding in the various Ni clusters involves the 4s’3d9 Ni configuration and is dominated by the Ni(4s) electrons, while the most favorable 3d9 configuration has the hole in the 3d shell taken to be delta-like with respect to the bond axis (axes). (See the discussion in ref.
i6bl.I 4.1. Ni20 From the above discussion, given (1) we expect the lowest 3d orbital occupancy to correspond to taking the 3d holes to be h-like with respect to the NiS bond axes u41. In these calculations we fixed the Ni-Ni distance at fi (where a is the nearest neighbor distance 2.49 A in Ni metal), as appropriate for next nearest neighbors on the Ni( 100) and Ni(ll0) surfaces. We then varied the NiO distance (retaining CZv symmetry). The resulting potential curve is shown in fig. 8, while the energies used
SP. W&h, W.A. Goddard III/Bonding af oxygen to models of (I&?/ Ni -0.0
623
-
-O.l-
-o.z-
3
hJ
-0.3-
s zl El
-O.u-
Fig. 8. Ni?O geometry optimization.
The calculated points are indicated.
to construct the curve are given in table 2. The optimum geometry from the potential curve corresponds to a distance above the surface of 0.31 A which leads to a NiO bond length of 1.79 A and a NiONi angle of 160.0’. Including only the two bond pairs (in the following discussion we include only the 4s electrons of each Ni atom), the GVB wavefunction corresponding to (1) is Table 2 Ni20 geometry variation da
1.5 1.2 1 .o 0.8 0.6 0.4
Energy CVB(2ipp) b
GVBWPPI c
-155.91732 -155.92398 -155.92644 -155.92197 -155.92842 -155.92818
-155.90678 -155.90909 -155.91034
a d is the perpendicular distance (in au) from the 0 to a line between the two Ni atoms. b This corresponds to wavefunction (5). The optimum geometry corresponds to a d value of 0.31 A which gives a NiO distance of 1.79 A and a NiONi angle of 160.0”. The De values are 3.87 eV and 4.37 eV for GVB and CI wavefunctions respectively. c This corresponds to wavefunction (8).
624
S.P. Watch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
written in terms of natural orbitals as (& - ~@;‘>(cl: - hG2) .
(9
where the two GVB pairs correspond to the localized bond pairs shown in fig. 2. An alternative way to correlate this wavefunction using symmetry orbitals is (la; - h2a:)flb:
- X!b:),
where
One may imagine (6) to correspond tion
to bonding the 0 atom in the following orienta-
0
~ NI 2
0
Y
(7)
* Nt 5
The bond pairs may then be qualitatively described as (1) an aI pair with one component essentially 0(2p&like and the other component corresponding to Ni2(4s) + Ni4(4s); (2) a bz pair with one component essentially 0(2p,)-like and the other component corresponding to Ni2(4s) - Ni4(4s). However, because of the ionic character of Ni20, we find that the at pair corresponds essentially to an 0(2p& doubly occupied orbital, leading to a wavefunction of the form la:(lb:
- h2bz),
(8)
which corresponds to the ionic configuration (2). For NizO (5) is lower in energy than (8) (see table 2). Thus, we optimized the geometry based on (5). However, from the populations it is clear that there is a large ionic col~ponent corresponding to (8). For larger clusters, we find that the presence of nearby Ni atoms restricts the correlation effects leading to a wavefunction of the form (8) being lower. We show the orbitals of (8) in fig. 9. From fig. 9 one sees that the Ia1 orbital (fig. SC) is essentially an O(2pJ orbital, while the bz pair has one component (fig. 9a) which is essentially 0(2p,)Jike, while the other component (fig. 9b) corre-
S.P. Walch, W.A. Goddard III/Bonding
NI*O
GVB(I/pp),
THE (a)
of oxygen to models of (100) Ni
C2v
BOND
625
S’fMMETRY
PAIR
(b)
024 ~-
ONE
I I
i
ONE
Cc) 02p,
6.0
Y
60
Fig. 9. The GVB orbitals for NizO using the wavefunction (8).
sponds to Ni2(4s) - Ni4(4s) but has built in a substantial amount of 0(2p,) character (indicating an ionic bond). To calculate the D, for the NizO cluster, we carried out a small configuration interaction (CI) calculation using the orbitals of (5). Here, we projected these orbitals onto (6), leading to basis functions which have the C,, symmetry of the molecule. In addition to these four orbitals, all the remaining occupied orbitals were included in the CI, leading to 17 basis functions (including the O(ls)-like orbital which was kept doubly occupied in all configurations). The configurations were generated by allowing all single excitations from the set of generating configurations in table 3.
a These orbit& correspor~d to the bond orbitofs 01‘ Nil 0 pmjccted PII ” The parenthesis indicate that WC take products of tlrc conl‘igurntion~ with those in the right pnrenthcscs, resulting in f’ocir ~~oni’ipuratlom.
( ‘2b“4rnmctr~ in the Ict’t parentheses
The resulting D, value is 4.37 eV as compared with a D, of 3.95 eV for a comparable Cl treatment for NiO (see reference [ 161) indicating that 0 prefers bridged sites on the Ni(lOO) surface as compared with bonding positions directly above a surface Ni atom.
Adding Ni atoms I and 3 leads to the Ni40 cluster. The electronic
configuration
is
---
0
Nl 1 x
(‘1)
where the bond orbitals (shown in the _r*zplane) correspond to the orbitals of(g). Adding to (8) the doubly-occupied 0 7px rxbital ( 1bf) and the 4s orbitals of Ni 1 and Ni3 which are triplet-tousled (3a, 1 2b: ,I leads to the overall ~OrlfigLlrati~~n [Xi]. la:(lbz
~- X2bi) lb: 21; 2bl .
(10)
Repulsive nonbonded interactions between the 0(7px) pair and Ni atoms 1 and 3 lead to an equilibrium geometry with the 0 0.56 A above the surface, 0.25 ‘4 higher than for Ni20. The resulting potential curve is slwwn in fig. 10, while the energies are given in table 4. In table 5, we show Mull&en populations for the various clusters. For NizO and Ni40 we see that Ni atoms 7I and 4 have populations corresponding to charges of -+0.5 electrons. Considering adsorbate ~aclsorbate interactions due to the other
S.P. Walch, W.A. Goddard III / Bonding of oxygen to models of (I 00) Ni
621
-o.o-
-O.l-
; w
-0.2-
z (3 E z
-0.3-
I
Fig. 10. Ni40 geometry
variation.
The calculated
points
are indicated.
oxygen atoms in the overlayer, we see from fig. 5 that, the overall charge distribution in our five Ni atom cluster is approximately described by an ion state where one 4s electron has been ionized from among the 4s orbitals of Nil and Ni3 [i.e., ionizing an electron from the 2ar or 2b 1 orbital of (lo)]. For the positively charged clusters, we anticipated that polarization effects in a direction perpendicular to the surface would be important. Therefore, we added the Ni atom beneath the surface, leading to the NiiO cluster as the model for 0 on Ni( 100).
Table 4 Ni40 geometry
variation
da
Energy
1.5 1.1 0.7
-237.02681 -237.03187 -237.02857
b
a d is the perpendicular distance (in au) from the 0 to the plane containing the four Ni atoms. b For a GVB(l/pp) wavefunction. The optimum geometry corresponds to ad of 0.56 A which corresponds to a NiO distance of 1.85 A and a NiONi angle of 144.7”. The De value is 2.98 eV for a GVB(l/pp) wavefunction. The basis set used here is [2s, lp, ld/3s, 2p] which we estimate to lead to an error in the energy of 0.239 eV (from comparison of NisO calculations using these basis sets) as compared with the [3s, lp, 2d/3s, 2p, Id] basis used for the NiO and NiaO calculations. Thus, this correction should be added to the De value to compare with the NiO and NisO calculations, leading to 3.22 eV as our best estimate for De.
628
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (I 00) Ni
Table 5 Mulliken populations for the N&O clusters a*b Niz 0
NisO
N&O
NisO
Nil0
10.00 9.55 10.00 9.55 10.08 8.82
9.15 9.52 9.75 9.52 9.85 8.61
._ Nil ’ Ni2 Ni3 Ni4 Ni5 0
_ 9.55 9.55 8.91
10.02 9.54 10.02 9.54 _ 8.88
9.57 _ 9.51 9.99 8.87
a Near the optimum geometry in each case, which corresponds to vertical displacements 0.1, 1.1, 1.2, and 1.8 au for NizO, NiaO, Ni40, NisO and NilO, respectively. b See ref. [ 151 in the text. c The numbering of the Ni atoms is as shown in fig. 6a [Ni(lOO)].
of 0.6,
4.3. Ni5 0, Ni: 0 We find for the neutral function [26] la:(lbz
NisO cluster that Ni5 is nonbonding,
- X2b:) lb: 2a] 3a] 2b; .
leading to a wave-
01)
We show the orbitals corresponding to (11) in fig. 3. The orbitals of the GVB pair (1 bi - h2bi) are shown in fig. 3ab, where one sees that they are similar to the corresponding orbitals of (8) (fig. 9a, b). The la; pair (fig. 3c) is essentially a doubly occupied 0(2p,) orbital. The 2ar orbital (fig. 3e) has bonding character on all three Ni atoms, while the 3ar orbital (fig. 3g) is essentially a 4s orbital on Ni5 and is antibonding in character. The 2br orbital (fig. 3f) corresponds approximately to Nil(4s)-Ni3(4s). The lowest ion state of the N&O cluster corresponds to ionizing the 3ar orbital leading to the wavefunction la:(lb:
- h2bz) lb: 2a: 2bf
(12.1
Near the equilibrium geometry for the neutral NisO cluster, the orbitals of (12) are very similar to the corresponding orbitals of (11) (as assumed in using Koopmans’ theorem). However, the Ni’, cluster has a larger effective electronegativity than the Nis neutral cluster, which leads to more covalent bonding for Ni;O than for NisO neutral. As expected from the discussion in section 4.1, this leads to an equilibrium geometry with the 0 further from the surface than for the Ni;O cluster. As the 0 atom moves from the equilibrium geometry for Ni50 neutral toward the equilibrium geometry for the Ni;O cluster, an electron is transferred from 0 back to the metal leading to the la: pair being mainly on the Ni (bonding orbital) while the 2ar orbital becomes a singly occupied 0(2p,) orbital. The resulting orbitals for the Nil0 cluster near its equilibrium geometry are
S.P. Walch, W.A. Goddard Ill/Bonding
of oxygen to models of (100) Ni
629
shown in fig. 4. Here one sees that the orbitals of the GVB pair (fig. 4a, b) are very similar to the corresponding orbitals of the N&O neutral cluster (fig. 3a, b). The doubly occupied la1 orbital (fig. 4e) has bonding character on all three Ni atoms and also shows NiO bonding character. The singly occupied 2aI orbital (fig. 4c) is
-0.0
-
-0.1
-
NljO
GEOMETRY
OPTIMIZRTION
N150
GEOMETRY
OPTIMIZRTIBN
ZI -o.z;: B Y
lLA -0.3-
Fig. 11. Ni50, NiiO geometry variation. The calculated points are indicated.
630
S.P.
Walch,
W.A.
Goddard III /Bonding of oxygen to models of (I OO}Ni
Table 6 N&O and Ni;O geometry variation Energy da Nis 0 ‘~ GVB
2.1 1.8 1.S 1.2 0.9 0.6
-
Ni;O -._..GVB c
“- --.- --.--~_-__I---~.. Koopmans theorem
-277.5567
-277.4016 -277.4044 -277.4023
-277.3854
-2ll.S588 -277.5564 -277.5517
-277.3988 -277.3932 -277.3853
-217.3851 --217.3794 -
d
a d in the perpendicular distance (in au) from the 0 to the plane containing the four surface Ni atoms. b For a GVB(l/ppf wavefunction. The optimum geometry corresponds to a d value of 0.65 A which leads to NiO distance of 1.88 A and a NiONi angle af 139.5”. The De value is 1.69 eV (see footnote b of table 4). c For a GVB(l/pp) wavefunction. The optimum geometry corresponds to a d value of 0.06 A which Ieads to a NiO distance of 2.01 A and a NiONi angle of 122.8”. The D, value is 2.85 eV (see footnote b of table 4). d The Koopmans” theorem energies Iead to an optimum geometry with the 0 atom 0.71 A above the surface.
essentially an 0(2p,) orbital and the 2bl orbital (fig. 4f) is similar to the corresponding orbital of (11) The ~ulliken populations (table 5) indicate that the Ni atoms involved in NiO bonds (Ni2 and Ni4) have Mulliken populations consistent with charges of -+0.5 electrons. From table 5 we see that the Ni:O cluster has a positive charge of -0.5 electron distributed between Nil and Ni3 as compared with -1.0 electron expected for Ni;O. Thus, we expect larger nonbonded repulsions between the 0(2p,) pair and the surface Ni atoms (1 and 3) for NiiO than for Ni;O. This effect, which derives from polarization effects involving Ni5, leads to an equilibrium geometry for Nil0 with the 0 atom 0.23 L%further from the surface than for NiiO. In fig. 11 we show the potential curves for the NisO and Ni:O clusters, whiIe the energies are given in table 6. As indicated in table 1r the NiiO cluster leads to a distance above the surface of 0.96 .A which is in excellent agreement with the results of dynamic LEED intensity analysis, 0.90 zi:0.10 A [S]. 4.4, NiJO Starting with the wavefunction (8) for NizO and adding the atom beneath the surface (Ni5) leads to the NiaO cluster. We find that NiS is nonbonding, leading to
631
Y L
--.-~____ -._I
-I-tiE BOND
(Cl)
.l_l.__._ “^___
T-""-"
PAIR
(b)
Fig. 12. Selected orbitals of the Ni30 cluster. Table 7 NW geometry variation da
Energy b
1.0 0.7 0.4 0.1 -0.2
-196.46073 -196.47057 -196.47960 -i96.48297 -196.47092
a d is the perpendicular distance (in au) from the 0 to a lime connecting Ni2 and Ni4. b For a GV~(~/pp) ~avefunct~on. The optimum geometry corresponds to a d value of 0.08 A which gives a NiO distance of 1.76 A and a NiONi angle of 174.8’. The De value is 3.08 eV (see footnote b of table 4).
S.P. Walch, W.A. Goddard I/I 1 Bonding of oxygen to models of (I 00) Ni
632 OS-
-0.2 -
-o.uL ;r g
-0.5-
6
I
I
-0.2
-0.1
I
-0.0
I DISTi&~
Fig. 13. Ni30 geometry
the qualitative
description
variation.
I
RNG;~AclN
la: 2a](lbi
I
0.5
I
0.6
are indicated.
L_-----+Y Nt2
l
to the GVB wavefunction
~ h2bi).
points
I
0.u
for NiaO:
0
which corresponds
I 0.3
The calculated
NI 4
0
1
NI 5
[27] (13)
We show the orbitals of (13) in fig. 12. Here one sees that the b, bond pair (fig. 12a, b) is qualitatively similar to the corresponding pair in NizO (fig. 9a, b), N&O (fig. 3a, b), and NiSO (fig. 4a, b). The 2ar orbital (fig. 12d) corresponds approximately to a 4s orbital on Ni5 but has hybridized away from the 0 atom. This leaves a partially exposed 3d9 core on Ni.5 which we expect to have an attractive interaction with the doubly occupied 0(2p,) orbital (as for the 50 orbital of CO upon bonding to Ni [21]). It is apparently this effect that leads to an equilibrium geometry for the NisO cluster with the 0 atom only 0.08 a above the surface, 0.23 i$ closer than for the NizO cluster [28]. The resulting potential curve is shown in fig. 13, while the energies used to construct fig. 13 are given in table 7.
S.P. Walch, W.A. Goddard III/Bonding
of oxygen to models of (100) Ni
633
In the case where the 0 bonds at the long edge of the (100) surface unit cell (fig. 6b), there are two Ni atoms below the surface (atoms 3 and 4 for geometry A), which can interact in the manner that Ni5 did for the Ni30 cluster. This leads to the expectation that for an 0 bridging Ni atoms 1 and 2 of fig. 6b there will be attractive interactions between the two doubly occupied p orbitals of the 0 atom and Ni atoms 3 and 4.
NI 3
N14
‘0
(14)
NI 1
Thus, for this registry with the surface, the oxygen would be expected to lie approximately in the plane of the surface (not more than 0.1 A above the surface).
References [ 11 (a) I.P. Batra and 0. Robaux, Surface Sci. 49 (1975) 653; (b) D.E. Ellis, H. Adacki, and F.W. Averill, Surface Sci. 58 (1976) 497. [2] See e.g. J.W.D. Connolly, in: Modern Theoretical Chemistry, Vol. 7, Ed. G.A. Segal (Plenum, New York, 1977) pp. 105-132. [3] The principal difficulty with the Xcz method for determining geometries is that usually only the muffin-tin approximation to the energy is evaluated. Errors in this approximation lead to very poor geometries (e.g. water is predicted to be linear [4a]). It is possible to make corrections to the muffin-tin energy leading to much better results [4b]. However, these corrections are often not carried out. [4] (a) J.W.D. Connolly and J.R. Sabin, J. Chem. Phys. 56 (1972) 5529. (b) J.B. Danese, Chem. Phys. Letters 45 (1977) 150. (c) C.H. Li and J.W.D. Connolly, Surface Sci. 65 (1977) 700. [S] J.E. Demuth, D.W. Jepsen and P.M. Marcus, Phys. Rev. Letters 31 (8) (1973) 540. [h] (a) S.P. Walch and W.A. Goddard III, Solid State Commun. 22 (1977) 907. (b) S.P. Walch and W.A. Goddard III, Surface Sci. 72 (1978) 645; see also ref. [21]. [7] (a) S.P. Walch and W.A. Goddard III, Surface Sci., submitted. (b) T.H. Upton and W.A. Goddard III, to be published. [8] (a) L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell University Press, New York, 1972) p. 93; (b) ibid, p. 260. [9] A.J.H. Wachters, J. Chem. Phys. 52 (1970) 1033. [lo] T.H. Dunning, Jr. and P.J. Hay, Gaussian Basis Sets for Molecular Calculations, in: Modern Theoretical Chemistry, Methods of Electronic Structure Theory, Vol. 3, Ed. H.F. Schaefer III (Plenum, New York, 1977) pp. l-27. The p functions are the same as in ref. [ 121, the tightest seven s functions are contracted into a single s function based on the 1s HF orbital, the second and third most diffuse are contracted into a basis function based on the 2s HF orbital; the most diffuse function is uncontracted.
634 [ 111
S.P. Walch, W.A. Goddard III/Bonding
S. Huzinaga,
unpublished. Jr., J. Chem. Phys.53 (1970) 2823. W.A. Goddard III. T.H. Dunning, Jr., W.J. Hunt and P.J. Hay, Accts. Chem. Res. 6 (1973) 368, S.P. Walch and W.A. Goddard III, J. Am. Chem. Sot. 100 (1978) 1338. This is from Mulliken populations. Generally, these populations indicate a greater charge transfer than would be indicated, for example, by the dipole moment. Thus, the populations although indicative of charge transfer should not be taken too literally. (a) B.J. Moss and W.A. Goddard III, J. Chem. Phys. 63 (1975) 3523: (b) B.J. MOSS, F.W. Bobrowicz and W.A. Goddard III, J. Chcm. Phys. 63 (1975) 4632. A wavefunction of the form (1) leads to an energy -0.5 eV below a wavefunction of the form (2). However, the qualitative description is like (2). J.E. Demuth, J. Colloid Interface Sci. 58 (1977) 185. The quoted atomic separations are obtained by taking a weighted average over the spectral levels corresponding to a given f, and S (spinorbit interactions are not included in our calculations). The values are from ref. [ 201. C.E. Moore, Atomic Energy Levels, Vol. II (National Bureau of Standards, 1952). S.P. Walch and W.A. Goddard III, J. Am. Chcm. Sot. 98 (1976) 7908. M.J. Sollenberger, M.S. thesis, California Institute of Technology (1975). T.H. Upton, W.A. Goddard III and C.F. Melius, J. Am. Chem. Sot., to be submitted. Them are two possible choices for the delta-like orbitals on each Ni. Their cncrgics arc within -0.04 eV and we chose to solve self-consistently for the case where each Ni 3d6 hole is asymmetric with rcspcct to the molecular plane, since this choice srmplifies the SCF calculations. The Ni(3d) holes for Ni atoms 2 and 4 (involved in Ni-0 bonds) were taken to be dcltalike with respect to the NiS bond axis and asymmetric with respect to the 1%: plane (containing Ni2, Ni4, and the S) which is the same orientation as for the NiaO calculation. The Ni(3d) holes for Nil and Ni3 were taken in 3d,, orbitals which are delta-like with respect to the x axis, which passes through Nil and Ni3. The Ni(3d) holes for Ni atoms l-4 are the same as for the Ni,O cluster (see ref. (251). The 3d hole for Ni5 is taken in a 3d,, orbital which is thus delta-like with respect to the z axis (regarded as the bond axis for bonding Ni5 to the surface Ni atoms). The Ni(3d) holes for Ni atoms 2 and 4 are the same as for the Ni,O calculation (see ref. [24]). The 3d hole for Ni5 is the same as for the NisO calculation (see ref. [26]). l:or the N&O cluster repulsive effects between the nonbonded Ni atoms (1 and 3) and the O(2pn) pair lead to a geometry with the 0 atom further above the surface than for Ni,O. Apparently, at larger distances stabilization of the 0(2p,) pair is less significant than nonbonded repulsion due to the Ni5(4s) orbital, leading to a slightly repulsive effect due to Ni5.
[12] T.H. Dunning, [13] [14]
[ 151
1161 [17] [18] [19]
[20] [21] [ 221 (231 [24]
(251
[ 261
[27] [28]
of oxygento models of (100) Ni