The surface chemistry of metal-oxygen interactions:

a first-principles study of O:Rh(110)

Kurt Stokbro1∗ and Stefano Baroni1,2∗∗

1 Istituto Nazionale di Fisica della Materia (INFM) and
arXiv:cond-mat/9605146v1 23 May 1996

Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Beirut 2/4, I-34014 Trieste, Italy.
2 Centre Européen de Calcul Atomique et Moléculaire (CECAM), ENS-Lyon, 46 Allée d’Italie,

F-69007 Lyon, France.

Abstract

We report on a computational study of the clean and oxygen-covered Rh(110)

surface, based on density-functional theory within the local-density approxi-

mation. We have used plane-wave basis sets and Vanderbilt ultra-soft pseu-

dopotentials. For the clean surface, we present results for the equilibrium

structure, surface energy, and surface stress of the unreconstructed and (1×2)

reconstructed structures. For the oxygen-covered surface we have performed

a geometry optimization at 21 , 1, and 2 monolayer oxygen coverages, and we

present results for the equilibrium configurations, workfunctions and oxygen

chemisorption energies. At half monolayer coverage, we find that oxygen in-

duces a (1 × 2) reconstruction of the surface, while at one monolayer coverage

the chemisorption energy is highest for the unreconstructed surface. Our re-

sults are rationalized by a simple tight-binding description of the interaction

between the O−2p orbitals and the metal valence states. The resulting bonds

are stronger when established with low coordinated metal atoms, and give

rise to an effective adsorbate-adsorbate interaction when two oxygen atoms

1
are bound to the same metal orbital.

Typeset using REVTEX

2
 I. INTRODUCTION

Oxygen is known to form strong bonds with metal surfaces, and the oxygen-metal inter-

action is one of the key elements in many technologically relevant catalytic reactions, such
as the oxidation of carbon or the reduction of nitrogen from their mono-oxides, occurring in
catalytic mufflers. As a first step towards an understanding of the microscopic mechanisms
responsible for the catalytic activity of some transition-metal surfaces, we present in this

paper a first-principles study of the interaction between oxygen and the Rh(110) surface.
From the calculations we extract simple chemical models of the metal-oxygen interaction,
which we believe to be of general relevance for adsorbate-metal systems.
The structure of the oxygen covered Rh(110) surface strongly depends on the oxygen
coverage [1–4]. At very low coverages oxygen is believed to occupy four-fold long-bridge
<
sites. At a certain critical coverage, θ = θc ∼ 1
monolayers, oxygen starts to induce a
2

(1 × 2) missing-row reconstruction of the surface, where the oxygen atoms occupy every
1
second three-fold site along the closed-packed top row. At θ = 2
the reconstruction is fully
developed, and at higher coverages the surface starts to deconstruct. At θ = 1 the rhodium

substrate is again unreconstructed and oxygen forms a (2 × 1) pattern. Our calculations,

performed at θ = 21 , 1, and 2 support for these coverages the picture given above.
From our self-consistent calculations we have extracted a simple chemical model of the
oxygen-metal interaction. From the model we identify a strong adsorbate-adsorbate inter-

action when two oxygen atoms are bound to the same metal orbital, and we discuss this
effect in connection with the calculations at θ = 1. We also show that the model predicts
stronger oxygen bonds with low coordinated metal atoms, and this is the force which drives
the oxygen induced reconstruction at θ = 21 .
The paper is organized as follows: In Section II we briefly describe the pseudopotential

method used for the calculations, and present our results for bulk Rh; in Section III we
report on our calculations for the clean Rh(110) surface, and in Section IV on the results
for the oxygen covered surface; in Section V we present the model of the rhodium-oxygen

3
bond; finally, Section VI contains our conclusions.

II. TECHNICAL DETAILS AND RESULTS FOR BULK RH

Our calculations are based on density-functional theory within the local-density approxi-
mation (LDA) [5,6]. Although the LDA is known to overestimate cohesive and chemisorption
energies, it has since long proven to be rather reliable as far as relative energies between
different bulk and surface geometries are concerned [7].

The electron-gas data used to implement the LDA are those by Ceperley and Alder [8],
as parameterized by Perdew and Zunger [9]. The single-particle Kohn-Sham equations are
solved using the plane-wave (PW) pseudopotential method. Isolated surfaces are modelled
by slabs in the supercell geometry. Due to the well known hardness of norm-conserving
pseudopotentials for first-row elements—such as O—and, to a lesser extent, for second-

transition-row atoms—such as Rh—, the use of ultrasoft (US) potentials [10] is mandatory
in order to keep the size of the PW basis sets manageable for the large supercells necessary
to model the surface. The oxygen US pseudopotential is essentially identical to that of
Ref. [11] with a core radius of 1.3 a.u. For rhodium we have used a newly developed

variant of the Vanderbilt scheme [10], where the norm conservation is released only for
those angular-momentum channels which would otherwise require very hard potentials (the
d-channel only in the present case) [12]. The pseudopotential is constructed from a scalar-
relativistic all-electron calculation, and it includes the 4d-, 5s- and 5p-valence states, for

which we used the core radii 1.6, 2.53 and 2.53 a.u. respectively. The 4d and 5s orbitals
were constructed in the atomic reference configuration 4d8 5s1 , while the 5p orbital was taken
from the reference configuration 4d7 5s0.75 5p0.25 . Basis sets including PW’s up to a kinetic-
energy cutoff Ecut ≈ 25–30 Ry yield very accurate results for both elements [11,12]. We
finally decided to adopt a cutoff of 30 Ry. This choice allows one to neglect the effects

of the finiteness of the basis sets even in those instances, such as e.g. the calculation of
the stress tensor [13], which are very sensitive to it. Brillouin-zone (BZ) integrations are

4
performed using the Gaussian-smearing special-point technique [14]. We have found that the
bulk properties are well converged using a Gaussian broadening of 0.3 eV and a Monkhorst-
Pack (444) mesh [15], which corresponds to 10 k points in the irreducible wedge of the BZ.

In order to test the convergence of our numerical BZ integrations, in many cases we have
made refined test calculations with a Gaussian broadening of 0.15 eV and a correspondingly
finer mesh. No significant differences were found in any of the cases examined. This fast
convergence with respect to BZ sampling is due to the relatively smooth Density of States

(DOS) at the Fermi energy, as shown in Fig. 1. In this figure we also show the projection of
the DOS onto individual atomic orbitals. There are 8.0 electrons per atom in the d bands,
while the remaining electron has mixed s and p character.
The calculated lattice constant is a0 = 3.81 Å and the bulk modulus B = 3.17 Mbar,

in good agreement with the experimental values (3.80 and 2.76 respectively) [16]. The
overestimation of the bulk modulus is also found in relativistic all-electron calculations, and
therefore it is not due to the use of pseudopotentials, but rather due to the LDA [12]. The
quality of the agreement between theory and experiment is of the same order as found for

most LDA calculations for metals and semiconductors.

III. THE CLEAN RH(110) SURFACE

The structural properties of the clean unreconstructed and (1 × 2) reconstructed surfaces

have been studied by minimizing the supercell total energy with respect to atomic positions,

using the Broyden-Fletcher-Goldfarb-Shanno minimization technique [17]. The value of the

workfunction was estimate by taking the difference between the calculated Fermi level and
the electrostatic potential in the middle of the vacuum region.
We denote the repeated-cell slab geometry by the notation (N + M), where N is the
number of atomic layers in the slab, and M the thickness of the vacuum region, in units

of the interlayer spacing normal to the surface. Different supercells—going from (5 + 5) to

(9 + 5) and (7 + 7)—where checked in order to test the convergence of our results. We found

5
no difference between the results obtained for M = 5 and M = 7, and also the dependence
upon N is very small. As for k-point sampling we tested a Gaussian broadening of 0.3 eV
and a Monkhorst-Pack (442) mesh [15]—which corresponds to 4 k points in the irreducible

wedge of the supercell BZ—and a Gaussian broadening of 0.15 eV in conjunction with a

(882) mesh. We find that the error introduced by using a (442) mesh is of the same order
as the finite size error by using a (7 + 5) cell.
In Table I we present the calculated atomic positions, workfunction, surface energy and

surface stress for the relaxed Rh(110) surface, and compare them with the corresponding
values obtained for the unrelaxed surface. The values were obtained from the (7 + 5) cell,
with the (442) k-point mesh, and the error estimate was based on calculations performed
with the (882) mesh and/or (9 + 5) supercell geometry. We observe a large inward relaxation

of the first layer, in analogy with what usually occurs at other open surfaces. However, the
calculated relaxation is almost one time and a half as large as the value obtained from LEED
structural analysis [18]. Since the calculated bulk modulus is 10% to large, one could have
expected an overestimate of the surface relaxations, but we also note that the experimental

value of [18] is probably is too small, since these authors only included relaxations of the first
two surface layers in their structural model. We find that the surface relaxations strongly
reduce the surface tension, indicating that the surface relaxation and surface tension are
determined by the same driving force. This is in qualitative agreement with the Effective-
Medium Theory of Ref. [19,20], according to which an inward relaxation of the outermost

atomic plane would decrease the surface energy by increasing the electron density at surface
atoms.
We now turn to the electronic structure of the Rh(110) surface. In Fig. 2a we compare
the projections of the DOS (PDOS) onto the surface atomic layer and onto an atomic layer

in the bulk. The main difference is the decreased band width and upward shift of the band
√
center of the first layer PDOS. This effect is in qualitative agreement with the N scaling
of the band width, where N is the coordination number, predicted by a simple one-band
tight-binding model. In Fig. 2b we show the PDOS of the surface d-orbitals, and we now

6
see the appearance of resonances in the spectrum caused by the broken metal-metal bonds.
The strongest resonance is caused by the yz orbital, and the significance of this orbital
is that it can only form weak δ bonds along the (110) surface row. In Section V we will

discuss the chemical bonding between oxygen and the rhodium surface and we will hint that
these resonances give an important contribution to the chemisorption energy. In analogy to
the terminology adopted for semiconductors, we will call these resonances metallic dangling
bonds.

Finally, we have considered the (1×2) missing-row reconstructed surface shown in Fig. 3.
This surface structure is not found to be stable in nature, but it can be produced in a meta-
stable state by first treating the surface with oxygen which afterwards is removed with
a strong reductant like CO [2]. Table II shows the calculated properties of the relaxed

surface, and the reported results were obtained with a (7 + 5) layer slab and a (882) k-point
mesh. Generally the relaxations are in good agreement with those obtained from the LEED
structural analysis of Ref. [2], and we predict an increase in the surface energy compared to
the unreconstructed surface of ≈ 0.1 eV/(1 × 2 cell), while there is no significant differences

in the surface stress.

IV. THE OXYGEN-COVERED RH(110) SURFACE

In this section we present calculations for the Rh(110) surface with a coverage of 21 , 1,
and 2 oxygen monolayers. Figure 4 shows the equilibrium configurations for the geometries

we have considered, and in Table III we report some key values of each chemisorption
1
geometry. At θ = 2
we find geometry h to be energetically favoured, while geometry k is
favoured for θ = 1. The structural data predicted by the present calculations compare well
with those determined experimentally [2,3]. The values of the workfunction and the relative
chemisorption energy of geometries h and k also compares well with the experimental data,

however, the chemisorption energy is overestimated by ∼ 1.2 eV, which is a typical error of
the LDA.

7
 A. Coverage 21 : the unreconstructed surface

We first discuss the stable chemisorption geometries on the unreconstructed rhodium

surface at θ = 12 . For the calculations we have used a (2 × 1) and a (1 × 2) surface cell and
for several different initial positions of the oxygen atom, we have relaxed the structure. We
have found six stable configurations, labeled a, b, c, d, e, and f in Fig. 4. The six oxygen
chemisorption sites can be divided into three groups: four-fold-coordinated long-bridge sites

(geometries a and b), three-fold-coordinated quasi-long-bridge sites (geometries c and d),

and three-fold-coordinated hollow sites(geometries e and f). In the quasi-long-bridge site
the oxygen atom has moved away from the long-bridge position towards a second-layer
atom in order to obtain three-fold coordination.
The chemisorption energy is highest in the three-fold coordinated hollow site. In these

structures most bond lengths between oxygen and rhodium first-layer atoms are nearly 2 Å;
the bonds with second-layer atoms are slightly longer for geometries c, d, e, and f indicating
a weaker bond, while there are no bonds with second-layer atoms in geometries a and b. The
main difference between the structures is in the bond angle between oxygen and first-layer

rhodium atoms, θO−1 . Inspection of Table III shows that the chemisorption energy decreases
when the bond angle departs from 900 . In section V we will provide some arguments which
indicate why this particular angle corresponds indeed to the strongest oxygen-metal bonds.
We also observe that there is almost no inward relaxation of the surface atoms below the

oxygen adsorbate.
Based on a HREELS study of the oxygen vibration frequencies for different oxygen
coverages of the Rh(110) surface, it was proposed in Ref. [1] that at low coverages oxygen
occupies the long-bridge site. This seems to be in disagreement with our calculations, since
we find the chemisorption energy in geometry f to be 0.26 eV higher than in geometry a.

However, our calculation is for θ = 21 , and at this coverage adsorbate-adsorbate repulsions

might disfavour certain geometries.

8
 B. Coverage 12 : The reconstructed surface

1
At θ = 2
the annealed surface shows a (2 × 2)pg LEED pattern [2,3], indicating that the

unit cell is (2 × 2) and must have a glide line in the (110) direction. Furthermore, there is
strong experimental evidence that the underlying rhodium substrate forms a (1×2) missing-
row structure [2,22]. If we assume that the rhodium atom sits in a three-fold site, there are
only three structures consistent with these experimental facts, and these are geometries h, i

and j shown in Fig. 4. The same three structures were considered in the LEED IV analysis
of Ref. [2]. We find geometry h to be energetically favoured, while the oxygen chemisorption
energy is 0.5 and 0.8 eV/atom lower in geometry i and j, respectively. Note that the energy
ordering of the three structures indicates that oxygen bonds with low coordinated rhodium
atoms are energetically favoured. In Table III we compare geometry h with two independent

LEED IV structural analyses, and the general agreement is rather good.

Since oxygen induce the (2 × 1) reconstruction on other transition metal surfaces [23] we
have also considered this structure. Initially we placed the oxygen atom in an asymmetrical
position above the long bridge site, but after relaxation oxygen occupied the symmetrical

position 0.4 Å above the rhodium surface, as shown in geometry g of Fig. 4. We now compare
the energetics of this reconstruction with the (1 × 2) reconstruction. Table III shows that
while each oxygen atom gains 0.5 eV/atom by forming the (1 × 2) reconstruction, the (2 × 1)
reconstruction is disfavoured by 0.1 eV/atom. It is interesting to divide this energy into

two contributions, the cost of reconstructing the substrate (∆σ/Θ) and the energy gain by
bonding oxygen to the reconstructed surface. The formation of the (1 × 2) reconstruction
only costs 0.2 eV/atom (the additional 0.1 eV compared to Table II is due to oxygen induced
strain), while the formation of the (2 × 1) reconstruction costs 1.4 eV/atom. By subtracting
the formation energy from the chemisorption energy we see that the oxygen bonding with

the (2 × 1) reconstructed surface is 0.6 eV stronger than the bonding with the (1 × 2)
reconstructed surface. The stronger bonding is due to the lower coordination of the surface
atoms, and in section V we will identify the electronic origin of this effect.

9
 Based on the above calculations we now discuss a possible origin of the different recon-
structions induced by nitrogen and oxygen on transition metal (110) surfaces. While oxygen
induces the (1 × 2) reconstruction of Rh(110) and the (2 × 1) reconstruction of Cu(110),

Ni(110) and Ag(110) [23], nitrogen has almost the reverse behaviour, i.e. it induces the (2×1)
reconstruction of Rh(110) [24] and a (1 × 3) reconstruction of the Cu(110) and Ni(110) sur-
faces where every third (110) row is missing [25–27]. To understand this behaviour we have
compared the geometry of the theoretical (2 × 1) reconstruction of O/Rh(110), with the

experimentally derived (2 × 1) structure of N/Rh(110) [24]. The comparison reveals a rather

large difference in the adatom-surface distance; while oxygen sits 0.4 Å above the surface
atoms, there is no height difference between nitrogen and the rhodium surface atoms. We
propose that an adsorbate positioned exactly in between the surface atom in the (100) row

may form the strongest bond, and since nitrogen is a smaller atom than oxygen, it can better
fit in between the rhodium surface atoms. This size argument can also explain the preference
of oxygen for the (2 × 1) reconstruction of silver, since the lattice constant of silver is 4.09
Å and the O-Ag bond length is 2.05 Å [28,29], oxygen fits perfectly in between the silver

atoms in the (100) row. A similar picture is found for copper, where the lattice constant
is 3.61 Å and the O-Cu bond length 1.81 Å [23]. The lattice constant of nickel is 3.52 Å
and the O-Ni bond length 1.77 Å [23], so in this case the oxygen atoms do not fit perfectly
in between the nickel atoms, and in Ref. [30] this was identified as a source for lowering
the chemisorption energy. Since nitrogen is a smaller molecule than oxygen it forms shorter

bonds with the metal atoms, and for copper and nickel the metal-metal separation gets too
large for nitrogen to form a strong bond with both metal atoms in the (100) row. However,
in the observed (2 × 3) structure on Cu(110) and Ni(110) it is possible for the surface atoms
to relax towards the nitrogen adsorbate, and nitrogen can thereby obtain an optimal bond

length with the surface atoms.

10
 C. Coverage 1 and 2

For θ = 1 we have only studied geometries where the oxygen atom is three-fold coordi-

nated. We find oxygen to have the highest chemisorption energy in geometry k of Fig. 4, in
good agreement with experimental findings [3]. The oxygen chemisorption site in geometry
k is very similar to that of geometry f, and we also find that the chemisorption energies
in the two structures are nearly identical. This suggests that there is little interaction be-

tween the oxygen atoms on the Rh(110) surface, which is rather surprising compared to the
strong oxygen-oxygen repulsion found on other transition metal surfaces at similar oxygen
coverages [31]. In section V we will show that this different behaviour can be explained by
a substrate mediated adsorbate-adsorbate interaction of electronic origin, whose strength is
related to the filling of the surface bands.

For θ = 2 we have considered two geometries: an oxygen dimer oriented in the (100)
direction (geometry m of Fig. 4), and an oxygen dimer oriented in the (110) direction (ge-
ometry n). We find geometry m to be energetically favourable, however, the chemisorption
energy is 1.1 eV lower than in geometry k. It is therefore questionable whether this structure

can be observed experimentally after high oxygen exposure, since the structure will not be
energetically favourable compared to geometry k plus molecular oxygen.
Geometrically the main difference between geometry k and geometry m, is the shift of
the oxygen bond with a second-layer rhodium atom to an oxygen-oxygen bond. This makes

the nature of the oxygen bonding in geometry m somewhat intermediate between those
occurring in geometry k and in molecular oxygen. This structure might therefore be an
important precursor state for oxygen dissociation.

V. THE CHEMISTRY OF THE RHODIUM-OXYGEN BOND

In this section we will analyse the oxygen chemisorption on rhodium in terms of a simple
tight-binding description. A tight-binding model of chemisorption has been put forward by

11
several authors [32–34].
The first step in building a tight-binding description of oxygen chemisorption is to identify
the metal and oxygen orbitals which are responsible for the bond formation. For the present

problem these consist of all the valence orbitals of rhodium (4d, 5s and 5p) and the O-2p
orbitals, while we can disregard the O-2s orbital, since its resonance is ≈ 19 eV below the
rhodium Fermi level. As in the model of Refs. [30,35] we describe the interaction between the
O-2p orbitals and the metal orbitals in two steps: First the unperturbed orbitals interact with

the rhodium Rh-5s and Rh-5p orbitals, and then the resulting renormalized O-2p orbitals
interact with Rh-4d orbitals. The different steps are illustrated in Fig 5. For the unperturbed
O-2p state we take the atomic eigenvalue and use the Rh(110) workfunction to position it
relative to the rhodium Fermi level (ǫ2p − ǫf = −4.1 eV). We note that the corresponding

unperturbed O-2s eigenstate is positioned −18.6 eV relative to the Fermi level, while the fully
selfconsistent calculation of geometry f has a O-2s resonance at −18.9 eV. The interaction
between oxygen and the broad metal sp bands is similar to the interaction between oxygen
and a Jellium surface. This interaction is well described by the weak coupling limit of the

Newns-Anderson model, and gives rise to a broadening and a shift of the O-2p level. The
interaction between the renormalized O-2p orbitals and the narrow d band is, on the other
hand, described by the strong coupling limit of the Newns-Anderson model, and gives rise to
a splitting of the levels into bonding–anti-bonding states, similar to the interaction between
two atomic orbitals.

By dividing the oxygen-metal interaction into an sp and a d part we obtain a simple

picture of the oxygen chemisorption energy on different transition metal surfaces. The
interaction with the metal sp bands gives a large contribution to the chemisorption energy,
however, due to the similarity of the transition metal sp bands this contribution is more

or less constant throughout the transition series. The d band contribution, on the other
hand, decreases with the filling of the band, and for the noble metals the O-2p – d anti-
bonding level will be filled [35] and in this case there will be a O-2p – d repulsion due to
orthogonalization. Figure 5c schematically shows that the O-2p – Rh-4d anti-bonding level

12
is well above the Fermi level, and the interaction with the rhodium d-band, therefore, gives a
large contribution to the chemisorption energy. We note that a substantial part of the O-2p
– Rh-4d bond is formed between the O-2p orbitals and localized Rh-4d states with energies

close to the Fermi level, i.e. metallic dangling bonds. This is illustrated in Figure 6 where
we show the Rh-4dyz PDOS for both the clean and oxygen covered Rh(110) surface. The
figure shows that the 4dyz dangling bond resonance at ǫd interacts with the renormalized
adsorbate adsorbate level at ǫa and forms a bonding state at ǫa − ∆1 and an anti-bonding
q
state at ǫd + ∆1 , where ∆1 = ∆20 + V 2 − ∆0 , ∆0 = (ǫd − ǫa )/2, and V is the O-2p – Rh-4d
coupling matrix element.
Since the O-2p level is below the Rh-4d band centre, the bonding state will have mostly
O-2p character. There will therefore be a charge transfer from the Rh-4d orbitals into the

O-2p orbitals. This charge transfer can be seen in Fig. 7, which shows the charge-density
difference between the oxygen+rhodium system and the two separated systems. The plot
shows a charge transfer from rhodium orbitals of symmetry d3z 2 −r2 (with z along the bond
axes) to the O-2p orbitals. We note that the rhodium d3z 2 −r2 orbitals have the largest overlap

with the the O-2p orbitals, and therefore give rise to the strongest rhodium-oxygen bonds.
In Fig. 8 we show the O-2p PDOS of geometries f and k, and in the spectrum of geometry
k we can identify 3 resonances. Apparently this is in conflict with the model developed in
the previous section which only predicted two resonances, corresponding to the bonding
and anti-bonding state of two interacting atomic orbitals. However, in geometry k two

O-2p orbitals couple to the same Rh-4d orbital, and the bonding is therefore related to
the interaction between three atomic orbitals, which give rise to a bonding resonance at
ǫa − ∆2 , an anti-bonding resonance at ǫd + ∆2 , and a non-bonding resonance at ǫa , where
q
∆2 = ∆20 + 2V 2 − ∆0 . From the positions of the three resonances(−6.8 eV, −5.2 eV, and

0.8 eV) we can determine the parameters of the atomic model. We find the renormalized
adsorbate level ǫa = −5.2 eV, the Rh-4d level ǫd = −0.8, and the O-2p–Rh-4d coupling
matrix element V = 2.2 eV. Compared to the unperturbed adsorbate level (ǫ2p − ǫf = −4.1
eV), the rhodium 4dyz resonance of Fig. 6, and the O-2p – Rh-4d coupling matrix element

13
obtained from Harrisons solid-state table [36] VHar = 2.0 eV, these values seem indeed
reasonable. We also note that for two interacting atomic orbitals the parameters predict a
bonding resonance at −6.1 eV, in good agreement with the O-2p PDOS of geometry f.

The above chemisorption model gives rise to a strong adsorbate-adsorbate interaction,

which can be either attractive or repulsive depending on the position of the metal state ǫd
relative to the Fermi level. If the metal state is empty (ǫd > ǫf ) the d-band contribution to
the chemisorption energy of non-interacting adsorbates is E1 = 2∆1 , while for interacting

adsorbates it is E2 = ∆2 , and since ∆1 > ∆2 /2 there is a repulsive adsorbate-adsorbate

interaction. However, if ǫf > ǫd + ∆1 then E1 = 0 and E2 = ∆2 − ǫf , and in this case
there is an adsorbate-adsorbate attraction. The crossover between repulsive and attractive
interaction happens in the range ǫd < ǫf < ǫd + ∆1 , where the difference in the d-band

contribution to the chemisorption energy is: E2 − E1 = (ǫd + ∆2 − ǫf ) − 2(ǫd + ∆1 − ǫf ).

From the model parameters we estimate an interaction energy of E2 − E1 = 0.6 eV, and
since two orbitals per oxygen atom contribute to the interaction, the d-band contribution to
the chemisorption energy is 1.2 eV larger in geometry k than in geometry f. However, the

model also predicts an adsorbate-adsorbate repulsion caused by the O-2p interaction with
the almost empty sp-band, and since we know from the full selfconsistent calculation that the
oxygen chemisorption energy is the same in the two structures, this sp-mediated repulsion
must compensate the d-mediated attraction. In geometry l of Fig. 4 two neighboring oxygen
atoms can only couple to the same metal s orbital, and there is only an s-mediated repulsion,

which gives rise to a 0.2 eV lower chemisorption energy than in geometry l.

Work is in progress to make the model more quantitative, and preliminary results show
that the model can account for the different adsorbate-adsorbate interaction on transition
metal and aluminum surfaces [37].
√
In Section III we showed that the bandwidth of the atom PDOS scale as N , where N
is the coordination of the atom, and that there is a corresponding shift of the band centre
which conserves the filling of the band. This was illustrated for the Rh(110) surface in Fig. 2,
and in the present context we note that the rhodium band centre is shifted upwards. This

14
shift gives rise to a similar shift of the rhodium–oxygen anti-bonding state, and since the
bond energy is given by the distance between the anti-bonding state and the rhodium Fermi
level the bond is strengthened. The energy gain by the oxygen induced (1×2) reconstruction

is therefore due to the oxygen bond with the the second layer rhodium atom, which on the
reconstructed surface has coordination 9 and on the unreconstructed surface coordination
11.

VI. CONCLUSIONS

In this paper we presented detailed first-principles calculations for the clean and half,
one and two monolayer oxygen-covered Rh(110) surface. At half monolayer oxygen coverage
we find a (1 × 2) reconstruction of the surface, contrary to the oxygen induced (2 × 1)
reconstruction of Cu(110), Ag(110) and Ni(110), but in good agreement with experimental

studies of O/Rh(110). Calculations for the theoretical (2 × 1) O/Rh(110) structure suggest

that this difference in behaviour is related to the scale between the lattice constant and
the oxygen-metal bond. Generally the calculations show that the oxygen chemisorption can
be rationalized in terms of a tight-binding model which include the O-2p interaction with

the rhodium valence states. This model give rise to a short ranged but strong adsorbate-
adsorbate interaction which can be either repulsive or attractive dependent of the filling of
the surface bands.

ACKNOWLEDGMENTS

We gratefully acknowledge many discussions with K. W. Jacobsen, J. K. Nørskov, R.

Rosei, and E. Tosatti. Thanks are due to R. Valente for porting our plane-wave ultra-soft
pseudopotential program to an IBM-SP2 parallel machine, and D. Vanderbilt for providing
an atomic program for the generation of ultra-soft pseudopotentials. Kurt Stokbro acknowl-

edges financial support from the European Union through HCM contracts ERBCHBGCT

15
920180 and ERBCHRXCT 930342. This work has been partially supported by the Italian
Consiglio Nazionale delle Ricerche within the Supaltemp project.

APPENDIX A: CALCULATION OF THE CHEMISORPTION ENERGY

To estimate the chemisorption energy relative to the O2 molecule we have used essen-
tially the same procedure as Ref. [21]. With the non-spinpolarized pseudopotential code we
have calculated the energy of the O/Rh(110) system (EO,Rh ) and the surface energy (ERh )

using the same super cell and k-point sampling. To find the reference molecular energy
we have used an atomic program to calculate the energy EOpol of a spin-polarized oxygen
atom, and from that subtracted the O2 atomization energy Eb = 3.74 eV/atom found by
Becke [38]. This value has to be corrected for the use of a finite basis set in the plane-wave
calculation, which we estimate to be Epw = 0.05 eV/atom. From these energies we calculate

the chemisorption energy, Echem , by

Echem = EOpol − Eb + Epw + ERh − EO,Rh . (A1)

16
 FIGURES
FIG. 1. The rhodium bulk DOS (solid line) and its projection onto sp and d atomic orbitals

(dotted lines).

FIG. 2. The DOS of the Rh(110) surface projected onto: a) layer 1 (solid line) and layer 4

(dashed line). b) The five d orbitals of layer 1.

FIG. 3. The geometry of the (1 × 2) missing row reconstruction.

1
FIG. 4. Oxygen binding geometries on the Rh(110) surface at coverage 2, 1 and 2. The

energetically favourable configurations at the three coverages are geometry h, k and m,

FIG. 5. a) The atomic O-2p eigenstate. b) Schematic O-2p PDOS for an oxygen atom coupling

to the rhodium 5s and 5p orbital. c) the O-2p PDOS of geometry f. d) the first layer PDOS of the

clean Rh(110) surface.

FIG. 6. The DOS of geometry f projected onto the the O-2p orbital and rhodium 4dyz orbital.

The solid lines show the PDOS of the interacting oxygen-rhodium system, while the dashed lines

show the PDOS of isolated oxygen and rhodium systems.

FIG. 7. Contour plot of the oxygen induced charge-density difference in geometry f. Dashed

contour lines indicate charge depletion. The top view shows the charge density difference in the

plane defined by the two first layer rhodium atoms(large grey circles) and the oxygen atom(small

solid circle). The side view shows the plane defined by the first and second layer rhodium atoms

and the oxygen atom.

FIG. 8. The O-2p PDOS of geometry f and k. The resonances in geometry f can be described

by the bond formation between two levels, ǫa and ǫd , coupled by V . In geometry k the resonances

can be described by the bond formation between three levels, where two levels at ǫa are coupled by
q q
V to a level at ǫd . The level shifts are given by ∆1 = ∆20 + V 2 − ∆0 and ∆2 = ∆20 + 2V 2 − ∆0 ,

where ∆0 = (ǫd − ǫa )/2.

17
 TABLES
TABLE I. Interlayer relaxations (∆d12 , ∆d23 , ∆d34 ), work function (W), surface energy (σ),

and surface tensions (σxx ,σyy ) of the Rh(110) surface (the x axis is oriented in the (110) direction).

The first row shows the available experimental data, while the second row shows the calculated

values before surface relaxation, and the the third row after relaxation. The numbers in parenthesis

indicate an estimate of the numerical error on the last displayed digit, due to the super-cell size

and k-point sampling.

∆d12 (%) ∆d23 (%) ∆d34 (%) W(eV) σ(eV/Å2 ) σxx (eV/Å2 ) σyy (eV/Å2 )

Expt. −7(1)a 2(1)a 5.1b

LDA unrelaxed 5.13(5) 0.198(5) 0.28(2) 0.25(2)

LDA relaxed −9.7(5) 3.6(8) −2.2(9) 5.14(5) 0.191(5) 0.20(2) 0.12(2)

a From Ref. [18]
b From Ref. [39]

TABLE II. Experimental and calculated surface properties of the (1 × 2) reconstructed surface.

For the definition of the symbols see Table I and Fig. 3. The workfunction, surface energy and

surface tension are given relative to the unreconstructed relaxed surface.

δy ∆d12 ∆d23 ∆d34 ∆d45 ∆W ∆σ ∆σxx ∆σyy

(%) (%) (%) (%) (%) (eV) (eV/Å2 ) (eV/Å2 ) (eV/Å2 )

Expt. 0.0a −11.4a −7.7a 11.2a −5.5a

LDA 0.6(2) −7.1(5) −6.7(5) 6(1) −3(1) 0.16(3) 0.004(1) 0.00(2) 0.01(2)
a From Ref. [2]

18
 TABLE III. Some key quantities describing the oxygen bonding in the geometries of Fig. 4. The

reported values are: The chemisorption energy Echem , substrate surface energy ∆σ/θ, workfunction

(∆W ), oxygen dipole (µ), oxygen-surface distance (zO−Rh1 ), the shortest bond length with a first

layer atom (dO−1 ), the shortest bond length with a second layer atom (dO−2 ), the bond angle

between bonds with first layer atoms (θO−1 ), the bond angle between bonds with a first layer atom

and a second layer atom (θO−2 ), and the first layer relaxation of the rhodium substrate(∆d12 ) (for

the geometries a, b, c, d, e, and f the surface atoms relax differently and we show the value of both

the smallest and the largest relaxation). Note that in geometry i the angle θO−1 is between the

oxygen bonds with second layer atoms, and in geometry j the bond lengths and bond angles are

reported for the oxygen bonds with second and third layer atoms. The oxygen dipole-moment was

derived from the oxygen induced workfunction change, and the calculation of the chemisorption

energy is described in Appendix A.

Echem ∆σ/Θ ∆W µ zO−1 dO−O dO−1 dO−2 θO−1 θO−2 ∆d12

(eV/O) (eV/O) (eV) (e Å/O) (Å) (Å) (Å) (Å) (%)

a) 1.97(4) 0.23 0.9(1) 0.11(1) 0.94(4) 2.69(1) 1.96(2) 2.77(3) 123(2)0 65(2)0 −15/10

b) 1.86(4) 0.15 0.50(5) 0.056(5) 0.57(3) 3.81(1) 1.99(2) 2.36(3) 147(3)0 77(3)0 −13/3

c) 1.89(4) 0.05 0.51 (5) 0.057(5) 0.62(3) 2.69(1) 2.06(2) 2.07(2) 131(2)0 80(2)0 −14/−2

d) 1.94(4) 0.16 0.38(2) 0.044(3) 0.53(1) 3.81(1) 2.03(1) 2.09(1) 140(1)0 82(1)0 −17/0

e) 2.03(3) 0.19 0.40(4) 0.046(4) 0.59(2) 2.69(1) 2.01(1) 2.02(1) 103(2)0 870 −11/2

f) 2.23(2) 0.11 0.44(5) 0.050(5) 0.71(1) 3.81(1) 2.00(1) 2.05(1) 93(2)0 82(1)0 −10/−3

g) 2.18 1.42 0.50 0.06 0.50 3.81 1.96 2.26 1510 790 −1

h) 2.75 0.19 0.85 0.10 0.60 3.78 2.00 2.00 850 850 −3

Expt. 1.54a 0.65b 0.074b 0.54c 3.82c 1.98c 1.97c 860c 880c −1c

Expt. 0.50d 3.89d 2.01d 1.88d 840d 870d −3d

i) 2.26 0.19 0.84 0.10 0.31 4.44 2.02 2.02 (850 ) 820 −12

j) 2.00 0.19 0.14 0.016 −0.61 2.98 (2.02) (2.06) (870 ) (840 ) −6

k) 2.23(2) 0.06 0.87(4) 0.049(3) 0.66(1) 2.96(1) 1.99(2) 2.06(2) 85(1)0 82(1)0 −3

19
Expt. 1.06a 0.73b 0.041b 0.60c 2.93c 1.98c 2.05c 860c 840c 1c

l) 2.06(2) 0.10 0.6(1) 0.034(5) 0.60(2) 2.69(1) 2.00(3) 2.03(3) 85(2)0 85(2)0 0

m) 1.1(1) 0.09 1.4(1) 0.040(4) 1.32(1) 1.32(1) 2.26(1) 2.84(2) 73(1)0 64(1)0 7

n) −1.1(1) 0.03 −0.65 1.81 1.15 2.74 3.16 880 530 −4

a Ref. [40]
b Ref. [4]
c Ref. [3]
d Ref. [2]

20
 REFERENCES

∗
Present address: Mikroelektronik Centret, Danmarks Tekniske Universitet, Bygning
345ø, DK-2800 Lyngby, Denmark. e-mail: stokbro@mic.dtu.dk

∗∗
e-mail: baroni@sissa.it or baroni@cecam.fr.

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21
[17] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes
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[19] K. W. Jacobsen, J. K. Nørskov, and M. J. Puska, Phys. Rev. B 35, 7423 (1987).

[20] K. Stokbro, N. Chetty, K. W. Jacobsen, and J. K. Nørskov, Phys. Rev. B 50, 10727
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[23] F. Besenbacher and J. K. Nørskov, Prog. In Surf. Sci 44, 5 (1993).

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22
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23
Projected DOS (states/eV) 3

total
2

1
d

sp

0
−8 −6 −4 −2 0 2
ε−εf (eV)
 δy

d12
x z d 23
d 34
d45

y y
TOP VIEW SIDE VIEW
 3
a) Layer 1
Layer 4
Projected DOS (states/eV) 2

b) dxz
1 Layer 1 dyz
dxy dxz dyz
d3z2−r2 dx2−y2

0
−8 −6 −4 −2 0 2
ε−εf (eV)
 1
Coverage 2

a) b)

c) d)

e) f)

g) h)

i) j)

Coverage 1

k) l)

Coverage 2

m) n)

TOP VIEW SIDE VIEW TOP VIEW SIDE VIEW

oxygen rhodium
 Schematic Schematic
O O/jellium O/Rh(110) Rh(110)
4
sp d
a) b) c) d)
2
int. int.
ε−εf (eV)

0
−2
−4
−6
−8
Projected DOS (arb. units)
 oxygen 2p rhodium 4dyz
4

2
εd+∆1
ε−εf (eV)

0 εd

−2

−4
εa
−6
εa−∆1
−8
X2
Projected DOS (arb. units)
TOP VIEW

SIDE VIEW
 geometry f geometry k
4

2
ε−εf (eV)

ε d + ∆1 ε d + ∆2
0 εd εd

−2

εa
−4 εa
εa
−6 ε a - ∆1 ε a - ∆2
−8
O2p Projected DOS (arb. units)