Karpov Institute of Physical Chemistry

10 Vorontsovo pole

105064, Moscow

Russia

with Atomic and Molecular Oxygen

**Keywords**: effective crystal field, transition metal oxides, d-d
spectra, oxygen adsorption.

Transition metal oxides (TMOs) are important for numerous reasons. These range from catalytic activity in oxygenation processes [] to superconductivity [] of some TMO-based materials. These unique properties of oxides are determined by their electronic structure. In this paper we analyse theoretically the pitfalls occuring throughout the description of the local d-states in the TMOs and relate this to analysis of some experimental data on the spectral properties of transition metal ions in oxides based on optical adsorption (OA) and electron energy loss spectroscopy (EELS). Information on the energy spectrum of the d-shell is of no direct use in chemistry. However, it can be shown that catalytic properties of the surface transition metal ions are governed by mixing of the electronic states of the catalyst's d-shell and those of reactants/products. So we give a sketch of the corresponding theory of potential energy surface (PES) of chemical transformation taking place in the coordination sphere of a transition metal ion (TMI). This analysis demonstrates how the ground state PES of a catalytic transformation depends on the weights of the excited and ionized states of the free reactants/products in it. Then a numerical analysis of the composition of the ground states of oxygen and dioxygen adsorbed by TMO surfaces is performed.

The electronic structure of the TMOs was extensively studied both
experimentally and theoretically (
Cox,Harrison,Morrison,Hufner,Parlebas,Tsuda to mention a few). The
spectrum of low-lying excitations controls the properties of TMOs: indeed
[] the relative energies of excitations d^{n}d^{n}®d^{n+1}d^{n-1} and d^{n}® L^{±}d^{n±1} are set as a basis
for classification of the oxides to Mott-Hubbard or charge-transfer
insulator (MHI and CTI respectively). This picture ignores other sets of
important excited states which are possible in oxides. According to Ref.
[] (and references therein) the electronic states of TMOs with
partially filled d-shells can be presented as band states of an ionic
insulator (like MgO or CaO) supplied with the local multiplets of the
d-electrons. Excitations inside the d-shell are responsible for the
structure of optical spectra []. Namely these excited states -
crystal field (CF) - excitations of the order of 1 - 3 eV shape the
properties of TMOs on this energy scale. Meanwhile the excitations
characteristic for the MHIs lay in the TMOs at 10 eV and higher and those
characteristic for CTIs above 5 eV (We do not mention the gapless
delocalized magnetic excitations - magnons - which are also characteristic
for TMOs being antiferromagnets).

Phenomenological model for the spectrum of the CF excitations dates back to
Bethe [] and is known as crystal field theory (CFT). In the
octahedral environment occurring in the above cited TMO all having the rock
salt crystal structure it is characterized by three empirical parameters D, B, and C of which the first describes the energy splitting of
one-electron d-levels and the orther two - the Coulomb interaction of
electrons in the d-shell. To improve the fitting of experimental spectra
additional orbital-deformation parameters l_{e} and l_{t} are
frequently introduced (for reference see [,]).
The general feature of all CFT implementations and extensions is that the
parameters mentioned above are considered as purely empirical. They cannot
be evaluated in the frame of the CFT itself since no real description of the
surrounding of the TMI is provided in its context except symmetry.

Thus there arises a problem of obtaining quantum chemical estimates for parameters of d-d excitations in TMOs. Two major obstacles must be mentioned here. First, the TMOs are of course infinite three-dimensional objects pertaining to the realm of solid state theory for which the account for the translational symmetry is indispensable. Second, the strong correlations of electrons in the d-shells are equally charateristic for TMOs as they are for other transition metal complexes. These correlations lead to problems for the self consistent field (SCF)-based methods when the latter are applied to spin and symmetry properties of the ground state of the transition metal complexes and to their d-d electron spectra. In fact, the single Slater determinant is poor even as a zero approximation to the structure of the ground state multiplet and electron correlation must be included explicitly - as a part of the wave function construct - to obtain correct results. Constructing the configuration interaction (CI) series based on the SCF orbitals does not solve the problem completely since they require a large number of configurations (most of them are to compensate the errors induced by the SCF approach at earlier stages of calculation) and converge slowly. Even more, when the solid state and correlation aspects ''collide'' in TMOs the result is completely disasterous: the one-electron band theory (the translation invariance compatible version of the SCF appfoximation) when applied to TMOs like MnO, CoO, and NiO predicts them to be partially filled d-band metals in sharp contrast with experiment (see Cox,Harrison,ZungerRev and references therein). Such a result perfectly shows how far the SCF description may be from the real state of things even in highly symmetric systems, simple in many other respects.

The general opinion in the literature is that the required quantum chemical
estimates can be obtained with use of the cluster approximation *i.e.*
by replacing the whole infinite three-dimensional crystal by the closest
surrounding of the TMI in question. The general argument here is that the
d-states are highly localized and thus their properties are controlled only
by their closest surrounding - the first coordination sphere. This
argument seems to be somewhat superficial, however. It is well known from
optical absorption (OA) spectroscopy of molecular transition metal complexes
that for the same set and spatial arrangment of donor atoms around the TMI
the OA spectrum (and even the ground state) may become different if
sufficient changes are chemically introduced to the peripheral groups of
bulk organic ligands. The source of such a mutability is not of course any
direct interaction between the peripheral groups and the TMI, but the
chemically induced variations in those electronic structure parameters
(ESPs) of the ligands which ultimately control the state of the d-shell.
Thus we see that the local character of the d-states does not suffice by
itself to justify the cluster approach and somewhat more elaborated
treatment is necessary.

An appropriate method for analysis of the parameters of the d-shells in
transition metal compounds is that of the effective Hamiltonian of the
crystal field (EHCF) one proposed about a decade ago []. It
allows to estimate the otherwise phenomenological D parameter of the
CFT provided a reasonable description of the ESPs of the ligands is given.
The EHCF methodology is based on the following features of electronic
structure of transition metal complexes: (i) the presence of localized
electrons in the open d-shell of transition metal atom; (ii) strong electron
correlations inside d-shell; (iii) only small amount of electron transfer
between d-shell and the ligands. All these features were implemented by
using the combination of McWeeny group function [] and effective
Hamiltonian (Löwdin partition) [] techniques and are based on
the subdividing the system into parts - correlated d-shell, effective
Hamiltonian of which is treated on the full CI level and the rest (ligands)
described in the semiempirical one-electron (SCF, single determinant)
approximation. These moves allowed also to construct a successful numerical
scheme reproducing experimental d-d spectra of transition metal complexes
with acceptable accuracy (the spin and symmetry properties of the ground and
low-lying excited states are always correct and the errors in the
determination of excitation energies are usually less than 1000 cm^{-1})
[]. This method was implemented in several incarnations
depending on particular procedures employed to estimate the ligands'
electronic structure parameters (ESPs, see below). The widest testing was
done for the CNDO estimates of the ligands' ESPs [], but the
attempts using the INDO [], SINDO1 [], and MINDO/3
[] also were quite successful.

According to the EHCF approach the matrix elements of the CF are dominated by the covalent contribution which actually takes into account the possibility of one-electron hopping between the d-shell and the ligands. In the form appropriate for the subsequent analysis they may be written as LECF/AOM:

| (1) |

| (2) |

| (3) |

Formally, the difference between ''molecular'' and ''crystal'' forms of the
EHCF theory should be minimal and the latter appears simply by replacing the
MOs by the band (Bloch) states:

| (4) |

Both in the molecular and in the solid state contexts the summation over all
one-electron eigenstates of the ligands (the | i
ñ MO
states or the Bloch states | n**k**
ñ ) must be
performed in Eq. (4). On the other hand it is clear that only
the states (say AOs) located at the nearest neighbor atoms have nonvanishing
one-electron hopping integrals with the d-shell of interest. This allows
[] to rewrite the matrix elements of the CF Eq. (
1) in a local form:

| (5) |

| (6) |

The local states relevant for the solid state context are the Wannier states [] defined by:

| (7) |

At a first glance this justifies applying the cluster approximation to calculation of the states of the d-shells interacting with the band states of an ionic insulator. The things are, however, not so simple since the band structure of the solid manifests itself in the system of the poles of the corresponding Green's functions. Indeed, as one can check the poles of the Green's function matrix elements in the local representation fill the whole range of energies which is spanned by the crystal band. In certain sense we face here the standard quantum mechanical situation: the things localized (measured) in one representation may be not localized in another one (for highly pedagogical discussion of this point see the book by Roald Hoffmann []). The Wannier states which are local in the coordinate (or site) representation are not local in the energy representation like the Bloch states are local in energy (they are the eigenstates of the corresponding Fock operator) and are not local in the coordinate (or site) representation and the question is to what extent this important feature of the real three-dimensional crystal is reproduced by the cluster calculation.

Thus, we see that the cluster calculations to be used to estimate the the
d-d spectra are subject to a very strong condition: they have to reproduce
somehow the effect of the whole set of band states. The last requirement in
fact is not strictly bound to the EHCF framework within which it has been
just formulated and applies irrespective to a specific technique used for
numerical modeling the solid with use of a cluster. In view of the above
analysis the case of minimal size clusters MO_{n}^{2(n-1)-}
Wahlgren,Janssen,Freitag,TchJMC seems to be the most suspicious. In the
crystals with the rock salt structure the filled band states of the e_{g}
symmetry mostly formed by the 2pO-states contribute to the splitting of
the d-orbitals. In the case of minimal cluster only one state (MO) of this
symmetry is provided by the ligands. Correspondingly the Green's function
has only one pole at the corresponding orbital energy value. A simple
analysis shows that in a three-dimensional rock-salt type solid at least two
states of the e_{g} symmetry appear from each band at each energy value in
the latter. The number of poles is corresponding *i.e. *infinite,
spanning the whole range of the respective energy bands. Generally, one pole
is not enough to reproduce the whole band with a non-zero width. In an
empirical approach one could of course tune an energy of a single level in
order to mimic the effect of the band, but on an *ab initio* level
precising the absolute position of the e_{g}-state energy in the cluster can
spoil the results on the splitting in the crystal since the exact energy of
this state can become far from the position most effective for reproducing
the interaction of the d-shell with the band.

We see that the key drawback of the minimal cluster models is the meagerness of the available spectrum of one-electron states on the ligands. On the other hand the rôle of the Madelung potential whose importance for accessing the sensible results on d-shell splitting in the minimal cluster approximation is frequently stressed [,] seems to be overestimated. Of course taking the Madelung potential is important in order to reproduce correctly the relative positions of the diagonal matrix elements of the ligands' Fock operator on the energy scale. This in its turn is important for determining the width of the valence band, the charge distribution and other ligand-related ESPs affecting the splitting, but by itself the Madelung potential only weakly influences the splitting of the d-shell since it is almost spherically symmetric. Indeed, our calculations show that the contribution of the charges beyond the first coordination shere (six charges) to the splitting of the d-states constitute only 3% per unit charge.

It is interesing to notice that the Madelung potential is sometimes
implicitly used within otherwise *ab initio *procedures as a fitting
parameter serving to improve the result. It is usually estimated with use of
the formal charges of the ions in the lattice. The effective charges of ions
can be, however, far from the formal ones due to electron delocalization
(band formation) in the crystal. For example, it was estimated that the
charges in the KCl are approximately only halves of the formal ones
Harrison. This effect is also very poorly reproduced by the minimal
cluster models due to lack of the translational symmetry. In the minimal
cluster calculations the effective charges residing respectively on the
metal and the oxygen are always different. For all these reasons we incline
to an opinion that the reasonable agreement between experimental data and
*ab initio* minumal cluster calculations (particularly those which
contain implicit adjustment schemes beyond otherwise strict *ab initio*
procedures) is an accidental coincidence.

The intrinsic drawbacks of the minimal cluster models can be reduced by increasing the size of the cluster since (i) the molecular orbitals of the larger clusters are closer to the band states of the solid and (ii) the atomic charges obtained are closer to the exact ones. The strong dependence of band gaps on the cluster size was demonstrated on the example of MgO and KCl clusters [] in the small size range.

Knowledge of electronic structure of the TMOs is important since it controls
their chemical properties including catalytic activity in oxygenation
processes []. In the absence of a catalyst these processes are
restricted due to spin conservation rules. It is usually believed that the
d-shell of a TMI serves as an electron donor or acceptor for the reactants
[]. Also, interactions between catalyst and reactants can change
their spin states getting around the spin conservation restriction without
significant charge transfer []. All this testifies that the
electron correlation in the d-shell and reactants of catalytic transition
metal complex (complex formed by catalyst and reactants coordinated to it)
must be taken into account simultaneously. The situation in general can be
described phenomenologically [,]. The Hamiltonian for
the entire catalytic complex is a sum of those for the free subsystems
(catalyst and reactants/products) and of their interaction:

| (8) |

| (9) |

| (10) |

| (11) |

In fact the EHCF method [] is designed to be a tool providing
the estimates for the CF phenomenological Hamiltonian. Though it does not
directly apply to the problem of catalysis since it assumes the number of
electrons in the d-shell to be a good quantum number (*i.e.* integer -
equal to the number of d-electrons in the free transition metal ion - and
constant) and the ligands wave function to be one of the ground state the
same principles can be used to construct the effective Hamiltonian for the
electron variables describing the d-shell and carefully chosen part of those
in the ligands. In the case of chemical process it is usually possible to
choose a small subset of orbitals responsible for the transformation. The
structure of these orbitals and/or their occupation numbers significantly
change in the course of reaction. We combine these orbitals into the r-subsystem (reactive one). For example, the isomerization of quadricyclane
to norboranadiene is a rearrangement of four-membered ring into two double
bonds. This reaction is forbidden according to the Woodward-Hoffmann rules
[] since the HOMO and LUMO of b_{1} and b_{2} symmetry of
quadricyclane and norbornadiene invert their occupancies in the course of
isomerization. Therefore, these two orbitals must be considered as active
and must be included into the r-subsystem. In the case of atomic oxygen
adsorption p_{x} and p_{y} atomic orbitals of oxygen bearing unpaired
electrons must be included into the r-subsystem since the electrons on
these orbitals determine the spin symmetry of the oxygen state and are
responsible for adding electrons to and removal from the oxygen atom.
Analogously, in the case of molecular oxygen adsorption, the degenerate p^{*} orbitals with unpaired electrons constitute the r-subsystem. In
general, using some number of highest occupied and some number of lowest
unoccupied molecular orbitals is a safe choice for the r-subsystem. Of
course this recommendation is of little value for someone who is interested
in numerical result only and can also afford large scale CIs. Our concern
here is largely to develop a semiquantitative tools supporting qualitative
understanding and explanation of catalysis phenomenon in intuitively
transparent terms.

To consider the transition metal complex with chemically active ligands we
divide the system in two parts: the first part (requiring correlated
description) is a combination of the d-shell and the r-subsystem. It is
denoted as dÅr and is assumed to be described on the full CI level.
The second part (environment) is presented by all the ligands without those
(molecular) orbitals of reactants which are included into the r-subsystem.
It is denoted as l\ominus r and is described in the SCF approximation. The
separation of the complex into above parts implies also the subdivision of
the Hamiltonian:

| (12) |

| (13) |

| (14) |

The wave function of the ligands (l-subsystem) is given by the antisymmetrized product of the molecular orbitals obtained by an SCF procedure applied to the ligands' Hamiltonian. After this some of the orbitals are ascribed to the r-subsystem while the rest forms the l\ominus r-subsystem and is used for averaging in Eq. (13).

The most important part is a construction of the effective Hamiltonian for
the dÅr-subsystem []. After it is constructed the
electronic energy of the k-th state of the whole complex can be found as a
sum of two averages:

| (15) |

We give now the explicit form of the effective Hamiltonian Eq. (13). It is a sum of one- and two-electron contributions:

| (16) |

| (17) |

| (18) |

| (19) |

The next contribution to the one-electron part Eq. (17)
describes one-electron transfers between the d-shell and the active
orbitals belonging to the r-subsystem. This operator is responsible for
variations of the occupation numbers for the d-shell and the r-subsystem:

| (20) |

| (21) |

| (22) |

Two-electron contributions are of three different types:

| (23) |

| (24) |

In order to substantiate our reasoning given above we performed calculations
of the parameters of the CF affecting the d-shells of TMIs in the
corresponding oxides by the EHCF method and of the spectra of d-d
excitations for TMIs in the different positions inside the TMOs clusters
with use of the EHCF estimated parameters. The structures of the clusters
were taken from the X-ray experiments for the bulk. Therefore, the
reconstruction of the crystal lattice near the surface was not taken into
account. We also did not change any parameters specially for the TMOs. So,
the Racah parameters B and C were taken the same as in the free ion. The
Burns' exponents for the metal d-orbitals were used and the resonance
parameters b^{M-O} were taken equal to those fitted to reproduce the
spectra of the hexaaquacomplexes [M(H_{2}O)_{6}]^{2+} [].

Preivously we studied the dependence of the EHCF results on the cluster
size. In Refs. [,] by studying a series including the
minimal cluster MO_{6}^{10-} and the cubic clusters representing fragments
of the oxide structure - M_{13}O_{14}^{2-}, M_{32}O_{32}, and M_{63}O_{62}^{2+} (3×3×3, 4×4×4, and 5×5×5 atoms in the cluster, respectively) have been
calculated. The relevant data are given in Table 1. The non-stoichiometry of
3×3×3 and 5×5×5 clusters can influence the
absolute positions of one-electron levels in the ligand system and the
d-shell. At the same time the formulation of the EHCF method requires only
their differences. In this case the role of non-stoichiometry of cluster is
rather small since the non-stoichiometry of the cluster leads to very close
shifts of the energy levels. First of all one can notice that there exists a
noticeable dependence of the calculated characteristics of the clusters with
their size. One can see that the convergence in atomic charges is
approximately achieved when the largest clusters in the series are used. It
indirectly suggests that the MOs and the corresponding orbital energies of
such a cluster sample the band states of the corresponding three-dimensional
crystal with sufficient accuracy. In addition to a well known dependency of
the calculated charges which reaches approximately the bulk value for the 5×5×5 clusters we notice that the values of 10Dq vary
nonmonotonously with increase of the cluster size at least for intermediate
cluster sizes. In fact the values obtained for the minimal clusters MO_{6}^{10-} are systematically closer to the experimental values than those
obtained for the 3×3×3 clusters. So we would come to a
conclusion that in the case of the octahedral clusters of minimal size
certain compensation of errors may take place. However, it is not clear
whether the same should always happen and whether we may expect a reasonable
result also for lower symmetry MO_{5}^{8-} clusters used to model the
surface TMIs. Indeed, our calculation using minimal cluster []
shows that in the case of the corresponding Co cluster the first excited
state ^{4}E has the energy 0.45 eV. This contradicts to the high-resolution
EELS experiment [] which positions this state at 0.05 eV. Use of 5×5×5 cluster allows to position this state correctly (0.03
eV in our calculation []). Meanwhile, it can be checked by
detailed analysis of the contributions to the EHCF that namely the covalent
contribution to the splitting between the lowest e- and the next in energy
b_{2}-orbitals of the Co ion is overestimated by an order of magnitude in
the minimal cluster calculation. This defect is lifted in the larger cluster
calculation where this splitting is significantly reduced.

On the basis of the above result we conclude that applying the clusters of
the size 5×5×5 would be a safer choice to be employed when
the interactions between the surface TMI with an adsobate is treated with
use of the effective Hamiltonian technique. For the purpose of testing we
consider the effect of NO adsorption on the (100) surface of NiO by the
effective Hamiltonian approach for transition metal complexes with
chamically transforming ligands. The r-subsystem is formed by two highest
occupied orbitals of the NO molecule containing together three electrons.
Let us consider the effect of NO adsorption on the ^{3}E surface state of
NiO. It is well established experimentally that the relative energy of this
state increases by 0.33 eV during the adsorption []. When the
VCI or MC-CEPA methods are applied to this process the shift obtained is 0.1
eV []. The shift of this level depends of course on the r(Ni-N)
distance and our calculations show that the experimental value is exactly
reproduced for r(Ni-N)=1.71 Å . This distance does not seem to be very
short since it is known, for example, that the experimentally determined
distance r(Fe-N) in complexes with NO is usually in the range 1.70¸1.75 Å .

In the previous subsection we considered the effective Hamiltonian
description of the local excitations in the TMOs. The acceptable agreement
between the calculated and experimental values in this case allows to hope
that the adsorption on the TMOs will be also reproduced adequately. The TMOs
and related materials are often used as oxidation catalysts in the processes
of detoxication of organic substances or carbon oxide utilization. The
mechanism of these reactions is not completely understood. It was
experimentally shown that the activation energy in the reaction of the
dihydrogen oxidation is proportional to the oxygen binding energy to the
surface of the TMO []. This observation allowed to make a
conslusion that the rate determining step in this oxidation process is an
interaction of dihydrogen with an oxygen atom adsorbed on the catalyst
surface:

| (25) |

We calculated the oxygen states on the surfaces of the TMOs by the hybrid
method of the electronic structure calculation for transition metal
complexes with chemically active ligands described in details above. In all
the cases the surface of the TMO was modeled by the 5×5×5
cluster and the oxygen 2p_{x}, 2p_{y} orbitals with unpaired electrons
constituted the r-subsystem. We studied the role of two structural
parameters on the electronic state of the oxygen - the metal-oxygen
distance and the exit of the transition metal ion from the surface plane
modeling the reaction of the surface on the adsorption (see Fig. 1). The
method gives the states of the dÅr-subsystem characterized by the
amplitudes of the configurations given by their Young tableaus. Our aim is
extracting the states of the adsorbed oxygen, *i.e.* of the r-subsystem. A set of Young tableaux corresponds to the definite state of the
whole system but not to that of the r-subsystem. If two electrons are on
the same orbital of the r-subsystem and other orbital is vacant the r-subsystem state is singlet. When both orbitals of the r-subsystem are
singly occupied, belong to different columns of the Young tableau and the
system has non-zero total spin the determination of the state of the r-subsystem is not so trivial. In this case the Young tableau of dÅr-subsystem contains a mixture of singlet and triplet states of the r-subsystem and to find the weights of the oxygen states the systems of two
inhomogeneous linear equations must be solved. The necessary subduction
coefficients were taken from Ref. [].

We choose the states map as a form of representation of the results on the
adsorption. In principle, the EHCF method is capable of geometry
optimization []. At the same time the geometry optimization gives
the electronic state only in one point. When we construct the map we have
more information since a) relatively small error in the optimized geometry
parameters can cause the incorrect result on the electronic state; b)
perturbation by other molecules can cause the change of the electronic
state. The states map for the atomic oxygen adsorbed on the (100) surface of
FeO (dependence of the system's electronic state on the structural
parameters) is given in Fig. 2. The interatomic distance Fe-O_{ads} was
varied in the range 1.2¸2.4 Å while the exit of the metal atom
from the plane was varied in the range 0.0¸0.5 Å . The positions of
the lines on the states map are given with precision of 0.01 Å . The
weights of singlet (W(O^{s})) and charge-transfer (one electron from the
d-shell to the r-subsystem, W(O^{-})) and the total charge on the oxygen
(Q(O)) are given for some representative points on the map. The same way
of construction is used for other states maps (see below). In the most cases
the position of the border between different states only slightly depends on
the exit of the metal ion from the plane. It means that these transitions
are mainly caused by the interaction of the d-shell with the adsorbed oxygen
atom. When the Fe-O distance is larger than 2.07 Å the state of the
oxygen is almost totally triplet with small admixture of the anion form. The
singlet state is totally absent. In the case of small values of r(Fe-plane)
the ground state is the ^{3}E state obtained from the quintet state of the
surface ion Fe^{2+} in the oxide and from the triplet state of the oxygen
atom. The exit of the metal ion from the surface plane changes the state of
the adsorption complex. The analogous change of the ground state can be
obtained for the free TMO due to changes in the crystal field. At the same
time in the case of adsorption these changes couple with crystal field
modifications due to the oxygen atom that leads to the non-trivial form of
the region ^{3}A_{2} on the states map. For the intermediate distances r(Fe-O)
the ground state is the ^{5}E state with noticeable weights of the singlet
and anion states of oxygen. In the case of small distances r(Fe-O) we can
see the singlet and triplet states with relatively large weights of the
singlet and charged forms of oxygen. Moreover, the weight of the
doubly-charged oxygen forms becomes noticeable. It should be noted that the
changes of weights of different states are not monotonous. For example, the
state ^{5}A_{1} in a small region near 1.5 Å along the r(M-O) coordinate
does not contain any singlet contribution at all, while its neighbour states
contain about 20% of the singlet oxygen weight. It is noteworthy that the
exit of the metal ion from the surface plane usually does not change
significantly the weights of different oxygen states if only the change of
the state of the whole complex does not occur under this condition.

In the case of atomic oxygen adsorption on the surface of CoO the states map
is somewhat simpler (Fig. 3). For large r(Co-O) distances the ground state
is the sextet (^{6}A_{1}) mainly formed by the quartet ground state of the
surface Co^{2+} ion in the oxide and by the triplet state of the oxygen
atom. This state prevails on the states map. As in the case of FeO the anion
form of the oxygen atom has significant weight for smaller and intermediate
r(Co-O) distances. At the same time the states with contribution from the
singlet oxygen are almost absent on this map. The singlet oxygen appears
only for the ^{2}E state occuring at very small distances r(Co-O) and for
the ^{4}E state which becomes the ground one only for large values of
r(Co-plane) and in a very small area of the map (Fig. 3). In the case of
adsorption of atomic oxygen on the NiO surface the states map is very
simple. The quintet state formed by the triplet states of the surface
transition metal ion in the oxide and of the oxygen atom is the ground one
for r(Ni-O) exceeding 1.38 Å . The singlet form of the oxygen atom appears
nowhere on the map. The amount of charge transfer between the oxide and the
oxygen atom is quite similar to that obtained for adsorption on the CoO. In
the case of atomic oxygen adsorption on the MnO the whole map is formed by
only one quartet state mainly constructed from the sextet state of the oxide
and the triplet state of the oxygen atom. The state of the d-shell conserves
the structure of the ground state of the free Mn^{2+} ion (^{6}S). The
singlet oxygen can be found in noticeable quantity even for medium values of
r(Mn-O). It should be noted that in the case of MnO the weight of
charge-transfer states is somewhat smaller than that for other oxides.

It is interesting to compare the main features of the adsorption of atomic
and molecular oxygen on the oxides. In the case of dioxygen adsorption the
structure of the r-subsystem orbitals is determined in the Coulomb field
of the oxide. There exists an opinion that the Coulomb field of the catalyst
can change the spin state of the oxygen molecule from the triplet one to the
singlet one []. At the same time the calculations show that
this effect can be achieved only for unphysically large Coulomb fields. The
molecular oxygen has more geometry degrees of freedom and the ionization
potentials and electron affinities are somewhat different from those of the
atomic oxygen. Moreover, in the case of molecular oxygen the vacant orbitals
can be important. It obviously affects the electronic structure of the
adsorption complex. We present here the states maps for two structures of
molecular oxygen adsorption on the (100) surface of CoO - the end-on one
(Fig. 4) and the side-on one (Fig. 5). In the case of the end-on adsorption
one can see that the general features of the states map representing
adsorption of atomic oxygen (Fig. 3) are conserved (including the origin of
the states and the positions of border lines between them) except the width
of the region of the ^{4}E state. It certifies that the changes of the
states are mainly caused by the crystal field induced by the doubly occupied
orbitals of the closest oxygen atom. The change of the atomic oxygen by the
molecular one leads to relatively small changes in the weights of different
configurations for equivalent points on the map. At the same time there are
some general trends: this change leads to decreasing of the weight of the
anionic oxygen and to increasing the weight of the singlet states of the
oxygen species. In the case of side-on adsorption the map differs
significantly from that for the end-on adsorption mainly due to difference
in the symmetry of the adosrption complex. It is noteworthy that significant
weight of singlet oxygen can be found in this case even for relatively large
interatomic distances. This form of adsorption is also more effective for
formation of negatively charged oxygen species. Moreover, for small
interatomic distances r(Co-O) the doubly charged oxygen has significant
weight - more than 8%.

We considered the problem of constructing local many-electron states in the TMOs and estimating their relative energies. The important statement here is that the correlated approximation of the d-shell electronic structure is necessary to describe the spectrum of d-d excitations. The EHCF approach was used as an appropriate method for this purpose. It allowed to reproduce the experimental data of the OA and EEL spectroscopy. In all the cases the reasonable agreement with the experiment was achieved by using larger cluster models without any special purpose parameterization process. The EHCF approach does not apply to the reactions in the coordination sphere of the transition metal ions since it does not take into account the electron correlation in the ligands. The natural modification of the EHCF approach was performed based on the effective Hamiltonian construction for a system consisting of the d-shell and active one-electron states of the ligands. This method can be applied to a wide range of problems in the adsorption and catalysis. We studied the states of the atomic and molecular oxygen species adsorbed on the transition metal oxides and have found that the weights of singlet, charge-transfer and triplet states strongly depend on the structural characteristics of the adsorption and on the nature of the transition metal atom forming the oxide. The entanglement of the states of the d-shell and oxygen is of particular importance and the model based only on the effect of the TMO Coulomb field on the state of the oxygen seems to be oversimplified.

**Acknowledgments.** This work has been performed with partial financial
support of RFBR through the grant 02-03-32087. Authors gratefully
acknowledge valuable discussions with Prof. A.A. Levin. The authors are
grateful to the Referee for his instructing comments.

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