Calculation of adsorption and interaction mechanisms of O 2 and CO 2 molecules on BaTiO 3 surface

The paper presents the results of quantum chemical calculations using the extended Huckel method for adsorption of O2 and CO molecules on BaTiO3 surface. It is shown that on (001) surface, the physical adsorption is dominant, whereas on (002) surface the chemical adsorption prevails, the Ti ions being the most active adsorption centres. The possible dissociation mechanisms of the adsorbed oxygen molecule and a heterogeneous oxidation reaction of CO in CO2 are considered.


Introduction
We have carried out the calculations for interaction of the adsorbate molecules with every surface point of clusters simulating the surface of BaTiO 3 crystal; and have built the energy surfaces corresponding to potential energy minimum of a complex "adsorbed molecule+cluster" (E ads = E min − E ∞ ).
The calculations were carried out using the Extended Huckel method (EHM) which takes into account only the electronic interaction energy.Here, a base program "Paramol-1" updated by us was used [1].Earlier we had used this method to calculate the adsorption of oxygen O 2 and hydrogen H 2 on small clusters of BaTiO 3 .We have also accounted for the interaction of thermal sputtering vapour components with the substrate surface in deposition and formation process of compound films [2][3][4].The modified EHM was used in [5] to calculate the geometry of polyatomic molecules.The use of large clusters resulted in a considerable decrease of the "edge" effects on the character of interaction of an adsorbed molecule with the adsorption centre.When choosing the clusters of BaTiO 3 single crystal surface, the shifts of ferroelectric and surface atoms were taken into account [6,7].While calculating the adsorption, the orientation of the adsorbate molecules relative to the adsorbent sur-face is to be taken into account.In case of adsorption of a two-atomic molecule O 2 and CO we have considered two basic orientations: a) a molecule axis is parallel to the adsorbent surface plane (s-type orientation adsorption); b) a molecule axis is normal to the adsorbent surface (c-type orientation adsorption).There are two possible orientations for CO molecule: by oxygen or carbon atoms towards the surface (the adsorption centre).The similar calculations for MgO and SnO 2 surfaces, accomplished ab initio like in the Hartree-Fock approximation, are presented in papers [8,9].
The "TiO 2 " surface layer of BaTiO 3 single crystal with TiO 2 adsorbing plane (a crystallographic plane (00 1  2 ) was modelled by a cluster of 32 atoms: 16 atoms of TiO 2 plane, 13 atoms of an underlying BaO plane, two O atoms and Ba atom of still more underlying planes for symmetry and electroneutrality of the cluster (106 valence electronic orbitals).The second cluster with BaO adsorbing plane consisted of 48 atoms: 18 Ba atoms, 26 O atoms and 4 Ti atoms (146 valence electronic orbitals).The coordinate axes X and Y are in the plane of the cluster surface and Z axis is normal to it coinciding with C axis of the crystal.
The calculations have shown the "BaO" cluster surface to be poorly active for adsorption; here the physical adsorption of O 2 and CO molecules dominates, which weakly influences the electric and physical properties of BaTiO 3 single crystal and the strongest electronic density redistribution takes place at adsorption on "TiO 2 " surface.Therefore, we present the results of the calculations of the interaction of the adsorbed molecules with various points of "TiO 2 " plane of BaTiO 3 adsorber as well as the possibility of O 2 dissociation and a heterogeneous oxidation reaction of CO in CO 2 .

Adsorption of O 2 and CO on the atomically pure surface
Figure 1 shows the minimum interaction energy surface of O 2 adsorbed molecule (c-type) with the "TiO 2 " cluster surface and the surface of the corresponding minimum distances R min .It is obvious that E min and R min sharply decrease in the vicinity of Ti atoms, changing slightly above the interstitial sites and oxygen atoms of the cluster.The potential wells in the vicinity of Ti are practically of a conic form.The potential energy E min sharply increases moving away for over 0.05 nm from Ti atom along X and Y axes that testifies to a distinct direction of binding O 2 absorbed molecule and Ti atom of the cluster.
We have also carried out similar calculations for O 2 s-type adsorption and CO adsorption on the atomically pure plane of the "TiO 2 " cluster.The values of binding energies of the adsorbed molecules with the cluster (E bind s = |E ads |) and their corresponding equilibrium distances from the surface adsorption centre are given in table 1.
The comparison of the data in figure 1 and in table 1 shows that the most energetically favourable adsorption centres for O 2 and CO molecules on the "TiO 2 " cluster surface are Ti atoms with c-type adsorption geometry and for CO moleculesby the oxygen downward (closer to Ti atom).The most pronounced redistribution of the electron density both inside adsorbate molecules and between the adsorbed ones takes place and the surface also corresponds to this localization geometry (table 2) [10].Below, a possibility of dissociation of O 2 molecule bound with Ti atom is considered.
The dissociation of O 2 molecule along Z-coordinate after a c-type adsorption on Ti (R ads = 0.1 nm) has been considered: one of the molecule atoms (O2) moves away from the other (O1, localized above Ti) in the direction normal to the surface; O1 in its turn changes the position above the surface reaching the potential energy mini- mum of the adsorption complex.The surface of minimum energies in Z-coordinates of O1 and O2 atoms was calculated.It was obtained that if O2 atom moves away from the surface, O1 atom approaches the surface, the depth of a dissociation potential well decreases approximately from 2.4 eV (note that the dissociation energy of O 2 isolated molecule is equal to 4 eV) to ≈ 1.6 eV, and R bond (O1) = 0.05-0.06nm (above Ti).If we take into account the energy equal to about 1 eV that can be liberated during adsorption and given to the molecule, then the additional dissociation energy becomes equal to 0.6-0.7 eV.This is much less compared to the isolated molecule dissociation, but total energy of the adsorption complex after desorption of O2 becomes larger (+0.3 eV) than before the interaction of O 2 with the surface.
According to EHM evaluations, the O1 atom becomes almost neutral (its charge is +0.2e and just −0.2e goes to Ti), and the desorbed O2 becomes doubly charged (it is given −0.5e from each of the four nearest O 2− ions of the TiO 2 surface) due to the closeness to Ti and due to strong overlap of the electron orbitals.The formation and desorption of such an ion are hardly possible.Therefore, we have also studied some other possible ways of O 2 dissociation.
At the O 2 absorption of s-type above Ti atom or above O lat oxygen atom of the cluster by O1 and O2 orientation in the direction of Ti atoms, the O 2 dissociation also becomes possible without the desorption of oxygen atom but with the localization of O1 and O2 atoms in a form of O − ions in the vicinity of O lat (the free migration radius of O ad above the atoms along the surface equals about 0.1 nm, R ads ≈ 0.16 nm, E bond = 0.4 eV, Q = −1e -figure 2) or, in the second case, approximately above the centre of the O-Ti bonds along the O-Ti-O line (see Y -coordinate in figure 2) at the height R ads ≈ 0.1 nm (E bond = 1.1 eV, Q = −0.85e).In both cases the energy barrier height equals ≈1 eV and with the account of the adsorption energy (see table 1) for the O 2 dissociation, an energy of E dis ≈ 0.7-0.8eV is needed.The O ad atom is charged by O lat electrons.In the first case O ad -O lat bond is like O 2 with −2e charge, and in the second case a complex O1-O lat -O2 (or O1-Ti-O2) is formed with a geometry similar to the water molecule H 2 O (H-O-H).After dissociation, the energy E min of "O-O-cluster" adsorption complex decreases to −0.4 eV (after O1 and O2 bond formation with O lat ) or before dissociation −1.1 eV (after localization of O1 and O2 between Ti and O lat ).After O 2 dissociation of s-type the activation desorption of one of the two oxygen ions can take place.Consequently, a free O 2− ion is formed and bound with the nearly neutral surface oxygen atom O ad .If O1 and O2 ions were situated in the vicinity of their neighbouring O lat , then one of them, getting about 0.65 eV, would be desorbed and the other one as a result of a charge loss, would be bound to the surface atom O 2− (R ads = 0.11 nm, total energy drop of "molecule-cluster" system E min = −0.7 eV).If O1 and O2 ions are definitely localized on Ti-O bond, then for desorption of O 2 , for example, 0.4-0.5 eV are needed with the simultaneous shift of O1 closer to Ti-O bond centre and decrease in height to R ads ≈ 0.01 nm, and the system energy decreases to E min = −1.5 eV.Thus, we see that if in the first case the desorption barrier exceeds "zero" energy E ∞ by ≈ +0.3 eV, then in the second case it does not.So, the desorption here is energetically more favourable.Both after the dissociation and the desorption of one of O 2 molecules for the atoms which remained O ad , it becomes energetically favourable to localize above Ti-O lat surface bond (figure 3, dark regions between Ti and O).

Adsorption of CO molecules at the presence of a chemosorbed oxygen on the surface
In practice, CO adsorption takes place on the surface that is already partially filled with molecules of other gases, in particular, oxygen molecules which have a large binding energy of c-type on Ti atoms (see figure 1 and table 1).Thus, we have calculated the potential interaction energy curves of CO molecules with adsorption centres O, Ti and M (interstitial site) of the "TiO 2 " surface cluster of BaTiO 3 single crystal in the presence of O 2 c-type localized molecule on the neighbouring titanium atom at a distance of R min = 0.11 nm, showing the possibility of a direct localization of CO on the adsorbed molecule O 2 .
For CO adsorption by s-type orientation on the partially oxidated TiO 2 plane, the potential energy minimum for the system "adsorbed molecule-cluster" is not reached.This energy minimum is attained only in case of c-type orientation -at CO localization on Ti the minimum is observed for both orientations of the adsorbed molecule, while for the rest of adsorption centres -only at CO orientation with carbon nearer to the surface.Thus, in the presence of an adsorbed oxygen on the surface, the energetically favourable is c-type adsorption of CO, which, however, has the opposite orientation in comparison with the adsorption on "TiO 2 " "pure" surface.The results of these evaluations are given in figure 4. The curve of O d is calculated for the case of CO localization on the surface oxygen atom distant from Ti atom with which O 2 molecule is c-type bound; the curve of O n is calculated for the interaction of CO with the oxygen atom of lattice nearest to Ti atom.It is seen that the binding energy of CO with such an "unclean" surface increases almost 10 times.The strongest decrease in the potential energy of the "adsorbed molecule-cluster" system is observed at the interaction of CO with O 2 c-type molecule localized on Ti.Possible mechanisms of the oxidation of CO into CO 2 are presented below.

Low degree of the surface covering with the adsorbate molecules (O 2 and CO); a non-dissociative form of oxygen adsorption
Let CO molecule on Ti2 atom be adsorbed, then on the nearest neighbouring Ti1 atom O 2 molecule of c-type is localized.For such a succession, the energetically favourable is c-type of CO orientation with O atom to Ti (E ads = −0.65 eV, see table 1).In the opposite case more probable is CO localization with carbon atom to titanium (see figure 4, E ads = −1.2eV), although the binding energy of opposite orientation is also large, approximately 0.7 eV (curve 5, figure 4).The oxygen atom of CO molecule is 0.14 nm away from Ti2 atom, R(C-O) = 0.11 nm, and O1 atom of O 2 adsorbed molecule is at a distance of 0.10 nm from Ti1.An equilibrium distance between O1-O2 of O 2 adsorbed molecule is equal to 0.16 nm (whereas far from the surface it is 0.12 nm).Thus, the O2 atom is 0.26 nm away from Ti1.The "extension" of O 2 molecule favours its dissociation.Along the coordinate Z, this leads to desorption of O2 atom with the activation energy of 0.7 eV.Along the coordinate Y (or X), the O2 atom migrates along the surface (figure 5) to CO molecule adsorbed on titanium with the formation along the axis Z (normal to the adsorbing plane) of Ti-O-C-O complex, i.e.CO 2 adsorbed molecule.It is seen that the system energy remains practically unchanged with quite large (±0.11nm) distances of O2 atom from a geometric centre above Ti1 atom, and permits it to approach CO "without difficulty".To form CO 2 adsorbed molecule (Ti2-O-C-O2) O2 atom needs to overcome a potential barrier about 0.6 eV high which is followed by an energy well, 8 eV deep (i.e. the reaction of oxidation of CO into CO 2 ).However, the bond of CO 2 with Ti is comparatively weak, E bond ≈ 0.4 eV.

Adsorption of CO with dissociative adsorption of oxygen on the "TiO 2 " cluster surface
As stated above, O 2 adsorbed molecule after having received additional energy of 0.6-0.8eV in the process of adsorption, can dissociate with localization of O ad on Ti or approximately above the binding line centre of the surface atoms Ti and O at a distance of 0.09 nm from the surface.The second case of dissociation process is energetically more probable.For this geometry of O ad , the calculations of CO interaction with the surface show that the potential energy minimum is observed neither at CO localization in the interstitial sites nor at s-type orientation on titanium or oxygen atoms.The energy minimum is attained only for c-type CO localization on O and Ti atoms of the surface, CO adsorption being of an activation character: at the adsorption on the lattice oxygen, the barrier height is the largest (≈ 1.8 eV), and on Ti atom it is the smallest (≈ 1 eV).In the latter case, an interesting effect was found: after c-type CO localization on Ti at a distance R bond = 0.17 nm, corresponding to E min ≈ −1.8 eV, the movement of the adsorbed molecule becomes energetically favourable.It is almost parallel to the Ti-O lat surface in the direction towards the atomically adsorbed ion of O ad oxygen at the height R ads = 0.09 nm above the "TiO 2 " surface and thus forms CO 2 .The total energy drop of the system is 3.7 eV.After having overcome a somewhat higher barrier (≈ 1.5 eV) CO molecule can also be localized directly above O ad with R bond ≈ 0.08 nm (E min ≈ −3.7 eV).In both cases, the desorption of CO 2 molecule being formed is energetically favourable.

CO adsorption at a high coverage of the "TiO 2 " surface with oxygen molecules
In such a case, a molecular form of c-type oxygen absorption on Ti atoms prevails (Ti-O1-O2).Energetically more favourable localization centre of CO is the O2 atom of c-type adsorbed oxygen (i.e.O 2 adsorbed molecule) with CO 2 molecule formation (O2-C-O, curve "O 2 " in figure 4).As it is seen from the curve 6 of the same figure, the simulation of a detachment of O-C-O2 molecule (i.e.CO 2 ) from Ti-O1 bond is accompanied by a further energy decrease of the system, and CO 2 molecule can either stay on the surface being localized above Ti-O1 bond with R ads = 0.14 nm and the energy decreases in the system additionally by 1 eV (total energy drop is 9.1 eV), or desorbs having overcome the potential barrier of 2 eV, which is considerably less than total energy drop due to CO molecule adsorption and its subsequent oxidation to CO 2 .

Conclusion
To explain the experimental data concerning the effect of the adsorption on electrical and physical properties of the solid states, it is important to know the charge "adsorbed molecule-adsorbent".For the atomically pure "TiO 2 " surface of BaTiO 3 crystal, c-type geometry adsorption on Ti atoms is the most energetically favourable for O 2 and CO molecules.A more obvious redistribution of the charges also corresponds to this geometry of adsorption (table 2).
1.It was obtained for a c-type absorption of O 2 in the interstitial site, that approaching E min (R min = 0.24 nm), the charge of a molecule is practically unchanged, and only a slight charge redistribution between the atoms of the molecule itself takes place.If an oxygen is c-type localized on Ti (R min = 0.1 nm), then the charges of all the nearest neighbours in the cluster change evidently as well as does the electronic charge density on the atoms of the adsorbed molecules.However, the lack of free electrons in a cluster predetermines a weakly pronounced donor mechanism of O 2 adsorption on a "pure" "TiO 2 " surface: the charge of −0.12 eV goes from O 2 on Ti, where the redistribution of electron density from the neighbouring oxygen atoms also takes place (−0.14e, i.e. approximately −0.035e from each of the four nearest surface atoms), decreasing titanium charge by 0.26e.The similar situation also takes place at CO absorption.Probably this explains a weak effect of O2 and CO adsorption on the electrical conductivity value of BaTiO 3 monocrystalline samples and their substantial effect on the spontaneous polarization value of the ferroelectric due to the appearance of the induced dipole moments of the adsorbed molecules [11].
2. Quite a different picture is obtained at CO adsorption on a "real" surface, when there is already an oxygen on it bound according to c-type on Ti atoms (see figure 4 and table 3, table 4).From the analysis of the calculation data it follows that: a) the charge of adsorbed molecules and surface atoms substantially changes in the process of adsorption and in many cases it does not change monotonously (see, e.g., curves Q in figure 4); b) CO molecule changes its charge state depending on the localization centre; c) if on a pure ideal surface the molecular adsorption of CO and O 2 follows a weak donor mechanism separately, then at CO, appearing on the surface, a charge of ≈ −1.5 eV is localized on O 2 adsorbed molecule, i.e. an acceptor mechanism of molecular adsorption of O 2 appears.
3. It is possible to predict the change in the charge state of a "weakly oxidated" surface on the whole depending on its occupation with CO molecules.Initially, i.e. at a small surface occupation, the most probable is localization of CO on O lat (figure 4).This causes a relocalization of the electron density from these atoms to O 2 , forming a surface negatively charged layer, and O lat and CO create, on the whole, a practically neutral adsorption pair O-CO, an external atom O of the adsorbed molecule CO having also the charge −1.1e (table 4).
The occupation of the surface with the adsorption atoms will lead to the interaction of CO with O 2 and to the formation of CO 2 .This causes the disappearance of a negative charge on O 2 and the appearance of a positive charge +1e on CO 2 (the total value with the centre O1 charge equals +0.34e).
In case of its desorption, there remains an oxygen ion localized on Ti with a charge equal to −0.85e.As it is seen from the calculations, this charge passes to it from O lat atoms surrounding the Ti.This should substantially effect the electrical conductivity of a crystal.
4. The calculations were carried out for a dielectric.Free electrons will be easily caught by the adsorbed molecules, -this should substantially effect the electrical conductivity of a crystal.

Figure 1 .
Figure 1.The minimum potential energy surfaces and the corresponding minimum distances (R min ) at the interaction of O 2 molecule (c-type orientation) with the atomic pure surface of the "TiO 2 " cluster of BaTiO 3 single crystal.(In figure the coordinates of Ti atoms are X, Y = ±0.2nm).

Figure 2 .
Figure 2. Potential curves of the interaction of O1 and O2 atoms of O 2 oxygen molecule with the cluster of "TiO 2 " surface: 1) at O1-O2 molecule dissociation along the surface on Y coordinate after its s-type localization above Ti (the numbers near points show the height (z) of O1 and O2 atoms above the surface plane; 2) at O2 atom desorption (the upper axis of Z-coordinates, the numbers near • points show the height z above O of atom O1 that remained; 3) at O 2 desorption after the two atoms localization (O1 and O2) in O ad position on both sides of Ti (curves series, Z-coordinates axis).4,5) the behavior of oxygen atoms charge of O 2 molecule (4) and the oxygen atom of the O lat lattice (5) which is approached by the molecule O2 atom in the process of its dissociation (see "1").

Figure 3 .
Figure 3.The chart of isoenergies migration levels of a dissociated oxygen atom (O1) along the "TiO 2 " cluster of BaTiO 3 surface.The second atom (O2) of O 2 molecule after its dissociation is localized above the O lat atom of the surface.The region of negative energies are shadowed.M -interstitial site.

Figure 4 .
Figure 4. c-type adsorption of CO molecule by C atom to the surface on the adsorption centres (M, Ti, O n , O d ) of "TiO 2 " cluster of BaTiO 3 surface and on the oxygen (O 2 ) adsorbed on the surface, which is also c-type localized above the titanium atom (by O1 atom to Ti, R min (O 2 − Ti) = 0.11 nm); on the right ordinate the change in the charges of CO molecule atoms (Q(C−) and Q(−O)) and O 2 (Q(O1) and Q(O2) at CO approaching O 2 is shown; curve 5 -CO adsorption on Ti by O atom to titanium; curve 6 -CO 2 desorption (i.e.O2-CO) from the surface after the interaction of CO with O 2 (O1 oxygen atom remains bound with Ti).

Figure 5 .
Figure 5.The minimum energy surface at dissociative movement above the "TiO 2 " surface of BaTiO 3 crystal of O2 atom of O 2 oxygen molecule c-type localized above the Ti atom to CO molecule which is also c-type bound with the neighboring Ti atom (with O atom to Ti).

Table 1 .
The energy (in eV) and length (in nm) of the adsorbed molecules bond on the most energetically favourable localization centres of "TiO 2 " surface for BaTiO 3 single crystal.ads E ads R ads E ads R ads E ads R ads E ads R ads

Table 2 .
Charges Q (in electron charge units, e) of localization centres and the atoms of molecules adsorbed on a "pure" "TiO 2 " surface of BaTiO 3 crystal.

Table 3 .
The charges (in e units) of atoms O 2 and CO molecules in the process of CO 2 desorption (figure4, curve 6) from the surface of "TiO 2 " cluster of BaTiO 3 crystal.