The chemical bonding in a series of nickel mixed oxides, namely Li2NiO2, Na2NiO2, tetragonal and orthorhombic La2NiO4 for Ni(II), LiNiO2, NaNiO2, LaNiO3 for Ni(III), BaNiO3 for Ni(IV) and LaNiO2, "LaSrNiO3" for Ni(I), is investigated from the results of electronic structure calculations, including both band structure and local properties i.e. atomic charges, covalent bond orders and atomic valences. The metallic contribution to the chemical bonding is modelled on the basis of the calculation of the delocalization degree of the covalent bond order, in terms of the existence of long range M-M interactions. As a main result, the increase of the formal oxidation state of nickel in these oxides involves an increase of both its atomic charge and its covalency.The highest covalency is found for the (III) and (IV) oxidation states, as the strongest ionicity is typical of Ni(I). A special emphasis is devoted to the chemical bonding in the perovskite like nickelates. In LaNiO3, the metallicity is a 3D property, as in LaNiO2 it is a 2D one. Comparing the chemical bonding in La2NiO4 and LaSrNiO3, evidences a decrease of the anisotropy of the perovskite-rocksalt intergrowth in the reduced nickelate.
Nickel mixed oxides bring an example of rich crystal chemical and physical properties as well, on the basis of the existence of various formal oxidation states of the Ni atoms, namely (I), (II), (III) and (IV). For example, the series LaNi(III)O3 - LaNi(I)O2 and La2Ni(II,III)O4+y - LaSrNi(I,II)O3.1 feature the perovskite and perovskite-rocksalt intergrowth structures respectively (1-4):they exhibit an extended range of oxygen deficient compositions, due to the presence of the strongly reduced Ni(I) oxidation state. In such case, the investigation of the chemical bonding and its correlation with the crystalline structure is of special interest. Up to now, the electronic structure calculations of nickel oxides are restricted to NiO and La2NiO4 ,which are found to be wide-gap semiconductors -energy gap 4.3 and 4 eV, respectively (5,6)-. A metallic character of the Ni-O bonding is identified in LaNiO3 and more generally, seems to be likely in Ni(III) containing compositions (7). Rather scarce information deals with the chemical bonding in oxidized Ni(III) and Ni(IV) compounds and nothing is reported on the strongly reduced oxides LaNiO2 and LaSrNiO3.1 .
Modelling the chemical bonding was performed in a series of mixed nickel oxides showing various oxidation states,. Electronic structure calculations included both band structure and local properties i.e. atomic charges, covalent bond orders and atomic valences. In order to get a better understanding of the metallic bonding, an investigation of the delocalization degree of the covalent bond orders was carried out. Consequently, the paper reports first on the difference in modelling the electron distribution in insulators and metals. Moreover, an analysis of the total covalency in terms of separated homoatomic and heteroatomic contributions is proposed. The as-calculated local properties are used to describe the chemical bonding, with a particular emphasis on the existence of Ni-Ni interactions i.e. a metallic property and O-O interactions i.e. a "peroxidic" like property.
1 ELECTRON DISTRIBUTION IN INSULATORS AND METALS.
1.1 Band theory for the transition metal oxides
In theory, the most usual way to investigate bonding in insulators and metals consists in band structure calculations of the electronic structure of the crystal under consideration. (8). Within the standard band theory, the full occupancy of one part of the one-electron bands (valence band) and the non-occupancy of another part of the bands (conduction band) results in an insulating property. The presence of one or some partly occupied bands allows to move electrons from the valence band to delocalized states in the conduction band without energy gap, thus this crystal shows a metallic property. This approach successfully predicts the type of bonding in some simple cases, for example, alkali halides or oxides, but for "3d"-metal compounds containing atoms with a partly occupied d-shell, it can lead to absurd results. For example, band structure calculations (9) for wide gap insulators "3d" metal monoxides with the rock salt structure (MnO, FeO, NiO) predict a metallic character of bonding.
Within the band theory, sometimes an a priori conclusion about the metallic character of bonding can be made without any calculation. For example, all crystals with an odd number of electrons per unit cell have to be metallic. This fact is in contradiction with a lot of examples of insulators with an odd number of electrons in the primitive unit cell of the crystal (10). The requirement of an even number of electrons per unit cell is not the only condition which provides an "insulating occupancy" of bands. In this respect, the metallic nature of the rock salt type NiO oxide which is found from the conventional spin-nonpolarized band theory, is a true difficulty. Even if there is one formula unit with 16 valence electrons per unit cell, the Oh crystal field splitting does not allow to separate occupied and non occupied bands, formed by the 3d, 4s Ni and 2s, 2p O orbitals, in all points of the Brillouin zone (BZ) (11). These contradictions between theory and experiment are not caused by restrictions of the band theory itself. If one considers the wave function of an electron subsystem with a reduced symmetry (in relation to the crystal symmetry), for example with a spin- or spatial- polarization, it is possible to transform the unit cell of the crystal or split some energy levels to provide another kind of band occupancy (11). The transformation of the face centered cubic lattice of NiO crystal to a rhombohedral one or consideration of spin-orbitals within an unrestricted Hartree-Fock scheme allows to disobey the mentioned symmetry restrictions and to provide either a "dielectric, or a metallic occupancy" of the bands. The final conclusion concerning the metallic or insulating properties of a crystal will be made after comparing the total energies of the two states with "metallic or insulating occupancy" of the bands.
Another kind of error in the determination of the nature of bonding -metallic or insulating, can be related to calculations using of a small set of (BZ) points. Usually, such a small set i.e. 64 or even 8 (BZ) points, well accounts for the main properties of the electronic structure of a crystal with a large forbidden energy gap (12). Enlarging this set only raises computer's efforts, but practically does not change the results of the calculations. However, for a crystal with a small number of states near the Fermi level, namely the case of the majority of the metallic "3d"-metal oxides, the choice of a small set of (BZ) points in which all the bands will have "an insulating occupancy", is not unrealistic. Including supplementary (BZ) points in the basis set for the calculations, results in slowly decreasing the forbidden energy gap; still, all the short range interactions between the nearest neighbours and the next neighbour atoms will not change significantly, for any set larger than 64 (BZ) points. Consequently, when considering a crystal with an unknown electronic structure, one is never sure that taking into account new (BZ) points will change the behavior of the bands. Thus, the analysis of the behavior of the dispersion curves cannot give unambiguously the complete knowledge of the metallic or insulating properties of a crystal. An additional information about these properties can be found in the investigation of the localization degree of the electronic density.
1.2 Calculation of the local properties: differences between metals and insulators.
The investigation of the electronic structure was made from a modified CNDO band structure analysis (Complete Neglect of the Differential Overlap) based on the LCAO approach, whose computational scheme is reported further in the text. As an outstanding feature of this method, it is possible to use the density matrix elements in the basis of the atomic orbitals, to calculate the local properties of the electronic structure in terms of atomic charges, covalent bond orders and atomic valences (13).
Using the density matrix elements in the orthogonal atomic basis, one can calculate the atomic charge QA within the Löwdin population analysis (14), and the covalent bond order WAB -Wiberg index-(15).
(2)
where ZA is the core charge, Pab the density matrix elements in the orthogonal atomic basis; a,b are the orbitals of the A and B atoms, respectively. As one can see from eq. (1) an absolute value of the calculated atomic charge is less than the maximal possible charge, which corresponds to the formal oxidation number. The ratio of the former to the latter can be considered as the ionicity degree of bonding. The Wiberg index describes an amount of electron pairs localized on a chosen bond. In the case of molecules with a strong covalent bonding - especially in organic molecules - the numerical values of the Wiberg index are close to integer numbers and merge into bond orders.
Extending these definitions from molecules to crystals is easy, if taking into account the transformation of the density matrix elements in a Bloch basis to that in a localized atomic basis:
(3)
where a', b' number the atomic orbitals which correspond to the a, b orbitals in one primitive unit cell with Rn - radius vector between cells. Integration in eq (3) is performed over VBZ the volume of the Brillouin zone.
Summing the Wiberg indexes WAB over all the atoms except A, in a molecule (15) or in a crystal (16, 13), gives a value of the covalency of the A atom, CA. The total atomic valency VA is related to the total number of A electrons which take part in forming the chemical bonds - both the ionic and the covalent one. The numerical values of the calculated atomic valency are proved to correlate in a rather good way with the classical values known for a large set of molecules and crystals (13).
(4)
(5)
Let us consider the differences between the electronic structure distribution in metals and insulators. Hereabove, a "molecular language" is used to model the electron distribution in a crystal. To describe the metallic bonding formed by electrons spread over all the volume of the crystal, it is sensible to study the delocalization degree of the covalent bond orders. In the case of a "dielectric occupancy" of the bands, the transformation calculated from eq.(3) is equal to unity. Within a one-band model, the matrix elements PaaRn are equal to zero (for n0) if an "insulating band occupancy" (independent of the k vector) is used.
(6)
Thus, in insulators all the non-zero density matrix elements and the Wiberg indexes to occur, regard an interband transition and consequently, a very fast vanishing of the covalent bond orders can be expected when the bond length increases.
For a metal with a partial band occupancy, it is possible to introduce a () region in BZ which is formed by a set of k-points with orbital energies less than the Fermi level Ef ((k)=2 for k, (k)Ef , and (k)=0 for k,(k)>Ef) and rewrite eq.(3) as:
(7)
From eq.(7), the density matrix elements PaaRn and thereby the Wiberg indexes WAA for a metallic compound, are found to decrease very slowly and not monotonically; as well as the -function of a crystal,and their actual behavior is determined by the structural properties of the crystal under consideration. As a useful consequence, one can expect the dependence of the Wiberg indexes WAB on the A-B interatomic distances, as measured by the variation of the covalent bond order, to be different for metals and for insulators:
-long range non-zero values for metals.
-rapidly decreasing values for insulators.
Therefore, the velocity of decrease of WAB can be assumed to be an additional criterion in the study of the nature of the bonding in a crystal.
The applicability of this approach can be exemplified on a model : the body centered structure of crystalline sodium, under a variable uniform dilatation or compression. To calculate the electronic structure of this crystal,the CNDO approximation is used with a standard parameterization for sodium atoms (17) and a basis set of 2048 BZ points ( 96 in its irreducible part). The obtained results do not differ from that in the calculation with 1024 points, thus the convergence is also achieved in the reduced basis set. As a result, the sodium crystals have a partly occupied band whose width varies from 40 eV to 3.0 eV- for crystals with a scaling factor in the range 0.6 to 3.0, respectively. Still, the delocalization degree is different for dense and extended crystals.(Fig. I) As the latter consist in weakly interacting atoms, the probability of "jumping" of electrons over atoms from bond to bond i.e. the metallic properties, progressively vanish. Thus, one can separate a rapidly decreasing covalent bonding on increasing the interatomic distance from a delocalized metallic contribution to bonding.
1.3 Homoatomic and heteroatomic covalency.
In the usual crystals which exhibit a mixed type of chemical bonding, it is useful to get a separate knowledge of the contributions to the overall covalency, namely the covalency between the same atoms - metal or non metal- i.e. an homoatomic covalency and the covalency in the metal-non metal pairs i.e. an heteroatomic covalency. A simple way to achieve this separation is based on the chemical meaning of the iono-covalent bonding in metal-non metal compounds: one can expect the main part of the covalency to be found in the metal-non metal pair i.e. the heteroatomic covalency which accompanies the purely ionic cation- anion bonding.
To calculate these two contributions, we can split the summation over all the atoms in a crystal modelled by eq.(4), into two parts: the first one includes the Wiberg indexes between atoms of the same element and gives the homoatomic contribution , the second one i.e. the Wiberg indexes related to all the different atomic pairs give the heteroatomic contribution to the overall covalency.
(8)
where A and A' atoms describe the same element.
When A is a metal, the homoatomic item in eq.(8) will be called the metallic contribution to the covalency. For ordinary insulating compounds, such contribution is expected to be very small, because the main part of the electronic density is localized in the anion-cation pair bonding. Conversely, the existence of some metallic character can be reasonably assumed, from the metal-metal interactions modelled by the homoatomic contribution to the overall covalency.
When A is a non metal, namely oxygen, the homoatomic part of the total oxygen covalency is related to oxygen-oxygen interactions which will be called "peroxidic" like oxygen bonding, as looking like the covalent O-O bond in the peroxide anion. Obviously, the occurrence of such "peroxidic" oxygen bonding has to be checked on the basis of the existence of short O-O distances, in the structure of the oxide under consideration.
Using the only heteroatomic covalency in the calculation of the atomic valency in eq.(5), results in a "corrected" atomic valency (18), whose value is assumed to fit the formal oxidation state. This will be further settled by the results of our calculations for mixed nickel oxides.
2. COMPUTATION SCHEME OF THE ELECTRONIC STRUCTURE CALCULATIONS.
To investigate the electronic structure, both band and local properties of mixed nickel oxides, a computation scheme built in the modified (CNDO) approximation was used. Within the (CNDO) approximation which is a semi-empirical scheme based on the Hartree-Fock (HF) method, most of the integrals containing atomic functions are either neglected or are approximated (17). The (CNDO) method does not use the local density approximation and thus is more favourable for crystals with open d-shells atoms, such as the transition metals (12).
The basic formalism of this approach is described in details in (12). Here, as regarding a crystal containing transition metal atoms, the construction of the Hamilton matrix is significantly changed in comparison with the standard molecule-oriented (CNDO) scheme (19). The standard (CNDO) approach refers to an ab initio (HF) calculation, in which some part of the core and Coulomb integrals is approximated. Including an atomic parameterization allows from one hand, to simplify the computation scheme and to calculate complex systems and from another hand, to obtain more realistic results, in comparison with the experimental data, as taking into account some part of the intraatomic correlation effects. In the hereby calculations, the main semi-empirical parameters for oxygen, nickel and non transition metal atoms were taken equal to that of the molecular calculations (18,20). However, to account for the long range character of the interactions in a crystal, an extended i.e. not a one-exponential basis function set is needed and consequently, the values of the bonding parameters must be recalibrated. In these calculations, the valence shell double- function is used as a basis for neutral atoms (21). To provide a correct behavior of the Coulomb integrals at large distances, when they are parameterized in the (CNDO) scheme, the values of AB parameters are modelled from the Ohno-Klopman approximation (22, 23).
As it was previously observed in the (HF) electronic structure calculations of NiO (24), the calculated value of the splitting between occupied and virtual 3dNi subbands (Hubbard parameters Udd), does not agree with the experimental data. This discrepancy is due to neglecting some part of the correlation effects, which are very strong for transition metal compounds. Partial including of the intraatomic correlation in terms of calibrated parameters decreases this splitting from 25 eV in (HF) to 15 eV in (CNDO) calculation. Some significant part of the interatomic correlation effects is assumed to be taken into account by means of a polarization correction for insulators. The interaction between the localized hole and the exited electron decreases the effective AA value. It must be noted, that taking into account the polarization correction is crucial for the conduction band: as a result, the position of the conduction band for the Ni(II) compounds, falls to approximately 7-8 eV, that corresponds to a more realistic band picture. Still, this practically does not change the valence band of a crystal; consequently, the calculation of the local properties according to eq.(1-2,4-5) does not depend significantly on the polarization correction.
In all the self-consistent calculations, the integration of the density matrix was made over 64 BZ points. For the oxides showing a metallic character of bonding, the reliability of this set was checked by comparing the results obtained for 64 BZ points with that obtained for 256 BZ points. Concerning NiO, as emphasized hereabove, in order to get the forbidden energy gap -there is a symmetry condition which prevents it (11)- the symmetry of the electron subsystem of the crystal was reduced and a spin-polarization technique was used.
3. CRYSTAL AND ELECTRONIC STRUCTURE OF NICKEL OXIDES UNDER CONSIDERATION .
As an example of crystals with a mixed type of bonding -ionic, covalent and metallic-, a series of complex nickel oxides was considered. This series includes the alkaline nickel mixed oxides M2Ni(II)O2 and MNi(III)O2 (M=Li, Na), the barium nickelate BaNi(IV)O3, the lanthanum nickelates: oxidized LaNi(III)O3 and reduced LaNi(I)O2, La2NiO4 in three forms - the tetragonal oxidized one, the orthorhombic reduced one-, the low temperature tetragonal structure-, and the lanthanum strontium nickelate in its reduced form LaSrNi(I,II)O3.1. NiO is also considered, for comparison.
3.1. Structural data.
An extended field of structural features and related crystal-chemical properties is displayed by these complex nickel oxides. For example, low dimensionality characteristics are present in NaNiO2 (25) -double octahedral layer- , in La2NiO4 (26, 27) and LaSrNiO3.1 (4) -perovskite- rocksalt intergrowth- and in LaNiO2 (2) -ordered lacunar perovskite-. As reported in Table 1, all the usual types of oxygen coordination of nickel atoms are considered, from the symmetrical VI octahedral one in LaNiO3 to the II+II distorted square one in LaSrNiO3.1. On to Figure 2 is reported a schematic drawing of the ideal models of the perovskite and perovskite-rocksalt intergrowth structures of LaNiO3, La2NiO4 (Fig.2a) and LaNiO2, LaSrNiO3.1 (Fig.2b), respectively. In the same way, the nearest Ni-Ni and O-O distances are spread over a wide range of values including small one, close to 2.4Å and 2.5Å respectively (Table 1), probably connected with some outstanding property of the chemical bonding.
3.2. Electronic structure of nickel oxides.
The main part of Ni(II) oxides is dielectric with a large forbidden energy gap (4-6 eV). The nature of the valence band structure and the origin of the energy gap are the matter of continuous discussions (31). Recent investigations (5) offer the following picture of the Ni(II) bonding in oxides: the top of the valence band is formed by hybrid 2p O and 3d Ni states, the occupied narrow 3dNi subband lies at approximately 1-2 eV below the Fermi level and the maximum width of the oxygen subband is 3-4 eV separated from the 3d Ni peak. In such results, which are obtained by using various approaches, the main difference regards the value of the splitting between the occupied and virtual i.e. unoccupied 3d Ni subbands. (HF) band theory calculations (24) for NiO predict a splitting close to 25 eV, as (CNDO) calculations in a standard molecular parameterization point to approximately 15 eV (17); in the Local Spin Density Approximation the value of 0.4 eV is obtained (32) and an absence of gap is found in (LDA) calculations (9), although the experimental data is near 7 eV.
The electronic structure of the ternary Ni(II) oxides has never been intensively studied. The introduction of nickel atoms as an "impurity" in MgO decreases the energy gap to 6 eV (5).More generally, the ternary nickel oxides are supposed to be dielectric with a slight increase of the energy gap, in comparison with NiO: this energy gap is formed by 3d Ni-3d Ni or 2p O-3d Ni transitions.
Compounds with a higher oxidation state of Ni, namely (III), are expected to display some metallic bonding. Still, a rather large concentration of defects in these crystals does not allow to obtain reliable information about their electronic structure.
4.1.Band structure of the nickel mixed oxides.
As calculated by the (CNDO) band theory approach, the band properties of the nickel mixed oxides under consideration (total and partial density of states, dispersion curves) were published previously (11,18). It must be noted that in this recent investigation, the intraatomic correlations were included in the computation scheme; as pointed out hereabove, the local properties in their dependence on the valence band structure, are never significantly changed.
For the quantum chemical description of highly oxidized and strongly reduced compounds as well, crystal structures which are used sometimes can be considered as model structures. For example, in the calculation of the oxygen deficient compound LaSrNiO3.1, the structural model corresponding to the limiting formula LaSrNi(I)O3 was used: in such case,there is a full ordering of the oxygen vacancies along the b axis and an ordering of the La and Sr cations.
The series of nickel mixed oxides listed in Table 2, show an extended range of electronic structure properties. LiNi(III)O2, NaNi(III)O2, LaNi(III)O3 and LaNi(I)O2 are found not to have a forbidden energy gap. A metallic property of the Ni-O bonding is known in LaNi(III)O3 (7) and is likely to occur in the Ni(III) containing oxides. In the reduced perovskite like LaNi(I)O2 no information is reported.
Otherwise, all the Ni(II) compounds, BaNi(IV)O3 and the reduced phase LaSrNi(I)O3 have forbidden energy gaps in the range 3-5 eV (Table 2) in rather good agreement with the available experimental data.
In all these nickel mixed oxides, the valence bands are formed by occupied 3d Ni and 2p O states, however, the relative positions of these subbands are different. In the dielectric compounds, the occupied 3d Ni states give a sharp peak of Density Of States, approximately 3-4 eV below the top of the valence band. The oxygen states lie nearly in the same energy region: as one can see from Table 2, the difference between the centers of gravity of the 3d Ni and the broad 2p O subbands, is less than 1-2 eV. In the metallic Ni(III) compounds, the 3d Ni subband is broader, and forms a wide (~10 eV) hybrid with the 2p O states of the valence band.
The bottom of the conduction band in the dielectric compounds is related to unoccupied 3d Ni states. In the lanthanum nickel oxides, there is a partial admixture of the 5d La states, in the bottom of the conduction band. The splitting between the occupied and the vacant d-states of nickel, the so-called Udd Hubbard parameter, depends on the formal nickel valence. For the Ni(II) compounds, the values which are obtained, are close to the value used in the Hubbard model for the description of NiO (7 eV) (31).
Concerning La2NiO4, no significant difference between the electronic structures of the two forms i.e. the tetragonal and orthorhombic R.T. one, is found, except a slight increase of the forbidden energy gap value, 4.5 and 5.0 eV respectively.
4.2 Local properties of the mixed nickel oxides.
The local properties, as calculated from the above described modelling, are reported in Table 3 , in terms of separate data for the nickel and oxygen atoms and also the lanthanum atoms, when considering the lanthanum containing oxides. Are successively presented for each oxide:
-QA the atomic charge i.e. the ionic part of the chemical bonding,
-Ctotal the total covalency as the sum of Chomo and Chetero the homoatomic and heteroatomic contributions i.e. the metal-metal or peroxidic like interactions and the metal-oxygen covalency respectively,
-VA the total atomic valency and VAcorr the same data obtained by considering the only Chetero contribution in eq.(5): the corrected data is supposed to fit the formal oxidation state.
Nickel atoms
QNi, the atomic charge of nickel, increases when the oxidation degree increases and, as a predictable data, QNi deviates the more from the oxidation degree for the formal most oxidized (IV) degree. Ni(II) is the most ionic in NiO, but its ionicity which is not significantly lowered in La2NiO4, is damaged in the two alkaline nickelates Li(Na)2NiO2 - 65 -; Ni(III) is found to be rather ionic -no less than 64 in NaNiO2- and the reduced Ni(I) degree identified in LaNiO2 and LaSrNiO3, is strongly ionic.
As featuring the addition of two independent contributions, the total covalency Ctotal cannot be easily related to QNi. The main contribution to the covalency i.e. the heteroatomic part Chetero is larger as the ionic character of the oxidation degree is lower: in this respect, the smallest and the largest heteroatomic covalencies are observed for the (I) and (IV) degrees, respectively. The homoatomic part of the nickel covalency Chomo which is assumed to originate in Ni-Ni metallic interactions, gets a significant value in three compounds: LiNi(III)O2, LaNi(III)O3 and LaNi(I)O2: this data cannot be immediately connected with the existence of short Ni-Ni distances (Table 1) and even more, the existence of such short distances, as in BaNi(IV)O3, does not result necessarily in Ni-Ni metallic interactions. Hereafter, an analysis of the Wiberg indexes i.e. the covalent bond orders, aims to clarify the problem of the dependence of both Chetero and Chomo on the Ni-O and Ni-Ni distances, respectively.
The atomic valency of nickel VNi does not differ significantly from the oxidation degree, for the usual Ni(II) degree. Otherwise, the general tendency is to get a higher value, except for NaNi(III)O2 and BaNi(IV)O3 which exhibit a rather strong lowering of the nickel valency. Considering VNicorr i.e. not taking into account the Ni-Ni covalency, results in values rather close to the (III) degree -LiNiO2 and LaNiO3- and the (I) degree -LaNiO2-. Finally, the "discrepancy" between the atomic valency and the formal oxidation state of nickel still remains in NaNi(III)O2 and BaNi(IV)O3: one can suppose the (IV) degree of nickel to have no physical meaning, but a similar statement cannot be proposed for the (III) degree. It can be assumed that some "uncertainty" in the structure determinations would result in a corresponding error in the calculations of the local properties: this cannot be precluded for NaNi(III)O2. Still, in both cases, the lowering of the nickel valency in these compounds has to be connected to a similar lowering of the oxygen valency.
Oxygen atoms
The following discussion of the local properties of the oxygen atoms does not take into account the detailed information reported for the different sets of atomic positions in La2NiO4 and LaSrNiO3: this is done further, in a specific discussion of the anisotropy of bonding of the perovskite like nickelates. As a general trend, the local properties of the oxygen atoms (Table 3) do not show a large extent of variation: the atomic charge QO is elevated and points to an ionicity not smaller than 80, except for BaNi(IV)O3 and NaNi(III)O2. The total covalency, when it only depends on the heteroatomic part, is well related to the atomic charge i.e. an increase of Ctotal accompanies a decrease of QO. A supplementary increase of the covalency is due to the homoatomic contribution: this occurs in four cases i.e. the two alkaline nickelates Li(Na)2Ni(II)O2, NaNi(III)O2 and BaNi(IV)O3. Contrarily to the Ni-Ni metallic interactions, the existence of an O-O homoatomic covalency is consistent with a systematic shortening of the dO-O distances -dO-O2.66Å(Table 1)- which results in some extent of peroxidic like bonding.
The atomic valency of oxygen VO is never significantly different from (II), if one takes into account the overall Ctotal covalency. When VO is restricted to the contribution of the heteroatomic covalency, VOcorr calculated in such way, gets the same behavior as VNicorr i.e. there is a "discrepancy" for NaNi(III)O2 and BaNi(IV)O3. This simultaneous lowering of the atomic valencies of the nickel and oxygen atoms is likely to mean that the total number of electrons to be involved in the heteroatomic Ni-O bonding, as predicted by the oxidation state , is not "used". Still, in no ways this unusual characteristic modifies the local properties of Na and Ba atoms, as evidenced by the calculation of their atomic charge, namely 1.01 for Na and 1.99 for Ba.
Lanthanum atoms
The local properties of the lanthanum atoms calculated in the four perovskite like oxides and in La2O3 for comparison (Table 3), evidence a rather elevated atomic charge, QLa, which points to an ionicity larger than 90 , except in LaSrNiO3 where a significant decrease is observed. As a result, the total covalency, which in any case is restricted to the heteroatomic contribution, is low, particularly in the perovskite like oxides and gets an increase only in LaSrNiO3: this is discussed further. Finally, the atomic valency of lanthanum VLa always fits in an excellent way the (III) oxidation degree, in agreement with the usual chemical data concerning this element.
Ni-O covalent bonding: dependence on the interatomic distances
The bond orders of the heterocovalent Ni-O bonding are reported in Table 4, in terms of the corresponding Wiberg indexes WNi-O. From this, a "rough" relationship between the Ni-O bond order and the Ni-O distance is evidenced: the shorter the distance is, the larger the bond order is. A continuous dependence cannot be observed, as the overall covalency of the Ni-O bond originates first in the kind of mixed oxide under consideration. Combining chemistry and structure allows a more relevant analysis of such a dependence. Thus, in any example of a distorted oxygen coordination of nickel, the decrease of the bond order is consistent with the increase of the Ni-O distance i.e. for the tetragonally elongated (NiO6) octahedra, for example, the covalent bond order of the apical bonds is smaller than that of the equatorial one (NaNiO2 and La2NiO4). Such a property is enhanced when considering a strong covalent Ni-O bonding, as in BaNiO3: the trigonal distortion of the octahedra results in a cooperative increase and decrease of the bond order: the very short Ni-O distances -1.74Å- are ten times more covalent than the long one -2.06Å-. This is likely to be the basis of the building of the (NiO3) chains of the so-called hexagonal compact two layers structure of BaNiO3. When considering a weak covalent Ni-O bonding as in LaNiO2 and LaSrNiO3, the dependence between the bond orders on the Ni-O distance occurs in a rather small extent and consequently is not easily informative. More generally, it must be emphasized that the systematic decrease of the covalent bond order for the larger interatomic Ni-O distances or for the lower oxidation state -Ni(I)-, gives evidence of the insulating property of such Ni-O bonds.
The comparison of the electronic structure in the tetragonal, orthorhombic and low temperature tetragonal structures of La2NiO4 shows slightly different changes of the Ni-O bonding. It is contradictory to the related cuprate La2CuO4 in which a strong redistribution of the electronic density under the tetragonal-orthorhombic transition, was found (11).
Metallic property of the Ni-Ni bonding: evidence of long range non-zero interactions
The knowledge of the dependence of the Wiberg indexes WNi-Ni on the Ni-Ni distances is assumed to be informative: a non-monotonic decrease of the homoatomic covalent bond orders and above all the existence of long range non-zero values of WNi-Ni will give evidence of a metallic property. Table 5 reports the values of WNi-Ni for the three compounds which show a significant homoatomic nickel covalency (Table 3), namely LiNi(III)O2, LaNi(III)O3 and LaNi(I)O2. The dependence on the Ni-Ni distances is analyzed in the following:
LiNi(III)O2: the largest value of WNi-Ni is observed at 5.75Å i.e. twice the shortest Ni-Ni distance and a progressive vanishing occurs for longer distances. If one takes into account the structural description of LiNiO2 in terms of a rocksalt like structure with a 1/1 ordering of the Li and Ni metals along the stacking direction, these data are meaningful: the significant maxima of WNi-Ni , including that one corresponding to the second neighbours give evidence of Ni-Ni interactions only in the "Ni planes" of the compact structure. Between two nearest "Ni planes" -5.013Å(Table 5)- i.e. across a "Li plane" because of the Ni/Li/Ni ordering, there is nearly no interaction. Under these conditions, the metallic property of the Ni-Ni bonding in LiNiO2 is a true 2D property.
LaNi(III)O3 and LaNi(I)O2: as expected on the basis of their same structural model, the perovskite one, these two compounds exhibit significant similarities in the dependence of their Ni-Ni bond orders. The largest values of WNi-Ni are observed for the first neighbours i.e. the Ni-O-Ni distances between two vertex sharing octahedra in LaNiO3 and between two vertex sharing squares in LaNiO2 (Figure 2). The main difference between LaNiO2 and LaNiO3 which is related to the systematic absence of the apical oxygen atoms in the "La" planes (Figure 2), concerns the decrease of the Ni-Ni distance -3.376Å- along the c axis of the unit cell of LaNiO2. Still, the bond order of the corresponding Ni-Ni bonding is not elevated: this is not so surprising, as such value of the Ni-Ni distance is too large to give a significant "direct" metal-metal bonding. The role of the long range Ni-Ni interactions in the equatorial planes in both cases, is confirmed by the values of WNi-Ni at double distance i.e. the Ni-O-Ni-O-Ni distances; as regards the "diagonal" Ni-Ni bonding i.e. the "ap2".distance in the equatorial planes, the bond order shows a secondary maximum in LaNiO3 and a nearly zero value in LaNiO2. This means that, once more in LaNiO2, any significant "direct" metal-metal bonding seems to be precluded. To summarize, the metallic property of the Ni-Ni bonding originates in the same basic structural picture, namely the equatorial planes: in LaNiO3, this is a 3D property, but in LaNiO2, owing to the absence of the apical oxygen atoms, the Ni-Ni interaction is rather weak and consequently, this is a 2D property.
4.3 Anisotropy of bonding in the oxidized and reduced perovskite like nickelates
The local properties calculated in the perovskite like nickelates can be used to appreciate the modifications of the Ni-O bonding, namely the occurrence of some axial anisotropy when going from the perovskite type to the perovskite-rocksalt intergrowth. Moreover, the dependence of this effect on the Ni oxidation state is tentatively studied on the basis of the data obtained for the oxidized series LaNiO3-La2NiO4 and the reduced one LaNiO2-LaSrNiO3.
The Ni-O bonding in La2NiO4 (tetragonal or orthorhombic form), as compared to the Ni-O bonding in LaNiO3, shows an axial anisotropy originating in the geometrical constraint due to matching a perovskite layer and a rocksalt one (33, 34): a significant decrease of the Ni-O apical covalent bond order is observed, as the Ni-O equatorial covalent bond order is slightly changed (Table 4). As usually reported in the studies of both the electron transport properties and the magnetic properties of LaNiO3 and La2NiO4 (35, 36), the dz2 level is empty in Ni(III) -LaNiO3- and half occupied in Ni(II) -La2NiO4-, as the dx2-y2 one is half occupied in both cases. This is consistent with this modelling of the covalency of the Ni-O bonding, in terms of an only decrease of the Ni-O apical bond order.
The covalency of the Ni-O bonding in the reduced nickelates LaNiO2 and LaSrNiO3 is weak. More precisely, it is the same in the four square planar Ni-O bonds of LaNiO2 and in the two remaining equatorial Ni-O bonds of LaSrNiO3 (Figure 2 and Table 4). The two apical Ni-O bonds which achieve the distorted square planar oxygen coordination of Ni in LaSrNiO3, on the basis of our calculations, show a different covalent bond order, depending on the kind of Ni-Oap-A bridge bond i.e. A=La or A=Sr: the Ni-O apical covalent bond order for A=La is unchanged with respect to the equatorial one and the Ni-O apical covalent bond order for A=Sr is further decreased (Table 4). This is easily understandable when considering the increase of ionicity of the Sr-O bonding, as compared to the La-O one. One has to emphasize that the four Ni-O bonds in LaSrNiO3 for the local situation A=La, show an isotropic covalency which is the same that in LaNiO2.
From these data, the anisotropy of the Ni-O bonding is better understood in terms of a local analysis of the mutual dependence of the various metal-oxygen bonds which are related to an oxygen atom of the structure under consideration. When the oxygen atom gets as first neighbors only nickel atoms, namely for LaNiO3 and the equatorial plane of the perovskite layer in La2NiO4 or for LaNiO2 and the two remaining equatorial Ni-O bonds of LaSrNiO3 respectively, the Ni-O covalent bond order is not changed and its value is fixed by the choice of the kind of oxidation degree of the nickel atoms i.e. oxidized or reduced. When the oxygen atom is simultaneously bonded to the nickel and A atoms, as for the apical oxygen of La2NiO4 and LaSrNiO3, the Ni-O apical covalent bond order is strongly dependent on the A-O apical one i.e. the nature of A and the value of the A-Oap distance which result in the own covalency of the A-Oap bond. In such case, the value of the covalency of the Ni-Oap bond is not fixed by the oxidational state of nickel but by the proper choice of the Ni-Oap-A bridge bond under consideration. In this respect, the comparison of the Ni-Oap-La bridge bond in La2NiO4 and LaSrNiO3 is rather instructive: despite the lower value of the heterocovalency of the nickel atom in LaSrNiO3 as compared to La2NiO4 ( Table 3), the Ni-O apical covalent bond order is larger in LaSrNiO3. The reason of such phenomenon is likely to be found in the covalency of both the apical oxygen and lanthanum atoms which is larger in LaSrNiO3 than in La2NiO4 (Table 3) . More generally, the modification in the anisotropy of the Ni-O bonding cannot be systematically deduced from the "rough" view based on the evolution of the dimensionality , when going from the 3D property of the perovskite structure to the 2D property of the perovskite-rocksalt intergrowth. From these results, the main contribution of the oxidation degree of the nickel atoms is evidenced in terms of a decrease of the anisotropic property of the perovskite-rocksalt intergrowth for the reduced nickelates.
Conclusion
As it results from electronic structure calculations, the increase of the formal oxidation state of the nickel atom in its oxide compounds, leads to increase both its atomic charge and its covalency. The nickel atom in Ni(I) compound forms essentially ionic bonds with oxygen, with a very small covalent contribution. In the more stable Ni(II) state, an intermediate character of the bonding with a main ionic contribution is found. In the Ni(III) compounds, a further increase of the atomic charge takes place, and the ionicity degree of the Ni-O bonding is less than in compounds with lower oxidation states of nickel. In some nickelates (LaNiO2 and all considered Ni(III) oxides) the metallic bonding is due to long range interactions between nickel atoms.
On the basis of these results, the current work aims to learn more about a comparison on Ni-O and Cu-O bonding, mainly in the perovskite like compounds. In this respect, the solid solutions La2(Ni1-xCux)O6-y - the oxidized and the reduced one- seem to be of relevant importance.
Acknowledgment This work is partly supported by the Russian Fundamental Research Foundation, grant 96-03-33991a
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Table 1. Crystal data of the nickel mixed oxides. (Only the nearest Ni-O, Ni-Ni and O-O distances (Å) are reported)
Compound Space group dNiO dNiNi dOO Ref.
Ni(II)O R-m (Fm3m)† 6*2.083 2.945 2.945
Li2Ni(II)O2 Immm 4*1.903 2.779 2.599 (28)
Na2Ni(II)O2 Cmc21 2*1.889 2.820 2.532 (28)
2*1.900
LiNi(III)O2 R-m 6*2.038 2.876 2.876 (25)
NaNi(III)O2 C2/m 4*1.951 2.860 2.656 (25)
2*2.167
BaNi(IV)O3 P63mc 3*1.744 2.404 2.534 (29)
3*2.063
LaNi(III)O3 R-c 6*1.933 3.832 2.704 (30)
LaNi(I)O2 P4/mmm 4*1.983 3.376 2.804 (2)
La2Ni(II)O4 I4/mmm 4*1.934 3.869 2.736 (26)
tetr. 2*2.243
La2Ni(II)O4 Cmca 4*1.948 3.890 2.734 (27)
orth. 2*2.240
LaSrNi(I)O3.1 Immm 2*1.926 3.566 2.810 (4)
2*2.046
†
- NiO undergoes a small rhombohedral distortion with a lattice angle equal to
60deg.12'Table 2 Band structure of nickel oxides (eV).
Ep-d- difference between centers of gravity of 3dNi and 2pO subbands.
Udd- Hubbard parameter for nickel atom,
Eg- forbidden energy gap: calculated and experimental values
Ep-d Udd Egcalc Egexp
Ni(II)O -1.6 6.6 4.4 4.3
Li2Ni(II)O2 -0.1 7.5 3.8 ~5
Na2Ni(II)O2 -0.5 7.9 4.3 ~5
LiNi(III)O2 1.0 11.5 0 metal
NaNi(III)O2 2.2 15.1 0 -------
BaNi(IV)O3 -1.0 6.5 4.8 -------
LaNi(III)O3 -0.3 11.2 0 metal
LaNi(I)O2 -4.2 9.5 0 -------
La2Ni(II)O4 -t -0.8 7.0 4.5 4
La2Ni(II)O4 -o -1.2 7.1 5.0 -------
LaSrNi(I)O3 -2.1 8.4 3.0 -------
Table 3 Local properties of the electronic structure in nickel mixed oxides.
Ni QNi Ctotal Chomo Chetero VNi VNicorr
Ni(II)O 1.77 0.44 0.02 0.42 2.00 2.00
Li2Ni(II)O2 1.20 1.07 0.01 1.06 1.85 1.85
Na2Ni(II)O2 1.37 0.94 0.00 0.94 1.92 1.92
LiNi(III)O2 2.57 1.92 1.15 0.76 3.70 2.98
NaNi(III)O2 1.91 0.65 0.02 0.62 2.27 2.25
BaNi(IV)O3 1.58 2.12 0.02 2.10 2.96 2.95
LaNi(III)O3 2.39 1.95 0.96 1.00 3.59 2.94
LaNi(I)O2 0.95 1.02 0.82 0.20 1.62 1.05
La2Ni(II)O4 -t 1.69 0.57 0.02 0.55 2.00 1.99
La2Ni(II)O4 -o 1.69 0.56 0.02 0.55 2.00 1.99
LaSrNi(I)O3 0.96 0.16 0.00 0.16 1.05 1.05
O QO Ctotal Chomo Chetero VO VOcorr
Ni(II)O -1.77 0.44 0.02 0.42 2.00 1.99
Li2Ni(II)O2 -1.56 0.79 0.19 0.60 2.00 1.89
Na2Ni(II)O2 -1.66 0.63 0.12 0.52 2.00 1.94
LiNi(III)O2 -1.78 0.42 0.04 0.38 2.00 1.99
NaNi(III)O2 -1.46 0.91 0.59 0.31 1.99 1.62
BaNi(IV)O3 -1.19 1.08 0.38 0.70 1.85 1.59
LaNi(III)O3 -1.75 0.45 0.04 0.41 1.99 1.97
LaNi(I)O2 -1.88 0.23 0.00 0.23 2.00 2.00
La2Ni(II)O4-t -1.78 0.42 0.02 0.40 2.00 1.99
i
-1.85 0.29 0.01 0.29 2.00 2.00
ii
La2Ni(II)O4-o i -1.77 0.43 0.02 0.41 2.00 1.99
-1.85 0.29 0.00 0.29 2.00 2.00
ii
LaSrNi(I)O3 -1.79 0.40 0.02 0.38 2.00 2.00
i
-1.83 0.33 0.01 0.32 2.00 2.00
ii'
-1.67 0.61 0.02 0.60 2.00 2.00
ii''
La QLa Ctotal Chomo Chetero VLa VLacorr
La2O3 2.73 0.53 0.01 0.52 3.01 3.00
LaNi(III)O3 2.87 0.25 0.00 0.25 3.00 3.00
LaNi(I)O2 2.81 0.37 0.04 0.32 3.00 2.98
La2Ni(II)O4-t 2.77 0.44 0.00 0.43 3.00 3.00
LaSrNi(I)O3 2.35 1.20 0.01 1.18 3.03 3.02
i.equatorial oxygen ii apical oxygen (')bonded to Sr, ('')
bonded to La Table 4 Wiberg indexes in insulator and metallic nickel oxides
dNi-O WNi-O dNi-Ni WNi-Ni
Ni(II)O 2.083 0.066 2.945 0.001
Li2Ni(II)O2 1.903 0.258 2.779 0.001
Na2Ni(II)O2 1.889 0.234 2.820 0.001
1.900 0.228
LiNi(III)O2 2.038 0.190 Table 5 Table 5
NaNi(III)O2 1.951 0.103 2.860 0.001
2.167 0.060
BaNi(IV)O3 1.744 0.629 2.404 0.004
LaNi(III)O3 1.933 0.150 Table 5 Table 5
LaNi(I)O2 1.983 0.033 Table 5 Table 5
La2Ni(II)O4-t 1.934 0.121 3.869 0.005
i
2.243 0.022
ii
La2Ni(II)O4-o i 1.948 0.121 3.890 0.005
2.240 0.019
ii
LaSrNi(I)O3 i 1.926 0.031 3.566 0.000
2.046 0.019
ii'
2.046 0.019
ii''
2.063 0.061
i equatorial oxygen; ii apical oxygen, (') bonded to Sr, ('').bonded to
La.Table 5 Ni-Ni Wiberg indexes in LiNi(III)O2, LaNi(III)O3 and LaNi(I)O2: dependence on the Ni-Ni distance(Å)
LiNi(III)O2 LaNi(III)O3 LaNi(I)O2
dNi-Ni WNiNi dNi-Ni WNiNi dNi-Ni WNiNi
2.876 0.041 3.832 0.071 3.376 0.032
4.981 0.020 5.384 0.012 3.966 0.119
5.013 0.002 5.454 0.016 5.208 0.000
5.751 0.165 6.551 0.003 5.609 0.003
5.780 0.011 6.665 0.004 6.546 0.004
6.456 0.008 7.664 0.023 6.752 0.000
7.630 0.002 7.932 0.023
8.154 0.008 8.621 0.003
8.778 0.003
8.868 0.014
10.417 0.022
11.217 0.001
11.714 0.031