The electronic structure of crystalline nickel oxides

Journal ofElectronSpectroscopy and Related Phenomena, 68 (1994) 5X-563 036%2048/94/$07.00 @ 1994 - Elsevier Science B.V. All rights reserved

The electronic structure of crystalline nickel oxides R.A. Evarestov, V.A. Veryazov, 1.1.Tupitsyn and V.V. A&nasiev Department of Quantum Chemistry, Chemical Institute, St.-Petersburg University, University pr. 2, St.-Petersburg 198904, Russia The electronic structure of eleven crystalline nickel oxides was investigated by band theory CNDO method. Both the band and local properties of the electronic structure were calculated and were used for the description of chemical bonding in Ni@) (NiO, Li2Ni02, Na2Ni02, K2Ni02, BaNi02, La2Ni04), Ni(III) (LiNi02, NaNiO2, LaNiO3) and Ni(IV) (BaNiO3) compounds.

l.Introduction The electronic structure of crystalline nickel oxides has been intensively studied by both theoretical and experimental treatments. As an example, simple nickel oxide - NiO is famous for the discrepancy between the band theory results and experimental descriptions of its dielectric properties. The discovery of high-temperature superconductivity has investigations of stimulated the lanthanum-nickel oxides, which are lanthanum-copper isomorphous to oxides. The electronic structure of other nickel oxides, especially with nickel in high oxidation state, is practically UlhOWIl.

In the present work, we calculated the electronic structure of eleven nickel oxides (with formal oxidation states of Ni atom - II, III and IV) within the band theory- CNDO (complete neglect of the differential overlap) approximation. We investigated not only the band structure properties (dispersion curves, total and partial densities of states, band widths and positions), but the chemical bonding (atomic charges, covalent bond orders, atomic valences) in these componnds. The crystal structures of ternary

SSDIO368-2048(94)02118-J

nickel oxides depend on the nature of additional atom (these data are summarized in Table 1). In its oxide compounds, the Ni(lI) atom has very different surroundings of oxygen atoms: octahedral (NiO, La2NiO4), square (Li2Ni02, BaNi02) or linear (K2Ni02) co-ordination (See Table 1). Thus, one can expect different electronic structure properties in the range of Ni(I1) oxides. However, the electronic structure has been studied only for NiO and La2Ni04 Different experimental Crystals. investigations show, that both NiO and La2NiO4 crystals are wide-gap semiconductors (with energy gap 4.3 [l] and 4 eV [2], respectively). The valence band in NiO crystal is formed by a narrow 3dNi subband and a wide 2p0 subband. The latter lies -2 eV below 3dNi peak [3]. The top of the valence band is formed by hybridized 2p0 and 3dNi states [4]. XPS measurements show, that the deep 2~0 states lie m 16 eV below 2p0 states and the width of upper valence band equals to 6-7 eV [3]. The bottom of conduction band is formed by 4sNi and non-occupied 3dNi states

[51. A lot of calculations of the electronic

555

Cmc2 1

w/mmln

Cmcm

Na2NiO2

K2NiO2

BaNi

C2/m

R?c

P63mc

JAG03

BaNi

5.631

8.285

9.026

4.808

5.59

5.535

12.664

4.755

12.838

01=60.9~

2.86

5.33 p=llo.Y

5.384

a=33.3O

12.547

9.19

10.141

2.779

a=60.2”

5.013

5.468

Cmca

RFrn

3.869

5.735

3.953

14/mmm

NaNiO2

LiNi02

Olth.

La2NiO4

La2NiO4 tetr.

3.843

Immm

Li2NiO2

2.820

2.946

lattice parameters , A a b C

R?-m

group

Space

NiO

Compound

K

(2a) 0 0 0.275

(6b) 0 0 0

(2a) 0 0 0

(3a) 0 0 0

(4a) 0 0 0

(2a) 0 0 0

(4a) 0 0 0

(2a) 0 0 0

(4a) 0 0.122 0

(2b) 0 x

(3a) 0 0 0

Ni

0 0.293

Me

(2b) g

g

(6a) 0 0 x

(2d) 0 x

(3b) 0 0 x g

0.25

(80 0 0.364 0.011

(4e) 0 0 0.372

(4c) 0 0.345 x

(4e) 0 0 0.657

(4a) 0 0.148 0.669 (4a) 0 0,394 0.847

(4j) x

Table 1. The crystal structure of the nickel oxide compounds. (L - number of bonds Ni-0)

x

0

0.008 s

(6~) 0.15 0.85 0.275

(18e) 0.547 0 &

(4i) 0.278 0 0.795

(6~) 0 0 %

(80 0 0.178 0.961

(8e) x

(4e) 0 0 0.177

(4c) 0 x

(8g) 0.25 0.08 j$

(4e) 0 0 0.869

(4a) 0 0.480 0.590 (4a) 0 0.280 0.408

(4i) 0 0 0.345

(3b) 0 0

0

6

6

6

L

1.95 2.17

2.04

1.95 2.24

1.93 2.24

2.00

1.69

1.89 1.90

1.90

2.09

%o

stru&ne of NiO crystal have been made (within LDA (local spin density approximation) [6], SIC-LSDA (selfinteraction corm&d local spin density approximation) [7], and HF (HartreeFock) [S] approximations). However, there is no calculation, which satisfactory describes all experimental facts. Nonspin polarized LDA [6] calculation of NiO crystal predicts the metallic bonding; including spin polarization [9] in the computation scheme leads to the formating of a very small energy gap between occupied and non-occupied 3dNi states. On the contrary, it was found in HF [S] calculation of NiO, that the top of the valence band is formed by 2p0 states, however, the relative position of 3dNi and 2pO subbands is contradicting to experimental density of states. There are only sparse studies of compounds with high oxidation states of Ni - (III) and (IV). It is known, that Ni(III) compounds are metals [lo]. However, even crystal structure investigations only give approximate results, because of the instability and possible oxygen nonstoichiometry in these compounds. 2. Band theory - CNDO calculation of the electronic structutre The complicated crystal structure of nickel oxides does not allow us to use the rigorous first-principle techniques for the calculation of their electronic structure. We used a semiempirical approximation, based on the Hartree-Fock method Within the CNDO. CNDO approximation most integrals containing atomic functions are either neglected or are approximated [l I]. Contrary to using local methods density approximation, in the CNDO method as

well as in HF, the crystalline potential includes nonlocal exchange and depends on the occupancy of an orbital. The latter is necessaryfor the correct description of the electronic structure of compounds with partially occupied d-states of transition metals [12]. Band theory- CNDO technique is described in detail in [ 131. The selfconsistent crystalline potential is obtained on the basis of Bloch sums of the atomic functions. In our calculation we used as a basis the valence shell double< function for neutral atoms (2p and 2s for oxygen, 3d and 4s for nickel, 6s and 5d for lanthanum, NS for alkali metals) [14]. The Hartree-Fock matrix elements in CNDO approximation depend on the set of atomic parameters. The semiempirical parameters for oxygen, lanthauum, barium and alkali metals were taken from our previous calculations [15, 161.Optimal values of nickel Coulomb integral - yNiNi=17eV and bonding parameters - p,= -5eV and gd= -10 eV - were calibrated to reproduce the main features of the experimental electronic structure of NiO crystal No additional variation of the potential was made during the investigation of Ni (II), (III) and (IV) oxides. In the self-consistent calculation for all crystals, with the exception of metallic Ni(II1)oxides, we used the set of 64 points in the Brillouin zone (ElZ), obtained by the LUC (large unit cell) method [171.We studied the dependence of the results of our calculations on the chosen set of BZ points, and found that this set reproducesthe main properties of electronic structure in the dielectric compounds. In the case of metallic

558

I I

3dNi

4

I I

w

n

, -20

. -10

9

3dNi

2PO

I I

I I

0

A.

1. h\

,

A &I

,

-10

0

-10

0

IOeV

-20

-10

0

-io b

3dNi

-20

-10

0

1OeV

Fig. 1. Total and pa.rtial3dNi and 2pO density of states in nickel oxides. a)-NiO, b)-LizNiC$, c)-NazNiOz, d)-KzNi02, e)lBaNiOz, f)-La2Ni04.C ,g)-L~~i04-0 h)-LiNi02,, i}-NaNi02, j)-LaNiaj

, k)-BaNi%

559

bonding, the integration over the BZ needs a more extended set of points. For metals with low density of states at the Fermi level (LiNiO2, NaNi and LaNiO3) we used a set of 216 points in the BZ. The main properties of the band structure of the nickel oxides are summarized in Table 2. Total and partial density of states in the crystals under consideration were calculated by interpolating scheme in-4096 points in BZ (See Fig.1). In our calculation of the electronic structure of the NiO crystal we used the RFm crystal structure with a small rhombohedraI distortion of the rock-salt cubic structure (See Table 1). As it was shown in [12], using this distortion allows one to eliminate symmetry restrictions and to obtain the dielectric gap in a non spin polarized calculationof NiO. As it is seen from Table 2 that the electronic structure of simple nickel oxide differs from that of ternary nickel (II) compounds. For the NiO crystal the centre of gravity of occupied 3dNi subband lies - 1 eV above the centre of gravity of the wide 2pO subband.The top of the valence band is formed by hybridized 3dNi and 2pO states, which confirms the conclusion [4] about the charge-transfercharacter of the dielectric gap in NiO. Indirect gap L+T equals 4.3 eV, and direct gap on the lYpoint equals 5.4 eV. The width of the upper valence band 6.6 eV correlates with photoemission data [3]. It was found in our calculation, that the bottom of the conduction band in NiO is formed by wide 4sNi,3dNi band. The centre of gravity of non-occupied 3dNi subband

lies -10 eV above the bottom of the conductionband. The value of this large splitting of 3dNi states is close to the value of the one-centreCoulombintegral yNiNi.We expect,that taking into account correlation effects on the nickel atom decreases the value of this unrealistic splitting, which was obtained both in CNDO and HF [8] calculations. However,we suppose, that including in the computation scheme the correlation effectson atomic-likenarrow nickel band mainly changes conduction, but not the valenceband. A correct descriptionof the latter is necessary to investigate the chemicalbonding in a crystal. As one can see from Table 2, alkalior alkali earth- nickel (II) oxides are typically charge transfer dielectrics with large energy gap. This result correlates with the estimation of the optical energy gap in the system Ni$lgl_,O (-6 eV) [4]. In lanthanum nickel (II) oxide, 3dNi and 21x0states lie approximately in the same energy region. We reproduce the experimentalenergy gap [2] in La2NiO4 crystal (it was found, that the indirect gap X-I’ equals 3.5 eV, and the direct gap 4.4 ev). The top of the valence band in La2Ni04 is fomxd by hybridized 3dNi and 2pO states. The difference in electronic structure properties between

tetragonal and orthorhombic phases of La2Ni04 is rather small, however, the latter has a forbidden energy gap of 3.9 eV. It was found in the CNDO calculation, that nickel (III) oxides are metals with low density of states on the Fermi level. As one can see from Fig.1, lanthanum nickel (III) oxide has a low density of states on the Fermi level. Inter band gap lies near low, partially occupied subbands, thus, the presence of crystal

560

structure defects (for example, oxygen non stoichiometry) may decrease the position of the Fermi level and change dielectric-metallic properties in this compound. As was found in CNDOcalculation in the only known nickel (IV) oxide BaNiO3,the 3dNi subband lies below the 2p0 subband,and a large energy gap is formed by the 2p0 and the non-occupied 3dNi states.

3. Chemical bonding in nickel oxides In the theol-y-C~O band approximation one can obtain selfconsistent density matrix elements on the basis of the atomic functions [131.Using the atomic basis allows to calculate the local properties of the electronic structure and to investigate the nature of chemical bonding in a crystal. The atomic charge on an atom can be found in LJiwdin population analysis [18]:

dependson the density matrix elements from the atomic block A-B and usually is associated with amount of electron pairs localized on the bondA-B.

(2) a&4 bcB

Covalency of an atom in a crystal is usually defined as a sum of the bond orders WABover all atoms B in a crystal rw.

CF = CWAB

We propose to divide this sum into two parts.

cy = Cw”‘Af A'#A

(1) where Z, is the core charge, a- the orbital of atom A, and P,, - the density matrix elements. As it was found in our CNDO calculation, the ionic&y of Ni(II) oxides is high, with Ni atomic charge 1.8 -1.9 e, which correlates with the results of HF calculation [S] and positron-annihilation measurement [19]. Increasing the formal oxidation state of nickel atom from Ni(II) to Ni(IV) leads to a very small increase of the nickel atomic charge from 1.8 to 2.4 e. The covalent bond order (Wiberg index [20]) between atoms A and B

(3)

A#B

CWBA B#A.A’

=MA+CA The first one contains the summation WAA,over the crystal , where atom A’ has the same chemicalnature as A, and the second part contains the remaining items. The former sum contains covalent interaction between atoms of the same elements and thus, may be called as metallic bonding M. We found that in the case of dielectric compound, this contribution is negligible small (less than O.Ole). But this contribution is the only one in the sum (4) for ordinary metal! We investigated the “composition” of covalency in nickel (III) metallic

561

Table 2. Centers of gravity of 2sO,2pO, 3dNi (occupied and filled) subbauds, width of upper valence band AEv , Fermi level I+, forbidden energy gap AEg and contribution of 3dNi states into the top of the valence baud.

Compound

2sO

2po

3dNi

3dNi

AEv

Ef

3dNi

cLEg

% NiO

-27.3

-10.4

-9.2

7.9

6.6

-7.1

4.3

45

Li2NiO2

-23:4

-6.5

-7.6

9.3

4.7

-4.7

9.0

d

Na2NiO2

-23.7

-6.5

-7.0

9.9

4.2

-5.0

8.0

d

K2NiO2

-23.7

-6.4

-9.6

7.2

4.4

-5.6

4.7

d

BaNi

-23.1

-5.9

-10.0

6.9

6.6

-4.0

6.0

d

La2NiO4 tetr

-24.4

-7.1

-7.1

9.9

7.1

-4.3

3.5

40

La2NiO4 orth

-24.6

-7.2

-6.7

10.3

5.8

-5.2

3.9

35

LiNi02

-26.6

-9.2

-11.4

-0.2

6.3

-2.9

0

80

NaNi

-26.8

-9.5

-10.7

4.8

3.8

-4.1

0

30

LaNiO3

-26.0

-8.6

-9.3

2.4

6.5

-0.6

0

90

BaNiOg

-27.3

-9.8

-12.5

1.6

6.5

-7.6

8.9

10

Table 3. “Metal correction” of nickel covalency and valency. M - metal-to-metal interaction, Ctot - total nickel covalency, C “corrected” non metal covalency V*- atomic valency, calculated with Ctot, V - non metallic valency (calculated with C)

Comoound

M

ctot

C

Vb

V

LiNiO2

0.88

2.22

1.34

3.54

2.94

NaNiO2

0.12

0.92

0.80

2.63

2.57

LaNiO3

0.93

2.13

1.20

3.63

3.01

562

compounds, and found, that the metallic contributions for lithium, sodium and oxygen atoms do not exceed 0.02e. The metallic contribution into covalence for the nickel atom in LiNi02, NaNiO2 and LaNiO3 crystals are shown in Table 3. The values of metal-to-metal interaction in these compounds are close to the metal-oxygeninteraction! In [22] the quantum chemical definition of the atomic valency VA was introduced. The value of the atomic valency corresponds to the total number of electrons, which take part in the forming of the chemical bonding (both covalent and ionic). The numerical values of the atomic valency in the wide row of molecules and crystals correlate well with the “classical chemical sense”

WI. V’ = ;(C,

+ (C; + 4Q9)

(5)

lf we use in this definition of the covalency Cfot (3), we obtain unrealistic results for the nickel vslency V* in metallic compounds (See Table 3). If we and metallic separate covalent contributions according to (4), and use in definition (5) only the former, we obtain more realistic results for the atomic valency V of nickel atom (See Table 3). It must be noted, that such “correction” for other atoms is negligibly small. Using the definition (l-5) we can divide all electrons from the valence shell of an atom into three parts: metallic (M), covalent (C) and ionic (Q). Two latter form “normal”atomic valency. 4. Conclusion The simple computational scheme, based on the semiempirical approximation of

the HF approach,- CNDO, allows one to reproduce the main properties of the electronic structure of nickel oxides. Calculated density of states and energy gap values correlate well with known experimental data. The elaborate investigation of the chemical bonding in Ni(II), Ni(III) and Ni(IV) oxides was made, especially in the case of metallic bonding. Acknowledgement We thauk Prof. J.Choisnet ( Centre de Recherche sur la Matiere Divisee, CNRS - Universite d’Orleans) for helpful discussions. One of us (V.A.V.) thanks Universite d’orleans for individual support. This work is supported by the Russian Fund of the Fundamental Research.

References 1. G.A. Sawatzky and J.W. Allen, Phys. Rev. Lett. 53 (1984) 2339. 2. H. Eisaki, S. Uchida, T. Mizokawa, H. Namatame, A. Fujimori, J. van Elp, P. Kuiper, G.A. Sawatzky, S Hosoya and H. Katayama-Yoshida,Phys. Rev. B45 (1992) 12513. 3. DE. Eastman and J.L. Freeouf, Phys. Rev. B34 (1975) 395. 4. S. Hufner Z. Phys. B 86 (1992) 207. 5. SHufner and GKWertheim Phys. Rev. B 8 (1973)4857. 6. L-F. Mattheiss, Phys. Rev. B5 (1972) 290. 7. A. Svane and O.Gunuarsson Phys. Rev. Letters 65 (1990) 1148. 8. W.C. Mackrodt, N.M. Harrison, V.R. Saunders, N-L. Allan, H.D. Towler, E. Apra, R.Dovesi Preprint Daresbury lab. N DL/SCI/P85IT

563

9.

10.

11.

12.

13.

14.

15.

(1992) Terakura, T. Ognchi, A.R Williams and JKubler, Phys. Rev. B30,4734 (1984). K. Sreedhar, J.M. Honig, M. Darvin, M. McElfresh, P.M. Shand, J.Xu, B.C. Crooker, J. Spalek Phys. Rev B 46 (1992) 6382 J.A. Pople and D.LBeveridge Approximate Molecular Orbital Theory, McGraw-Hill Publ. Co, New York 1970. J. Choisnet, R.A. Evarestov, 1.1. Tupitsin, V.A. Veryazov, Physica Status Solidi (to be published). R.A. Evarestov and V.A. Veryazov, Rev. Solid State Science 5 (1991) 415. E.Clementi and C.Ro&ti Atomic Data and Nuclear Data Table 14 (1974) 197. McLean and R.C. McLean, Atomic Data and Nuclear Data Table 26 (1981) 328. R.A. Evarestov and V.A. Veryazov, Phys. Status Solidi (b) 157 (1990) 281, (b) 158 (1990) 201 . K.

16. R.A. Evarestov, A.V. Leko, 1-V. Murin, A.V. Petrov and V.A. Veryazov, Phys. Status Solidi (b) 170 (1992) 145 17. RA. Evarestov and V.P.Smimov Phys. Status Solidi (b) 119 (1983) 9. 18. P. Lowdin Adv. Quantum Chem. 5 (1970) 185. 19. A.L.Wachs, P.E.A. Turchi, RH. Howell, Y.C. Jean, M.J. Fluss, J.H. Kaiser, R.N. West, K.L. Merkle and A. Revcolevschi Phys. Rev. B 40 (1989) 1. 20. K.B. Wibcrg,Tetrahedron 24 (1%8) 1083. 21. D.R. Armstrong, P.G. Perkins and J.J.P. Stewart, J. Chem, Sot. Dalton Trans., (1973) 838. 22. RA. Evarestov and V.A. Veryazov, Theor. Chim. Acta 81(1991) 95.