Band-structure description of Mott insulators (NiO, MnO, FeO, CoO)

Band-structure description of Mott insulators (NiO, MnO, FeO, CoO)

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J. Phys.: Condens. Matter 2 (1990) 3973-3987. Printed in the UK Band-structure description of Mott insulators (NiO, MnO, FeO, COO) V I Anisimov, M A Korotin and E Z Kurmaev Institute of Metal Physics, Academy of Sciences of the USSR, Ural Division, Sverdlovsk GSP-170, USSR Received 28 June 1989, in final form 12 October 1989 Abstract. The unoccupied-states potential correction (USPC) in the local spin-density-func- tional (LSDF) formalism is proposed as a way to take correlation effects into account approxi- mately. The method is based on using different potentials for the electrons in valence and conduction bands. When applied to antiferromagnetic transition-metal oxides (NiO, MnO, FeO, COO), it solved the long-standing problem of reproducing the experimental values of the band gaps, which are underestimated in normal Lswcalculations. Fe0 and COO become insulators, in contrast to the metallic ground state obtained in the usual LSDF calculations. Moreover, the calculated magnetic properties improved considerably due to introduction of the USPC. It is shown that band-structure calculations using the USPC provide a correct description of available data from spectral measurements (ultraviolet photoelectron spectro- scopy, x-ray photoelectron spectroscopy, bremsstrahlung isochromate spectroscopy) for these compounds. 1. Introduction Among the 3d-metal monoxides with the NaCl crystal structure, the compounds with metallic conductivity (TiO, VO) are easily distinguished from those with insulating properties and antiferromagnetic ordering (NiO, MnO, FeO, COO). The latter are most interesting for solid-state theory in connection with the problem of the description of their electron structure and electronic and magnetic properties. It is expected that oxygen 2p states are occupied, metal 4s states are empty and metal 3d states are partially occupied in these compounds. The last circumstance causes the main problem in explaining the insulating properties of these materials. which asserts that This contradiction is removed by use of Mott-Hubbard theory [l], the strong intra-atomic d-d Coulomb interaction is much greater than the 3d bandwidth. As a result, a gap is formed between the filled and empty 3d states. The existing discrepancies concerning the value of the Coulomb interaction and 2p + 3d type gap in these compounds, analysis of spectral data lead to ideas about an 0 which means a gap with charge transfer [2,3]. The assumption of strong correlation effects, which are described in terms of configuration-interaction theory, is an essential condition for such a situation to occur [4,5]. In spite of some success of one-electron spin-polarised band-structure calculations in describing the electron structure of 3d-metal magnetic monoxides [6], as a whole they do not reproduce band-gap values and underestimate values of local magnetic moments 0953-8984/90/173973 + 15 $03.50 @ 1990 IOP Publishing Ltd 3973 3974 V I Anisimov et a1 (approximately 1.5 times for NiO). In connection with this, it is asserted that one-particle band-structure theory is not applicable to the analysis of electron structure and magnetic properties of compounds with strong electron-electron correlation. The last affirmation is very important in connection with the discovery of high-T, oxide superconductors, which also belong to this class of compounds. Owing to the above, an attempt to rehabilitate one-electron band-structure methods for the analysis of electron structure and magnetic properties of such materials is of exceptional interest. Earlier in [7] a method of taking correlation effects into account in the frame of the local spin-density-functional (LSDF) formalism was suggested by us. The method is based on the use of different potentials for the electrons in valence and conduction bands. The use of this method for calculation of electron structure and magnetic properties of La2Cu04 allowed us to obtain for the first time a stable anti- a band gap of about ferromagnetic solution with a spin magnetic moment pcu = 0.38pB, 0.78 eV and a narrow peak in the density of states near the Fermi energy, the existence of which was predicted in many experimental works. In the same work, some preliminary results of using this method for the electron structure calculations of NiO are presented [7]. Complete data of self-consistent spin-polarised band-structure calculations for 3d- metal magnetic monoxides (MnO, FeO, COO, NiO) with and without taking account of correlation effects are reported in the present paper. It was shown that calculations including the correlation effects give band-gap values and local magnetic moments that are in agreement with experimental data and provide the correct description of all available spectral measurements (ultraviolet photoelectron spectroscopy (UPS), x-ray bremsstrahlung isochromate spectroscopy (BIS) , etc) photoelectron spectroscopy (XPS) , for these compounds. It is very important that the ground-state calculations reproduce In our all spectral data without using the configuration-interaction theory as in [4,5]. opinion, the approach suggested by us not only provides the rehabilitation of band- structure theory for the analysis of such materials, but also has important consequences for the interpretation of spectral data, and in particular shows the possibility of extracting information about the density-of-states distribution in the ground state of the system under investigation. 2. Method of calculation It is necessary to point out that failure in the application of standard band-structure methods to the analysis of the electron structure of the given compounds stimulated activity in both model and LSDF calculations with account taken of correlation effects. First of all, work should be mentioned [SI in which model calculations of the electron structure of transition-metal oxides and halides were performed in the frame of the Anderson model using intra-atomic Coulomb integral values (U) and charge transfer energy (A) determined from spectral experiments. Calculations of d8+ d9 and d8+ d7 excitation energies for NiO by the supercell method with a self-consistent account of charge redistribution around an atom having an excited shell were presented in [9]. The U and A parameters obtained were in agreement with experimental data, which indicates the possibility of determining in principle the parameters of the Anderson model in the LSDF approach. The method of accounting for the correlation effects in band-structure calculations by introducing a self-interaction correction (SIC) was proposed in [lo]. In the SIC method Band-structure description of Mott insulators 3975 the potential created by the charge density of the electron itself is subtracted from the total LSDF potential, which leads to lower energies of the occupied states. The SIC correction is not applied to the unoccupied states because they do not contribute to the electron density. As a result, the SIC method gives an increased energy difference between filled and empty states, in good agreement with experimental data (it was demonstrated for solid Ar in [lo]). We have performed similar calculations for NiO. In this case the valence band, in contrast to Ar, is formed by states with different degrees of spatial localisation. Therefore, the SIC correction must have different values for p and d states and be greater for the latter due to their greater spatial localisation. Self- consistent band-structure calculations for NiO with the SIC for all states forming the occupied band gave a band gap increased to 4 eV, which agrees with the experimental value [2, 111. However, in addition to this, a redistribution of states in the valence band took place, i.e. the d states of Ni fell below the 02p states, which contradicts the photoemission data [2,11]. This disagreement with experimental data calls for greater caution in the application of the SIC especially to transition-metal oxides. It is generally accepted that the LSDF approach correctly describes the characteristics of the ground state (charge and spin density), but gives a systematic error in the determination of the excitation energies. It leads to underestimated values of band gaps for the 3d-metal oxides under consideration. In general, the electrons of valence and conduction bands must be affected by potentials of different configurations, i.e. the conduction band electrons must be affected by the potential of a shell containing one electron more than that for the valence band electrons (see [123). However, the standard LSDF approach requires the same potential for all electrons in both occupied and un- occupied parts of the band. The use of the SIC allows us to decrease by one the number of electrons interacting with an electron in the valence band, thus providing different potentials for electrons in the valence and conduction bands. However, as mentioned above, the energies of different occupied states lower non-uniformly, which can lead to redistribution of the valence band states and hence to distortion of the ground-state results. Using the method suggested by us [7], it is possible to obtain the required difference of potentials for the electrons of valence and conduction bands. However, in contrast to the sxmethod, in this case the number of electrons acting on the electrons in occupied states remains unchanged, and the number of electrons with which an electron in the conduction band interacts is increased by one. As in the SIC method, the band gap between occupied and unoccupied states should be expected to increase; however, this would not be accompanied by any distortion of the ground-state characteristics, because the potential for valence band states does not change. We named this method the ‘unoccupied-states potential correction’ (USPC). The scheme of the USPC method is as follows. Let dhgy be a d orbital with spin projection (J and orbital momentum projection m, where n,, is its population in the ground state. The corresponding band is completely occupied if nmo = 1, and the potential obtained in the LSDF is the average potential that acts upon the electron on the given orbital. If nmo = 0, the corresponding band is empty and it is necessary to put an electron on the given orbital and to calculate the potential created by the charge and spin density corresponding to the excited configuration, thus obtaining the potential that affects the electron in this state. # 0 because of hybrid- It may happen that the band would be unoccupied but nmo isation effects. In this case the dhp configuration corresponds to the ground state, and dhu to excited state. This can be interpreted as follows. The ground-state configuration 3976 V I Anisimov et a1 d;%g is realised with probability nmo and the excited-state configuration d;, with prob- n,,) if the electron is on a d,,orbital. Therefore, the average configuration ability (1 - from which the potential for the electron on a d,, orbital is constructed will be d;gonmo+(l-nmo). Calculations were performed by the linearised muffin-tin orbitals method in the atomic sphere approximation (LMTO-ASA) [13], and the ratio of metal and non-metal sphere radii was chosen self-consistently in such a way that the atomic spheres were neutral. If, for the ground state of magnetic oxides, the configuration of metal atoms is dX(s, p)\"-\n being the number of valence electrons, then for the excited state it will be dx+y(s, p)n-x-y, with y being the d-orbital contribution to the wavefunction of the unoccupied band. In this approach, a change in d-shell charge is screened by changes in number of s and p electrons in the metallic atom sphere. For narrow-band materials (to which the oxides under consideration belong) one can distinguish sub-bands, cor- responding to specific d orbitals. Therefore the potential will be orbital-dependent. For tig and ed states of Ni, instance, in NiO (see figure 2) the valence band is formed by t&, and the conduction band by e/ states. This means that the potential obtained for the ground-state configuration is used for all oxygen states and for all nickel states except and the potential of an excited configuration is taken only for the e/ orbital. e/ , 131, the main system of equations can be written as follows: In the LMTO-ASA method [ Here Bil,(k) are LMTO expansion coefficients for Bloch functions (i is an atomic index, 1 an angular momentum index and m the angular momentum projection index), sii' /m,l,mf(k) is a structure matrix of the LMTO method and P,,,(E) is the LMTO potential matrix is determined only by the crystal structure and does not depend function. The S(k) on the atomic potentials. The potential functions Pilm(E) depend only on the ith atom potential and are determined by the value of the logarithmic derivatives of the radial wavefunction on the surface of the atomic sphere for the angular momentum value 1. If are inde- we are using the same potential for all orbitals of the ith atom, then Pirm(E) pendent of the index m and, for example, the same potential function corresponds to t?g orbitals. But it is possible to use different potentials for different m values, as is and eg done in our approach. This method of calculating potential functions corresponds to the introduction of an orbital-dependent potential, and the new Hamiltonian will be defined by equations (1). It was shown in [14] that equations (1) are equivalent to a secular equation of the form: [H(k) - E]B(k) = 0 (2) with energy-independent Hamiltonian matrix H(k). The problem of the non-orthogonality of the unoccupied states with the occupied ones appears when one uses different potentials for these states. But this is not the case in the Hamiltonian construction procedure suggested by us. Different potentials were but not for the used in calculations of potential parameters for different basis orbitals, resulting bands. The Hamiltonian matrix was constructed from the calculated potential parameters and structure constants, and all states, for both occupied and unoccupied bands, were eigenstates of the same Hamiltonian and hence were orthogonal to each other. To exclude possible misunderstanding, one must distinguish clearly between the unoccupied band and the basis orbital that gives the major contribution to that band. Band-structure description of Mott insulators 3977 I 0 I I I I\"] Y rz K UK Y rz K UK Figure 1. First Brillouin zone and E(k) curves for antiferromagnetic (AFZ) NiO. The Fermi level E, is shown by a broken line. The right-hand side shows the results of calculations with the unoccupied-states potential correction (computation 2) and the left-hand side the results without this correction (computation 1). 3. Results and discussion The results of band-structure calculations for NiO, MnO, Fe0 and COO are presented in figures 1-8: dispersion curves E(k), total density-of-electron-states curves N(E) and eg- and tZg-state distributions with different spin projections are shown. The curves represent the results obtained in calculations: without (computation 1) and with (com- putation 2) the USPC. The calculatedvalues of the band gaps and local magnetic moments and 2. for magnetic oxides are given later in tables 1 It is necessary to point out that the use of the standard self-consistent spin-polarised method, when applied to the oxides mentioned above, gives energy bands with metallic and energy bands that are underestimated in comparison conductivity for Fe0 and COO with the experimental data values of the band gap for MnO and NiO. In this respect, the results obtained are fully identical to those formerly published in [6]. The use of the USPC leads to essential reconstruction of the electron structure of magnetic oxides. First of all, a gap appears in all oxides, which naturally corresponds to their insulating properties. The application of the USPC resulted not only in the appear- ance of gaps with width close to the experimental one (see table l), but also in drastic reduction of the hybridisation between e: d states and oxygen p states. This leads to a smaller contribution of d electrons with 'spin down' to the occupied bands and, respect- ively, to increased spin magnetic moments on metal atoms (e.g. on Ni in NiO, the to 1.63pB, which is considerably closer to the experi- moment increased from 1.11,~~ mentally observed values 1.64,~~ [15] and 1.77~~ [16]). Let us recall that a stable magnetic solution for NiO had been obtained in [6] only structure, but for antiferromagnetic AF1 and ferromagnetic for antiferromagnetic AF~ 3978 V I Anisimou et a1 't ,\\ -. E lev1 -5 E lev) 0 Figure 2. Total (upper pair) and partial densities (lower pair) of states for Ni d orbitals in (t2J contributions. The arrows denote 'spin-up' and NiO. The full (broken) curves denote eg 'spin-down' states. The Fermi level (vertical lines) was placed in the middle of the energy gap. The right-handside corresponds to the calculations with theunoccupied-states potential correction (computation 2) and the left-hand side to calculations without this correction (computation 1). structures, the values of the Ni magnetic moment were zero, which indicates the itinerant nature of the magnetic moment in this compound. We obtained the same results in our calculations without the USPC. Self-consistent band-structure calculations for NiO with Band-structure description of Mott insulators 3979 Y rz K UK Y rz K UK Figure 3. E(k) curves for MnO. The notations are the same as in figure 1. ferromagnetic structure were performed by us with the USPC and a stable magnetic solution with magnetic moment 1.7 pB was obtained. This result agrees with the localised nature of magnetic moments in NiO. Consider, now, the general structure of energy bands of magnetic 3d-metal oxides obtained in the present calculations. Oxygen 2s states form the lowest energy band (not shown in figures 1-8), separated from the 0 2p band by a gap of about 8-9 eV width. The use of the USPC does not change the energy position of this band (at E = -20 eV in the energy scale adopted in figures 1-8) nor its structure. An 0 2p band in all oxides, according to computation 1, is separated by a gap from higher-lying tJg states. The USPC slightly modifies the structure of the 0 2p band, giving no shift in its centre of gravity. Its top is raised to higher energies. The tIg band hits in the same energy region as the top 2p band (because of an increase in magnetic moment resulting in an increase in of the 0 energy splitting of 'spin-up' and 'spin-down' d states), which leads to mixing of 0 2p and tJg states. The energy of the e: band is lowered on average by 1 eV in computation 2, as compared to computation 1. In the regions of partly occupied and unoccupied states, the order of the d bands remains the same: tig and e! . It is necessary to point out that the e: band overlaps with the 4s4p band. Inclusion of the USPC leads to an increase in the energy of the unoccupied tig and e: bands on average by 2-3 eV. On the whole, the energy band structures of all the oxides considered (figures 1-8) are similar with respect to the shape of the total and partial density-of-states curves. Concluding this section, let us discuss the origin of the band gap in magnetic oxides on the basis of our calculated band structures. The ratios of atomic sphere radii obtained from the electroneutrality condition were equal to RMe/Ro = 1.5-1.6. If the presence ions is assumed (usually the ratio of ionic radii is equal to OS), such a of Me2+ and 02- distribution of charge density in atomic spheres corresponds to partial inclusion of the oxygen-ion charge density in metal atomic spheres and its approximation by s and p electrons of the metal. Consequently, a decrease in the s- and p-electron number with increasing occupancy of d orbitals in an excited state can be interpreted as the result of transfer of electrons from oxygen ions to the metal d shell. This corresponds to a d\"+ d\"+'L transition or 2p + 3d transition, i.e. to a transition with charge transfer. 4. Comparison with experiment The results of a comparison of experimental values of band gaps and local magnetic moments with those obtained in the given calculations for magnetic oxides are presented 3980 VI Anisimov et a1 6 i -5 0 E lev1 5 Figure 4. Total and partial densities of states for MnO. The notations are the same as in figure 2. in tables 1 and 2. Also listed for the sake of comparison are data obtained in [6]. Analysis of these results leads to the conclusion that the suggested USPC method gives an opportunity to obtain for the first time good enough agreement with experiment within the frame of the LSDF approach. It is interesting also to compare the results obtained with data from spectroscopic experiments. To date, only MnO [22] and NiO [2, 11,231 have been investigated fully. Fe0 has been examined less thoroughly [24], mostly Band-structure description of Mott insulators 3981 Y rz K UK Y rz K UK Figure 5. E(k) curves for FeO. The notations are the same as in figure 1. Table 1. Energy gaps (ev). MnO Without USPC With USPC Experiment Fe0 coo 0 2.66 =3[19,20] NiO 0.41 3.90 4.0[11],4.3 [2] 0.82 0 2.50 3.59 3.6-3.8 [17,18] - because of difficulties in growing non-defect single crystals. We know only earlier papers [25,26]. for COO MnO. The results of angle-dependent UPS for two polarisations, a = 80\" and a = 45\and of UPS with varied excitation energy (30-80 eV) have been published recently in [22]. Unfortunately, BIS measurements for MnO are absent; therefore, in this case the occupied part of the energy bands can be compared with experiment only on a relative energy scale (for comparison with experiment, the results of computation 2 with the USPC were taken). According to experimental UPS spectra, the separation between eV, which is close to the the centres of gravity of e$ and t& occupied bands is about 1.8 calculated value (~1.6 eV). The bottom of the 0 2p band is separated from the top of the e$ band, according to experiment, by -8 eV, which practically coincides with the theoretical estimates. We have pointed out that taking into account the USPC results in the e: band falling by approximately 1.0 eV. Just such an energy shift was artificially assigned to the theoretical bands obtained in [6] for good agreement with experimental in [22]). In our case, this shift was found as a result of self-consistent data [22] (see figure 1 calculations without the introduction of any correction, allowing for relaxation effects. According to angle-dependent UPS data [22], no noticeable dispersion of 3d states was observed for MnO throughout the Brillouin zone. This conclusion on the whole correlates with the E(k) curves presented in figure 3. Appreciable dispersion of 0 2p states in the Brillouin zone is revealed in both calculations and experiment. The conclusion that the shape of the main spectrum has an antiresonance character near the excitation threshold energy (2p3d) was made from analysis of resonance UPS data for MnO [22]. This suggested that a configuration 3d5L appears in the final state of the photoemission process, the latter thus being a 2p3d transition. As mentioned above, 3982 V I Anisimov et a1 I “I”’“”’’ I E levi Figure 6. Total and partial densities of states for FeO. The notations are the same as in figure 2. T 5 I ji, / E lev) a similar conclusion about the insulating gap origin was also made from theoretical calculations. NiO. A full set of spectroscopic data are available for this compound, including UPS with varied excitation energy [2], BIS [2, 111 and angle-dependent UPS [23]. Note first of all that the band-gap value, determined from UPS and BIS (AE 4.0-4.3 eV), is in full =L Band-structure description of Mott insulators 3983 0 -5 Y rz K UK Y rz K UK Figure 7. E@) curves for COO. The notations are the same as in figure 1. Table 2. Local magnetic moments ( pB). MnO Terakura et a1 [6] Without USPC With USPC Experiment 4.45 4.47 4.74 4.79[16] Fe0 3.43 3.42 3.72 COO 2.35 2.29 2.70 3.35 [21] NiO 1.09 1.05 1.68 1.64 [15], 1.77 [16] - agreement, with the calculated one (AE = 3.9 eV). The UPS, measured at E = 66 eV (figure 9), is most convenient for comparison with calculated bands. In this case both 0 2p and Ni 3d states are clearly revealed owing to a favourable relation between the photoionisation cross sections. In the experimental spectrum five peaks are clearly B, C, D, E). Two high-energy (D, E) peaks have mainly 3d character, distinguished (A, 2p character (figure 9). It and two others (B, C) are of mixed (Ni 3d-0 2p) or purely 0 is typical that a structure similar to that described above is also observed in the density of states. Moreover, the energy separation of the peaks and their genesis are in satisfactory agreement. It is important that, as with MnO, the experimental spectrum can be interpreted on the basis of calculations performed for the ground state without the use of ideas about many configurational interactions. FeO. UPS spectra measured with variation of excitation energy (35-120 eV) [24] were chosen for comparison with experiment. Like NiO, five overlapping sub-bands are 55 eV), which can be identified distinguishable in this case (see figure 2 in [24] for E = with the maxima on the N(E) curve presented in figure 6. COO. UPS data obtained at E = 30 and 1486eV have been reported in [25,26]. The UPS for COO and FeO, as shown in [25], is very similar. general structure of experimental We have noted above the similarity of the energy band structures of these compounds (see figures 5 and 7). This means that the conclusions about correspondence between experimental and theoretical spectra that were made for Fe0 are applicable also for coo. 3984 V Z Anisimov et a1 t 4&=@+ 1 I -5 0 E lev) E lev) Figure 8. Total and partial densities of states for COO. The notations are the same as in figure 2. While the increase of the energy gaps follows naturally from our potential correc- tions, which raise the unoccupied states on the energy scale relative to the occupied states, the improvement of the calculated magnetic parameters was rather surprising as a result of including the (table 2). Magnetic moment values increase by (0.3-0.6)~~ USPC. Moreover, the magnetic solution for NiO now exists independently of the type of Band-structure description of Mott insulators 3985 Figure 9. The calculated total densities of states t#r~l.lll,,,11~8 lI,tllI~-f -20 -10 0 10 20 (computation 2) and the experimental spectra 121 __ Energy above E, lev1 i for N~O. magnetic structure, which confirms the localised nature of the Ni magnetic moment. The cause of these changes is the raising of energy of the unoccupied ‘spin-down’ d orbitals, which leads to decreasing p-d hybridisation for the ‘spin-down’ electrons. As aresult, the contribution of d orbitals to the occupied part of the valence band decreases and the magnitude of the magnetic moment becomes closer to the integer ionic value. It is commonly recognised that, although the LSDF calculations can give wrong excitation energies, the ground-state characteristics, such as total energy, charge and spin electron densities, must be described correctly. Our results show that the correction to the potential of the unoccupied states can significantly improve the ground-state characteristics. We believe that correct determination of the p-d energy difference is important not only for excitation energies but also for the correct description of the p-d hybridisation and, hence, of the values of magnetic moments and exchange inter- action parameters. For MnO and NiO, the changes in the electron structure arising from the USPC are quantitative, since energy gaps also existed in the calculations without the correction (although for NiO the energy-gap value has increased more than 10 times). But for COO and Fe0 the electron structure changes drastically, having transformed from metallic to insulating type. In figures 5 and 7 three tig bands crossing the Fermi level split due to and two for Fe0 the USPC into occupied and empty bands, and one empty band for COO move up in the energy scale. For NiO and MnO the calculated magnetic moment values are close to the exper- the experimental value is 0.65~~ greater than imental data (see table 2), while for COO the calculated one. It is known that there is unquenched orbital angular momentum in COO. For its estimation it is necessary to calculate the contribution of different d orbitals to the occupied bands. The standard LSDF gives three degenerate tjg orbitals, of which 3986 VI Anisimov et a1 any three independent linear combinations can be used. The USPC removes this degener- acy and raises the energy of the empty states. But which linear combinations of t2,0rbitals correspond to empty or occupied states remains uncertain. Following the analysis in the occupied bands will be formed by an xy orbital and a [6] we accept that for COO linear combination of xz and yz orbitals, which corresponds to an orbital angular momentum projection m = +1, and the empty band corresponds to the combination 1. As a result, the orbital angular momentum value for a CO atom will be 1. with m = - In reality this value can be less than 1 due to the not purely t2, origin of the bands in question. It is interesting to compare our approach with the Anderson impurity model cal- culation of McMahan et a1 [27]. The main problem in both cases was to take into account different d configurations of the metal atom with different energies in contrast to the one-electron LSDF calculations with an average d configuration and average energy of d orbitals. In [27] only the model parameters were calculated in the LSDF and the correlation effects were treated directly in the impurity approximation. In our approach, different d configurations are related to different d spin-orbitals. (This is possible only when each unoccupied band is formed mainly by a certain d spin-orbital.) After that the degeneracy in the energy of d orbitals is removed and the usual band-structure calculations are performed. We think that our approach can be considered as a rather simple and natural realisation of the idea of ‘lower and upper Hubbard bands’ in the frame of band-structure calculations. We present here the results of the application of our approach to four transition- metal compounds. (The results of calculations for La2CuOQ are presented in [7].) One can ask what would be found if this approach were applied to solids with a different type of electronic structure such as a transition metal, an insulator and a semiconductor? The simplest case is an insulator, for which the valence and conduction bands are formed by different orbitals, but here the problem of the correct description of the excited shell screening can appear. In a semiconductor both bands are formed by the same orbitals and one must take as a basis set the Wannier-type functions and not the atomic-like LMTO orbitals. As for metals and compounds with a metallic type of electronic structure, the main question is as follows. Are the correlation effects strong enough to produce a gap between the occupied and unoccupied bands? if this is not the case, then our approach cannot be applied because it is necessary to have a totally unoccupied band corresponding to the certain orbital for our method. 5. Conclusions In the present paper we suggest a method to take account approximately of correlation effects in electronic structure calculations for narrow-band transition-metal compounds. The core of the method is the unoccupied-states potential correction. The application of this method to the electronic structure calculations for the antiferromagnetic 3d-metal not only gave for all these compounds an insulating monoxides NiO, MnO, Fe0 and COO type of band structure with correct band gaps, but also significantly improved the values of their magnetic parameters. We believe that one-electron methods of band-structure calculations based on the local spin-density-functional approach, after rather simple modifications, can be applied to systems with strong electron correlations. Band-structure description of Mott insulators References 3987 [1] Hubbard J 1964 Proc. R. Soc. A 277 237; 1964 Proc. R. Soc. A 281 401 [2] Sawatzky G A and Allen J W 1984 Phys. Reu. Lett. 53 2339 J. Magn. Magn. Mater. 54-57 [3] Zaanen J, Sawatzky G A and Allen J W 1985 Phys. Reu. Lett. 55 418; 1986 607 [4] Fujimori A, Minami F and Sugano S 1984 Phys. Rev. B 29 5225 [5] Fujimori A and Minami F 1984 Phys. Rev. B 30 957 [6] Terakura K, Oguchi T, Williams A R and Kubler J 1984 Phys. Reu. B 30 4734 [7] Anisimov V I, Korotin M A and Afanasyev I V 1989 Physica C 161 59 [8] Van der Laan G, Zaanen J and Sawatzky G A 1986 Phys. Reu. B 33 4253 [9] Norman M R and Freeman A J 1986 Phys. Reu. B 33 8896 [lo] Perdew J P and Zunger A 1981 Phys. Reu. B 23 5048 [ll] Hufner S, Ostenvalder J, Riesterer T and Hulliger F 1984 Solid State Commun. 52 793 [12] Mott N F 1974 Metal-Insulator Transitions (London: Taylor and Francis) [13] Andersen 0 K 1975 Phys. Reu. B 12 3060 Jepsen 0 and Andersen 0 K 1983 Phys. Reu. B 27 7144 [14] Gunnarson 0, [15] Alperin H A 1962 J. Phys. Soc. Japan Suppl. B 17 12 [16] Fender B E F, Jacobson A J and Wedgwood J FA 1968 Chem. Phys. 48 990 [17] Iskenderov RN, DrabkinIA, Emel’yanovaLTand KsendzovYaM 1969Sou. Phys.-Solidstate 102031 [18] Huffman D R, Wild R L and Shinmei J 1969 Chem. Phys. 50 4092 [19] Powell R J and Spicer W E 1970 Phys. Reo. B 2 2182 [20] Hufner S and Wertheim G K 1973 Phys. Reo. B 7 5086 (211 Khan D C and Erickson RA 1970 Phys. Reu. B 12243 [22] Lad R J and Henrich V E 1988 Phys. Reu. B 38 10860 [23] McKay J M and Henrich V E 1984 Phys. Rev. Lett. 53 2343 [24] Fujimori A, Kimizuka N, Tanigushi M and Suga S 1987 Phys. Reu. B 36 6691 [25] Kim K S 1975 Phys. Rev. B 11 2177 395 [26] Eastman D E and Freeouf J L 1975 Phys. Reo. B 34 [27] McMahan A K, Martin R M and Satpathy S 1988 Phys. Reu. B 38 6650