Density Functional Theory pp 525-548 | Cite as

# Local Density Functional and Strong On-Site Correlations: The Electronic Structure of La_{2}CuO_{4}

Chapter

## Abstract

The density functional (DF) theory has been a most successful theoretical method for describing ground state properties in solid state physics since the beginning of seventies [1, 2]. An enormous amount of applications of the local density approximation (LDA) to the DF can be found in the literature for the description of a wide range of phenomena in a wide range of materials (see e.g. references within Refs. [1, 2] and reviews [3, 4]). Unfortunately the class of materials where the LDA does not work properly is also growing rapidly including those with the most startling physical properties.

## Keywords

Local Density Approximation Unoccupied State Lower Hubbard Band Slater Integral Apex Oxygen## Preview

Unable to display preview. Download preview PDF.

## References

- [1]
*Theory of the Inhomogeneous Electron Gas*edited by S. Lundqvist and N.H. March, (Plenum, 1983).Google Scholar - [2]G.D. Mahan and K.R. Subbaswamy,
*Local Density Theory of Polarizability*, (Plenum, 1990).Google Scholar - [3]R.O. Jones and O. Gunnarsson, Rev. Mod. Phys.
**61**, 689 (1989).ADSCrossRefGoogle Scholar - [4]W.E. Pickett, Rev. Mod. Phys.
**62**, 433 (1989).ADSCrossRefGoogle Scholar - [5]D.C. Langreth and J.P. Perdew, Phys. Rev. B
**21**, 5469 (1980).ADSGoogle Scholar - D.C. Langreth and M. J. Mehl, Phys. Rev. B
**28**, 1809 (1983).ADSGoogle Scholar - J.P. Perdew and Y. Wang, Phys. Rev. B
**33**, 8800 (1986).ADSGoogle Scholar - [6]J.P. Perdew and A. Zunger, Phys. Rev. B
**23**, 5048 (1981).ADSGoogle Scholar - [7]J.P. Perdew in
*Advances in Quantum. Chemistry*, Vol. 21, edited by S.B. Trickey, p. 113 (Academic Press, 1990), and the references therein.Google Scholar - [8]V.I. Anisimov, J. Zaanen, and O.K. Andersen, Phys. Rev. B
**44**, 943 (1991).ADSGoogle Scholar - [9]J.P. Perdew, R.G. Parr, M. Levy, and J.L. Balduz, Jr, Phys. Rev. Lett.
**49**, 1691 (1982).ADSCrossRefGoogle Scholar - [10]A.R. Williams, J. Kübier, and C.D. Gelatt, Jr, Phys. Rev. B
**19**, 6094 (1979).ADSGoogle Scholar - [11]M.T. Czyżyk, R.A. de Groot, G. Dalba, P. Fornasini, A. Kisiel, F. Rocca, and E. Burattini, Phys. Rev. B
**39**, 9831 (1989).ADSGoogle Scholar - J. Ghijsen, L.H. Tjeng, J. van Elp, H. Eskes, J. Westerink, G.A. Sawatzky, and M.T. Czyżyk, Phys. Rev. B
**38**, 11322 (1988).ADSGoogle Scholar - M. Grioni, M.T. Czyżyk, F.M.F. de Groot, J.C. Fuggle, and B.E. Watts, Phys. Rev. B
**39**, 4886 (1989).ADSGoogle Scholar - M.T. Czyżyk, and R.A. de Groot, in
*Proceedings of the Second European Conference on Progress in X-ray Synchrotron Radiation Research Research, Rome, Italy 1989*, edited by A. Balerna, E. Bernieri, and S. Mobilio, (Italian Physical Society, Bolonia 1990), p.47.Google Scholar - P.J.W. Weijs, M.T. Czyżyk, J.F. van Acker, W. Speier, J.B. Goedkoop, H. van Leuken, H.J.M. Hendrix, R.A. de Groot, G. van der Laan, K.H.J. Buschow, G. Wiech and J.C. Fuggle, Phys. Rev. B
**41**, 11899 (1990).ADSGoogle Scholar - [12]H. van Leuken, A. Lodder, M.T. Czyżyk, F. Springelkamp, and R.A. de Groot, Phys. Rev. B
**41**, 5613 (1990).ADSGoogle Scholar - [13]M.T. Czyżyk, K. Lawniczak-Jabloriska, and S. Mobilio, Phys. Rev. B
**45**, 1581 (1992);.ADSGoogle Scholar - [14]M.T. Czyżyk, R. Potze, and G.A. Sawatzky, Phys. Rev. B
**46**, 3729 (1992).ADSGoogle Scholar - [15]O.K. Andersen, Phys. Rev. B
**12**, 3060 (1975).ADSGoogle Scholar - H.K. Skriver,
*The LMTO Method*, (Berlin, 1984).Google Scholar - [16]O.K. Andersen and O. Jepsen, Phys. Rev. Lett.
**53**, 2571 (1984).ADSCrossRefGoogle Scholar - [17]E.U. Condon and G.H. Shortley,
*The Theory of Atomic Spectra*, (Cambridge, 1953).Google Scholar - [18]J.S. Griffith,
*The Theory of Transition-Metal Ions*, (Cambridge, 1961).Google Scholar - [19]A.M. Oles and G. Stollhoff, Phys. Rev. B
**29**, 314 (1984).ADSGoogle Scholar - [20]J.B. Grant and A.K. McMahan, Phys. Rev. B
**46**, 8440 (1992).ADSGoogle Scholar - [21]M.M. Steiner, R.C. Albers, and L.J. Sham, Phys. Rev. B
**45**, 13272 (1992).ADSGoogle Scholar - [22]V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyżyk, and G.A. Sawatzky, to appear in Phys. Rev. B. (Dec.‘93).Google Scholar
- [23]A.K. McMahan, R.M. Martin, and S. Satpathy, Phys. Rev. B
**38**, 6650 (1988).ADSGoogle Scholar - [24]O. Gunnarsson, O.K. Andersen, O. Jepsen, and J. Zaanen, Phys. Rev. B
**39**, 1708 (1989).ADSGoogle Scholar - [25]M.S. Hybertsen, and M. Schlüter, Phys. Rev. B
**39**, 9028 (1989).ADSGoogle Scholar - [26]A.K. McMahan, J.F. Annett, and R.M. Martin, Phys. Rev. B
**42**, 6268 (1990).ADSGoogle Scholar - [27]One should be a bit careful when comparing the values of
*U*reported in the literature, because of the different, often only implicitly assumed conventions which are used. All values obtained by constrained-LDA calculations involving atomic-sphere (muffin-tin) approximation should be identified with*screened*Slater monopole integral*F*^{0}_{eff.}So we do, see Appendix. The diagonal values of Coulomb interaction*U*_{mm}, m =*x*^{2}—*y*^{2}, 3*z*^{2}—*r*^{2},*xy, etc*, are, however, different. In terms of Racah*A, B*and*C*parameters they read:*U*_{d}=*F*^{0}_{eff.},*A*+ 7/5*C*, and*U*_{mm}= A + 4*B*+ 3*C*. As an example,*U*_{d}= 7.42 eV in Ref. [26] and*U*(*d*_{x}^{2}−_{y}^{2}) = 8.96 eV in Ref. [20] are in fact the same. Of course, values of*B*and*C*have to be known. The authors of references used in this example did not confuse that matter, but it seems that ambiguity about these values exists in the literature.Google Scholar - [28]V.I. Anisimov, M.A. Korotin, J. Zaanen, and O.K. Andersen, Phys. Rev. Lett.
**68**, 345 (1992).ADSCrossRefGoogle Scholar - [29]V.l. Anisimov, private communication.Google Scholar
- [30]C.E. Moore,
*Atomic Energy Levels*, Natl. Bur. Stand. (U.S.), No. 467 (Washington, D.C. 1958), Vols. 1-3.Google Scholar - [31]H. Eskes, L.H. Tjeng, and G.A. Sawatzky, Phys. Rev. B
**41**, 288 (1990).ADSGoogle Scholar - [32]H. Eskes, and G.A. Sawatzky, Phys. Rev. B
**44**, 9656 (1991).ADSGoogle Scholar - [33]F.M.F. de Groot, J.C. Fuggle, B.T. Thole, and G.A. Sawatzky, Phys. Rev. B
**42**, 5459 (1990).ADSGoogle Scholar - [34]J.B. Mann,
*Atomic structure calculations*, Los Alamos Scientific Laboratory Reports No.LASL-3690 (1967).Google Scholar - [35]S.L. Cooper, G.A. Thomas, A.J. Millis, P.E. Sulewski, J. Orenstein, D.H. Rapkine, S-W, Cheong, and P.L. Trevor, Phys. Rev. B
**42**, 10785 (1990).ADSGoogle Scholar - [36]J. Zaanen, G.A. Sawatzky, and J.W. Allen, Phys. Rev. Lett.
**55**, 418 (1985).ADSCrossRefGoogle Scholar - [37]F. Barriquand, and G.A. Sawatzky, submitted to Phys. Rev. B.Google Scholar
- [38]E. Manousakis, Rev. Mod. Phys.
**63**, 1 (1991).ADSCrossRefGoogle Scholar - [39]Y. Gao, T.J. Wagener, J.H. Weaver, A.J. Arko, B. Flandermeyer, D.W. Capone II, Phys. Rev. B
**36**, 3971 (1987).ADSGoogle Scholar - [40]F.C. Zhang, and T.M. Rice, Phys. Rev. B
**37**, 3759 (1988).ADSGoogle Scholar - [41]E. Pellegrin, N. Nücker, J. Fink, S.L. Molodtsov, A. Gutierrez, E. Navas, O. Strebel, Z. Hu, M. Domke, G. Kaindl, S. Uchida, Y. Nakamura, J. Markl, M. Klauda, G. Saemann-Ischenko, A. Krol, J.L. Peng, Z.Y. Li, and R.L. Greene, Phys. Rev. B
**47**, 3354 (1993). The experimental spectra presented in Fig. 6 differ slightly from those published by Pellegrin*et al.*We used spectra which were corrected for the self-absorption effect and which were kindly provided to us by E. Pellegrin after publication.Google Scholar - [42]C.T. Chen, L.H. Tjeng, J. Kwo, H.L. Kao, P. Rudolf, F. Sette, and R.M. Fleming, Phys. Rev. Lett.
**68**, 2543 (1992).ADSCrossRefGoogle Scholar - [43]We used such a broadening procedure successfully in many occasions. See e.g. Ref. [11, 13] and [14].Google Scholar
- [44]Such an expectation is based on our previous experience with self-consistent calculations of the core-hole effects on the XAS spectra in semiconductors and metals. See: M.T. Czyżyk, and R.A. de Groot, Proc. of ”2nd European Conf. on Progress in X-ray Synchrotron Radiation Research, p. 47, Rome, Italy, October 1989; P.J.W. Weijs, M.T. Czyèyk, J.F. van Acker, W. Speier, J.B. Goedkoop, H. van Leuken, H.J.M. Hendrix, R.A. de Groot, G. van der Laan, H.J. Buschow, G. Wiech, J.C. Fuggle, Phys. Rev. B
**41**, 11899 (1990).ADSGoogle Scholar - [45]Z-X. Shen, J.W. Allen, J.J. Yeh, J.-S. Kang, W. Ellis, W. Spicer, I. Lindau, M.B. Maple, Y.D. Dalichaouch, M.S. Torikachvili, J.Z. Sun, and T.H. Geballe Phys. Rev. B
**36**, 8414 (1987).ADSGoogle Scholar - [46]A. Fujimori, E. Takayama-Muromachi, Y. Uchida, and B. Okai, Phys. Rev. B
**35**, 8814 (1987).ADSGoogle Scholar - [47]J. Ghijsen, L.H. Tjeng, J. van Elp, H. Eskes, J. Westerink, G.A. Sawatzky, and M.T. Czyżyk, Phys. Rev. B
**38**, 11322 (1988).ADSGoogle Scholar - [48]H. Eskes and G.A. Sawatzky, Phys. Rev. Lett.
**61**, 1415 (1988).ADSCrossRefGoogle Scholar - [49]J.A. Gaunt, Phil.Trans. A.
**228**, 151 (1929).ADSMATHCrossRefGoogle Scholar - [50]D.A. Varshslovich, A.N. Moskalev, and V.K. Khersonskii,
*Quantum Theory of Angular Momentum*, (World Scientific, 1989).Google Scholar

## Copyright information

© Springer Science+Business Media New York 1995