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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## 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).ADSzbMATHCrossRefGoogle 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