Projector Self-Consistent DFT+U Using Nonorthogonal Generalised Wannier Functions

  • David Daniel O’Regan
Part of the Springer Theses book series (Springer Theses)


The DFT+U energy functional depends not only on the electronic density and the Hubbard interaction parameters, but additionally on a set of projections which delineate the correlated subspaces.


Electric Dipole Moment Axial Ligand Magnetic Dipole Moment Wannier Function Iron Porphyrin 
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  1. 1.
    D.D. O’Regan, N.D.M. Hine, M.C. Payne, A.A. Mostofi, Projector self-consistent DFT+U using nonorthogonal generalized Wannier functions. Phys. Rev. B 82(8), 081102 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    V.I. Anisimov, J. Zaanen, O.K. Andersen, Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44(3), 943 (1991)ADSCrossRefGoogle Scholar
  3. 3.
    V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czy zyk, G.A. Sawatzky, Density-functional theory and NiO photoemission spectra. Phys. Rev. B 48(23), 16929 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, G. Kotliar, First-principles calculations of the electronic structure and spectra of strongly correlated systems: dynamical mean-field theory. J. Phys. Condens. Matter 9(35), 7359 (1997)ADSCrossRefGoogle Scholar
  5. 5.
    A.I. Lichtenstein, M.I. Katsnelson, Ab initio calculations of quasiparticle band structure in correlated systems: LDA++ approach. Phys. Rev. B 57(12), 6884 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    M. Cococcioni, S. de Gironcoli, Linear response approach to the calculation of the effective interaction parameters in the LDA + U method. Phys. Rev. B 71(3), 035105 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    H.J. Kulik, M. Cococcioni, D.A. Scherlis, N. Marzari, Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach. Phys. Rev. Lett. 97(10), 103001 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    T. Miyake, F. Aryasetiawan, Screened Coulomb interaction in the maximally localized Wannier basis. Phys. Rev. B 77(8), 085122 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57(3), 1505 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    O. Eriksson, J.M. Wills, M. Colarieti-Tosti, S. Lebgue, A. Grechnev, Many-body projector orbitals for electronic structure theory of strongly correlated electrons. Int. J. Quantum Chem. 105, 160–165 (2005)Google Scholar
  11. 11.
    D.D. O’Regan, M.C. Payne, A.A. Mostofi, Subspace representations in ab initio methods for strongly correlated systems. Phys. Rev. B 83(24), 245124 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    A.A. Mostofi, J.R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, N. Marzari, Wannier90: a tool for obtaining maximally localised Wannier functions. Comp. Phys. Comm. 178, 685 (2008)ADSzbMATHCrossRefGoogle Scholar
  13. 13.
    W.E. Pickett, S.C. Erwin, E.C. Ethridge, Reformulation of the LDA+U method for a local-orbital basis. Phys. Rev. B 58(3), 1201 (1998)ADSCrossRefGoogle Scholar
  14. 14.
    M.J. Han, T. Ozaki, J. Yu, O(N) LDA + U electronic structure calculation method based on the nonorthogonal pseudoatomic orbital basis. Phys. Rev. B 73(4), 045110 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    K.K.H. Eschrig, I. Chaplygin, Density functional application to strongly correlated electron systems. J. Solid State Chem. 176(2), 482 (2003)ADSCrossRefGoogle Scholar
  16. 16.
    S. Fabris, S. de Gironcoli, S. Baroni, G. Vicario, G. Balducci, Reply to comment on taming multiple valency with density functionals: a case study of defective ceria. Phys. Rev. B 72(23), 237102 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    R.D. King-Smith, M.C. Payne, J.S. Lin, Real-space implementation of nonlocal pseudopotentials for first-principles total-energy calculations. Phys. Rev. B 44(23), 13063 (1991)ADSCrossRefGoogle Scholar
  18. 18.
    S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, First principles methods using CASTEP. Zeitschrift für Kristallographie 220(5–6), 567 (2005)CrossRefGoogle Scholar
  19. 19.
    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, Quantum espresso: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21(39), 395502 (2009)CrossRefGoogle Scholar
  20. 20.
    E. Clementi, D.L. Raimondi, Atomic screening constants from SCF functions. J. Chem. Phys. 38, 2686 (1963)ADSCrossRefGoogle Scholar
  21. 21.
    N. Marzari, D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56(20), 12847 (1997)ADSCrossRefGoogle Scholar
  22. 22.
    I. Souza, N. Marzari, D. Vanderbilt, Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65(3), 035109 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    F. Lechermann, A. Georges, A. Poteryaev, S. Biermann, M. Posternak, A. Yamasaki, O.K. Andersen, Dynamical mean-field theory using Wannier functions: a flexible route to electronic structure calculations of strongly correlated materials. Phys. Rev. B 74(12), 125120 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    V.V. Mazurenko, S.L. Skornyakov, A.V. Kozhevnikov, F. Mila, V.I. Anisimov, Wannier functions and exchange integrals: the example of \(\hbox{LiCu}_{2}\hbox{O}_{2}.\) Phys. Rev. B 75, 224408 (2007)Google Scholar
  25. 25.
    M. Posternak, A. Baldereschi, S. Massidda, N. Marzari, Maximally localised Wannier functions in antiferromagnetic MnO within the FLAPW formalism. Phys. Rev. B 65, 184422 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    B. Amadon, F. Lechermann, A. Georges, F. Jollet, T.O. Wehling, A.I. Lichtenstein, Plane-wave based electronic structure calculations for correlated materials using dynamical mean-field theory and projected local orbitals. Phys Rev B 77(20), 205112 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    C.-K. Skylaris, P.D. Haynes, A.A. Mostofi, M.C. Payne, Introducing ONETEP: linear-scaling density functional simulations on parallel computers. J. Chem. Phys. 122, 084119 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    P.D. Haynes, C.-K. Skylaris, A.A. Mostofi, M.C. Payne, Elimination of basis set superposition error in linear-scaling density-functional calculations with local orbitals optimised in situ. Chem. Phys. Lett. 422, 345 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    R. McWeeny, Some recent advances in density matrix theory. Rev. Mod. Phys. 32(2), 335 (1960)MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    X.-P. Li, R.W. Nunes, D. Vanderbilt, Density-matrix electronic-structure method with linear system-size scaling. Phys. Rev. B 47(16), 10891 (1993)ADSCrossRefGoogle Scholar
  31. 31.
    R.W. Nunes, D. Vanderbilt, Generalization of the density-matrix method to a nonorthogonal basis. Phys. Rev. B 50(23), 17611 (1994)ADSCrossRefGoogle Scholar
  32. 32.
    M.S. Daw, Model for energetics of solids based on the density matrix. Phys. Rev. B 47(16), 10895 (1993)ADSCrossRefGoogle Scholar
  33. 33.
    D.G. Anderson, Iterative procedures for nonlinear integral equations. J. ACM 12(4), 547 (1965)zbMATHCrossRefGoogle Scholar
  34. 34.
    C.G. Broyden, A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19(92), 577 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    D.A. Scherlis, M. Cococcioni, P. Sit, N. Marzari, Simulation of heme using DFT+U: a step toward accurate spin-state energetics. J. Phys. Chem. B 111(25), 7384 (2007)CrossRefGoogle Scholar
  36. 36.
    M. Bernien, J. Miguel, C. Weis, M.E. Ali, J. Kurde, B. Krumme, P.M. Panchmatia, B. Sanyal, M. Piantek, P. Srivastava, K. Baberschke, P.M. Oppeneer, O. Eriksson, W. Kuch, H. Wende, Tailoring the nature of magnetic coupling of Fe-porphyrin molecules to ferromagnetic substrates. Phys. Rev. Lett. 102(4), 047202 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    P.M. Panchmatia, B. Sanyal, P.M. Oppeneer, GGA+U modeling of structural, electronic, and magnetic properties of iron porphyrin-type molecules. Chem. Phys. 343(1), 47 (2008)ADSCrossRefGoogle Scholar
  38. 38.
    A.M.P. Sena, V. Brázdová, D.R. Bowler, Density functional theory study of the iron-based porphyrin haem(b) on the Si(111):H surface. Phys. Rev. B 79(24), 245404 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    L.G.G.V. Dias da Silva, M.L. Tiago, S.E. Ulloa, F.A. Reboredo, E. Dagotto, Many-body electronic structure and Kondo properties of cobalt-porphyrin molecules. Phys. Rev. B 80(15), 155443 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    M. Palummo, C. Hogan, F. Sottile, P. Bagalá, A. Rubio, A binitio electronic and optical spectra of free-base porphyrins: the role of electronic correlation. J. Chem. Phys. 131(8), 084102 (2009)ADSCrossRefGoogle Scholar
  41. 41.
    J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77(8), 3865 (1996)ADSCrossRefGoogle Scholar
  42. 42.
    A.M. Rappe, K.M. Rabe, E. Kaxiras, J.D. Joannopoulos, Optimized pseudopotentials. Phys. Rev. B 41(2), 1227 (1990)ADSCrossRefGoogle Scholar
  43. 43.
    V.L. Campo Jr, M. Cococcioni, Extended DFT+U+V method with on-site and inter-site electronic interactions. J. Phys. Condens. Matter 22(5), 055602 (2010)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1. Cavendish LaboratoryTCM Group, University of CambridgeCambridgeUK

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