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Calculation of x-ray absorption spectra

Calculation of x-ray absorption spectra. Christian Brouder Institut de Minéralogie et de Physique des Milieux Condensés. Theoretical approaches. A bit of history One body Two bodies Many bodies. The malediction of XAFS calculations. Kronig (1931) Petersen (1932) Bogdanovich (1937)

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Calculation of x-ray absorption spectra

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  1. Calculation of x-ray absorption spectra Christian Brouder Institut de Minéralogie et de Physique des Milieux Condensés

  2. Theoretical approaches A bit of history One body Two bodies Many bodies

  3. The malediction of XAFS calculations Kronig (1931) Petersen (1932) Bogdanovich (1937) Natoli (1980)

  4. The main approaches One-body calculation Two-body calculations Many-body calculations

  5. One-body s(E) = 4p2a E Sn|<fn|e.r|f0>|2d(en-e0-E) (-D + V(r)) fn(r) = enfn(r) V = Vc+VxcDFT LDA Kohn-Sham V = Vc+SGreen function theory f0(r) core-hole wavefunction

  6. Multiple-scattering theory Indra’s net Avatamsaka sutra The book of Buddha garlands (~400) Lord Rayleigh (1892) Kasterin (1897) Korringa (1945,1947) Kohn Rostoker (1953)

  7. The muffin-tin approximation Spherical atoms in a constant interstitial potential

  8. The muffin-tin approximation Spherical atoms in a constant interstitial potential

  9. Muffin-tin programs CONTINUUM (Natoli, 1980) ICXANES (Durham et al., 1982) http://cpc.cs.qub.ac.uk/summaries/AARR.html FEFF8 (Rehr et al., 1991) http://leonardo.phys.washington.edu/feff/ SPRKKR (Ebert et al., 1998) relativistic olymp.cup.uni-muenchen.de/ak/ebert/SPRKKR/ MXAN (Benfatto et al., 2002) maurizio.benfatto@lnf.infn.it PY-LMTO (Antonov et al., 2001) relativistic LMTO yaresko@mpipks-dresden.mpg.de

  10. Non muffin-tin

  11. Non-muffin-tin programs FPX (Foulis, 1986-2002) Non-muffin-tin multiple scattering www.esrf.fr/computing/scientific/fpx/fpx.htm WIEN2k (Blaha et al., 1998) FP-LAPW www.wien2k.at/ FDMNES (Joly, 2001) Finite difference method 147.173.148.95/LDC/LE_LABORATOIRE/Equipes_de_recherche/EQUIPE_SPECTROSCOPIE/SIMUL/EtudFond_Prog.asp

  12. Non-muffin-tin programs PARATEC (Cabaret et al., 2002) pseudopotential www-ext.lmcp.jussieu.fr/~cabaret/xanes.html EXC!TING (Dewhurst et al., 2006) FP-LAPW exciting.sourceforge.net/ STOBE (Saint-Amant et al., 1992) LCAO www.fhi-berlin.mpg.de/th/th.html

  13. Two-body Bethe-Salpeter L=L0+L0KL L0(12;1’2’)=G(1,2’)G(2,1’) The dielectric response (x,y)  <0|[j(x),j(y)]|0> can be obtained from L

  14. BS + TDDFT programs ADF (Stener et al., 2003) TDDFT www.scm.com/ DP (Olevano et al., 1999) TDDFT pseudopotential theory.polytechnique.fr/codes/dp/dp.html EXC Bethe-Salpeter pseudopotential theory.polytechnique.fr/codes/exc/exc.html NBSE (Shirley, 1998) Bethe-Salpeter pseudopotential physics.nist.gov/Divisions/Div844/staff/Gp4/shirley.html

  15. Many-body Many-body states s(E) = 4p2a E Sn|<Fn|e.r|F0>|2d(en-e0-E) (-D + SiVn(ri) + SijVe(rij)) |Fn> = en |Fn> |F0> many-bodyground state

  16. Multiplet programs TT-MULTIPLETS (Thole et al., 1990) www.anorg.chem.uu.nl/people/staff/FrankdeGroot/ttmultiplets.htm/ Cluster (Kotani et al., 1992) theo.phys.okayama-u.ac.jp/~okada/index_e.html/ AMARCORD (Mirone, 2000) www.esrf.fr/computing/scientific/people/mirone/amarcord/

  17. Problems Green functions and KS-(TD)DFT One-particle orbitals are occupied or not Restricted to closed shell systems Multiplets parametrized very small systems

  18. Unifying approaches Multichannel multiple scattering Krüger and Natoli (2004) TDDFT for open shells in progress (E.K.U Gross and coll.) Green functions with correlation in progress

  19. Long-term program CORRELATION

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