Calculation of x-ray absorption spectra

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 Snltfne.rf0gt2 d(en-e0-E) (-D
V(r)) fn(r) en fn(r) V VcVxc DFT LDA
Kohn-Sham V VcS Green function
theory f0(r) core-hole wavefunction
6
Multiple-scattering theory
Indras 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/AAR
R.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_at_lnf.infn.it PY-LMTO (Antonov et
al., 2001) relativistic LMTO
yaresko_at_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/scie
ntific/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_SPECTROSC
OPIE/SIMUL/EtudFond_Prog.asp

12
Non-muffin-tin programs
PARATEC (Cabaret et al., 2002)
pseudopotential www-ext.lmcp.jussieu.fr/cabare
t/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 LL0L0KL L0(1212)G(1,2)G(2,1
) The dielectric response ?(x,y) ?
lt0j(x),j(y)0gt 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/d
p/dp.html EXC Bethe-Salpeter pseudopotential
theory.polytechnique.fr/codes/exc/exc.html NBSE
(Shirley, 1998) Bethe-Salpeter
pseudopotential physics.nist.gov/Divisions/Div8
44/staff/Gp4/shirley.html

15
Many-body
Many-body states
s(E) 4p2a E SnltFne.rF0gt2 d(en-e0-E) (-D
SiVn(ri) SijVe(rij)) Fngt en Fngt F0gt
many-body ground state
16
Multiplet programs
TT-MULTIPLETS (Thole et al., 1990)
www.anorg.chem.uu.nl/people/staff/FrankdeGroot/ttm
ultiplets.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