Calculation of x-ray absorption spectraCalculation of x-ray absorption spectra

Christian BrouderChristian BrouderInstitut de Minéralogie et de Physique des Milieux CondensésInstitut de Minéralogie et de Physique des Milieux Condensés

A bit of historyA bit of historyOne bodyOne bodyTwo bodiesTwo bodiesMany bodiesMany bodies

Theoretical approachesTheoretical approaches

Kronig (1931)Kronig (1931)Petersen (1932)Petersen (1932)Bogdanovich (1937)Bogdanovich (1937)Natoli (1980)Natoli (1980)

The malediction of The malediction of XAFS calculationsXAFS calculations

One-body calculationOne-body calculation

The main approachesThe main approaches

Two-body calculationsTwo-body calculations

Many-body calculationsMany-body calculations

One-bodyOne-body

nn||nn||.r.r||00>|>|22 ((nn--

00-E)-E)

V(V(rr)) )) nn((rr) = ) = nn nn((rr) )

V = VV = Vcc+V+Vxcxc DFT LDA Kohn-ShamDFT LDA Kohn-Sham

V = VV = Vcc++ Green function theoryGreen function theory

00((rr) core-hole wavefunction ) core-hole wavefunction

The book of Buddha garlands (~400)The book of Buddha garlands (~400)Lord Rayleigh (1892)Lord Rayleigh (1892)Kasterin (1897)Kasterin (1897)Korringa (1945,1947)Korringa (1945,1947)Kohn Rostoker (1953)Kohn Rostoker (1953)

Multiple-scattering theoryMultiple-scattering theory

Indra’s netIndra’s netAvatamsaka sutraAvatamsaka sutra

The muffin-tin approximationThe muffin-tin approximation

Spherical atoms in a constant interstitial potential

The muffin-tin approximationThe muffin-tin approximation

Spherical atoms in a constant interstitial potential

CONTINUUM (Natoli, 1980)CONTINUUM (Natoli, 1980)ICXANES (Durham et al., 1982)ICXANES (Durham et al., 1982) http://cpc.cs.qub.ac.uk/summaries/AARR.html

FEFF8 (Rehr et al., 1991)FEFF8 (Rehr et al., 1991) http://leonardo.phys.washington.edu/feff/

SPRKKR (Ebert et al., 1998)SPRKKR (Ebert et al., 1998) relativistic olymp.cup.uni-muenchen.de/ak/ebert/SPRKKR/

MXAN (Benfatto et al., 2002)MXAN (Benfatto et al., 2002) maurizio.benfatto@lnf.infn.it

PY-LMTO (Antonov et al., 2001)PY-LMTO (Antonov et al., 2001) relativistic LMTO yaresko@mpipks-dresden.mpg.de

Muffin-tin programsMuffin-tin programs

Non muffin-tinNon muffin-tin

Non-muffin-tin programsNon-muffin-tin programs

FPX (Foulis, 1986-2002)FPX (Foulis, 1986-2002) Non-muffin-tin multiple scattering

www.esrf.fr/computing/scientific/fpx/fpx.htm

WIEN2k (Blaha et al., 1998)WIEN2k (Blaha et al., 1998) FP-LAPW

www.wien2k.at/

FDMNES (Joly, 2001)FDMNES (Joly, 2001) Finite difference method 147.173.148.95/LDC/LE_LABORATOIRE/Equipes_de_recherche/EQUIPE_SPECTROSCOPIE/SIMUL/EtudFond_Prog.asp

Non-muffin-tin programsNon-muffin-tin programs

PARATEC (Cabaret et al., 2002)PARATEC (Cabaret et al., 2002) pseudopotential

www-ext.lmcp.jussieu.fr/~cabaret/xanes.html

EXC!TING (Dewhurst et al., 2006)EXC!TING (Dewhurst et al., 2006) FP-LAPW

exciting.sourceforge.net/

STOBE (Saint-Amant et al., 1992)STOBE (Saint-Amant et al., 1992) LCAO

www.fhi-berlin.mpg.de/th/th.html

Bethe-SalpeterBethe-SalpeterL=LL=L00+L+L00KLKL

LL00(12;1’2’)=G(1,2’)G(2,1’)(12;1’2’)=G(1,2’)G(2,1’)

The dielectric response The dielectric response (x,y) (x,y) <0|[j(x),j(y)]|0> <0|[j(x),j(y)]|0>can be obtained from Lcan be obtained from L

Two-bodyTwo-body

BS + TDDFT programsBS + TDDFT programsADF (Stener et al., 2003)ADF (Stener et al., 2003) TDDFT

www.scm.com/

DP (Olevano et al., 1999)DP (Olevano et al., 1999) TDDFT pseudopotential

theory.polytechnique.fr/codes/dp/dp.html

EXCEXC Bethe-Salpeter pseudopotential

theory.polytechnique.fr/codes/exc/exc.html

NBSE (Shirley, 1998)NBSE (Shirley, 1998) Bethe-Salpeter pseudopotential

physics.nist.gov/Divisions/Div844/staff/Gp4/shirley.html

Many-body statesMany-body states

Many-bodyMany-body

nn||nn||.r|.r|00>|>|22 ((nn--00-E)-E)

iiVVnn((rrii) ) ijijVVee((rrijij)) |)) |nn> = > = nn | |nn> >

||00> > many-bodymany-body ground stateground state

Multiplet programsMultiplet programs

TT-MULTIPLETS (Thole et al., 1990)TT-MULTIPLETS (Thole et al., 1990) www.anorg.chem.uu.nl/people/staff/FrankdeGroot/ttmultiplets.htm/

Cluster (Kotani et al., 1992)Cluster (Kotani et al., 1992) theo.phys.okayama-u.ac.jp/~okada/index_e.html/

AMARCORD (Mirone, 2000)AMARCORD (Mirone, 2000) www.esrf.fr/computing/scientific/people/mirone/amarcord/

ProblemsProblems

Green functions and KS-(TD)DFTGreen functions and KS-(TD)DFT One-particle orbitals are occupied or not

Restricted to closed shell systems

MultipletsMultiplets parametrized very small systems

Unifying approachesUnifying approaches

Multichannel multiple scatteringMultichannel multiple scattering Krüger and Natoli (2004)

TDDFT for open shellsTDDFT for open shells in progress (E.K.U Gross and coll.)

Green functions with correlationGreen functions with correlation in progress

Long-term programLong-term program

CORRELATION