OCEAN and AI2NBSE OCEAN and AI2NBSE postprocessors of ABINIT for postprocessors of ABINIT for

Core and Valence SpectraCore and Valence Spectra

J.J.RehrJ.J.Rehr11,, John VinsonJohn Vinson11, E.L.Shirley, E.L.Shirley22

J.J. KasJ.J. Kas1 1 and F. Vilaand F. Vila1 1

11U. of Washington Seattle, WAU. of Washington Seattle, WA22N.I.S.T. Gaithersburg, MDN.I.S.T. Gaithersburg, MD

aka SKWIGGLiEaka SKWIGGLiE

SSpectra from pectra from KK-space -space WWave-ave-functions with functions with IInteractions, nteractions,

GGradually radually GGetting etting LiLike ke EExperimentxperiment

Hybrid approach to core Hybrid approach to core spectroscopyspectroscopy GW/BSE for GW/BSE for XAS, NRIXS, EELS, …XAS, NRIXS, EELS, … PAW Pseudo-potential / planewave DFT PAW Pseudo-potential / planewave DFT

Includes self energy damping, Includes self energy damping, multiplets … …multiplets … …

OObtaining btaining CCore ore EExcitationxcitation spectra usingspectra usingAABINIT andBINIT andNNBSEBSE

1. OCEAN*

*Phys. Rev. B 83, 115106 (2011)

2. Optical-UV Spectra AI2NBSE* (ABINIT + NIST BSE)

*Phys. Rev. B 78, 205108 (2008)

Bethe-Salpeter EquationBethe-Salpeter Equation

Particle-Hole HamiltonianParticle-Hole Hamiltonian H = EH = E00 + V + Vc c + W+ W

Bubble Bubble VVcc is unscreened is unscreened Ladder Ladder WW is screened is screened

Bubble Ladder

Bethe-Salpeter EquationBethe-Salpeter Equation

MultipletsCentral term

Dielectric Response < Dielectric Response < BSEBSE

H H particle-hole Hamiltonian including: particle-hole Hamiltonian including:

many-pole GW self-energy many-pole GW self-energy ΣΣ Algorithm: Haydock recursion Algorithm: Haydock recursion

Standard Density-Functional TheoryStandard Density-Functional Theory Pseudopotential, Plane-wave, LDAPseudopotential, Plane-wave, LDA ABINITABINIT (www.abinit.org) (www.abinit.org)

Well-documented shortcomings; Well-documented shortcomings; improvements:improvements: GWGW XC + UXC + U

Core to pseudo transitions with PAWCore to pseudo transitions with PAW Following Blöchl, PRB 50, 17953 (1994)Following Blöchl, PRB 50, 17953 (1994)

Ground-stateGround-state

ABINITABINIT (Plane-wave, pseudo-potential)* (Plane-wave, pseudo-potential)* LDA (Ceperley-Alder) LDA (Ceperley-Alder) VVxcxc

Zero Temp / Frozen latticeZero Temp / Frozen lattice

Regular grid in Regular grid in kk-space-space Size required varies with BZ volumeSize required varies with BZ volume

Core states from NIST HF atomic Core states from NIST HF atomic codecode

*Other PW/PP DFT codes may also work*Other PW/PP DFT codes may also work

Kohn-Sham Wave-Kohn-Sham Wave-FunctionsFunctions

Electron-hole pair Electron-hole pair approximationapproximation

Conduction electron

Core hole

……

PAW Matrix Elements PAW Matrix Elements

Core-Hole ScreeningCore-Hole Screening

Core response from self-consistent Core response from self-consistent HF HF

Use neutralizing shell to divide Use neutralizing shell to divide valencevalence RPA for short rangeRPA for short range Model dielectric for long rangeModel dielectric for long range

Hybersten and Louie, Phys Rev B 35, 5585 (1987)

GW Many-pole self-GW Many-pole self-energyenergy

Extension of Hedin-Lundqvist Extension of Hedin-Lundqvist plasmon-poleplasmon-pole

MPSE (Kas et al.*)MPSE (Kas et al.*) Calculate loss functionCalculate loss function

with with AI2NBSEAI2NBSE Model as a series Model as a series

of (many) polesof (many) poles Apply as convolutionApply as convolution

J.J. Kas et. al, Phys Rev B 76, 195116 (2007)

LiF loss

OCEAN PackageOCEAN Package

Structure DFT/ABINIT HFAtom

BSESpectra

Example: Li Example: Li KK-edge XAS of LiF-edge XAS of LiF

1000 k-points

100 Ha. cut-off

Expt. data from K. Handa et. al, Memoires Sr. Center Ritsumeika Univ 7 (2005)

1000 k-points

100 Ha. cut-off

Example:Example: Li Li KK-edge XAS of LiF -edge XAS of LiF Comparison with EXC!TING* (Comparison with EXC!TING* (NO NO

MPSE)MPSE)

*W. Olovsson et. al, Phys Rev B 79, 041102(R) (2009)

NO MPSE

Example: F Example: F KK-edge XAS in LiF-edge XAS in LiF

Expt. data from E. Hudson et. al, Phys. Rev. B 49, 3701 (1994)

1000 k-points

100 Ha. cut-off

Ice: Ice: O K edge XAS

8 molecule cells

216 k-points

50 Ha. cut-off

Expt. data from P. Wernet et. al, Science 304, 995 (2004)

Example: L-edge Spectra – Multiplet effects Ti L2,3 edge SrTiO3

HB SE = Hh +He +Heh

Heh = V®(r) +g(i; j )

cf. De Groot et al – Atomic model + crystal-field parametersHh = ¡ ²®+L ¢S(p)

He = p2

2m +L ¢S(d) +H xtalK S Hat = Hav +L ¢S(p)

+L ¢S(d) +Hxtalf ield +g(i; j )

*J. Elec.Spect. Rel. Phen. 144, 1187(2005)

alá E. Shirley: BSE + KS crystal potentialab initio – no parameters

PRL 45, 397 (1980)

V L23

Ni L23

L23 Transition Elements

di 2

coth0

22

recursion Lanczos step6

22

ii QDQ

3. Ab initio XAS Debye Waller Factors e-2σ2 k2

*Phys. Rev. B 76, 014301 (2007)

Ψ

Many Pole model

for phonons

*

VDOS ρ

D ynamical matrix D from ABINIT

Example: XAFS Debye-Waller Factor of GeExample: XAFS Debye-Waller Factor of Ge

Expt: Dalba et al. (1999)

F. Vila et al. Phys. Rev. B76, 014301 (2007)

ConclusionsConclusions Core & Valence BSE+GW packagesCore & Valence BSE+GW packages

OCEAN & AI2NBSEOCEAN & AI2NBSE

NRIXS, EELS, XAS, NRIXS, EELS, XAS,

Includes GW self-energy, multiplets, ..Includes GW self-energy, multiplets, ..

Future: RIXS, XPS, DW factors, etc.Future: RIXS, XPS, DW factors, etc.

AcknowledgmentsAcknowledgments

J. Vinson (UW)J. Vinson (UW) J. Kas (UW)J. Kas (UW) F. Vila (UW)F. Vila (UW) K. Jorissen (UW)K. Jorissen (UW) H. Lawler (Vanderbilt)H. Lawler (Vanderbilt) E. Shirley (NIST)E. Shirley (NIST)

Thanks to

Supported by DOE BES Grant DEFG03-97ER45623DOE BES Grant DEFG03-97ER45623& DOE Computational Materials Science Network& DOE Computational Materials Science Network

X. Gonze, UC de LouvainA. Soininen (U. Helsinki) L. Reining (E. Polytechnique)C. Ambrosch-Draxl (U. C. Ambrosch-Draxl (U. Leobon)Leobon)T. Ahmed (UW)

Rehr Group & collaborators