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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
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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
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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)
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2. Optical-UV Spectra AI2NBSE* (ABINIT + NIST BSE)
*Phys. Rev. B 78, 205108 (2008)
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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
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Bethe-Salpeter EquationBethe-Salpeter Equation
MultipletsCentral term
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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
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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
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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
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Electron-hole pair Electron-hole pair approximationapproximation
Conduction electron
Core hole
……
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PAW Matrix Elements PAW Matrix Elements
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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)
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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
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OCEAN PackageOCEAN Package
Structure DFT/ABINIT HFAtom
BSESpectra
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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)
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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
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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
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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)
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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
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PRL 45, 397 (1980)
V L23
Ni L23
L23 Transition Elements
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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
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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)
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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.
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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