XSPECTRA A Tool for X-ray Absorption Spectroscopy...

XSPECTRAA Tool for X-ray Absorption Spectroscopy

Calculations

Oana Bunău

School on Numerical Methods for Materials Science Related to Renewable EnergyApplications

Trieste28th November 2012

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XAS is a probe of the empty states projected on theabsorbing atom

σ(ω) = 4π2α~ω∑j

∑f ,g

|〈f |Ô|g〉|2 δ (~ω − (Ef − Eg ))

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About XSPECTRA

Scope: provides interpretation of XAS spectra

within the single particle approximation

near edge XAS @ K and L1 edges with linear polarization

distributed within the Quantum Espresso package

free (GNU licence)

Please acknowledge:

C. Gougoussis, M. Calandra, A. P. Seitsonen, and F. Mauri in Phys. Rev.B 80, 075102 (2009)

P. Giannozzi et al. in J. Phys. Condens. Matter 21, 395502 (2009)

M. Taillefumier, D. Cabaret, A. M. Flank, F. Mauri in Phys. Rev. B 66,195107 (2002)

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1 The PAW theory

2 The Lanczos algorithm

3 Hands on XSPECTRA

4 Examples

5 Summary

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1 The PAW theory


3 Hands on XSPECTRA

4 Examples

5 Summary

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The PAW methodWe need to reconstruct the all electron states

Both the probed states |f 〉 and the core level |g〉 are all electron statesWith pseudopotentials we normally get pseudo states.

To reconstruct the all electron ones, use:

The projector augmented wave method PAW

All electron Pseudo

|Ψ〉 mapping←−−−→ |Ψ̃〉

P. E. Blochl, Phys. Rev. B 50, 17953 (1994)

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PAW for XASM. Taillefumier et al. in Phys. Rev. B 66, 195107 (2002)

By using |f 〉 = T |f̃ 〉 and the localization of |g〉:


∑f ,g

|〈f̃ |Φ̃R0〉|2 δ (~ω − (Ef − Eg ))

where |Φ̃R0〉 =∑

n |p̃nR0〉〈φnR0 |Ô|g〉

|g〉 the all electron initial (core) level, without hole|φnR0〉 the all electron partial waves, localized on the absorberÔ = � · r + 12 (� · r)(k · r) the transition operator|p̃nR0〉 the PAW projectorsR0 the position of the absorbing atom

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PAW for XASM. Taillefumier et al. in Phys. Rev. B 66, 195107 (2002)

|Φ̃R0〉 =∑n

|p̃nR0〉〈φnR0 |Ô|g〉

The sum runs over a complete set ⇔ infinite number of projectors

In practice a finite number of projectors is enough.

1 projector/channel (l)

generally yields wrong intensitieswrong dipole/quadrupole ratio

2 projectors/channel (l)

correct intensities in the near edge region (≈ 50 eV above the edge,in most of the cases)need to be linearly independent (i.e. ⇔ span a 2×2 subspace)

To simulate the extended edge (EXAFS) more projectors are needed, butthen you might want to use another method

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1 The PAW theory


3 Hands on XSPECTRA

4 Examples

5 Summary

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The sum over the empty states


∑f ,g

|〈f̃ |Φ̃R0〉|2 δ (~ω − (Ef − Eg ))

The direct sum over the empty states f is very expensive.

Instead, re-write (δ → 0):

σ(ω) = 4πα~ω∑j

∑g

|〈Φ̃R0 |Im(H̃ − Eg − ~ω − iδ)−1|Φ̃R0〉|2

with H̃ = T †HT the pseudo-Hamiltonian

Solve by using the Lanczos algorithm and the continued fraction.

Advantage: the empty states are not calculated explicitly. The sum overempty states depends on the occupied bands only.

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The Lanczos algorithm and the continued fraction

M(E ) = 〈Φ̃R0 |Im(H̃ − E − iδ)−1|Φ̃R0〉 = ? (E = Eg + ~ω)

Scope: Calculate without brute force diagonalization

1. Use the Lanczos recursive algorithm to bring H̃ in a tridiagonal form.2. Use the continued fraction to evaluate the matrix element above.

See more in:C. Lanczos in J. Res. Natl. Bur. Stand. 45, 255 (1950)C. Lanczos in J. Res. Natl. Bur. Stand. 49, 33 (1952)R. Haydock, V. Heine and M. Kelly in J. Phys C 5, 2845 (1972)M. Taillefumier, D. Cabaret, A. M. Flank, F. Mauri in Phys. Rev. B 66, 195107(2002)B. Walker and R. Gebauer in J. Chem. Phys 127 164106 (2007)C. Gougoussis, M. Calandra, A. P. Seitsonen, and F. Mauri in Phys. Rev. B 80,075102 (2009)

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The Lanczos basis {|ui 〉}:

|u0〉 =|Φ̃R0〉√〈Φ̃R0 |Φ̃R0〉

H̃|ui 〉 = ai |ui 〉+ bi+1|ui+1〉+ bi |ui−1〉

H̃ =

a0 b1 0 0 0b1 a1 b2 0 00 b2 a2 b3 0

0 0 b3. . .

. . .

0 0. . .

. . .. . .

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The Lanczos basis {|ui 〉}:

|u0〉 =|Φ̃R0〉√〈Φ̃R0 |Φ̃R0〉

H̃|ui 〉 = ai |ui 〉+ bi+1|ui+1〉+ bi |ui−1〉

M(E ) =〈Φ̃R0 |Φ̃R0〉

a0 − E − iδ −b21

a1−E−iδ−b22

...

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Lanczos within XSPECTRASome useful input parameters

M(E ) =〈Φ̃R0 |Φ̃R0〉

a0 − E − iδ −b21

a1−E−iδ−b22

a2−E−iδ−b23···

will eventually converge when the Lanczos space is large enough.

Related keywords:

xniter = maximum number of iterations (maximum dimension of theLanczos basis)

xerror = convergence threshold on the integral of the XAS crosssection

xcheck conv = number of iteration between two convergence checks

xgamma = Lorentzian broadening (related to the core-hole lifetime)

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Lanczos within XSPECTRASome useful input parameters

M(E ) =〈Φ̃R0 |Φ̃R0〉

a0 − E − iδ − b21

a1−E−iδ−b22

a2−E−iδ−b23···

will eventually converge when the Lanczos space is large enough.

Related keywords:

xsave = save file storing the Lanczos a and b parameters

terminator = .true. imposes the use of a terminator ⇔(ai , bi ) = (aN , bN) for i > N, allowing an analytical form of thecontinued fraction

The convergence depends strongly on the broadening parameter

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Case of multiple absorbers

If the unit cell contains several absorbers: σtot =∑

j σj

If two or more equivalent atoms, calculate one of them and infer thecross section of the peers by using group theory ( see C. Brouder in J.Phys.: Condens. Matter 2 70138, 1990)

If two or more non-equivalent atoms of the absorbing species, you needto run as many calculations (pw + XSPECTRA) as the number ofnon-equivalent atoms.Mind the core-level shift (see S. Gao et al. in Phys. Rev. B 77 115122,2008).

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1 The PAW theory


3 Hands on XSPECTRAPrepare the GIPAW pseudopotentialsExtracting the core wavefunctionPrepare the (supercell) SCF input fileRun a SCF calculationRun XSPECTRA

4 ExamplesC K edge in diamondSi K edge in SiO2Ni K edge in NiO

5 Summary

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cp -r $WORKSHOP/Tutorial XSpectra /scratch/cd /scratch/Tutorial XSpectra/

Directory structure:

./input/ input files for the examples

./outdir/ tmp output

./pseudo/ pseudopotentials for this tutorialthe script upf2plotcore.sh

./Gipaw pseudo generation/ input files necessary to generate GIPAWpseudopotentials with and without a core-hole

./solutions/ reference outputs for the files in ./input/

./References/ relevant papers, the .pdf of these lecturesmanual page INPUT XSPECTRA

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Steps to run XSPECTRA

1 Prepare the GIPAW pseudopotentials2 Extract the core wavefunction ./upf2plotcore.sh pseudo.UPF3 Prepare the (supercell) SCF input file4 Run a SCF calculation: pw.x < prefix.scf.in > prefix.scf.out5 Run XSPECTRA: xspectra.x < prefix.xspectra.in > prefix.xspectra.out

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1 The PAW theory




5 Summary

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GIPAWGauge independent PAW pseudopotential

The GIPAW pseudopotential includes all the reconstruction informationneeded to run XSPECTRA

needed for the absorbing atom only (non-absorbing atoms acceptany kind of pseudopotential)

contains the following information on the absorbing atom:

the core wavefunction without holethe all electron atomic statesthe Blochl projectors

can be obtained with the atomic code ld1.x

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Exercise: Generate a C GIPAW in order to calculate the dipolarcontribution at the C K edge in diamond

Projector 1st projector 2nd projectorchannel energy energy

optional s 2s 3smandatory p 2p 3p

Remember that a minimum of 2 projectors/channel is needed !!

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Generating GIPAW pseudopotentialNo core hole

File ./Gipaw Pseudo Generation/C.ld1.in

&input

title=’C’, ! atomic symbol

prefix=’C’, ! prefix

zed=6.0, ! atomic number

config=’1s2 2s2 2p1.5 3s0 3p0’, ! atomic configuration

iswitch=3,

dft=’PBE’, ! xc functional

rel=1

/

........

”!” marks the beginning of a comment

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&input





iswitch=3,


rel=1

/

........

Atomic configuration of the isolated atom.In the case of C needs a bit of ionization.Since we want to generate projectors at the 2s, 2p, 3s, 3p energies thesestates need to be included.

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&input





iswitch=3,


rel=1

/

........

Exchange correlation functional.Must be the same for all the atoms.

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&input





iswitch=3,


rel=1

/

........

Defaults.No need to touch

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Generating GIPAW pseudopotentialWith hole

File ./Gipaw Pseudo Generation/C/Ch.ld1.in

&input

title=’Ch’, ! atomic symbol




iswitch=3,


rel=1

/

........

Keep the same atomic number and put the hole on the 1s state.You can of course define fractional holes (e.g. 1s0.5) but use with care !!

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File ./Gipaw Pseudo Generation/Ch.ld1.in

........

&inputp

file pseudopw=’C.star1s-pbemt gipaw.UPF’,

pseudotype=2 ! type of pseudopotential

lloc=1, ! angular momentum of

! the local channel

tm=.true., ! Trouiller-Martins pseudization

lgipaw reconstruction=.true., ! include GIPAW information

/

........

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........

&inputp




! the local channel



/

........

2 for norm conserving3 for ultrasoft

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........

&inputp




! the local channel



/

........

This flag is needed to insert GIPAW reconstruction information

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........

2 ! number of states

2S 1 0 2.0 0 1.5 1.5 ! standard C valence states for

2P 2 1 1.5 0 1.5 1.5 ! pseudization

&test

/

4 ! number of projectors

2S 1 0 2.0 0 1.5 1.5 ! list of projectors

2P 2 1 1.5 0 1.5 1.5

3S 2 0 0.0 0 1.5 1.5

3P 3 1 0.0 0 1.5 1.5

EOF

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Generating GIPAW pseudopotentialAvailability

Now run:

ld1.x < C.ld1x.in > C.ld1x.out

ld1.x < Ch.ld1x.in > Ch.ld1x.out

to get C.pbe-mt gipaw.UPF and C.star1s.pbe-mt gipaw.UPF pp files

About the notation system:

starNs = core-hole in the Ns state

PBE = the exchange correlation functional

gipaw = contains GIPAW information

Some GIPAW pseudopotentials are already available in the QuantumEspresso pseudopotential table, e.g. Ni.star1s-pbe-sp-mt gipaw.UPF

If not, you may find pslibrary on www.qe-forge.org useful. Add thereconstruction information (gipaw flag + list of projectors) to the existingld1 inputs and generate your own GIPAW pseudopotentials.

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1 The PAW theory




5 Summary

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Extracting the core wavefunction

The core wavefunction without hole can be obtained with the ld1.x codeby performing an all electron calculation on the isolated atom.

Alternatively, if you have a GIPAW pseudopotential without core hole youcan use the script upf2plotcore.sh

./upf2plotcore.sh C.pbemt gipaw.UPF > C.wfc

→ C.wfc is needed by XSPECTRA→ a copy of upf2plotcore.sh is saved in ./pseudo

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1 The PAW theory




5 Summary

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Generating the SCF inputsCalculations with core hole require a supercell

1 use the GIPAW pseudopotentials with core hole for each atom of theabsorbing species

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Generating the SCF inputsCalculations with core hole require a supercell

1 use the GIPAW pseudopotentials with core hole for each atom of theabsorbing species

2 build a supercell to eliminate spurious interaction between thecore-hole and its periodic images

3 increase gradually the supercell’s dimension until convergence isachieved

Typically 6 to 7 Å are needed between the core hole and its images

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1 The PAW theory




5 Summary

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Electronic structure generation

File ./Diamond/diamondh.scf.in

&control

calculation=’scf’,

pseudo dir = ’$PSEUDO_DIR/’,

outdir=’$TMP DIR/’,

prefix=’diamondh’,

/

..........

Flag to be specified when performing the electronic structure calculation

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Electronic structure generationFile ./input/diamondh.scf.in

..........

&system

ibrav = 1, ! type of Bravais lattice

celldm(1) = 6.740256, ! cell parameter

nat=8, ! number of atoms

ntyp=2, ! number of atom types

nbnd=16, ! number of bands

tot charge = 1, ! charge of the cell

ecutwfc=40.0, ! cutoff energy

/

..........

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File ./input/diamondh.scf.in

..........

&system








/

..........

8 atom supercellThe total charge of the cluster needs to be specified when the core holeis present, to compensate for the extra electron in the empty states.

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File ./input/diamondh.scf.in

..........

&system








/

..........

The absorbing atom needs to be considered different from the other Catoms. The core hole breaks the symmetry of the crystal.

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File ./Diamond/diamondh.scf.in

........

ATOMIC SPECIES

C h 12.0 Ch PBE TM 2pj.UPF

C 12.0 C PBE TM 2pj.UPF

ATOMIC POSITIONS crystal

C h 0.0 0.0 0.0

C 0.0 0.5 0.5

C 0.5 0.0 0.5

C 0.5 0.5 0.0

C 0.75 0.75 0.25

C 0.75 0.25 0.75

C 0.25 0.75 0.75

C 0.25 0.25 0.25

K POINTS automatic

4 4 4 0 0 0

EOF

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1 The PAW theory




5 Summary

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XSPECTRA input file

File ./input/diamondh.xspectra.in

&input xspectra

calculation=’xanes dipole’, ! type of calculation



xepsilon(1)=1.0; xepsilon(2)=0.0, ! polarization

xepsilon(3)=0.0; xcoordcrys=.true. ! polarization

xiabs=1, ! type of the absorber

ef r=$FERMI LEVEL, ! Fermi energy in Ry

/

........

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XSPECTRA input file


&input xspectra








/

........

’xanes dipole’,’xanes quadrupole’If ’xanes quadrupole’, both ~� and ~k need to be specified

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XSPECTRA input file


&input xspectra








/

........

Same as for the SCF calculationThe Fermi energy, or LUMO, must be taken from the previous step.Alternatively, it can be calculated in XSPECTRA by settingcalculation=’fermi level’ (insulating case only)

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XSPECTRA input file


&input xspectra








/

........

Projections of the polarization vectorxcoordcrys=.true. ⇒ crystal basexcoordcrys=.false. ⇒ cartesian

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XSPECTRA input file


&input xspectra








/

........

Rank of the absorbing atom under ATOMIC SPECIES in the electronicstructure calculation input.

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XSPECTRA input fileParameters controlling the Lanczos process

File ./input/diamond.xspectra.in

&input xspectra

x save file=’diamondh.xspectra.sav’,

xerror=0.001,

xniter=1000,

xcheck conv=50,

xonly plot=.false.

/

........

See explanations on slide no. 12Use xonly plot=.true. to replot spectra from a previous run(stored in the .sav file)

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XSPECTRA input fileParameters for the plot


..........

&plot

xnepoint=300, ! number of energy points

xgamma=0.8, ! core hole linewidth in eV

xemin=-10.0, ! energy min in eV

xemax=30.0, ! energy max in eV

terminator=.true., ! use a terminator for Lanczos (faster!)

cut occ states=.true., ! treatment of occupied states

/

.......

The cut occ states flag controls whether transition below the Fermi levelare considered or not in calculating the cross section.Only cut occ states=.true. has a physical meaning

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..........

&pseudos

filecore=’C.wfc’, ! the core wfc

r paw(1)=3.2, ! PAW radius for l=1 channel

/

&cut occ

cut desmooth=0.1,

/

4 4 4 0 0 0

EOF

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..........

&pseudos



/

&cut occ

cut desmooth=0.1,

/

4 4 4 0 0 0

EOF

Obtained at the previous step with ./upf2plotcore.sh.

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..........

&pseudos



/

&cut occ

cut desmooth=0.1,

/

4 4 4 0 0 0

EOF

Radius of the augmentation regionA good choice in general is rpaw = 1.5*rcut with rcut the cutoff radius inthe norm conserving generationDecrease if projectors are linearly dependentDo not touch if in doubt...

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..........

&pseudos



/

&cut occ

cut desmooth=0.1,

/

4 4 4 0 0 0

EOF

Parameters specifying how to cut smoothly the occupied states (if metal).Full explanation in Ch. Brouder, M. Alouani, K.H. Bennemann in Phys.Rev. B 54 7334 (1996)Accurate but time-consuming. Alternative: use xgamma=0.1 andconvolute as post-process.

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..........

&pseudos



/

&cut occ

cut desmooth=0.1,

/

4 4 4 0 0 0

EOF

The k point sampling is not necessarily the same as in the SCF run.

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XSPECTRA output files

prefix.xspectra.out is the talkative file containing information aboutthe run

prefix.xspectra.dat contains the XAS spectrum and can be visualizedwith usual plotting tools (gnuplot, xmgrace)

prefix.xspectra.sav is the save file, containing information on theLanczos process (a and b vectors)

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# final state angular momentum: 1

# broadening parameter (in eV): 0.1

# absorbing atom type: 1

# Energy (eV) sigma

-10.00000000 0.00219117

-9.88988989 0.00229325

-9.77977978 0.00240286

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Keep the save file if you want to:

resume a previously interrupted run

replot spectrum with different

broadeningenergy range

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1 The PAW theory


3 Hands on XSPECTRA


5 Summary

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The effect of the core holeC K edge in diamond

Task 1 Apply the previous steps to obtain the spectra with and withoutcore hole, at the C K edge in diamond.

What you’ve already done:generate GIPAW pseudopotentials for C, with and without core holegenerate the core wavefunction without hole C.wfc

What you need to do now:1. Make sure that the C.wfc and C*UPF are in the right directory2. Make sure you have the correct paths in *.scf.in and *.xspectra.in3. Run the SCF calculation:

pw.x < diamond.scf.in > diamond.scf.outpw.x < diamondh.scf.in > diamondh.scf.out

4. Run the XAS calculation:xspectra.x < diamond.xspectra.in > diamond.xspectra.outxspectra.x < diamondh.xspectra.in > diamondh.xspectra.out

What can you tell about the importance of the core hole ?, 40/62

The effect of the core holeC K edge in diamond

0.00

0.05

0.10

0.15

0.20

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XA

S (

u.a

.)

Energy (eV)

C K edge in diamond

with core holeno hole

The effect of the core hole is huge.

It is usually the case when the Fermilevel lies in the same band probed bythe XAS.

What happens when you increase the size of the supercell ?

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Increasing the size of the supercell

Task 21. Write the SCF input for a larger supercell.2. Perform a XSPECTRA calculation with core hole on this newstructure.

For instance, double the 8 atom supercell in one of the directions⇓

16 atoms.

Check your input with xcrysden –pwi prefix.scf.in

For the sake of comparison, keep a k point sampling equivalent to theone of the 8 atom supercell, both for SCF and XAS calculations.

Precaution For accurate calculations always choose supercells that obeythe symmetry of the crystal. In this case, the 2×2×2 instead of the2×2×1

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8 atoms supercell

ibrav = 1,

nat=8,

celldm(1) = 6.740256,

celldm(2) = 1,

celldm(3) = 1,

K POINTS automatic

4 4 4 0 0 0

16 atoms supercell

ibrav = 8,

nat=16,

celldm(1) = 6.740256,

celldm(2) = 1,

celldm(3) = 2

K POINTS automatic

4 4 2 0 0 0

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from M. Taillefumier et al.

Phys. Rev. B 66, 195107 (2002)

+ The appropriate treatment ofthe core hole requires thesolution of the two bodyproblem (Bethe Salpeterequation), but this is veryexpensive.

+ Usually taking into account thecore hole self-consistently is areasonable approximation.

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C K edge in diamond

Choose one of the two cases (with or without hole).

Task 31. Add another projector to the l = 1 channel.2. Re-run the SCF and XAS calculations.3. Check the linear dependence of the projectors (see *xspectra.out)

Task 4 Eliminate one of the projectors for the l = 0 channel. Whathappens ?

Task 5 Calculate the dipolar spectrum for another polarization direction,e.g. (123), and compare to the (100). Use the 8 atom supercell.

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Number of projectorsC K edge in diamond

0.00

0.05

0.10

-5 0 5 10 15 20 25 30

XA

S (

u.a

.)

Energy (eV)

C K edge in diamond

3 proj l=12 proj l=1

This is a typical example where 3 projectors / l=1 channel are needed.

Adding a projector will never shift the positions of peaks in the spectra,at most it affects intensities.

Projectors for the l=0 channel are not important @ K edges.

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Polarization effectsTensor formalism

+ The XAS of non cubic samples depends on the orientation of thepolarization.

+ The absorption tensor of the crystal obeys the symmetry of thespace group

+ The atomic absorption tensors obey the specific point groupsymmetry

Cubic (e.g. diamond):

σ =

σ0 0 00 σ0 00 0 σ0

Hexagonal (e.g. SiO2):

σ =

σ|| 0 00 σ|| 00 0 σ⊥

for dipolar E1-E1 transitions only !

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Polarization effectsTensor formalism

+ The XAS of non cubic samples depends on the orientation of thepolarization.

+ The absorption tensor of the crystal obeys the symmetry of thespace group

+ The atomic absorption tensors obey the specific point groupsymmetry

(�∗x �∗y �∗z )

σxx σxy σxzσyx σyy σyzσzx σzy σzz

�∗x�∗y�∗z

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1 The PAW theory




5 Summary

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Si K edge in SiO2Linear dichroism

Task 6 Calculate the spectra for in plane (σ||) and out of plane (σ⊥)polarizations.

1. ./upf2plotcore.sh Si PBE TM 2pj.UPF > Si.wfc2. pw.x < SiO2.scf.in > SiO2.scf.out3. xspectra.x < SiO2.xspectra plane.in > SiO2.xspectra plane.out4. xspectra.x < SiO2.xspectra c.in > SiO2.xspectra c.out

Task 7 Check that the spectra are invariant for any � ⊥ Oz

Task 8 Try to restart the Lanczos from a previously interrupted run (fileSiO2.xspectra restart 1.in). Check the manual page(./References/INPUT XSPECTRA.txt) for more information.

1. Use the time limit keyword to interrupt a run2. Use restart mode = ’restart’ to resume3. Check the output *.out

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Si K edge in SiO2Linear dichroism

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0.0025

0.0050

0.0075

-5 0 5 10 15 20 25 30 35 40

XA

S (

u.a

.)

Energy (eV)

Si K edge in SiO2

in planeout of plane

The dipolar spectrum for a given polarization direction can be expressed as alinear combination of these two elementary spectra.

The dipolar spectrum for a powder: σiso =σ100+σ010+σ001

3

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Si K edge in SiO2Converged results

C. Gougoussis et al. in Phys. Rev. B 80, 075102 (2009)

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1 The PAW theory




5 Summary

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Ni K edge in NiOThe magnetic primitive cell

File ./input/NiO.scf.in:

&system

ibrav = 5, celldm(1) =9.67155, celldm(4)=0.8333333333,

starting magnetization(1)=1.0, starting magnetization(2)=-1.0,

tot magnetization = 0

/

ATOMIC SPECIES

Ni 58.6934 Ni PBE TM 2pj.UPF

B 58.6934 Ni PBE TM 2pj.UPF

O 15.9994 O PBE TM.UPF

ATOMIC POSITIONS crystal

Ni 0.0000000000 0.0000000000 0.0000000000

B -.5000000000 1.5000000000 -.5000000000

O 0.7500000000 -.2500000000 -.2500000000

O -.7500000000 0.2500000000 0.2500000000

The magnetic primitive cell contains two Ni atoms AF-coupled., 53/62

Ni K edge in NiODipolar E1-E1 and quadrupolar E2-E2 contributions

Task 10 Calculate the dipolar and quadrupolar contributions to thespectra for one of the absorbing Ni.

1. ./upf2plotcore.sh Ni PBE TM 2pj.UPF > Ni.wfc2. pw.x < NiO.scf.in > NiO.scf.out3. xspectra.x < NiO.xspectra fermi.in > NiO.xspectra fermi.out4. xspectra.x < NiO.xspectra dip.in > NiO.xspectra dip.out5. xspectra.x < NiO.xspectra qua.in > NiO.xspectra qua.out

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Ni K edge in NiODipolar E1-E1 and quadrupolar E2-E2 contributions

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0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0 5 10 15 20

XA

S (

u.a

.)

Energy (eV)

Ni K edge in NiO

quadrupole x 15dipole

Dipolar contribution always dominates, due to the higher overlap withthe 1s radial function.

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Ni K edge in NiOSpin resolved signal

Plot the up and down contributions to the spectra.File NiO *.dat:

# final state angular momentum: 1

# broadening parameter (in eV): 0.900000000000

# absorbing atom type: 1

# Energy (eV) sigmatot sigmaup sigmadown

-10.00000000 0.00001279 0.00000644 0.00000635

-9.89966555 0.00001289 0.00000649 0.00000640

-9.79933110 0.00001298 0.00000654 0.00000645

-9.69899666 0.00001308 0.00000659 0.00000650

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0

4

8

12

16

0 5 10 15 20

XA

S (

u.a

.)

Energy (eV)

Ni K edge in NiO

dipole E1-E1

updown

0.0

0.5

1.0

1.5

2.0

-2 0 2 4 6 8 10 12 14

XA

S (

u.a

.)

Energy (eV)

Ni K edge in NiO

quadrupole E2-E2

updown

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Task 11 Calculate the second Ni atom and compare with the first one.

Hint: use xiabs = 2 in NiO.xspectra-qua.in

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0.0

0.5

1.0

1.5

2.0

-2 0 2 4 6 8 10 12 14

XA

S (

u.a

.)

Energy (eV)

Ni K edge in NiO

Up states in

quadrupole E2-E2

transitions

Ni1 upNi2 up

Ni1 ↑ = Ni2 ↓Ni1 ↓ = Ni2 ↑

+Ni1 ≡ Ni2

Calculating only one of the two Ni is enough, since they are symmetry related(time reversal symmetry)

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0.0

0.5

1.0

1.5

2.0

-2 0 2 4 6 8 10 12 14

XA

S (

u.a

.)

Energy (eV)

Ni K edge in NiO

Up states in

quadrupole E2-E2

transitions

Ni1 upNi2 up

Ni1 ↑ = Ni2 ↓Ni1 ↓ = Ni2 ↑

+Ni1 ≡ Ni2

Task 12 Turn the antiferromagnet into a feeble ferrimagnet.

Hint: Lower the accuracy in the SCF run (pedagogical purpose only).Check what happens.

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1 The PAW theory


3 Hands on XSPECTRA

4 Examples

5 Summary

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XSPECTRA features

calculates K and L1 edges (dipole E1-E1 and quadrupole E2-E2 withlinear polarization)

supports all standard DFT functionals available in QuantumEspresso (PZ,PBE,PZ+U,PBE+U)

supports both ultrasoft and norm conserving pseudopotentials

the pseudopotential of the absorbing species must containinformation on the core states (GIPAW)

the all electron reconstruction is performed within GIPAW

the summation over the empty states is done using a Lanczosalgorithm and a continued fraction approach

a supercell is needed to model the core hole

Not yet supported:

spin-orbit coupling

circular polarization

hybrid functionals

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History

First implementation of XAS calculation using the PAW method belongsto M. Taillefumier, D. Cabaret, A. M. Flank, F. Mauri in Phys. Rev. B66, 195107 (2002).

norm conserving

dipolar E1-E1 transitions

The method was improved and ported in Quantum Espresso by C.Gougoussis, M. Calandra, A. P. Seitsonen, and F. Mauri in Phys. Rev. B80, 075102 (2009).

norm conserving and ultrasoft pseudopotentials

dipolar E1-E1 and quadrupolar E2-E2 transitions

supports DFT+U

Please cite these works if you use XSPECTRA results in yourpublications, as well as P. Giannozzi et al. in J. Phys. Condens. Matter21, 395502 (2009)

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Please feel free to contact me: bunau at unizar.es

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The PAW theoryThe Lanczos algorithmHands on XSPECTRAPrepare the GIPAW pseudopotentialsExtracting the core wavefunctionPrepare the (supercell) SCF input fileRun a SCF calculationRun XSPECTRA

ExamplesC K edge in diamondSi K edge in SiO2Ni K edge in NiO

Summary

XSPECTRA A Tool for X-ray Absorption Spectroscopy...

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