XSPECTRA A Tool for X-ray Absorption Spectroscopy Calculations

Transcription

1 XSPECTRA A Tool for X-ray Absorption Spectroscopy Calculations Oana Bunău School on Numerical Methods for Materials Science Related to Renewable Energy Applications Trieste 28th November 2012, 1/62

2 XAS is a probe of the empty states projected on the absorbing atom σ(ω) = 4π 2 α ω j f Ô g 2 δ ( ω (E f E g )) f,g, 1/62

3 About XSPECTRA Scope: provides interpretation of XAS spectra within the single particle approximation near edge K and L 1 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, (2009) P. Giannozzi et al. in J. Phys. Condens. Matter 21, (2009) M. Taillefumier, D. Cabaret, A. M. Flank, F. Mauri in Phys. Rev. B 66, (2002), 2/62

4 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA 4 Examples 5 Summary, 3/62

5 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA 4 Examples 5 Summary, 4/62

6 The PAW method We need to reconstruct the all electron states Both the probed states f and the core level g are all electron states With pseudopotentials we normally get pseudo states. To reconstruct the all electron ones, use: The projector augmented wave method PAW All electron Ψ mapping Pseudo Ψ P. E. Blochl, Phys. Rev. B 50, (1994), 5/62

7 The PAW method P. E. Blochl in Phys. Rev. B 50, (1994) Ψ = T Ψ T is linear T ˆ1 in the core (augmentation) region only, 6/62

8 The PAW method P. E. Blochl in Phys. Rev. B 50, (1994) Ψ = T Ψ T is linear T ˆ1 in the core (augmentation) region only ˆT = ˆ1 + R T R = ˆ1 + R ( Φ Rn Φ Rn ) p Rn R the coordinates of nuclei Φ Rn the all electron partial waves Φ Rn the pseudo partial waves The PAW projectors p Rn are defined as: p Rn Φ R n = δ RR δ nn inside 0 outside the augmentation region, 6/62

9 PAW for XAS M. Taillefumier et al. in Phys. Rev. B 66, (2002) By using f = T f and the localization of g : σ(ω) = 4π 2 α ω f Φ R0 2 δ ( ω (E f E g )) j f,g where Φ R0 = n p nr 0 φ nr0 Ô g g the all electron initial (core) level, without hole φ nr0 the all electron partial waves, localized on the absorber Ô = ɛ r (ɛ r)(k r) the transition operator p nr0 the PAW projectors R 0 the position of the absorbing atom, 7/62

10 PAW for XAS M. Taillefumier et al. in Phys. Rev. B 66, (2002) Φ R0 = n p nr0 φ nr0 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 intensities wrong 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, but then you might want to use another method, 8/62

11 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA 4 Examples 5 Summary, 9/62

12 The sum over the empty states σ(ω) = 4π 2 α ω j f Φ R0 2 δ ( ω (E f E g )) The direct sum over the empty states f is very expensive. f,g, 10/62

13 The sum over the empty states σ(ω) = 4π 2 α ω j f Φ R0 2 δ ( ω (E f E g )) The direct sum over the empty states f is very expensive. f,g Instead, re-write (δ 0): σ(ω) = 4πα ω Φ R0 Im( H E g ω iδ) 1 Φ R0 2 j g with H = 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 over empty states depends on the occupied bands only., 10/62

14 The Lanczos algorithm and the continued fraction M(E) = Φ R0 Im( H E iδ) 1 Φ R0 =? (E = E g + ω) Scope: Calculate without brute force diagonalization 1. Use the Lanczos recursive algorithm to bring H 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, (2002) B. Walker and R. Gebauer in J. Chem. Phys (2007) C. Gougoussis, M. Calandra, A. P. Seitsonen, and F. Mauri in Phys. Rev. B 80, (2009), 11/62

15 The Lanczos algorithm and the continued fraction M(E) = Φ R0 Im( H E iδ) 1 Φ R0 =? (E = E g + ω) Scope: Calculate without brute force diagonalization 1. Use the Lanczos recursive algorithm to bring H in a tridiagonal form. 2. Use the continued fraction to evaluate the matrix element above. The Lanczos basis { u i }: u 0 = Φ R0 Φ R0 Φ R0 H u i = a i u i + b i+1 u i+1 + b i u i 1 a 0 b b 1 a 1 b H = 0 b 2 a 2 b b , 11/62

16 The Lanczos algorithm and the continued fraction M(E) = Φ R0 Im( H E iδ) 1 Φ R0 =? (E = E g + ω) Scope: Calculate without brute force diagonalization 1. Use the Lanczos recursive algorithm to bring H in a tridiagonal form. 2. Use the continued fraction to evaluate the matrix element above. The Lanczos basis { u i }: u 0 = Φ R0 Φ R0 Φ R0 H u i = a i u i + b i+1 u i+1 + b i u i 1 Φ R0 Φ R0 M(E) = b1 a 0 E iδ 2 a 1 E iδ b2 2..., 11/62

17 Lanczos within XSPECTRA Some useful input parameters Φ R0 Φ R0 M(E) = a 0 E iδ a 1 E iδ b 2 1 b 2 2 a 2 E iδ b2 3 will eventually converge when the Lanczos space is large enough. Related keywords: xniter = maximum number of iterations (maximum dimension of the Lanczos basis) xerror = convergence threshold on the integral of the XAS cross section xcheck conv = number of iteration between two convergence checks xgamma = Lorentzian broadening (related to the core-hole lifetime), 12/62

18 Lanczos within XSPECTRA Some useful input parameters Φ R0 Φ R0 M(E) = a 0 E iδ a 1 E iδ b 2 1 b 2 2 a 2 E iδ b2 3 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 (a i, b i ) = (a N, b N ) for i > N, allowing an analytical form of the continued fraction The convergence depends strongly on the broadening parameter, 12/62

19 Case of multiple absorbers If the unit cell contains several absorbers: σ tot = j σ j, 13/62

20 Case of multiple absorbers If the unit cell contains several absorbers: σ tot = j σ j If two or more equivalent atoms, calculate one of them and infer the cross section of the peers by using group theory ( see C. Brouder in J. Phys.: Condens. Matter , 1990) If two or more non-equivalent atoms of the absorbing species, you need to run as many calculations (pw + XSPECTRA) as the number of non-equivalent atoms. Mind the core-level shift (see S. Gao et al. in Phys. Rev. B , 2008)., 13/62

21 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 14/62

22 cp -r $WORKSHOP/Tutorial XSpectra /scratch/ cd /scratch/tutorial XSpectra/, 15/62

23 cp -r $WORKSHOP/Tutorial XSpectra /scratch/ cd /scratch/tutorial XSpectra/ Directory structure:./input/./outdir/./pseudo/./gipaw pseudo generation/./solutions/./references/ input files for the examples tmp output pseudopotentials for this tutorial the script upf2plotcore.sh input files necessary to generate GIPAW pseudopotentials with and without a core-hole reference outputs for the files in./input/ relevant papers, the.pdf of these lectures manual page INPUT XSPECTRA, 15/62

24 Steps to run XSPECTRA 1 Prepare the GIPAW pseudopotentials 2 Extract the core wavefunction./upf2plotcore.sh pseudo.upf 3 Prepare the (supercell) SCF input file 4 Run a SCF calculation: pw.x < prefix.scf.in > prefix.scf.out 5 Run XSPECTRA: xspectra.x < prefix.xspectra.in > prefix.xspectra.out, 16/62

25 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 17/62

26 GIPAW Gauge independent PAW pseudopotential The GIPAW pseudopotential includes all the reconstruction information needed to run XSPECTRA needed for the absorbing atom only (non-absorbing atoms accept any kind of pseudopotential) contains the following information on the absorbing atom: the core wavefunction without hole the all electron atomic states the Blochl projectors can be obtained with the atomic code ld1.x, 18/62

27 Exercise: Generate a C GIPAW in order to calculate the dipolar contribution at the C K edge in diamond Projector 1st projector 2nd projector channel energy energy optional s 2s 3s mandatory p 2p 3p Remember that a minimum of 2 projectors/channel is needed!!, 19/62

28 Generating GIPAW pseudopotential No 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, 20/62

29 Generating GIPAW pseudopotential No 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 /... 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 these states need to be included., 20/62

30 Generating GIPAW pseudopotential No 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 /... Exchange correlation functional. Must be the same for all the atoms., 20/62

31 Generating GIPAW pseudopotential No 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 /... Defaults. No need to touch, 20/62

32 Generating GIPAW pseudopotential With hole File./Gipaw Pseudo Generation/C/Ch.ld1.in &input title= Ch,! atomic symbol prefix= C,! prefix zed=6.0,! atomic number config= 1s1 2s2 2p1.5 3s0 3p0,! atomic configuration iswitch=3, dft= PBE,! xc functional 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!!, 21/62

33 Generating GIPAW pseudopotential With hole 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 /..., 22/62

34 Generating GIPAW pseudopotential With hole 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 /... 2 for norm conserving 3 for ultrasoft, 22/62

35 Generating GIPAW pseudopotential With hole 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 /... This flag is needed to insert GIPAW reconstruction information, 22/62

36 Generating GIPAW pseudopotential With hole File./Gipaw Pseudo Generation/Ch.ld1.in... 2! number of states 2S ! standard C valence states for 2P ! pseudization &test / 4! number of projectors 2S ! list of projectors 2P S P EOF, 23/62

37 Generating GIPAW pseudopotential Availability 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, 24/62

38 Generating GIPAW pseudopotential Availability 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 Quantum Espresso pseudopotential table, e.g. Ni.star1s-pbe-sp-mt gipaw.upf If not, you may find pslibrary on useful. Add the reconstruction information (gipaw flag + list of projectors) to the existing ld1 inputs and generate your own GIPAW pseudopotentials., 24/62

39 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 25/62

40 Extracting the core wavefunction The core wavefunction without hole can be obtained with the ld1.x code by performing an all electron calculation on the isolated atom. Alternatively, if you have a GIPAW pseudopotential without core hole you can 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, 26/62

41 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 27/62

42 Generating the SCF inputs Calculations with core hole require a supercell 1 use the GIPAW pseudopotentials with core hole for each atom of the absorbing species, 28/62

43 Generating the SCF inputs Calculations with core hole require a supercell 1 use the GIPAW pseudopotentials with core hole for each atom of the absorbing species 2 build a supercell to eliminate spurious interaction between the core-hole and its periodic images 3 increase gradually the supercell s dimension until convergence is achieved Typically 6 to 7 Å are needed between the core hole and its images, 28/62

44 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 29/62

45 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, 30/62

46 Electronic structure generation File./input/diamondh.scf.in... &system ibrav = 1, celldm(1) = , nat=8, ntyp=2, nbnd=16, tot charge = 1, ecutwfc=40.0, /...! type of Bravais lattice! cell parameter! number of atoms! number of atom types! number of bands! charge of the cell! cutoff energy, 31/62

47 Electronic structure generation File./input/diamondh.scf.in... &system ibrav = 1, celldm(1) = , nat=8, ntyp=2, nbnd=16, tot charge = 1, ecutwfc=40.0, /...! type of Bravais lattice! cell parameter! number of atoms! number of atom types! number of bands! charge of the cell! cutoff energy 8 atom supercell The total charge of the cluster needs to be specified when the core hole is present, to compensate for the extra electron in the empty states., 31/62

48 Electronic structure generation File./input/diamondh.scf.in... &system ibrav = 1, celldm(1) = , nat=8, ntyp=2, nbnd=16, tot charge = 1, ecutwfc=40.0, /...! type of Bravais lattice! cell parameter! number of atoms! number of atom types! number of bands! charge of the cell! cutoff energy The absorbing atom needs to be considered different from the other C atoms. The core hole breaks the symmetry of the crystal., 31/62

49 Electronic structure generation 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 C C C C C C C K POINTS automatic EOF, 32/62

50 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 33/62

51 XSPECTRA input file File./input/diamondh.xspectra.in &input xspectra calculation= xanes dipole,! type of calculation prefix= diamondh, outdir= $TMP DIR/, xepsilon(1)=1.0; xepsilon(2)=0.0,! polarization xepsilon(3)=0.0; xcoordcrys=.true.! polarization xiabs=1,! type of the absorber ef r=$fermi LEVEL,! Fermi energy in Ry /..., 34/62

52 XSPECTRA input file File./input/diamondh.xspectra.in &input xspectra calculation= xanes dipole,! type of calculation prefix= diamondh, outdir= $TMP DIR/, xepsilon(1)=1.0; xepsilon(2)=0.0,! polarization xepsilon(3)=0.0; xcoordcrys=.true.! polarization xiabs=1,! type of the absorber ef r=$fermi LEVEL,! Fermi energy in Ry /... xanes dipole, xanes quadrupole If xanes quadrupole, both ɛ and k need to be specified, 34/62

53 XSPECTRA input file File./input/diamondh.xspectra.in &input xspectra calculation= xanes dipole,! type of calculation prefix= diamondh, outdir= $TMP DIR/, xepsilon(1)=1.0; xepsilon(2)=0.0,! polarization xepsilon(3)=0.0; xcoordcrys=.true.! polarization xiabs=1,! type of the absorber ef r=$fermi LEVEL,! Fermi energy in Ry /... Same as for the SCF calculation The Fermi energy, or LUMO, must be taken from the previous step. Alternatively, it can be calculated in XSPECTRA by setting calculation= fermi level (insulating case only), 34/62

54 XSPECTRA input file File./input/diamondh.xspectra.in &input xspectra calculation= xanes dipole,! type of calculation prefix= diamondh, outdir= $TMP DIR/, xepsilon(1)=1.0; xepsilon(2)=0.0,! polarization xepsilon(3)=0.0; xcoordcrys=.true.! polarization xiabs=1,! type of the absorber ef r=$fermi LEVEL,! Fermi energy in Ry /... Projections of the polarization vector xcoordcrys=.true. crystal base xcoordcrys=.false. cartesian, 34/62

55 XSPECTRA input file File./input/diamondh.xspectra.in &input xspectra calculation= xanes dipole,! type of calculation prefix= diamondh, outdir= $TMP DIR/, xepsilon(1)=1.0; xepsilon(2)=0.0,! polarization xepsilon(3)=0.0; xcoordcrys=.true.! polarization xiabs=1,! type of the absorber ef r=$fermi LEVEL,! Fermi energy in Ry /... Rank of the absorbing atom under ATOMIC SPECIES in the electronic structure calculation input., 34/62

56 XSPECTRA input file Parameters 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. 12 Use xonly plot=.true. to replot spectra from a previous run (stored in the.sav file), 35/62

57 XSPECTRA input file Parameters for the plot File./input/diamondh.xspectra.in... &plot xnepoint=300, xgamma=0.8, xemin=-10.0, xemax=30.0, terminator=.true.,! number of energy points! core hole linewidth in ev! energy min in ev! energy max in ev! 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 level are considered or not in calculating the cross section. Only cut occ states=.true. has a physical meaning, 36/62

58 XSPECTRA input file Parameters for the plot File./input/diamondh.xspectra.in... &pseudos filecore= C.wfc,! the core wfc r paw(1)=3.2,! PAW radius for l=1 channel / &cut occ cut desmooth=0.1, / EOF, 37/62

59 XSPECTRA input file Parameters for the plot File./input/diamondh.xspectra.in... &pseudos filecore= C.wfc,! the core wfc r paw(1)=3.2,! PAW radius for l=1 channel / &cut occ cut desmooth=0.1, / EOF Obtained at the previous step with./upf2plotcore.sh., 37/62

60 XSPECTRA input file Parameters for the plot File./input/diamondh.xspectra.in... &pseudos filecore= C.wfc,! the core wfc r paw(1)=3.2,! PAW radius for l=1 channel / &cut occ cut desmooth=0.1, / EOF Radius of the augmentation region A good choice in general is r paw = 1.5*r cut with r cut the cutoff radius in the norm conserving generation Decrease if projectors are linearly dependent Do not touch if in doubt..., 37/62

61 XSPECTRA input file Parameters for the plot File./input/diamondh.xspectra.in... &pseudos filecore= C.wfc,! the core wfc r paw(1)=3.2,! PAW radius for l=1 channel / &cut occ cut desmooth=0.1, / 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 (1996) Accurate but time-consuming. Alternative: use xgamma=0.1 and convolute as post-process., 37/62

62 XSPECTRA input file Parameters for the plot File./input/diamondh.xspectra.in... &pseudos filecore= C.wfc,! the core wfc r paw(1)=3.2,! PAW radius for l=1 channel / &cut occ cut desmooth=0.1, / EOF The k point sampling is not necessarily the same as in the SCF run., 37/62

63 XSPECTRA output files prefix.xspectra.out is the talkative file containing information about the run prefix.xspectra.dat contains the XAS spectrum and can be visualized with usual plotting tools (gnuplot, xmgrace) prefix.xspectra.sav is the save file, containing information on the Lanczos process (a and b vectors), 38/62

64 XSPECTRA output files prefix.xspectra.out is the talkative file containing information about the run prefix.xspectra.dat contains the XAS spectrum and can be visualized with usual plotting tools (gnuplot, xmgrace) prefix.xspectra.sav is the save file, containing information on the Lanczos process (a and b vectors) # final state angular momentum: 1 # broadening parameter (in ev): 0.1 # absorbing atom type: 1 # Energy (ev) sigma , 38/62

65 XSPECTRA output files prefix.xspectra.out is the talkative file containing information about the run prefix.xspectra.dat contains the XAS spectrum and can be visualized with usual plotting tools (gnuplot, xmgrace) prefix.xspectra.sav is the save file, containing information on the Lanczos process (a and b vectors) Keep the save file if you want to: resume a previously interrupted run replot spectrum with different broadening energy range, 38/62

66 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 39/62

67 The effect of the core hole C K edge in diamond Task 1 Apply the previous steps to obtain the spectra with and without core hole, at the C K edge in diamond. What you ve already done: generate GIPAW pseudopotentials for C, with and without core hole generate 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 directory 2. Make sure you have the correct paths in *.scf.in and *.xspectra.in 3. Run the SCF calculation: pw.x < diamond.scf.in > diamond.scf.out pw.x < diamondh.scf.in > diamondh.scf.out 4. Run the XAS calculation: xspectra.x < diamond.xspectra.in > diamond.xspectra.out xspectra.x < diamondh.xspectra.in > diamondh.xspectra.out What can you tell about the importance of the core hole?, 40/62

68 The effect of the core hole C K edge in diamond C K edge in diamond with core hole no hole The effect of the core hole is huge. XAS (u.a.) It is usually the case when the Fermi level lies in the same band probed by the XAS Energy (ev) What happens when you increase the size of the supercell?, 41/62

69 Increasing the size of the supercell Task 2 1. Write the SCF input for a larger supercell. 2. Perform a XSPECTRA calculation with core hole on this new structure. 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 the one of the 8 atom supercell, both for SCF and XAS calculations. Precaution For accurate calculations always choose supercells that obey the symmetry of the crystal. In this case, the instead of the 2 2 1, 42/62

70 Increasing the size of the supercell 8 atoms supercell ibrav = 1, nat=8, celldm(1) = , celldm(2) = 1, celldm(3) = 1, K POINTS automatic atoms supercell ibrav = 8, nat=16, celldm(1) = , celldm(2) = 1, celldm(3) = 2 K POINTS automatic , 43/62

71 Increasing the size of the supercell The appropriate treatment of the core hole requires the solution of the two body problem (Bethe Salpeter equation), but this is very expensive. from M. Taillefumier et al. Phys. Rev. B 66, (2002) Usually taking into account the core hole self-consistently is a reasonable approximation., 44/62

72 C K edge in diamond Choose one of the two cases (with or without hole). Task 3 1. 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. What happens? Task 5 Calculate the dipolar spectrum for another polarization direction, e.g. (123), and compare to the (100). Use the 8 atom supercell., 45/62

73 Number of projectors C K edge in diamond proj l=1 2 proj l=1 C K edge in diamond XAS (u.a.) Energy (ev) 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 K edges., 46/62

74 Polarization effects Tensor formalism The XAS of non cubic samples depends on the orientation of the polarization. The absorption tensor of the crystal obeys the symmetry of the space group The atomic absorption tensors obey the specific point group symmetry Cubic (e.g. diamond): σ = σ σ σ 0 Hexagonal (e.g. SiO 2 ): σ = σ σ σ for dipolar E1-E1 transitions only!, 47/62

75 Polarization effects Tensor formalism The XAS of non cubic samples depends on the orientation of the polarization. The absorption tensor of the crystal obeys the symmetry of the space group The atomic absorption tensors obey the specific point group symmetry (ɛ x ɛ y ɛ z ) σ xx σ xy σ xz ɛ x σ yx σ yy σ yz ɛ y σ zx σ zy σ zz ɛ z, 47/62

76 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 48/62

77 Si K edge in SiO 2 Linear 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.wfc 2. pw.x < SiO2.scf.in > SiO2.scf.out 3. xspectra.x < SiO2.xspectra plane.in > SiO2.xspectra plane.out 4. xspectra.x < SiO2.xspectra c.in > SiO2.xspectra c.out Task 7 Check that the spectra are invariant for any ɛ Oz Task 8 Try to restart the Lanczos from a previously interrupted run (file SiO2.xspectra restart 1.in). Check the manual page (./References/INPUT XSPECTRA.txt) for more information. 1. Use the time limit keyword to interrupt a run 2. Use restart mode = restart to resume 3. Check the output *.out, 49/62

78 Si K edge in SiO 2 Linear dichroism Si K edge in SiO in plane out of plane XAS (u.a.) Energy (ev) The dipolar spectrum for a given polarization direction can be expressed as a linear combination of these two elementary spectra. The dipolar spectrum for a powder: σ iso = σ100+σ010+σ001 3, 50/62

79 Si K edge in SiO 2 Converged results C. Gougoussis et al. in Phys. Rev. B 80, (2009), 51/62

80 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA Prepare the GIPAW pseudopotentials Extracting the core wavefunction Prepare the (supercell) SCF input file Run a SCF calculation Run XSPECTRA 4 Examples C K edge in diamond Si K edge in SiO 2 Ni K edge in NiO 5 Summary, 52/62

81 Ni K edge in NiO The magnetic primitive cell File./input/NiO.scf.in: &system ibrav = 5, celldm(1) = , celldm(4)= , starting magnetization(1)=1.0, starting magnetization(2)=-1.0, tot magnetization = 0 / ATOMIC SPECIES Ni Ni PBE TM 2pj.UPF B Ni PBE TM 2pj.UPF O O PBE TM.UPF ATOMIC POSITIONS crystal Ni B O O The magnetic primitive cell contains two Ni atoms AF-coupled., 53/62

82 Ni K edge in NiO Dipolar E1-E1 and quadrupolar E2-E2 contributions Task 10 Calculate the dipolar and quadrupolar contributions to the spectra for one of the absorbing Ni. 1../upf2plotcore.sh Ni PBE TM 2pj.UPF > Ni.wfc 2. pw.x < NiO.scf.in > NiO.scf.out 3. xspectra.x < NiO.xspectra fermi.in > NiO.xspectra fermi.out 4. xspectra.x < NiO.xspectra dip.in > NiO.xspectra dip.out 5. xspectra.x < NiO.xspectra qua.in > NiO.xspectra qua.out, 54/62

83 Ni K edge in NiO Dipolar E1-E1 and quadrupolar E2-E2 contributions quadrupole x 15 dipole Ni K edge in NiO XAS (u.a.) Energy (ev) Dipolar contribution always dominates, due to the higher overlap with the 1s radial function., 55/62

84 Ni K edge in NiO Spin resolved signal Plot the up and down contributions to the spectra. File NiO *.dat: # final state angular momentum: 1 # broadening parameter (in ev): # absorbing atom type: 1 # Energy (ev) sigmatot sigmaup sigmadown , 56/62

85 Ni K edge in NiO Spin resolved signal 16 up down Ni K edge in NiO 12 XAS (u.a.) 8 dipole E1-E Energy (ev) 2.0 up down Ni K edge in NiO 1.5 XAS (u.a.) 1.0 quadrupole E2-E Energy (ev), 57/62

86 Ni K edge in NiO Spin resolved signal Task 11 Calculate the second Ni atom and compare with the first one. Hint: use xiabs = 2 in NiO.xspectra-qua.in, 58/62

87 Ni K edge in NiO Spin resolved signal Task 11 Calculate the second Ni atom and compare with the first one. Hint: use xiabs = 2 in NiO.xspectra-qua.in Ni K edge in NiO 2.0 Ni 1 up Ni 2 up XAS (u.a.) Up states in quadrupole E2-E2 transitions Ni 1 = Ni 2 Ni 1 = Ni Ni 1 Ni Energy (ev) Calculating only one of the two Ni is enough, since they are symmetry related (time reversal symmetry), 58/62

88 Ni K edge in NiO Spin resolved signal Task 11 Calculate the second Ni atom and compare with the first one. Hint: use xiabs = 2 in NiO.xspectra-qua.in Ni K edge in NiO 2.0 Ni 1 up Ni 2 up XAS (u.a.) Up states in quadrupole E2-E2 transitions Ni 1 = Ni 2 Ni 1 = Ni Ni 1 Ni Energy (ev) Task 12 Turn the antiferromagnet into a feeble ferrimagnet. Hint: Lower the accuracy in the SCF run (pedagogical purpose only). Check what happens., 58/62

89 1 The PAW theory 2 The Lanczos algorithm 3 Hands on XSPECTRA 4 Examples 5 Summary, 59/62

90 XSPECTRA features calculates K and L 1 edges (dipole E1-E1 and quadrupole E2-E2 with linear polarization) supports all standard DFT functionals available in Quantum Espresso (PZ,PBE,PZ+U,PBE+U) supports both ultrasoft and norm conserving pseudopotentials the pseudopotential of the absorbing species must contain information on the core states (GIPAW) the all electron reconstruction is performed within GIPAW the summation over the empty states is done using a Lanczos algorithm and a continued fraction approach a supercell is needed to model the core hole, 60/62

91 XSPECTRA features calculates K and L 1 edges (dipole E1-E1 and quadrupole E2-E2 with linear polarization) supports all standard DFT functionals available in Quantum Espresso (PZ,PBE,PZ+U,PBE+U) supports both ultrasoft and norm conserving pseudopotentials the pseudopotential of the absorbing species must contain information on the core states (GIPAW) the all electron reconstruction is performed within GIPAW the summation over the empty states is done using a Lanczos algorithm and a continued fraction approach a supercell is needed to model the core hole Not yet supported: spin-orbit coupling circular polarization hybrid functionals, 60/62

92 History First implementation of XAS calculation using the PAW method belongs to M. Taillefumier, D. Cabaret, A. M. Flank, F. Mauri in Phys. Rev. B 66, (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. B 80, (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 your publications, as well as P. Giannozzi et al. in J. Phys. Condens. Matter 21, (2009), 61/62

93 Please feel free to contact me: bunau at unizar.es, 62/62