1 / 54

XSPECTRA

XSPECTRA. A tool for X-ray absorption spectra (XAS) calculations. Matteo Calandra. / afs/ictp/public/shared/qetutorial/Matteo /References/Lectures_XAS.pdf. C. Gougoussis , M. Calandra, A. P. Seitsonen , and F. Mauri Phys. Rev . B 80 , 075102 (2009).

marcel
Download Presentation

XSPECTRA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. XSPECTRA A tool for X-ray absorption spectra (XAS) calculations Matteo Calandra /afs/ictp/public/shared/qetutorial/Matteo/References/Lectures_XAS.pdf C. Gougoussis, M. Calandra, A. P. Seitsonen, and F. Mauri Phys. Rev. B 80, 075102 (2009) P. Giannozzi et al., J. Phys. Condens. Matter21, 395502 (2009).

  2. XSPECTRA (General questions) Whatisit ? XSPECTRA calculate K and L1X-ray absorption dipolar and quadrupolar cross sections in the pre-edge to near-edgeregion. Wherecan I find XSPECTRA ? XSPECTRA isdistributed in the QUANTUM-ESPRESSO package. Can I use it ? XSPECTRA isdistributedunder the GNU licence, soyoucan use it for free. Pleaseremember to cite the followingpapers to acknowledge people building the software: P. Giannozzi et al., J. Phys. Condens. Matter21, 395502 (2009). C. Gougoussis, M. Calandra, A. P. Seitsonen, and F. Mauri, Phys. Rev. B 80, 075102 (2009) How doesitwork ? This iswhatwewilllearntoday…

  3. Outline XAS in a nutshell. XSPECTRA Theory (PAW) The LanczosMethod Running XSPECTRA Tutorials Diamond SiO2 Conclusion

  4. Outline XAS in a nutshell. XSPECTRA Theory (PAW) The LanczosMethod Running XSPECTRA Tutorials Diamond SiO2 Conclusion

  5. Whatis XAS ? Crystal X-ray source (synchrotron) Incident X-ray beam TransmittedX-ray Beam Detector

  6. Whatis XAS ? XSPECTRA wasbuilt to answerthis question.

  7. XAS Physicalprocess Challenge: describecore-hole attraction from first principles.

  8. Chemical and Orbital selectivity The choice of the incident photon energy selects the coreelectronexcited. It permits to choose (i) the atomfromwhich the electronisexcited (absorbingatom). (ii) the atomiclevelfromwhich the electronisexcited. Example: Eu L1, L2, L3edges Edgename Core state Intensity (Arb. Units.) Incident photon energy

  9. Chemical and Orbital selectivity The choice of the incident photon energy selects whichcoreelectronisexcited. Experimentalists are then free to choose: (i) the atomfromwhich the electronisexcited (absorbingatom). (ii) the atomiclevelfromwhich the electronisexcited. Note thatcore-satebindingenergies of atoms are verydifferent: For more see http://xdb.lbl.gov/

  10. Name of XAS structures XANES EXAFS edge pre-edge XANES=X-raynearedge structures. EXAFS=Extended X-Ray Absorption Fine Structure.

  11. Name of XAS structures XSPECTRA calculation XANES EXAFS edge pre-edge XANES=X-raynearedge structures. EXAFS=Extended X-Ray Absorption Fine Structure.

  12. XAS cross section From Fermi golden-rule: Final state with a core-hole Initial state: no core-hole Incident-photon energy The matrixelementis: 1s p states 1s d states See Ch. Brouder, J. Phys. Cond. Matt. 2, 701 (1990) for more details.

  13. XAS cross section In the absence of a magneticfield the cross section canbeseparated in dipolar and quadrupolarterms (cross terms are zero in this case): with: and the twotermscanbecalculatedseparately. The quadrupolar part is in the pre-edgeregion.

  14. Outline XAS in a nutshell. XSPECTRA Theory (PAW) The LanczosMethod Running XSPECTRA Tutorials Diamond SiO2 Conclusion

  15. XAS cross section needsall-electron states Final state with a core-hole Initial state: no core-hole Incident-photon energy ALL ELECTRON STATES Howeverwe have pseudopotentials and we do not have all-electron states! How to solvethisproblem ? Use the projectedaugmentedwave (PAW) method! P. E. Blöchl, Phys. Rev. B 50, 17953 (1994)

  16. PAW for XAS – short explanation As we use pseudopotentials, the electronwavefunctionthatweobtain in our simulation isdifferentfrom the all-electronwavefunction: ALL ELECTRON PSEUDO MAPPING Assume that a linearmappingexistsbetween the twowavefunctions: Nucleus As the pseudowavefunctiondiffersfrom the AE one only in the augmentation region (coreregion) then the mappingoperatoris differentfrom the identityonly in the augmentation region. Augmentation region P. E. Blöchl, Phys. Rev. B 50, 17953 (1994)

  17. PAW for XAS – short explanation The mappingiswritten as: R= coordinates of the nuclei with AE PARTIAL WAVES (e.g. AE atomic wavefunctions) PAW Projectors identified by the condition PSEUDO PARTIAL WAVES (e.g. atomic pseudo Wavefunctions) The projectors are non-zero only in the augmentation region. P. E. Blöchl, Phys. Rev. B 50, 17953 (1994)

  18. PAW for XAS – short explanation Replacing in the XAS cross section and using the localization of the weobtain core state where and andR0 isthe position of the absorbingatom. Thus in order to calculate the matrix-element one needs: ψi= The corewavefunction of the absorbingatom (e. g. 1s state for K-edge) WITHOUT A CORE-HOLE. .1. .2. φ = The AE partial wavescentered on the absorbingatom (e.g. AE atomic states) .3. PAW projectors. M. Taillefumieret al. PRB 66, 195107 (2002)

  19. PAW for XAS – short explanation WARNING: The sum isactually over a complete set (infinitenumber) of projector (unfeasible). In practice we have to reduce the number of projectors to a finitenumber. You needtwoprojectors per channel (i.e. per angularmomentum l) in order to have correct XAS intensity up to ~ 50 eV from the Fermi level. Use of a single projectorgives incorrect dipole/quadrupole ration and in most of the case giveswrongintensities. Projectors have to belinearlyindipendent, namelythey must reallyspan a dimension 2 subsbace. M. Taillefumieret al. PRB 66, 195107 (2002)

  20. XSPECTRA (The lanczosmethod) In the XAS cross-sectionyouneed to perform a sum over all empty states This is of course verydemanding if done in a brute-forceway. XSPECTRA use the lanczosmethod. Rewriting: And thiscanbecomputedusing the Lanczosmethod and the continous fraction. Thus in the XSPECTRA input wewill have to specify: xniter=Maximal number of iteration to beused in the lanczosmethod. xerror=Convergence threashold for the Lanczosmethod (On the integral of the XAS cross section). xcheck_conv=Number of iterationbetweentwo convergence checks. xgamma=Lorentzianbroadening (core-holelinewidth)

  21. Outline XAS in a nutshell. XSPECTRA Theory (PAW) The LanczosMethod Running XSPECTRA Tutorials Diamond SiO2 Conclusion

  22. Beforegoing on… Login cd/scratch/ Create a directory withyourname: mkdiryourname cp /afs/ictp/public/shared/qetutorial/Matteo/ /scratch/yourname/

  23. Directory structure Subdirectory ./Binaries/ Here all the Binariesneeded to runxspectra are included. PLEASE USE THESE BINARIES. Subdirectory ./Gipaw_Pseudo_Generation/ Here all the input files necessary to generate GIPAW pseudopotentials with and without a core-hole are included. Subdirectory ./Diamond/ /Diamond_nohole/ /SiO2/ Examples and exercises. Subdirectory ./References/ Relevant paperswithfullyconvergedresults and these lectures.

  24. Running XSPECTRA Prepare GIPAW pseudo and supercellscf input file 1 2 ./pw.x < prefix.scf.in > prefix.scf.out Generatecore state of the absorbingatom (upf2plotcore.sh) 3 4 ./xspectra.x < prefix.xspectra.in > prefix.xspectra.out

  25. Running XSPECTRA Prepare GIPAW pseudo and supercellscf input file 1 2 ./pw.x < prefix.scf.in > prefix.scf.out Generatecore state of the absorbingatom (upf2plotcore.sh) 3 4 ./xspectra.x < prefix.xspectra.in > prefix.xspectra.out

  26. (GI)PAW – what do weneed ? ψi= The corewavefunction of the absorbingatom (e. g. 1s state for K-edge) WITHOUT A CORE-HOLE .1. .2. φ = The AE partial wavescentered on the absorbingatom (e.g. AE atomic states) .3. Blochlprojectors. All thesequantitiescanbecalculatedfrom the atomic code as theyinvolveonly the solution for an isolatedatom. These informations are contained in (GI)PAW pseudopotentials. A GIPAW pseudopotentialisneededonly for the absorbingatom, for the otheratomicspecies use anyotherpseudopotentialavialable Nowwesee how to generatethem in the case of Carbon.

  27. Generation of (GI)PAW pseudopotentials Wegenerate a pseudopotential to studydipolarK-edge XAS transition in diamond, soweneed to generate a pseudopotentialwithtwo p projectors. As an exercise (even if not needed) wealsoincludetwo s projectors. Wechoose to generate the projectors as follows:

  28. Generation of (GI)PAW pseudopotentials [C]=1s2 2s2 2p2 File ./Gipaw_Pseudo_Generation/C/C.ld1.in NO CORE-HOLE Carbonnuclear charge is of course unchanged. &input title='Ch', prefix='Ch', zed=6.0, config='1s2 2s2 2p1.5 3s0 3p0 ', iswitch=3, dft=’PBE', rel=1, / …. As wewant to generateprojectors at the energies of 2s,3s,2p and 3p states weneed to put these states here. To bindthese states we have to ionize a bit, namely 1s2 2s2 2p1.5 iswitch=3, means: generation of a pseudopotential

  29. Generation of (GI)PAW pseudopotentials [C]=1s2 2s2 2p2 File ./Gipaw_Pseudo_Generation/C_Hole/Ch.ld1.in WITH CORE-HOLE Carbonnuclear charge is of course unchanged. &input title='Ch', prefix='Ch', zed=6.0, config='1s1 2s2 2p1.5 3s0 3p0 ', iswitch=3, dft=’PBE', rel=1, / …. Core-hole As wewant to generateprojectors at the energies of 2s,3s,2p and 3p states weneed to put these states here. iswitch=3, means: generation of a pseudopotential

  30. Generation of (GI)PAW pseudopotentials File ./Gipaw_Pseudo_Generation/C_Hole/Ch.ld1.in &inputp pseudotype=2, lloc=1, file_pseudopw=’ C.star1s-pbe-mt_gipaw.UPF', tm=.true., lgipaw_reconstruction=.true., / 2 2S 1 0 2.00 0.00 1.5 1.5 2P 2 1 1.50 0.00 1.5 1.5 &test / 4 2S 1 0 2.00 0.00 1.5 1.5 3S 2 0 0.00 0.00 1.5 1.5 2P 2 1 1.50 0.00 1.5 1.5 3P 3 1 0.00 0.00 1.5 1.5 This flag isneeded to insert (GI)PAW reconstruction information. Standard valence states configuration for Carbon pseudopotentialgeneration Total number of PAW projectors Projectors

  31. Generation of (GI)PAW pseudopotentials Thenperforming ./ld1.x < Ch.ld1.in > Ch.ld1.out generate the pseudopotentialC.star1s-pbe-mt_gipaw.UPF of the QE-XSPECTRA distribution. Inside the pseudo all the informations needed to perform an XSPECTRA calculation are contained.

  32. Pseudopotentialname notation Pseudopotentialsincluding (GI)PAW informations are alreadyavailable in the QUANTUM-ESPRESSO pseudopotential table, for example: Ni.star1s-pbe-sp-mt_gipaw.UPF starNsmeans a core-hole in the s state with principal quantum number N. PBE is the exchange-correlationfunctionalused gipawmeansthatgipaw informations are included in the absorbingatom.

  33. XSPECTRA (Modeling the corehole) Aftergeneration of the core-holepseudopotential, buildyour structure withyour pseudopotentialstarNsgipawin the absorbingatom position. As weworkwithpbcwealsoneed to build a supercell to minimize the interaction between the core-hole and itsperiodic image

  34. XSPECTRA (Modeling the corehole) Aftergeneration of the core-holepseudopotential, buildyour structure withyour pseudopotentialstarNsgipawin the absorbingatom position. As weworkwithpbcwealsoneed to build a supercell to minimize the interaction between the cote-hole and itsperiodic image How big must the supercellbe ? Performdifferentcalculations for differentsupercells and seewhen the result converges. Rule of thumb: usuallyyouneedat least 6-7 Angstrom distance between the core-hole and itsperiodic image.

  35. Running XSPECTRA Prepare GIPAW pseudo and supercellscf input file 1 ✓ 2 ./pw.x < prefix.scf.in > prefix.scf.out Generatecore state of the absorbingatom (upf2plotcore.sh) 3 4 ./xspectra.x < prefix.xspectra.in > prefix.xspectra.out

  36. Step 2 – electronicdensitygeneration Dir: ./Diamond/ file: diamond.scf.in &control calculation='scf', pseudo_dir = '$PSEUDO_DIR/', outdir='$TMP_DIR/', prefix='diamondh', / &system ibrav = 1, celldm(1) = 6.740256, nat=8, ntyp=2, nbnd=16, tot_charge=+1.0, ecutwfc=40.0, / &electrons / ATOMIC_SPECIES …. SCF calculation to obtain the electronic charge density 8 atomssupercell. Note ntyp=2 as the absorbingatom MUST isconsidereddifferentfrom the otheratomic types. Needs to bespecifiedwhen a core-holeispresenttpcompensate for the additionalelectron in empty states.

  37. Step 2 – electronicdensitygeneration Dir: ./Diamond/ file: diamond.scf.in … &electrons / ATOMIC_SPECIES Ch 12.0 Ch_PBE_TM_2pj.UPF C 12.0 C_PBE_TM_2pj.UPF ATOMIC_POSITIONS crystal Ch 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 Pseudopotential for all atom types. Ch = Carbonwithcore-hole. Atomic positions of the toosmallsupercell.

  38. Running XSPECTRA (more details) Prepare GIPAW pseudo and supercellscf input file 1 ✓ 2 ✓ ./pw.x < prefix.scf.in > prefix.scf.out Generatecore state of the absorbingatom (upf2plotcore.sh) 3 4 ./xspectra.x < prefix.xspectra.in > prefix.xspectra.out

  39. Extracting the core-wavefunction Final state with a core-hole Initial state: no core-hole The corewavefunctionψiIN THE ABSENCE OF A CORE-HOLEcanbeobtainedusing the ld1.x code and performing an all-electroncalculation on the isolatedatom. Alternatively, if you have a (GI)PAW pseudopotentialwithoutcore-holeyoucan use the script upf2plotcore.sh XSpectra/upf2plotcore.sh C.pbe-mt_gipaw.UPF > C.wfc C.wfcisneeded by the XSPECTRA program. A copy of upf2plotcore.sh issaved in the directory with the C pseudopotentialwithoutcore-hole.

  40. Running XSPECTRA (more details) Prepare GIPAW pseudo and supercellscf input file 1 ✓ 2 ✓ ./pw.x < prefix.scf.in > prefix.scf.out Generatecore state of the absorbingatom (upf2plotcore.sh) 3 ✓ 4 ./xspectra.x < prefix.xspectra.in > prefix.xspectra.out

  41. Step 4 – XSPECTRA input file &input_xspectranamelist, herewespecify the main information to control the job: &input_xspectra calculation='xanes_dipole', prefix='diamondh', outdir='$TMP_DIR/', xonly_plot=.false., xniter=1000, xcheck_conv=50, xerror=0.001, x_save_file='diamondh.xspectra.sav', ef_r=${FERMI_LEVEL}, xiabs=1, xepsilon(1)=1.0, xepsilon(2)=0.0, xepsilon(3)=0.0, / xanes_dipole/xanes_quadrupole Perform a full continous fraction calculation Theseparameters control the Lanczos. File where the a and b coefficients of the Lanczosmethod are saved. In Rydberg:sets the energyzero in the final spectra. Read thisfromstep 1 output. Type of the absorbingatom. Polarizationvector of the incident beam

  42. Step 4 – XSPECTRA input file &plot namelist, isused to specify the plot of the cross-section &plot xgamma=0.8, xnepoint=1000, xemin=-10.0, xemax=30.0, terminator=.true., cut_occ_states=.true., / Core-holelinewidth (atomic data) Number of ω points to beused for σ(ω) Range of ω for σ(ω) Use a terminator for the Lanczos (faster) Eliminate the occupied states from the cross section. The states are eliminatedbelow the Fermi levelspecified in the previousslide.

  43. Step 4 – XSPECTRA input file &pseudos namelist, isused to specify the initial state wavefunction and the pax radius &pseudos filecore='C.wfc', r_paw(1)=3.2, / Name of the file with the core-state wavefunctiongeneratedatstep 3 Radius defining the augmentation region. This isusefulwhenyourprojectors are almostlinearlydependent. Do not use it if you do not know what to do. Generally a good choice for r_pawisr_paw=3 r_cut/2 or greater, and r_cutis the radius used in a normconservinggeneration of the pseudo.

  44. Step 4 – XSPECTRA input file &cut_occnamelistspecifies how to cutsmoothlyoccupied states &cut_occ cut_desmooth=0.1, cut_stepl=0.01, / This isdoneusingfollowingref. Ch. Brouder, M. Alouani, K. H. Bennemann, Phys. Rev. B 54 (1996) p.7334-49. Most of the times theseparametersworks. Howeverthey do not necessaryrepresent the most efficient choice in term of CPU time. These and otherparameters control the smoothcut of occupied states. It issuggestedthat beforemodifyingthemyouread the referenceabove.

  45. Running XSPECTRA (more details) Prepare GIPAW pseudo and supercellscf input file 1 ✓ 2 ✓ ./pw.x < prefix.scf.in > prefix.scf.out Generatecore state of the absorbingatom (upf2plotcore.sh) 3 ✓ 4 ✓ ./xspectra.x < prefix.xspectra.in > prefix.xspectra.out

  46. Output files Besidesprefix.xspectra.outtwoother files are produced: prefix.xspectra.dat Contains the XANES cross section. It is a file of the kind: # final state angularmomentum: 1 # broadeningparameter (in eV): 0.800000000000 # absorbingatom type: 1 # Energy (eV) sigma -10.00000000 0.02722740 -9.86622074 0.02766810 -9.73244147 0.02789281 -9.59866221 0.02791267 The file canbevisualizedwithxmgrace / gnuplot or similar. prefix.xspectra.sav Contains all the informations of the Lanczosprocess (a and b ectors) and canbeused to replot the cross section (differentbroadening/energy range) or to continue the Lanczos. Alwayskeepthis file for replotting.

  47. Outline XAS in a nutshell. XSPECTRA Theory (PAW) The LanczosMethod Running XSPECTRA Tutorials Diamond SiO2 Conclusion

  48. Diamondwith and withoutcore-hole Repeatsteps 2,3,4 to obtain the XANES spectrum of Diamondwithout a core-hole in the final state (see directory ./Diamond_nohole/ ). Note the hugecore-holeeffect!!!! Whathappensincreasing the supercell size ?

  49. Increasingsupercell size Verybigsize-effects, the simulation converges with 250 atoms. Note thatpeak A is not welldescribed in DFT. The iswellknown in literature. M. Taillefumieret al. PRB 66, 195107 (2002)

  50. αquartz (SiO2) Hexagonal cell – in-planepolarization.

More Related