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NSRRC September 12 program

NSRRC September 12 program. Charge Transfer Multiplet program Used for the analysis of XAS, EELS, Photoemission, Auger, XES, ATOMIC PHYSICS  GROUP THEORY  MODEL HAMILTONIANS. X-ray Absorption Spectroscopy. Excitations of core electrons to empty states

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NSRRC September 12 program

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  1. NSRRC September 12 program

  2. Charge Transfer Multiplet program Used for the analysis of XAS, EELS, Photoemission, Auger, XES, ATOMIC PHYSICS  GROUP THEORY  MODEL HAMILTONIANS

  3. X-ray Absorption Spectroscopy Excitations of core electrons to empty states The XAS spectrum is given by theFermi Golden Rule

  4. X-ray Absorption Spectroscopy Excitations of core electrons to empty states The XAS spectrum is given by theFermi Golden Rule 1s

  5. X-ray Absorption Spectroscopy 2p 2s Phys. Rev. B.40, 5715 (1989)

  6. X-ray Absorption Spectroscopy oxygen 1s > p DOS Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)

  7. X-ray Absorption Spectroscopy oxygen 1s > p DOS Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)

  8. 1-particle: 1s edges (DFT + core hole +U) 2-particle: + all edges of closed shell systems (TDDFT, BSE) many-particle: open shell systems (CTM4XAS) Interpretation of XAS

  9. XAS: multiplet effects Fermi Golden Rule: IXAS = |<f|dipole| i>|2 [E=0] Single electron (excitation) approximation: IXAS = |< φ empty|dipole| φcore>|2 

  10. XAS: multiplet effects Overlap of core and valence wave functions  Single Particle model breaks down 3d <2p3d|1/r|2p3d> 2p3/2 2p1/2 Phys. Rev. B. 42, 5459 (1990)

  11. XAS: recent first principles developments for L edges X-ray absorption: core hole effect • DFT to cluster Wannier multiplet (Haverkort) • Restricted-Active-Space (Odelius, Koch, Broer, Lundberg) • Extensions of TD-DFT with 2h-2e (Neese, Roemelt) • ab-initio multiplets [‘RAS-DFT’] (Ikeno, Uldry) [ See http://www.anorg.chem.uu.nl/FXS2013/]

  12. CTM4XAS (semi-empirical)

  13. Charge Transfer Multiplet program Used for the analysis of XAS, EELS, Photoemission, Auger, XES, ATOMIC PHYSICS  GROUP THEORY  MODEL HAMILTONIANS

  14. Atomic Multiplet Theory

  15. Atomic Multiplet Theory =E • Kinetic Energy • Nuclear Energy • Electron-electron interaction • Spin-orbit coupling

  16. Atomic Multiplet Theory =E X X • Kinetic Energy • Nuclear Energy • Electron-electron interaction • Spin-orbit coupling

  17. Term Symbol • 2S+1L

  18. Term Symbols of a two-electron state 1s2s-configuration Term symbols 1s: 2S Term symbols 2s: 2S Term symbols 1s2s: multiply L and S separately L2p=0, L3p=0>> LTOT = 0 S2p=1/2, S3p=1/2

  19. Term Symbols 1s2s-configuration S2p=1/2, S3p=1/2 What are the values of the total S (STOT) ? =0 or 1 Singlet or triplet: ↑↓ or ↑↑, but the degeneracies are 1 and 3

  20. Term Symbols Singlet or triplet

  21. Spin-orbit coupling • Couple L and S quantum numbers • L and S loose their exact meaning as quantum numbers • Only the total moment J is a good quantum number Valence Spin-orbit coupling

  22. Quantum numbers • Main n 1,2,3,…. • Azimuthal L (orbital moment) • Spin S • Magnetic mL (orbital magnetic moment) • Spin magnetic mS (spin magnetic moment) • Total moment J • Total magnetic mJ

  23. Term Symbols • Term symbols of a 2p13d1 configuration • 2p1 2P1/2, 2P3/2 (S=1/2, L=1) • 3d1 2D3/2, 2D5/2 (S=1/2, L=2) • 2p13d1 STOT = 0 or 1 •  LTOT = 1 or 2 or 3 •  1P1 + 3P0, 3P1, 3P2 •  1D2 + 3D1, 3D2, 3D3 •  1F3 + 3F2, 3F3, 3F4 • [(2J+1)=3+1+3+5+5+3+5+7+7+5+7+9=60]

  24. Term Symbols • Term symbols of a 2p2 configuration

  25. Configurations of 2p2

  26. Term Symbols of 2p2 LS term symbols:1S, 1D, 3P LSJ term symbols: 1S0 1D2 3P0 3P13P2

  27. The electron-electron interaction • Electron-electron interaction acts on 2 electrons • It can couple 4 different wave function a, b, c and d

  28. The electron-electron interaction • Split wave functions into radial and angular part • Split operator into radial and angular part • Use series expansion of 1/r12

  29. Coulomb integral • Special case: a=c and b=d • >> the two electron are in the same shell • Fk is called a Slater integral • It is a number that is calculated from first principles

  30. Atomic Multiplet Theory Electron-electron interactions of Valence States Valence Spin-orbit coupling

  31. CTM4XAS version 5.2

  32. CTM4XAS version 5.2

  33. Atomic Multiplet Theory Core Valence Overlap Core Spin-orbit coupling

  34. Multiplet Effects (Ni2+) 1s 2s 2p 3s 3p 0.07 0 5 0 8 17 13 0 17 2 Core Valence Overlap Core Spin-orbit coupling

  35. 2p XAS of TiO2 • Ground state is 3d0 • Dipole transition 3d02p53d1 • Ground state symmetry: 1S0 • Final state symmetry: 2P2D gives • 1P, 1D, 1F, and3P, 3D, 3F

  36. 2p XAS of TiO2 • Final state symmetries: 1P, 1D, 1F, and3P, 3D, 3F • Transition <1S0|J=+1| 1P1, 3P1 , 3D1> • 3 peaks in the spectrum

  37. Exercise: Calculate the 2p XAS spectrum of a Ti atom

  38. Hunds rules • Term symbols with maximum spin S are lowest in energy, • Among these terms: Term symbols with maximum L are lowest in energy • In the presence of spin-orbit coupling, the lowest term has • J = |L-S| if the shell is less than half full • J = L+S if the shell is more than half full 3d1 has 2D3/2 ground state 3d2 has 3F2 ground state 3d9 has 2D5/2 ground state 3d8 has 3F4 ground state Give the Hund’s rule ground states for 3d1 to 3d9

  39. Exercise: Calculate the 2p XAS spectrum of Fe Fe atom: Ground state: 3d6 (4s2) 5D j=4

  40. Term Symbols and XAS Fe atom: Ground state: 3d6 (4s2) Final state: 2p53d7 Dipole transition: p-symmetry 3d6-configuration: 5D, etc. j=42p53d7-configuration: 110 states j’= 3,4, 5 p-transition: 1P j=+1,0,-1 ground state symmetry: 5D 5D4 transition:5D1P = 5PDF possible final states: 68 states

  41. Term Symbols and XAS Fe atom: Ground state: 3d6 (4s2) 5D j=4 5D0 5D 5D4

  42. Term Symbols and XAS NiII ion in NiO: Ground state: 3d8 Final state: 2p53d9 Dipole transition: p-symmetry 3d8-configuration: 1S, 1D, 3P,1G, 3Fj=42p53d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4 p-transition: 1P j=+1,0,-1 ground state symmetry: 3F 3F4 transition:3F1P = 3DFG two possible final states:3D, 3F 3D3,3F3,3F4,1F3

  43. 3d8 XAS calculation +LS3d : > 3F4 +LS2p 0 +FK, GK: > 3F

  44. Atomic multiplets

  45. Charge Transfer Multiplet program ATOMIC PHYSICS  GROUP THEORY  MODEL HAMILTONIANS

  46. Crystal Field Effects eg states t2g states

  47. in symmetrical field in octahedral ligand field eg x2-y2 z2 t2g yz xz xy Octahedral crystal field splitting metal ion in free space x2-y2 yz z2 xz xy

  48. Crystal Field Effects in CTM 0 7 = 2.13 eV

  49. Crystal Field Effects SO3 Oh (Mulliken) S 0 A1 P 1 T1 D 2 E+T2 F 3 A2+T1+T2 G 4 A1+E+T1+T2

  50. 2p XAS of TiO2 (atomic multiplets) TiIV ion in TiO2: 3d0-configuration: 1S, j=02p13d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4 p-transition: 1P j=+1,0,-1 Write out all term symbols: 1P11D21F3 3P03P13P2 3D13D23D3 3F23F33F4 1 3 4 3 1

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