NSRRC September 12 program Part 1 CTM4XAS Atomic Multiplet, crystal fields and charge transfer Part...
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Transcript of NSRRC September 12 program Part 1 CTM4XAS Atomic Multiplet, crystal fields and charge transfer Part...
NSRRC September 12 program
Part 1CTM4XAS
Atomic Multiplet, crystal fields and charge transfer
Part 2 CTM4RIXS
Charge Transfer Multiplet program
Used for the analysis of XAS, EELS,
Photoemission, Auger, XES,
ATOMIC PHYSICS
GROUP THEORY
MODEL HAMILTONIANS
if EEiffXAS reI
2ˆ~
Excitations of Excitations of core electrons core electrons to empty statesto empty states
The XAS spectrum The XAS spectrum is given by theis given by the
Fermi Golden RuleFermi Golden Rule
X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy
Excitations of Excitations of core electrons core electrons to empty statesto empty states
The XAS spectrum The XAS spectrum is given by theis given by the
Fermi Golden RuleFermi Golden Rule
symmetrysiteXAS MI ,2~
X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy
1s1s
22pp22ss
Phys. Rev. B.40, 5715 (1989)Phys. Rev. B.40, 5715 (1989)
X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy
X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy
Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)
oxygen 1s > p DOSoxygen 1s > p DOS
X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy
Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)
oxygen 1s > p DOSoxygen 1s > p DOS
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 XASInterpretation of XAS
Fermi Golden Rule:IXAS = |<f|dipole| i>|2 [E=0]
Single electron (excitation) approximation:IXAS = |< φ empty|dipole| φcore>|2
22
ˆˆ iqiiqf recre
2
ˆ?? creq
XAS: multiplet effectsXAS: multiplet effects
2p2p3/23/2
2p2p1/21/2
Overlap of core and valence wave functionsOverlap of core and valence wave functions
Single Particle model breaks downSingle Particle model breaks down
3d3d
<2p3d|1/r|2p3d><2p3d|1/r|2p3d>
XAS: multiplet effectsXAS: multiplet effects
Phys. Rev. B. 42, 5459 (1990) Phys. Rev. B. 42, 5459 (1990)
X-ray absorption: core hole effectX-ray absorption: core hole effectXAS: recent first principles XAS: recent first principles developments for L edgesdevelopments for L edges
• 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/]
Charge Transfer Multiplet program
Used for the analysis of XAS, EELS,
Photoemission, Auger, XES,
ATOMIC PHYSICS
GROUP THEORY
MODEL HAMILTONIANS
Niii
pairsre
NrZe
Nmp slrH
iji
i )(222
2
Atomic Multiplet TheoryAtomic Multiplet Theory
=E
• Kinetic Energy• Nuclear Energy• Electron-electron interaction• Spin-orbit coupling
Niii
pairsre
NrZe
Nmp slrH
iji
i )(222
2
Atomic Multiplet TheoryAtomic Multiplet Theory
X X
=E
• Kinetic Energy• Nuclear Energy• Electron-electron interaction• Spin-orbit coupling
Term Symbols of a two-electron stateTerm 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
Term SymbolsTerm 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
N
iiipairs
re
ATOM slrHij
)(2
Spin-orbit couplingSpin-orbit coupling
Valence 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
• 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
Quantum numbersQuantum numbers
• 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]
Term Symbols
Configurations of 2p2
1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1
1 0 -1
1 0 -1 1 0 -1
1 0 -1 1 0 -1
LS term symbols: 1S, 1D, 3PLSJ term symbols:
MS=1 MS=0 MS=-1
ML= 2 0 1 0
ML= 1 1 2 1
ML= 0 1 3 1
ML=-1 1 2 1
ML=-2 0 1 0
Term Symbols of 2p2
1S0 1D2
3P0 3P1 3P2
pairs
reij
H2
The electron-electron interactionThe electron-electron interaction
• Electron-electron interaction acts on 2 electrons• It can couple 4 different wave function a, b, c and d
The electron-electron interactionThe electron-electron interaction
1. Split wave functions into radial and angular part2. Split operator into radial and angular part3. Use series expansion of 1/r12
Coulomb integralCoulomb 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
N
iiipairs
re
ATOM slrHij
)(2
k
kk
k
kkJ
Sre
JS GgFfLL 1212 ||
12
2
Atomic Multiplet TheoryAtomic Multiplet Theory
Electron-electron interactions of Valence States
Valence Spin-orbit coupling
N
iiipairs
re
ATOM slrHij
)(2
k
kk
k
kkJ
Sre
JS GgFfLL 1212 ||
12
2
Atomic Multiplet TheoryAtomic Multiplet Theory
Core Valence Overlap
Core Spin-orbit coupling
1s 2s 2p 3s 3p
0.07
0
5
0
8
17
13
0
17
2Core Spin-orbit coupling
Multiplet Effects (NiMultiplet Effects (Ni2+2+))
Core Valence Overlap
2p XAS of TiO2p XAS of TiO22
• Ground state is 3d0
• Dipole transition 3d02p53d1
• Ground state symmetry: 1S0
• Final state symmetry: 2P2D gives
• 1P, 1D, 1F, and 3P, 3D, 3F
• Final state symmetries:
1P, 1D, 1F, and 3P, 3D, 3F
• Transition <1S0|J=+1| 1P1, 3P1 , 3D1>
• 3 peaks in the spectrum
2p XAS of TiO2p XAS of TiO22
• 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 state3d9 has 2D5/2 ground state 3d8 has 3F4 ground state
Hunds rulesHunds rules
Give the Hund’s rule ground states for 3d1 to 3d9
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, 5p-transition: 1P j=+1,0,-1
ground state symmetry: 5D 5D4
transition: 5D 1P = 5PDFpossible final states: 68 states
Term Symbols and XASTerm Symbols and XAS
NiII ion in NiO: Ground state: 3d8 Final state: 2p53d9 Dipole transition: p-symmetry
3d8-configuration: 1S, 1D, 3P,1G, 3F j=4
2p53d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4p-transition: 1P j=+1,0,-1
ground state symmetry: 3F 3F4
transition: 3F 1P = 3DFGtwo possible final states: 3D, 3F 3D3,3F3,3F4, 1F3
Term Symbols and XASTerm Symbols and XAS
Octahedral crystal field splitting
metal ionin free space
in symmetrical field
t2g
yz xz xy
eg
in octahedral ligand field
x2-y2 z2
x2-y2 yz z2 xz xy
SO3 Oh (Mulliken)
S 0 A1
P 1 T1
D 2 E+T2
F 3 A2+T1+T2
G 4 A1+E+T1+T2
Crystal Field EffectsCrystal Field Effects
TiIV ion in TiO2: 3d0-configuration: 1S, j=02p13d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4p-transition: 1P j=+1,0,-1
Write out all term symbols:1P1 1D2 1F3
3P0 3P1 3P2
3D1 3D2 3D3
3F2 3F3 3F4
1 3 4 3 1
2p XAS of TiO2 (atomic multiplets)
J in SO3 Deg.
0 1
1 3
2 4
3 3
4 1
12
Crystal Field Effect on XAS
<1S0|dipole|1P1> goes to <A1|T1|T1>
J in SO3 Deg. Branchings
0 1 A1
1 3 3T1
2 4 4E, 4T2
3 3 3A2, 3T1,3T2
4 1 A1, E, T1, T2
12
Crystal Field Effect on XAS
<1S0|dipole|1P1> goes to <A1|T1|T1>
J in SO3 Deg. Branchings in Oh Deg.
0 1 A1 A1 2
1 3 3T1 A2 3
2 4 4E, 4T2 T1 7
3 3 3A2, 3T1,3T2 T2 8
4 1 A1, E, T1, T2 E 5
12 25
Crystal Field Effect on XAS
<1S0|dipole|1P1> goes to <A1|T1|T1>
• 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 state3d9 has 2D5/2 ground state 3d8 has 3F4 ground state
Hunds rulesHunds rules
Energy
Symmetries Oh Total symmetry
1S 4.6 eV
1A1
3P 0.2 eV
3T1
1D -0.1 eV
1E + 1T2
3F -1.8 eV
3A2 + 3T1 + 3T2
1G 0.8 eV
1A1+1T1+
1T2+1E
Crystal Field Effects on 3dCrystal Field Effects on 3d88 states states
SO3 Oh (Butler) Oh (Mulliken)
S 0 0 A1
P 1 1 T1
D 2 2 + ^1 E+T2
F 3 ^0+ 1 +^1 A2+T1+T2
G 4 0 + 1 + 2 + ^1 A1+E+T1+T2
Crystal Field EffectsCrystal Field Effects
Energy
Symmetries Oh Total symmetry
1S 4.6 eV
1A1
3P 0.2 eV
3T1
1D -0.1 eV
1E + 1T2
3F -1.8 eV
3A2 + 3T1 + 3T2
1G 0.8 eV
1A1+1T1+
1T2+1E
Double group symmetry Double group symmetry
A1A1=A1
T1T2= T1+ T2+ E+ A2
Ground state of a transition metal system3dN at every site
Charge fluctations
Charge Transfer Effects
Hubbard U for a 3d8 ground state:U= E(3d7) + E(3d9) – E(3d8) – E(3d8)
Ligand-to-Metal Charge Transfer (LMCT):= E(3d9L) – E(3d8)
Charge Transfer Effects
Charge Transfer Effects
= E(3d9L) – E(3d8)
E(3d10LL‘) – E(3d8)Two times charge transfer: 2 Extra 3d3d interaction: U
2 +U
Charge Transfer Effects in XASE(3d9L) – E(3d8) = E(3d10LL‘) – E(3d8) = 2 +U
2p XAS: 3d8 2p5 3d9
E (2p53d9) = E2p+
2p XAS: 3d9L 2p5 3d10L
E (2p53d10L) = E2p- Q +2+U
Energy difference: E2p- Q +2+U- E2p - = +U-QQ U+2 eV
3d5
MnO: Ground state: 3d5 + 3d6LEnergy of 3d6L: Charge transfer energy
2p53d6
Charge Transfer Effects
3d6L
3d5
MnO: Ground state: 3d5 + 3d6LEnergy of 3d6L: Charge transfer energy
2p53d7L
2p53d6
+U-Q
Charge Transfer Effects
3d6L
• Transition metal oxide: Ground state: 3d5 + 3d6L• Energy of 3d6L: Charge transfer energy
XAS
2p53d7L
+U-Q
2p53d6
3d5
2p53d6L
XPS
2p53d5
-Q
Ground State
Charge transfer effects in XAS and XPS
NiO: Ground state: 3d8 (3d8 )
+ 3d9L Charge transfer energy
+ 3d93d7 Hubbard U
+ 3d10L2 2+U
+ 3d7L Metal-ligand CT MLCT
Charge Transfer Effects
Spectral shape:
(1) Multiplet effects
(2) Charge Transfer
J. Elec. Spec.J. Elec. Spec.67, 529 (1994)67, 529 (1994)
X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy
=10
NiO
La2Li½Cu½O4
30% 3d8
1A1
30% 3d8
3A2=-5
=5
=0
=-10
3d8 + 3d9L
Charge Transfer effects
Chem. Phys. Lett. 297, 321 (1998)
=10
NiO
La2Li½Cu½O4
30% 3d8
1A1
30% 3d8
3A2=-5
=5
=0
=-10
3d8 + 3d9L
Charge Transfer effects
Calculate the 2p XAS spectrum of Cs2KCuF6
3d6L
3d5
2p53d7L
2p53d6
+U-Q
FeIII: Ground state: 3d5 + 3d6L
C NM
filled d-orbital
empty *-orbital
M C N
filled -orbital
empty d or p orbital
(i) -C?C?N distance
C NM
filled d-orbital
empty *-orbital
M C N
filled -orbital
empty d or p orbital
(i) C?
C NM
filled d-orbital
empty *-orbital
M C N
filled -orbital
empty d or p orbital
(i) -C?C?N distance
C NM
filled d-orbital
empty *-orbital
M C N
filled -orbital
empty d or p orbital
(i) C?
(i) donation (ii) back-donation
empty d-orbital
filled orbital
LMCT and MLCT: - bonding - bonding
with Ed Solomon (Stanford) JACS 125, 12894 (2003), JACS 128, 10442 (2006), JACS 129, 113 (2007)
3d4L
3d6L
3d5
FeIII: Ground state: 3d5 + 3d6L + 3d4L
2p53d5L
2p53d7L
2p53d6
+U-Q - 2
-U+Q + 2
with Ed Solomon (Stanford) JACS 125, 12894 (2003), JACS 128, 10442 (2006), JACS 129, 113 (2007)
LMCT and MLCT: - bonding - bonding
-2
0
2
4
6
8
10
700 705 710 715 720 725 730
Energy (eV)
No
rmal
ized
Ab
sorp
tio
n
Fit X
Series2
FeIII(tacn)2
FeIII(CN)6
with Ed Solomon (Stanford) JACS 125, 12894 (2003), JACS 128, 10442 (2006), JACS 129, 113 (2007)
LMCT and MLCT: - bonding - bonding
Resonant Inelastic X-ray SpectroscopyResonant Inelastic X-ray Spectroscopy
2p XAS of CaF2
3d0
’
3s13d1
2p53d1
Phys. Rev. B.Phys. Rev. B.53, 7099 (1996)53, 7099 (1996)
Resonant Inelastic X-ray ScatteringResonant Inelastic X-ray Scattering
2p3s RIXS of CaF2
3d0
’
3s13d1
2p53d1
Butorin Butorin J. Elec. Spec 110, 213 (2000)J. Elec. Spec 110, 213 (2000)
Resonant Inelastic X-ray SpectroscopyResonant Inelastic X-ray Spectroscopy
Exercise: Repeat these calculations
Phys. Rev. B.Phys. Rev. B.57, 14584 (1998)57, 14584 (1998)
dd spin-flip‘spin-flip’
MSS
2p3d RIXS of NiO
Soft x-ray RIXS and magnetismSoft x-ray RIXS and magnetism
What does the progam do?
What does the program do?
Nothing, really… no multiplets, no group theory, no angular dependence, …)
Takes output of two separate ctm4xas calculations and combines them in Kramers-Heisenberg Formula
CTM4RIXSCTM4RIXS
• Load in absorption and emission files → Extract information and save energies, symmetries and transition matrix elements (saved as .sm file).
• >> These matrices are calculated with CTM4XAS if the RIXS option is chosen
AbsorptionTriad
GS → T1 → IS
EmissionTriad
IS → T2 → FS
|g>, Eg
|n>, En
|f>, Ef
CTM4RIXSCTM4RIXS
A first CTM4RIXS calculationA first CTM4RIXS calculation
Choose the name_abs that has been calculated with CTM4XAS
A first CTM4RIXS calculationA first CTM4RIXS calculation
Set L intermediate to 0.4 and click button at bottom
A first CTM4RIXS calculationA first CTM4RIXS calculation
Set Delta to 0.1 (two times) and click button at bottomChoose a name in the pop-up window.
A first CTM4RIXS calculationA first CTM4RIXS calculation
Set Delta NOT to a small number >> CTM4RIXS crashes
A first CTM4RIXS calculationA first CTM4RIXS calculation
Start the calculation with the RIXS buttonA pop-up window tracks the progress.
• The RIXS calculation is finished.
• Next the RIXS plane can be plotted with the screen on the right.
CTM4RIXSCTM4RIXS
Plotting a CTM4RIXS calculationPlotting a CTM4RIXS calculation
Select the file button and next the select the file you calculated;GOTO the name_RIXS directoryGOTO the name_matrices directorySELECT name_Ms
Plotting a CTM4RIXS calculationPlotting a CTM4RIXS calculation
This is the 2p3d RIXS plane of Ni2+ with 10Dq=1.0 eV.
Plotting a CTM4RIXS calculationPlotting a CTM4RIXS calculation
Enlarge a region of the 2D map with this button & select the region.
Plotting a CTM4RIXS calculationPlotting a CTM4RIXS calculation
Final state energy to set the vertical axis to energy loss. (& enlarge/select the region).
Selecting a cross-sectionSelecting a cross-section
Choose a vertical cross section & select energy.The screen on the right shows the cross section (= RXES)
• 2D RIXS plane
• Cross sections, including
resonant XESselective XASHERFD
partial FY
What is calculated with CTM4RIXSWhat is calculated with CTM4RIXS
• No interatomic exchange (can be included)
• Only 3dN > 2p5 3dN+1 > 3dN channel• (as yet) no charge transfer
• Fluorescence is not included
What is NOT calculated with CTM4RIXSWhat is NOT calculated with CTM4RIXS
Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface
Calculation of 2p3d RIXS without charge transfer
(note: this is a repetition of CTM4XAS, now with the original DOS commands)
1.Do a CTM4XAS calculation for 2p3d RIXS, for example for Co2+, 10dq=1 eV, using co2 as filename.2.Copy the files co2_ems.rcg, co2_abs.rcg, co2_ems.rac and co2_abs.rac to the directory c:cowan/batch 3.Open the DOS prompt command window, for type cmd in “search programs”4.Goto the directory c:/cowan/batch by typing ‘cd ..’, ‘cd ..’, ‘cd cowan’, ‘cd batch’ 5.type ‘rcg2 co2_ems’ and ‘rac2 co2_ems’. Same for the _abs files.6.Open the ora-files with CTM4RIXS and make a plot (same as with CTM4XAS files)7.(shift the excitation energy and the emission energy to the correct values)
Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface
Calculation of 2p3s RIXS (without charge transfer)
1.Do a CTM4XAS calculation for 2p3d RIXS, for example for Co2+, 10dq=1 eV.2.Do a RCN calculation using hco23s.rcn within c/cowan/batch; The output is written in the file hco23s.rcf3.Open the file co2p3s_ems.rcg and change the line P_5__D_8 to P_5__D_8__S_2 (keep the same number of spaces indicated by _). Change the line P_6__D_7 to P_6__D_8__S_1.4.Open the file hco23s.rcf and copy the line starting with “Co2+ 3s01 3d08” and replace in co2p3s_ems the line starting with “Co2+ 2P06 3D07”.5.Change the energy to 0.0000 (from a value around -600).6.Re-run the rcg and rac files for 2p3s RIXS.7.Open the ora-files with CTM4RIXS and make a plot.8.(shift the excitation energy and the emission energy to the correct values)9.(Note that the integrated XES spectrum now gives exactly the XAS spectral shape because it is a core-core channel)
Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface
Calculation of 2p3d RIXS with charge transfer (MATLAB is needed)
Step 1: run CTM4XAS•RUN an XAS calculation with CTM4XAS, including charge transfer. •Use any name. I use nitest1, with 10Dq=1, DELTA=3, Udd=6, Upd=7, rest=default.•Copy the files nitest1.rcg and nitest1.ban to cowan/batch•Copy in cowan/batch rni2.rac to nitest1.rac
Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface
Calculation of 2p3d RIXS with charge transfer (MATLAB is needed)
Step 2: Run the calculations for absorption•Copy BANEX2.BAT to cowan/batch #see below#•Copy banderex.exe to cowan/bin ##•Open the DOS prompt•Change the directory to c:cowan/batch•Type Rcg2 nitest1•Type Rac2 nitest1•Type Banex2 nitest1•The result is in the file nitest1.oba
(## this is a modified executable file using exact diagonalization as created by Robert Green; ask me to send it to you)
Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface
Calculation of 2p3d RIXS with charge transfer (MATLAB is needed)
Step 3a: Create the inputfiles for the x-ray emission step and run the calculations Copy nitest1.rcg to nitest1x.rcgEdit the file nitest1x.rcg
Invert lines 4 and 5 (line 4 is D08 P06)Invert lines 12 and 13Invert block 4 with block 3.
[Each block starts with 0 80998080 …. and ends with -99999999.]Save the file nitest1x.rcgCopy nitest1.rac to nitest1x.racCopy nitest1.ban to nitest1x.ban
Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface
Calculation of 2p3d RIXS with charge transfer (MATLAB is needed)
Step 3b: Edit the file nitest1x.banChange the lines def EG2 = 3.000 unity def EF2 = 2.000 unityto def EG2 = 2.000 unity def EF2 = 3.000 unityChange for the triads the first sign from + to – and the last sign from – to +Change erange 0.3 to erange 999Type Rcg2 nitest1xType Rac2 nitest1xType Banex2 nitest1xThe result is in the file nitest1x.oba
Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface
Calculation of 2p3d RIXS with charge transfer (MATLAB is needed)
Step 4: Run the Kramers-Heisenberg calculation(for the moment use this procedure; all parameters are set in racin.m)•Copy nitest1.oba to rni2.oba•Copy nitest1x.oba to rni2x.oba•Start MATLAB•Type dorixs•The RIXS matrix is saved in rni2_MS•Change the name rni2_MS to rni2_MS.mat
Step 5: Plot with CTM4RIXSLoad the file rni2_Ms.mat
2p 3/2
2p 1/2
2s
1s
fluorescent radiation
2p 3/2
2p 1/2
2s
1s
Fluorescence Auger
Core Hole DecayCore Hole Decay
5880 5900 5920 6480 6520 6560Fluorescence Energy [eV]
x 8
x 500
K1,3
K1
K2
K''
K2,5
K'
K
K Main Lines K Satellite LinesMnO
1s X-ray emission1s X-ray emission
Tot
al E
nerg
y
2p53dn
3p53dn
1s13dn
Core Hole
Valence hole
Photoionizationor
K capture
5880 5900 5920 6480 6520 6560Fluorescence Energy [eV]
x 8
x 500
K1,3
K1
K2
K''
K2,5
K'
K
K Main Lines K Satellite Lines
K KMain Lines
K Satellites
3dnGround State
1s X-ray emission1s X-ray emission
Etotal
K Fluorescence
Strong interaction between
unfilled 3p and 3d shells!
3d1s
3d3p
Photoionization
Multiplet effects in 1s3p XES (KMultiplet effects in 1s3p XES (Kββ))
Spin-selectivity in the K line
K1,3
3p
3d
3p
3d
K’
?5P
7P
Multiplet effects in 1s3p XES (KMultiplet effects in 1s3p XES (Kββ))
3p XPS and K XES
Free Mn atom3p XPS
MnF2 K
A
F
B
Identical final state configuration:3p53d5
Multiplet effects in 1s3p XES (KMultiplet effects in 1s3p XES (Kββ))
1s2p and 1s3p XES spectra
Approximations:
- 3dN ground state (+ CT)
- XES only from lowest energy 1s13dN state (+CT)
- Charge transfer energy is -Q
3d6L
• Transition metal oxide: Ground state: 3d5 + 3d6L• Energy of 3d6L: Charge transfer energy
Pre-edge
1s13d7L
+U-Q
1s13d6
3d5
1s13d6L
edge
1s13d5
-Q
Ground State
Charge transfer in 1s pre-edge and edge
1s2p and 1s3p XES spectra
Approximations:
- 3dN ground state (+ CT)
- XES only from lowest energy 1s13dN state (+CT)
- Charge transfer energy is -Q
- Neglect 1s3d exchange interaction (needed for spin-pol.)
- Neglect of excitation process (a better approximation is to
describe the excitation process with XPS)
Fe K pre-edgesFe K pre-edges
Westre et al. JACS 119, 6297 (1997); Heyboer et al. J.Phys.Chem.B. 108, 10002 (2004)
Exercise: Repeat these calculations
Pre-edge and edge
Only quadrupole peaks visible3d7 1s13d8 2p53d8
Only correct with interference effects ONOnly correct with interference effects ON
CoO
high-spin CoII
3d7 [4T2]
Exercise: Repeat these calculations
Non-local screening peaks RIXS-MCD at the K pre-edge
XMCD at high-pressureSikora, PRL 105, 037202 (2010)
X-MCDX-MCD
L=2, S=1/2 2DJ=5/2 or 3/2More than half-full2D5/2
Cu2+: 3d9 2p53d10
L=1, S=1/2 2PJ=3/2 or 1/2
2P3/2 or 2P1/2
J= +1 or 0 or -1light polarization q = mJ
3d5
MnO: Ground state: 3d5 + 3d6LEnergy of 3d6L: Charge transfer energy
2p53d6
Charge Transfer Effects
3d6L
3d5
MnO: Ground state: 3d5 + 3d6LEnergy of 3d6L: Charge transfer energy
2p53d7L
2p53d6
+U-Q
Charge Transfer Effects
3d6L
• Transition metal oxide: Ground state: 3d5 + 3d6L• Energy of 3d6L: Charge transfer energy
XAS
2p53d7L
+U-Q
2p53d6
3d5
2p53d6L
XPS
2p53d5
-Q
Ground State
Charge transfer effects in XAS and XPS