1. NSRRC September 12 program
Part 1
CTM4XAS
Atomic Multiplet, crystal fields and charge transfer
Part 2
CTM4RIXS

2. Charge Transfer Multiplet program
Used for the analysis of XAS, EELS,
Photoemission, Auger, XES,
ATOMIC PHYSICS 
GROUP THEORY
MODEL HAMILTONIANS
The TT-multiplets program can be used to explain the spectral shapes of all core level spectroscopies. XAFS, photoemission, auger, etc.
The program combines three advanced computer codes, an atomic physics code to describe all atomic interactions, a group theory code to describe the local symmetry (think of crystal fields) and model Hamiltonians to describe many body effects correlated systems.
AS A SIDE REMARK I WOULD LIKE TO MENTION that the active site in a catalyst is a perfect example of a correlated system. (in biocatalysis this is often realised)
The integrated program gives accurate descriptions of core level spectra, from a set of uniform electronic structure parameters.
The program is important for all of the new spectroscopies that I will describe.
The program is distributed from my homepage and it is used at some 50 institutes worldwide.

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

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

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

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

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

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

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

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) 10

11. X-ray absorption: core hole effect
XAS: recent first principles
developments 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 11

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
The TT-multiplets program can be used to explain the spectral shapes of all core level spectroscopies. XAFS, photoemission, auger, etc.
The program combines three advanced computer codes, an atomic physics code to describe all atomic interactions, a group theory code to describe the local symmetry (think of crystal fields) and model Hamiltonians to describe many body effects correlated systems.
AS A SIDE REMARK I WOULD LIKE TO MENTION that the active site in a catalyst is a perfect example of a correlated system. (in biocatalysis this is often realised)
The integrated program gives accurate descriptions of core level spectra, from a set of uniform electronic structure parameters.
The program is important for all of the new spectroscopies that I will describe.
The program is distributed from my homepage and it is used at some 50 institutes worldwide.

14. Atomic Multiplet Theory

15. Atomic Multiplet Theory
Kinetic Energy
Nuclear Energy
Electron-electron interaction
Spin-orbit coupling

16. Atomic Multiplet Theory
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)
2p13d  STOT = 0 or 1
 LTOT = 1 or 2 or 3
 1P1 + 3P0, 3P1, 3P2
 1D2 + 3D1, 3D2, 3D3
 1F3 + 3F2, 3F3, 3F4
[(2J+1)= =60]

24. Term Symbols
Term symbols of a 2p2 configuration

25. Configurations of 2p2 1  0  -1  1  0  -1  1  0  -1  1  0 

26. 1S0 1D2 3P0 3P1 3P2 Term Symbols of 2p2 MS=1 MS=0 MS=-1 ML= 2 1 ML= 11
ML= 1 2
ML= 0 3
ML=-1
ML=-2
LS term symbols: 1S, 1D, 3P
LSJ term symbols:
1S0 1D2 3P0 3P1 3P2

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+)
0.07 5 8 17 13 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, and 3P, 3D, 3F

36. 2p XAS of TiO2 Final state symmetries: 1P, 1D, 1F, and 3P, 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 Give the Hund’s rule ground states for 3d1 to 3d9
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 d2 has 3F2 ground state
3d9 has 2D5/2 ground state d8 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=4 2p53d7-configuration: 110 states j’= 3,4, 5
p-transition: 1P j=+1,0,-1
ground state symmetry: 5D D4
transition: 5D 1P = 5PDF
possible final states: states

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

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, 3F j=4 2p53d9-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
+FK, GK: > 3F

44. Atomic multiplets

45. Charge Transfer Multiplet program
ATOMIC PHYSICS 
GROUP THEORY
MODEL HAMILTONIANS
The TT-multiplets program can be used to explain the spectral shapes of all core level spectroscopies. XAFS, photoemission, auger, etc.
The program combines three advanced computer codes, an atomic physics code to describe all atomic interactions, a group theory code to describe the local symmetry (think of crystal fields) and model Hamiltonians to describe many body effects correlated systems.
AS A SIDE REMARK I WOULD LIKE TO MENTION that the active site in a catalyst is a perfect example of a correlated system. (in biocatalysis this is often realised)
The integrated program gives accurate descriptions of core level spectra, from a set of uniform electronic structure parameters.
The program is important for all of the new spectroscopies that I will describe.
The program is distributed from my homepage and it is used at some 50 institutes worldwide.

46. Crystal Field Effects
eg states
t2g states

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

48. Crystal Field Effects in CTM
7 = 2.13 eV

49. Crystal Field Effects SO3 Oh (Mulliken) S A1 P 1 T1 D 2 E+T2 F 3A1 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=0 2p13d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4
p-transition: 1P j=+1,0,-1
Write out all term symbols:
1P1 1D2 1F3
3P0 3P1 3P2
3D1 3D2 3D3
3F2 3F3 3F4

51. Crystal Field Effect on XAS
J in SO3
Deg. 1 3 2 4  12
<1S0|dipole|1P1> goes to <A1|T1|T1>

52. Crystal Field Effect on XAS
J in SO3
Deg.
Branchings 1 A1 3
3T1 2 4
4E, 4T2
3A2, 3T1,3T2
A1, E, T1, T2  12
<1S0|dipole|1P1> goes to <A1|T1|T1>

53. Crystal Field Effect on XAS
J in SO3
Deg.
Branchings
 in Oh 1 A1 2 3
3T1 A2 4
4E, 4T2 T1 7
3A2, 3T1,3T2 T2 8
A1, E, T1, T2 E 5  12 25
<1S0|dipole|1P1> goes to <A1|T1|T1>

54. Effect of 10Dq on XAS:3d0

55. Comparison with Experiment

56. Comparison with Experiment

57. CTM4XAS version 5.2

58. CTM4XAS version 5.2

59. Turning multiplet effects off

60. 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 d2 has 3F2 ground state
3d9 has 2D5/2 ground state d8 has 3F4 ground state

61. Crystal Field Effects on 3d8 states
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

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

63. Double group symmetry A1A1=A1 T1T2= T1+ T2+ E+ A2 Symmetries Oh
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
A1A1=A1
T1T2= T1+ T2+ E+ A2

64. Crystal Field Effects: Tanabe-Sugano

65. Effect of 10Dq on XAS:3dN

66. High-spin or Low-spin 10Dq > 3J (d4 and d5) 10Dq > 2J

67. 2p XAS of Mn2+

68. 3d spin-orbit coupling
Exercise: Calculate the 2p XAS spectrum of CoO

69. 3d spin-orbit coupling

70. Charge Transfer Effects
Ground state of a transition metal system
3dN at every site
Charge fluctations

71. 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)

72. Charge Transfer Effects
= E(3d9L) – E(3d8)
E(3d10LL‘) – E(3d8)
Two times charge transfer: 2
Extra 3d3d interaction: U
2 +U

73. Charge Transfer Effects

74. Charge Transfer Effects in XAS
E(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-Q
Q  U+2 eV

75. Charge Transfer Effects in XAS
+U-Q 

76. Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d5
2p53d6

77. Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d6L
3d5
2p53d7L
2p53d6 
+U-Q  

78. Charge Transfer Effects in XPS
-Q 

79. Charge transfer effects in XAS and XPS
Transition metal oxide: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d6L
XPS
2p53d5
XAS
2p53d7L 
3d5
-Q
Ground State
+U-Q  
2p53d6L
2p53d6

80. Charge Transfer Effects
NiO: Ground state: 3d8 (3d8 )
+ 3d9L Charge transfer energy 
+ 3d93d7 Hubbard U
+ 3d10L2 2+U
+ 3d7L Metal-ligand CT MLCT

81. Charge Transfer Multiplets of Ni2+
=3
=9
=0
=6

82. Exercise: perform a series of charge transfer calculations changing  from +10 to -10.

83. X-ray Absorption Spectroscopy
Spectral shape:
(1) Multiplet effects
(2) Charge Transfer
J. Elec. Spec.
67, 529 (1994)

84. Charge transfer

85. Charge transfer

86. Charge transfer

87. Charge Transfer effects
3d8 + 3d9L
=10
30% 3d8
1A1
=5
NiO
=0
30% 3d8
3A2
La2Li½Cu½O4
=-5
=-10
Chem. Phys. Lett. 297, 321 (1998)

88. Charge Transfer effects
3d8 + 3d9L
=10
30% 3d8
1A1
=5
NiO
=0
30% 3d8
3A2
La2Li½Cu½O4
=-5
=-10
Calculate the 2p XAS spectrum of Cs2KCuF6

89. LMCT and MLCT:  - bonding
FeIII: Ground state: 3d5 + 3d6L
3d6L
3d5
2p53d7L
2p53d6
+U-Q   
with Ed Solomon (Stanford) JACS 125, (2003),
JACS 128, (2006), JACS 129, 113 (2007)

90. LMCT and MLCT:  - bonding
FeIII: Ground state: 3d5 + 3d6L + 3d4L
2p53d5L
2p53d7L
2p53d6
3d4L
3d6L
3d5
-U+Q   + 2  
+U-Q   - 2
with Ed Solomon (Stanford) JACS 125, (2003),
JACS 128, (2006), JACS 129, 113 (2007)

91. LMCT and MLCT:  - bonding
FeIII(tacn)2
FeIII(CN)6
with Ed Solomon (Stanford) JACS 125, (2003),
JACS 128, (2006), JACS 129, 113 (2007)

92. RIXS

93. RIXS
Butorin, J. Elec. Spec. 110, 213 (2000)

94. Resonant Inelastic X-ray Spectroscopy
dd excitation

95. Resonant Inelastic X-ray Spectroscopy
2p XAS of CaF2
3d0 
’
3s13d1
2p53d1

96. Resonant Inelastic X-ray Scattering
2p3s RIXS of CaF2
3d0 
’
3s13d1
2p53d1
Phys. Rev. B.
53, 7099 (1996)

97. Resonant Inelastic X-ray Spectroscopy
Butorin
J. Elec. Spec 110, 213 (2000)
Exercise: Repeat these calculations

98. Soft x-ray RIXS and magnetism
NiII 3d8 []  2p53d9[jj]  3d8[]

99. Soft x-ray RIXS and magnetism
MS dd
‘spin-flip’
spin-flip
Phys. Rev. B.
57, (1998)
2p3d RIXS of NiO

100. CTM4RIXS

101. CTM4RIXS 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

102. CTM4RIXS

103. CTM4RIXS
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
Emission
Triad
IS → T2 → FS
Absorption
Triad
GS → T1 → IS
|g>, Eg
|n>, En
|f>, Ef W w
W - w

104. A first CTM4RIXS calculation
Choose the name_abs that has been calculated with CTM4XAS

105. A first CTM4RIXS calculation
Choose ‘1’ in the pop-up menu

106. A first CTM4RIXS calculation
Choose ‘1’ in the pop-up menu

107. A first CTM4RIXS calculation
Click button at bottom

108. A first CTM4RIXS calculation
Set L intermediate to 0.4 and click button at bottom

109. A first CTM4RIXS calculation
Set Delta to 0.1 (two times) and click button at bottom
Choose a name in the pop-up window.

110. A first CTM4RIXS calculation
Set Delta NOT to a small number >> CTM4RIXS crashes

111. A first CTM4RIXS calculation
Start the calculation with the RIXS button
A pop-up window tracks the progress.

112. CTM4RIXS The RIXS calculation is finished.
Next the RIXS plane can be plotted with the screen on the right.

113. Plotting a CTM4RIXS calculation
Select the file button and next the select the file you calculated;
GOTO the name_RIXS directory
GOTO the name_matrices directory
SELECT name_Ms

114. Plotting a CTM4RIXS calculation
This is the 2p3d RIXS plane of Ni2+ with 10Dq=1.0 eV.

115. Plotting a CTM4RIXS calculation
Enlarge a region of the 2D map with this button
& select the region.

116. Plotting a CTM4RIXS calculation
Final state energy to set the vertical axis to energy loss.
(& enlarge/select the region).

117. Selecting a cross-section
Choose a vertical cross section & select energy.
The screen on the right shows the cross section (= RXES)

118. What is calculated with CTM4RIXS
2D RIXS plane
Cross sections, including
resonant XES selective XAS HERFD
partial FY

119. What is NOT 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

120. A first CTM4RIXS calculation

121. Calculations without the CTM4XAS interface

122. Calculations without the CTM4XAS interface
Calculation of 2p3d RIXS without charge transfer
(note: this is a repetition of CTM4XAS, now with the original DOS commands)
Do a CTM4XAS calculation for 2p3d RIXS, for example for Co2+, 10dq=1 eV, using co2 as filename.
Copy the files co2_ems.rcg, co2_abs.rcg, co2_ems.rac and co2_abs.rac to the directory c:cowan/batch
Open the DOS prompt command window, for type cmd in “search programs”
Goto the directory c:/cowan/batch by typing ‘cd ..’, ‘cd ..’, ‘cd cowan’, ‘cd batch’
type ‘rcg2 co2_ems’ and ‘rac2 co2_ems’. Same for the _abs files.
Open the ora-files with CTM4RIXS and make a plot (same as with CTM4XAS files)
(shift the excitation energy and the emission energy to the correct values)

123. Calculations without the CTM4XAS interface
Calculation of 2p3s RIXS (without charge transfer)
Do a CTM4XAS calculation for 2p3d RIXS, for example for Co2+, 10dq=1 eV.
Do a RCN calculation using hco23s.rcn within c/cowan/batch; The output is written in the file hco23s.rcf
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.
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”.
Change the energy to (from a value around -600).
Re-run the rcg and rac files for 2p3s RIXS.
Open the ora-files with CTM4RIXS and make a plot.
(shift the excitation energy and the emission energy to the correct values)
(Note that the integrated XES spectrum now gives exactly the XAS spectral shape because it is a core-core channel)

124. Calculations 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

125. Calculations 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)

126. Calculations 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.rcg
Edit the file nitest1x.rcg
Invert lines 4 and 5 (line 4 is D08 P06)
Invert lines 12 and 13
Invert block 4 with block 3.
[Each block starts with …. and ends with ]
Save the file nitest1x.rcg
Copy nitest1.rac to nitest1x.rac
Copy nitest1.ban to nitest1x.ban

127. Calculations without the CTM4XAS interface
Calculation of 2p3d RIXS with charge transfer (MATLAB is needed)
Step 3b:
Edit the file nitest1x.ban
Change the lines
def EG2 = unity def EF2 = unity to
def EG2 = unity
def EF2 = unity
Change for the triads the first sign from + to – and the last sign from – to +
Change erange 0.3 to erange 999
Type Rcg2 nitest1x
Type Rac2 nitest1x
Type Banex2 nitest1x
The result is in the file nitest1x.oba

128. Calculations 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 CTM4RIXS
Load the file rni2_Ms.mat

129. XES calculations

130. X-ray absorption and X-ray photoemission

131. Core Hole Decay
Fluorescence Auger

132. X-ray emission

133. Resonant X-ray emission spectroscopy

134. 1s X-ray emission MnO explain axes Start with K alpha
address resolution -> no solid state detector
Nomenclature from early days of x-ray spectroscopy of high Z materials (Kb3 3p1/2, Kb2 4p, Kb5 3d)

135. 1s X-ray emission 1s13dn Total Energy 2p53dn 3p53dn Core HoleKa K
Main Lines K
Satellites
Total Energy
2p53dn
Photoionization or
K capture
Transitions that give rise to the fluorescence lines
Spectra repeated for orientation
total energy of the atom on y-axis
Dipole selection rules
Kb satellites
Core hole final states
In this talk I will focus on Kbeta emission
3p53dn
Core Hole
Ground State
Valence hole
3dn

136. Multiplet effects in 1s3p XES (Kβ)
Etotal 3d 1s
Kb Fluorescence
Photoionization 3d 3p
Strong interaction between unfilled 3p and 3d shells!

137. Spin-selectivity in the Kb line
Multiplet effects in 1s3p XES (Kβ)
Spin-selectivity in the Kb line 3d 7P 3p 5P ? 3d 3p
Kb1,3
Kb’

138. Multiplet effects in 1s3p XES (Kβ)
3p XPS and Kb XES
Multiplet effects in 1s3p XES (Kβ)
Identical final state configuration:
3p53d5 A
Free Mn atom
3p XPS B
MnF2 Kb F

139. 1s2p and 1s3p XES spectra

140. 1s2p and 1s3p XES spectra Approximations: 3dN ground state (+ CT)
XES only from lowest energy 1s13dN state (+CT)
Charge transfer energy is -Q

141. Charge transfer in 1s pre-edge and edge
Transition metal oxide: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d6L
edge
1s13d5
Pre-edge
1s13d7L 
3d5
-Q
Ground State
+U-Q  
1s13d6L
1s13d6

142. 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)

143. Charge transfer in XES spectra
Pieter Glatzel et al. Phys. Rev. B. 64, (2001)

144. Charge transfer in XES spectra
Pieter Glatzel et al. Phys. Rev. B. 64, (2001)

145. RIXS at metal K edges

146. Fe K pre-edges Exercise: Repeat these calculations
Westre et al. JACS 119, 6297 (1997); Heyboer et al. J.Phys.Chem.B. 108, (2004)

147. Pre-edge and edge Exercise: Repeat these calculations CoO
high-spin CoII
3d7 [4T2]
Only quadrupole peaks visible
3d7  1s13d8  2p53d8
Only correct with interference effects ON

148. Non-local screening peaks RIXS-MCD at the K pre-edge

149. Non-local screening peaks RIXS-MCD at the K pre-edge

150. Non-local screening peaks RIXS-MCD at the K pre-edge

151. Non-local screening peaks RIXS-MCD at the K pre-edge of Fe3O4

152. RIXS-MCD at the K pre-edge Non-local screening peaks

153. Non-local screening peaks RIXS-MCD at the K pre-edge
XMCD at high-pressure
Sikora, PRL 105, (2010)

154. MCD

155. X-MCD

156. light polarization q = mJ
X-MCD
Cu2+: 3d  p53d10
L=2, S=1/2  2D
J=5/2 or 3/2
More than half-full
2D5/2
L=1, S=1/2  2P
J=3/2 or 1/2
 2P3/2 or 2P1/2
J= +1 or 0 or -1
light polarization q = mJ

157. X-MCD
Cu2+: 3d9

158. X-MCD Exercise: Repeat these calculations mJ=-5/2 MCD to mJ’=-3/2
no LS
MCD
Exercise: Repeat these calculations

159. X-MCD
MCD
no LS
MCD
+ crystal field

160. X-MCD
MCD
3F LS
3F no LS

161. XPS

162. X-ray photoemission

163. Charge transfer effects in XPS

164. Charge Transfer Effects in XAS
+U-Q 

165. Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d5
2p53d6

166. Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d6L
3d5
2p53d7L
2p53d6 
+U-Q  

167. Charge Transfer Effects in XPS
-Q 

168. Charge transfer effects in XAS and XPS
Transition metal oxide: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d6L
XPS
2p53d5
XAS
2p53d7L 
3d5
-Q
Ground State
+U-Q  
2p53d6L
2p53d6

169. Charge transfer effects in XPS
Exercise: Calculate the 2p XPS spectrum of NiCl2