NSRRC September 12 program
Part 1
Part 2
CTM4XAS
Atomic Multiplet, crystal fields and charge transfer
CTM4RIXS
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
The XAS spectrum
is given by the
Fermi Golden Rule
I XAS ~  f  f eˆ  r i
2
E
f
 Ei 
X-ray Absorption Spectroscopy
Excitations of
core electrons
to empty states
The XAS spectrum
is given by the
Fermi Golden Rule
1s
I XAS ~ M    site ,symmetry
2
X-ray Absorption Spectroscopy
2p
2s
Phys. Rev. B.40, 5715 (1989)
X-ray Absorption Spectroscopy
oxygen 1s > p DOS
Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)
X-ray Absorption Spectroscopy
oxygen 1s > p DOS
Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)
Interpretation of XAS
1-particle:
1s edges
(DFT + core hole +U)
2-particle:
+ all edges of closed
shell systems
(TDDFT, BSE)
many-particle:
open shell systems
(CTM4XAS)
XAS: multiplet effects
Fermi Golden Rule:
IXAS = |<f|dipole| i>|2 [E=0]
 f eˆq  r i
2
 i c eˆq  r i
 ??  eˆq  r c
2
Single electron (excitation) approximation:
IXAS = |< φ empty|dipole| φcore>|2 
2
XAS: multiplet effects
Overlap of core and valence wave functions
3d
 Single Particle model breaks down
<2p3d|1/r|2p3d>
2p3/2
2p1/2
Phys. Rev. B. 42, 5459 (1990)
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 http://www.anorg.chem.uu.nl/FXS2013/]
CTM4XAS (semi-empirical)
Charge Transfer Multiplet program
Used for the analysis of XAS, EELS,
Photoemission, Auger, XES,
ATOMIC PHYSICS

GROUP THEORY

MODEL HAMILTONIANS
Atomic Multiplet Theory
Atomic Multiplet Theory
=E
H 
N
pi2
2m

N
 Ze 2
ri


pairs
e2
rij
   (ri ) li  si
N
• Kinetic Energy
• Nuclear Energy
• Electron-electron interaction
• Spin-orbit coupling
Atomic Multiplet Theory
=E
H 
pi2
2m
X
N

N
 Ze 2
ri
X


pairs
e2
rij
   (ri ) li  si
N
• Kinetic Energy
• Nuclear Energy
• Electron-electron interaction
• Spin-orbit coupling
Term Symbol
2S+1L
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
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
Term Symbols
Singlet or triplet
Spin-orbit coupling
H ATOM 

pairs
e2
rij
  (ri ) li  si
N
• 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
Quantum numbers
• Main
n
1,2,3,….
• Azimuthal
L
(orbital moment)
• Spin
S
• Magnetic
mL
• Spin magnetic mS
• Total moment
J
• Total magnetic mJ
(orbital magnetic moment)
(spin magnetic moment)
Term Symbols
• Term symbols of a 2p13d1 configuration
• 2p1 
2P , 2P
1/2
3/2
(S=1/2, L=1)
• 3d1 
2D , 2 D
3/2
5/2
(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
• Term symbols of a 2p2 configuration
Configurations of 2p2
11
00 -1-1
11
00 -1-1
111  000  -1-1-1 
11 0 00 -1 -1-1
11
110000-1-1-1-1
11
110000-1-1-1-1
11
1  000  -1-1-1 
11
-1-1
11 00

0
-1  1 
1
0
0
-1 
-1 
1
1
0
0
-1 
-1 
1
1
0
0
-1 
-1 
Term Symbols of 2p2
MS=1
ML= 2
0
ML= 1
1
ML= 0
1
MS=0 MS=-1
1
0
2
1
3
1
ML=-1
1
2
1
ML=-2
0
1
0
LS term symbols: 1S, 1D, 3P
LSJ term symbols:
1S
1D 3P 3P 3P
0
2
0
1
2
The electron-electron interaction
H

2
e
rij
pairs
• Electron-electron interaction acts on 2 electrons
• It can couple 4 different wave function a, b, c and d
The electron-electron interaction
1. Split wave functions into radial and angular part
2. Split operator into radial and angular part
3. Use series expansion of 1/r12
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
Atomic Multiplet Theory
2 S 1
L   f k F   gk G
e2 2 S 1
J
r12
LJ | |
k
k
k
Electron-electron interactions of Valence States
H ATOM 

pairs
e2
rij
  (ri ) li  si
N
Valence Spin-orbit coupling
k
CTM4XAS version 5.2
CTM4XAS version 5.2
Atomic Multiplet Theory
2 S 1
L   f k F   gk G
e2 2 S 1
J
r12
LJ | |
k
k
k
Core Valence Overlap
H ATOM 

pairs
e2
rij
  (ri ) li  si
N
Core Spin-orbit coupling
k
Multiplet Effects (Ni2+)
1s
0.07
2s
5
2p
8
3s
3p
13
17
Core Valence Overlap
0
0
17
0
Core Spin-orbit coupling
2
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
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
Exercise:
Calculate the 2p XAS spectrum of a Ti atom
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
3d9 has 2D5/2 ground state
3d2 has 3F2 ground state
3d8 has 3F4 ground state
Give the Hund’s rule ground states for 3d1 to 3d9
Exercise: Calculate the 2p XAS spectrum of Fe
Fe atom:
Ground state:
3d6 (4s2) 5D j=4
Term Symbols and XAS
Fe atom:
Ground state:
Final state:
Dipole transition:
3d6 (4s2)
2p53d7
p-symmetry
5D, etc.
3d6-configuration:
2p53d7-configuration: 110 states
1P
p-transition:
ground state symmetry: 5D
5D 1P = 5PDF
transition:
possible final states:
j=4
j’= 3,4, 5
j=+1,0,-1
5D
4
68 states
Term Symbols and XAS
Fe atom:
Ground state:
3d6 (4s2) 5D j=4
5D
0
5D
5D
4
Term Symbols and XAS
NiII ion in NiO:
Ground state:
Final state:
Dipole transition:
3d8-configuration:
2p53d9-configuration:
p-transition:
3d8
2p53d9
p-symmetry
1S 1D, 3P,1G, 3F
,
2P2D = 1,3PDF
1P
ground state symmetry: 3F
3F 1P = 3DFG
transition:
two possible final states: 3D, 3F
j=4
j’=0,1,2,3,4
j=+1,0,-1
3F
4
3D ,3F ,3F 1F
3
3
4,
3
3d8 XAS calculation
+LS3d : > 3F4
+LS2p
0
+FK, GK: > 3F
Atomic multiplets
Normalized Intensity
1
0
850
855
860
865
Energy (eV)
870
Charge Transfer Multiplet program
ATOMIC PHYSICS

GROUP THEORY

MODEL HAMILTONIANS
Crystal Field Effects
eg states
t2g states
Octahedral crystal field splitting
metal ion
in free space
in symmetrical field
in octahedral ligand field
eg
x2-y2 z2
t2g
yz
x2-y2 yz z2 xz xy
xz
xy
Crystal Field Effects in CTM
0
7 = 2.13 eV
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
2p XAS of TiO2 (atomic multiplets)
TiIV ion in TiO2:
3d0-configuration:
2p13d9-configuration:
p-transition:
1S
,
2P2D
1P
Write out all term symbols:
1P
1D
1F
1
2
3
3P
3P
3P
0
1
2
3D
3D
3D
1
2
3
3F
3F
3F
2
3
4
1
3
4
3
1
= 1,3PDF
j=0
j’=0,1,2,3,4
j=+1,0,-1
Crystal Field Effect on XAS
J in SO3
Deg.
0
1
1
3
2
4
3
3
4
1

12
<1S0|dipole|1P1> goes to <A1|T1|T1>
Crystal Field Effect on XAS
J in SO3
Deg.
Branchings
0
1
A1
1
3
3T1
2
4
4E, 4T2
3
3
3A2, 3T1,3T2
4
1
A1, E, T1, T2

12
<1S0|dipole|1P1> goes to <A1|T1|T1>
Crystal Field Effect on XAS
J in SO3
Deg.
Branchings
 in Oh
Deg.
0
1
A1
A1
2
1
3
3T1
A2
3
2
4
4E, 4T2
T1
7
3
3
3A2, 3T1,3T2
T2
8
4
1
A1, E, T1, T2
E
5

12
<1S0|dipole|1P1> goes to <A1|T1|T1>
25
Effect of 10Dq on XAS:3d0
Comparison with Experiment
Comparison with Experiment
CTM4XAS version 5.2
CTM4XAS version 5.2
0.0
0.0
0.0
Turning multiplet effects off
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
3d9 has 2D5/2 ground state
3d2 has 3F2 ground state
3d8 has 3F4 ground state
Crystal Field Effects on 3d8 states
Energy
Symmetries Oh
1S
4.6
eV
1A
3P
0.2
eV
3T
1
1D
-0.1
eV
3F
-1.8
eV
1G
0.8
eV
1E
3A
2
1A
1
+ 1T2
+ 3T1 + 3T2
1T +1T +1E
+
1
1
2
Total symmetry
Crystal Field Effects
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
Double group symmetry
Energy
Symmetries Oh
1S
4.6
eV
1A
3P
0.2
eV
3T
1
1D
-0.1
eV
3F
-1.8
eV
1G
0.8
eV
1E
3A
2
1A
1
Total symmetry
A1A1=A1
+ 1T2
+ 3T1 + 3T2
1T +1T +1E
+
1
1
2
T1T2= T1+ T2+ E+ A2
Crystal Field Effects: Tanabe-Sugano
Effect of 10Dq on XAS:3dN
High-spin or Low-spin
10Dq > 3J
(d4 and d5)
10Dq > 2J
(d6 and d7)
2p XAS of Mn2+
3d spin-orbit coupling
Exercise: Calculate the 2p XAS spectrum of CoO
3d spin-orbit coupling
Charge Transfer Effects
Ground state of a transition metal system
3dN 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
= E(3d9L) – E(3d8)
E(3d10LL‘) – E(3d8)
Two times charge transfer:
Extra 3d3d interaction:
2
U
2 +U
Charge Transfer Effects
Energy (eV)
15
2+U
3U-2
10
5

U-
0
6
7
8
9
10
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
Charge Transfer Effects in XAS
Energy (eV)
15
+U-Q
10
5

0
6
7
8
9
10
Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d5
2p53d6
Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d6L

3d5
2p53d7L
+U-Q  
2p53d6
Charge Transfer Effects in XPS
Energy (eV)
15
10
-Q

5
0
6
7
8
9
10
Charge transfer effects in XAS and XPS
• Transition metal oxide: Ground state: 3d5 + 3d6L
• Energy of 3d6L: Charge transfer energy 
3d6L
XPS
XAS

2p53d5
3d5
-Q
Ground State
2p53d6L
2p53d7L
+U-Q  
2p53d6
Charge Transfer Effects
NiO: Ground state: 3d8 (3d8 )
+ 3d9L
+ 3d93d7
+ 3d10L2
+ 3d7L
Charge transfer energy 
Hubbard U
2+U
Metal-ligand CT MLCT
Charge Transfer Multiplets of Ni2+
=3
=9
=0
=6
Exercise: perform a series of charge transfer
calculations changing  from +10 to -10.
X-ray Absorption Spectroscopy
Spectral shape:
(1) Multiplet effects
(2) Charge Transfer
J. Elec. Spec.
67, 529 (1994)
Charge transfer
Charge transfer
Charge transfer
Charge Transfer effects
=10
3d8 + 3d9L
30% 3d8
=5
NiO
=0
La2Li½Cu½O4
=-5
1A
1
30% 3d8
3A
2
=-10
Chem. Phys. Lett. 297, 321 (1998)
Charge Transfer effects
=10
3d8 + 3d9L
30% 3d8
=5
1A
1
NiO
=0
La2Li½Cu½O4
30% 3d8
=-5
=-10
Calculate the 2p XAS spectrum of Cs2KCuF6
3A
2
LMCT and MLCT:  - bonding
FeIII: Ground state: 3d5 + 3d6L
M
C
emptyempty
d or p
orbital
d-orbital
3d6L
N
filled filled
orbital
orbital

(i) - (i)  donation
3d5
C
M
N
filled
d-orbital
empty
*-orbital
2p53d7L
(ii)  back-donation
+U-Q  
?C?N distance
5
6
2p 3d
with Ed Solomon (Stanford) JACS 125, 12894 (2003),
JACS 128, 10442 (2006), JACS 129, 113 (2007)
LMCT and MLCT:  - bonding
FeIII: Ground state: 3d5 + 3d6L + 3d4L
2p53d5L
3d4L
-U+Q   + 2

3d6L

3d5
2p53d7L
+U-Q   - 2
2p53d6
with Ed Solomon (Stanford) JACS 125, 12894 (2003),
JACS 128, 10442 (2006), JACS 129, 113 (2007)
LMCT and MLCT:  - bonding
FeIII(tacn)2
Normalized Absorption
10
8
Fit X
Series2
FeIII(CN)6
6
4
2
0
700
-2
705
710
715
720
725
730
with Ed Solomon (Stanford) JACS 125, 12894 (2003),
Energy
(eV)
JACS 128, 10442
(2006),
JACS 129, 113 (2007)
RIXS
RIXS
Butorin, J. Elec. Spec. 110, 213 (2000)
Resonant Inelastic X-ray Spectroscopy
dd excitation
Resonant Inelastic X-ray Spectroscopy
2p XAS of CaF2
3d0

2p53d1
’
3s13d1
Resonant Inelastic X-ray Scattering
2p3s RIXS of CaF2
3d0

2p53d1
’
3s13d1
Phys. Rev. B.
53, 7099 (1996)
Resonant Inelastic X-ray Spectroscopy
Butorin
J. Elec. Spec 110, 213 (2000)
Exercise: Repeat these calculations
Soft x-ray RIXS and magnetism
NiII 3d8 []  2p53d9[jj]  3d8[]
Soft x-ray RIXS and magnetism
S
‘spin-flip’
dd
2p3d RIXS of NiO
MS
spin-flip
Phys. Rev. B.
57, 14584 (1998)
CTM4RIXS
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
CTM4RIXS
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
Absorption
Triad
GS → T1 → IS
|n>, En
W

|f>, Ef
W
|g>, Eg
Emission
Triad
IS → T2 → FS
A first CTM4RIXS calculation
Choose the name_abs that has been calculated with CTM4XAS
A first CTM4RIXS calculation
Choose ‘1’ in the pop-up menu
A first CTM4RIXS calculation
Choose ‘1’ in the pop-up menu
A first CTM4RIXS calculation
Click button at bottom
A first CTM4RIXS calculation
Set L intermediate to 0.4 and click button at bottom
A first CTM4RIXS calculation
Set Delta to 0.1 (two times) and click button at bottom
Choose a name in the pop-up window.
A first CTM4RIXS calculation
Set Delta NOT to a small number >> CTM4RIXS crashes
A first CTM4RIXS calculation
Start the calculation with the RIXS button
A pop-up window tracks the progress.
CTM4RIXS
• The RIXS calculation is finished.
• Next the RIXS plane can be plotted with the screen on the right.
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
Plotting a CTM4RIXS calculation
This is the 2p3d RIXS plane of Ni2+ with 10Dq=1.0 eV.
Plotting a CTM4RIXS calculation
Enlarge a region of the 2D map with this button
& select the region.
Plotting a CTM4RIXS calculation
Final state energy to set the vertical axis to energy loss.
(& enlarge/select the region).
Selecting a cross-section
Choose a vertical cross section & select energy.
The screen on the right shows the cross section (= RXES)
What is calculated with CTM4RIXS
• 2D RIXS plane
• Cross sections, including
resonant XES
selective XAS
HERFD
partial FY
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
A first CTM4RIXS calculation
Calculations without the
CTM4XAS interface
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)
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 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.rcf
3. 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 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 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 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 0
80998080
Save the file nitest1x.rcg
Copy nitest1.rac to nitest1x.rac
Copy nitest1.ban to nitest1x.ban
…. and ends with
-99999999.]
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 = 3.000 unity
def EF2 = 2.000 unity
to
def EG2 = 2.000 unity
def EF2 = 3.000 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
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
XES calculations
X-ray absorption and X-ray photoemission
Core Hole Decay
Fluorescence
Auger
3
/
2
2
p
1
/
2
2
p
2
s
1
s
3
/
2
2
p
1
/
2
2
p
2
s
f
l
u
o
r
e
s
c
e
n
t
r
a
d
i
a
t
i
o
n
1
s
X-ray emission
Resonant X-ray emission spectroscopy
1s X-ray emission
MnO
K Main Lines
K Satellite Lines
K1,3
K2,5
K''
K1
x 500
K2
K'
x8
K
5880
5900
5920
6480
6520
Fluorescence Energy [eV]
6560
1s X-ray emission
K Main Lines
K Satellite Lines
K1,3
K2,5
K''
x 500
K2
K'
x8
K
K
5880
1s13dn
5900
5920
6480
6520
6560
K
Main Lines
K
Satellites
Fluorescence Energy [eV]
2p53dn
Photoionization
or
K capture
3p53dn
Core Hole
Valence hole
Ground State
3dn
Total Energy
K1
Multiplet effects in 1s3p XES (Kβ)
Etotal
3d
1s
K Fluorescence
Photoionization
3d
3p
Strong
interaction
between
unfilled 3p and
3d shells!
Multiplet
effects in 1s3p
Spin-selectivity
inXES
the (Kβ)
K line
7P
3d
3p
5P
?
3d
3p
K’
K1,3
3p XPS and K XES
Multiplet effects in 1s3p XES (Kβ)
Identical final state configuration:
3p53d5
A
MnF2 K
F
B
Free Mn atom
3p XPS
1s2p and 1s3p XES spectra
1s2p and 1s3p XES spectra
Approximations:
- 3dN ground state (+ CT)
- XES only from lowest energy 1s13dN state (+CT)
- Charge transfer energy is -Q
Charge transfer in 1s pre-edge and edge
• Transition metal oxide: Ground state: 3d5 + 3d6L
• Energy of 3d6L: Charge transfer energy 
3d6L
edge
Pre-edge

1s13d5
3d5
-Q
Ground State
1s13d6L
1s13d7L
+U-Q  
1s13d6
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)
Charge transfer in XES spectra
Pieter Glatzel et al. Phys. Rev. B. 64, 045109 (2001)
Charge transfer in XES spectra
Pieter Glatzel et al. Phys. Rev. B. 64, 045109 (2001)
RIXS at metal K edges
Fe K pre-edges
Exercise: Repeat these calculations
Westre et al. JACS 119, 6297 (1997); Heyboer et al. J.Phys.Chem.B. 108, 10002 (2004)
Exercise: Repeat these calculations
CoO
Pre-edge and edge
high-spin CoII
3d7 [4T2]
Only quadrupole peaks visible
3d7  1s13d8  2p53d8
Only correct with interference effects ON
Non-local
peaks
RIXS-MCD screening
at the K pre-edge
Non-local
peaks
RIXS-MCD screening
at the K pre-edge
Non-local
peaks
RIXS-MCD screening
at the K pre-edge
Non-local
screening
peaks
RIXS-MCD
at the
K pre-edge
of Fe3O4
Non-local
peaks
RIXS-MCD screening
at the K pre-edge
Non-local
peaks
RIXS-MCD screening
at the K pre-edge
XMCD at high-pressure
Sikora, PRL 105, 037202 (2010)
MCD
X-MCD
X-MCD
Cu2+: 3d9
L=2, S=1/2  2D
J=5/2 or 3/2
More than half-full
2D5/2

2p53d10
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
X-MCD
Cu2+: 3d9
X-MCD
MCD
mJ=-5/2
to
mJ’=-3/2
MCD
no LS
Exercise: Repeat these calculations
X-MCD
MCD
no LS
MCD
+ crystal field
X-MCD
MCD
3F
4
3F
LS
no LS
XPS
X-ray photoemission
Charge transfer effects in XPS
Charge Transfer Effects in XAS
Energy (eV)
15
+U-Q
10
5

0
6
7
8
9
10
Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d5
2p53d6
Charge Transfer Effects
MnO: Ground state: 3d5 + 3d6L
Energy of 3d6L: Charge transfer energy 
3d6L

3d5
2p53d7L
+U-Q  
2p53d6
Charge Transfer Effects in XPS
Energy (eV)
15
10
-Q

5
0
6
7
8
9
10
Charge transfer effects in XAS and XPS
• Transition metal oxide: Ground state: 3d5 + 3d6L
• Energy of 3d6L: Charge transfer energy 
3d6L
XPS
XAS

2p53d5
3d5
-Q
Ground State
2p53d6L
2p53d7L
+U-Q  
2p53d6
Charge transfer effects in XPS
Exercise: Calculate the 2p XPS spectrum of NiCl2