# Example: LFDFT: XMCD 3d-4f transitions in Er 3+¶

```
#!/bin/sh
# Application of the Ligand Field DFT approach for the calculation
# of the X-ray Magnetic Circular Dichroism (XMCD) for lanthanide ion and complexes.
# This example calculates the XMCD spectra of the Er3+ ion
# for an Er 4f^11 (ground state) -> Er 3d^9 4f^12 transition, in which case a 3d core
# electron is promoted to the 4f shell.
# First an average of configuration calculation (AOC) is performed, where 11
# electrons are equally distributed over the 7 orbitals that have the most
# dominant Er 4f character. Depending on the electron configuration this might
# be a non-trivial task.
# Symmetry NOSYM should be specified.
SCM_LFDFT="$AMSHOME/examples/adf/Er_LFDFT_MCD/LFDFT"
export SCM_LFDFT
AMS_JOBNAME=GS $AMSBIN/ams <<eor
System
Atoms
Er 0.0000000000 0.0000000000 0.0000000000
End
Charge +3
End
task SinglePoint
Engine adf
Unrestricted No
Symmetry NOSYM
IrrepOccupations
A 54 1.571428571428571 1.571428571428571 1.571428571428571 1.571428571428571 1.571428571428571 1.571428571428571 1.571428571428571
End
basis
Core None
Type TZP
End
XC
GGA PBE
End
EndEngine
eor
# When the AOC calculation is ready, you need to make sure that indeed the
# partially occupied orbitals are dominantly f orbitals. In the ADF output you
# can find the character of the MOs in the list of all MOs, ordered by energy,
# with the most significant SFO gross populations.
# Next the LFDFT calculation is performed including a magnetic field of 1 Tesla
# in the z-direction (Bfield 0 0 1),
# which is needed for the XMCD calculation. In this case there is 1
# shell, and the nlval for 4f is '4 3'. The MO indices should be the
# fractionally occupied levels of the AOC calculation (in this case 28 29 30 31 32 33 34).
$AMSBIN/lfdft << eor
adffile GS.results/adf.rkf
nshel 1
nlval 4 3
MOind 28 29 30 31 32 33 34
soc 1.0
Bfield 0.0 0.0 1.0
DegeneracyThreshold 1.0E-8
eor
# Then, we need to calculate the electronic structure corresponding to the Er
# core electron excitation. In this case, we promote 1 electron from 3d orbitals
# to the 4f. Therefore, an average of configuration calculation (AOC) is
# performed, where 9 electrons are equally distributed over the 5 orbitals
# that have the most dominant Er 3d character; and 11+1 electrons are
# equally distributed over the 7 orbitals that have the most dominant Er 4f
# character. Symmetry NOSYM should be specified.
AMS_JOBNAME=ES $AMSBIN/ams <<eor
System
Atoms
Er 0.0000000000 0.0000000000 0.0000000000
End
Charge +3
End
task SinglePoint
Engine adf
Unrestricted No
Symmetry NOSYM
IrrepOccupations
A 18 1.8 1.8 1.8 1.8 1.8 26 1.714285714285714 1.714285714285714 1.714285714285714 1.714285714285714 1.714285714285714 1.714285714285714 1.714285714285714
End
basis
Core None
Type TZP
End
XC
GGA PBE
End
EndEngine
eor
# When the AOC calculation is ready, you need to make sure that indeed the
# partially occupied orbitals are dominantly d and f orbitals. In the ADF output you
# can find the character of the MOs in the list of all MOs, ordered by energy,
# with the most significant SFO gross populations.
# Next the LFDFT calculation is performed, again including a magnetic field of 1 Tesla
# in the z-direction (Bfield 0 0 1),
# which is needed for the XMCD calculation. In this case there are 2
# shells, and the nlval for 3d is '3 2' and 4f is '4 3'. The MO indices should be the
# fractionally occupied levels of the AOC calculation
# (in this case 10, 11, 12, 13, and 14 for the 3d; and 28, 29, 30, 31, 32, 33, and 34 for 4f).
$AMSBIN/lfdft << eor
adffile ES.results/adf.rkf
nshel 2
nlval1 3 2
nlval2 4 3
MOind1 10 11 12 13 14
MOind2 28 29 30 31 32 33 34
soc 1.0 1.0
Bfield 0.0 0.0 1.0
DegeneracyThreshold 1.0E-08
eor
# Finally, we use lfdft_tdm to calculate the oscillator strengths for the
# Er 4f^11 (ground state) -> 3d^9 4f^12 transitions.
# Input for lfdft_tdm are the 2 adf.rkf files that were
# calculated previously. Results of the excitation energies are added on the
# adf.rkf file belonging to state2.
$AMSBIN/lfdft_tdm << eor
STATE1 GS.results/adf.rkf
STATE2 ES.results/adf.rkf
eor
```