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
# 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

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

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