# Example: ESR spin-restricted and spin-unrestricted: TiF3¶

```
#!/bin/sh
# You calculate Electron Spin Resonance properties with the keywords ESR and
# QTENS. ESR is a block-type key and is used to compute the G-tensor or the
# Nuclear Magnetic Dipole Hyperfine interaction. QTENS is a simple key and
# invokes the computation of the Nuclear Electric Quadrupole Hyperfine
# interaction.
# Proper usage of the key ESR requires that you do one of the following:
# (a) A Spin-Orbit calculation, spin-restricted, with exactly one unpaired
# electron, or
# (b) A Spin-Orbit calculation, spin-unrestricted in the collinear
# approximation, or
# (c) No Spin-Orbit terms and spin-unrestricted.
# In case (a) and (b) you obtain the G-tensor. In case (b) and (c) you get the
# Magnetic Dipole Hyperfine interaction.
# Note: in case (a) the program also prints a Magnetic Dipole Hyperfine
# interaction data, but these have then been computed without the terms from the
# spin-density at the nucleus. Note: in case (b) and (c) one can have more than
# one unpaired electron. Note: in case (b) one has to use symmetry NOSYM.
# Five calculations are performed:
# - Scalar relativistic spin-restricted
# - Scalar relativistic open shell spin-restricted
# - Scalar relativistic spin-unrestricted
# - Spin-Orbit relativistic spin-restricted
# - Spin-Orbit relativistic spin-unrestricted collinear
# First a scalar relativistic spin-restricted calculation is performed. The
# results of this calculation are used as a fragment in the next spin-
# unrestricted calculation, using only 0 SCF iterations, which is a way to get
# the scalar relativistic spin-restricted open shell result for the magnetic
# dipole hyperfine interaction.
AMS_JOBNAME=TiF3_SR $AMSBIN/ams <<eor
System
atoms
Ti 0 0 0
F 1.780 0 0
F -0.89 1.5415252187363007 0
F -0.89 -1.5415252187363007 0
end
end
Task SinglePoint
Engine ADF
title TiF3 scalar relativistic restricted
basis
core None
type TZ2P
CreateOutput Yes
end
noprint sfo frag functions
relativity
level scalar
formalism ZORA
end
xc
gga Becke Perdew
end
EndEngine
eor
AMS_JOBNAME=TiF3_SR_0 $AMSBIN/ams <<eor
System
atoms
Ti 0 0 0 adf.f=TiF3
F 1.780 0 0 adf.f=TiF3
F -0.89 1.5415252187363007 0 adf.f=TiF3
F -0.89 -1.5415252187363007 0 adf.f=TiF3
end
end
Task SinglePoint
Engine ADF
title TiF3 scalar relativistic open shell restricted
esr
end
fragments
TiF3 TiF3_SR.results/adf.rkf
end
noprint sfo frag functions
qtens
relativity
level scalar
formalism ZORA
end
scf
iterations 0
end
spinpolarization 1
unrestricted
xc
gga Becke Perdew
end
EndEngine
eor
# Next a spin-unrestricted SCF calculation is performed to get the scalar
# relativistic spin-unrestricted result for the magnetic dipole hyperfine
# interaction.
AMS_JOBNAME=TiF3_SR_unrestricted $AMSBIN/ams <<eor
System
atoms
Ti 0 0 0 adf.f=TiF3
F 1.780 0 0 adf.f=TiF3
F -0.89 1.5415252187363007 0 adf.f=TiF3
F -0.89 -1.5415252187363007 0 adf.f=TiF3
end
end
Task SinglePoint
Engine ADF
title TiF3 relativistic open shell unrestricted
esr
end
fragments
TiF3 TiF3_SR.results/adf.rkf
end
noprint sfo frag functions
qtens
relativity
level scalar
formalism ZORA
end
spinpolarization 1
unrestricted
xc
gga Becke Perdew
end
EndEngine
eor
# Then, for the same molecule, we compute the G-tensor in a Spin-Orbit run
# (spin-restricted).
# The here-computed and printed Dipole Hyperfine interaction misses the terms
# from the spin-density at the nucleus: compare with the outcomes from the first
# calculation.
# In each of the calculations, the QTENS key invokes the computation of the
# Electric Quadrupole Hyperfine interaction.
# Note that an all-electron calculation is carried out. This is relevant for the
# computation of the A-tensor, the nuclear magnetic dipole hyperfine
# interaction, where an accurate value of the spin-polarization density at the
# nucleus is important. For the G-tensor (and also for the Q-tensor) this plays
# a minor role, but for reasons of consistency both calculations use the same
# basis set and (absence of) frozen core.
AMS_JOBNAME=TiF3_SO $AMSBIN/ams <<eor
System
atoms
Ti 0 0 0 adf.f=TiF3
F 1.780 0 0 adf.f=TiF3
F -0.89 1.5415252187363007 0 adf.f=TiF3
F -0.89 -1.5415252187363007 0 adf.f=TiF3
end
end
Task SinglePoint
Engine ADF
title TiF3 relativistic spinorbit open shell restricted
esr
end
fragments
TiF3 TiF3_SR.results/adf.rkf
end
noprint sfo frag functions
qtens
relativity
level spin-orbit
formalism ZORA
end
xc
gga Becke Perdew
end
EndEngine
eor
# Finally a spin-orbit coupled spin-unrestricted calculation is performed using
# the collinear approximation. Note that symmetry NOSYM is used.
AMS_JOBNAME=TiF3_SO_unrestricted $AMSBIN/ams <<eor
System
atoms
Ti 0 0 0 adf.f=TiF3
F 1.780 0 0 adf.f=TiF3
F -0.89 1.5415252187363007 0 adf.f=TiF3
F -0.89 -1.5415252187363007 0 adf.f=TiF3
end
end
Task SinglePoint
Engine ADF
title TiF3 relativistic spinorbit open shell unrestricted collinear
esr
end
fragments
TiF3 TiF3_SR.results/adf.rkf
end
noprint sfo frag functions
qtens
relativity
level spin-orbit
formalism ZORA
spinorbitmagnetization collinear
end
symmetry nosym
unrestricted
xc
gga Becke Perdew
end
EndEngine
eor
```