TiF₃: ESR g-tensor, A-tensor, Q-tensor

Sample directory: adf/ESR_TiF3/

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-unrestricted
• Spin-Orbit relativistic spin-restricted
• Scalar relativistic spin-restricted
• Scalar relativistic open shell spin-restricted
• Spin-Orbit relativistic spin-unrestricted collinear

After the preliminary calculations (DIRAC, to get the relativistic TAPE12 file with relativistic potentials, and the Create runs), we first calculate the Dipole Hyperfine interaction: a spin-unrestricted calculation without Spin-Orbit coupling.

$ADFBIN/adf << eor
title  TiF3  relativistic open shell unrestricted
noprint sfo,frag,functions

DEFINE
 RTIF = 1.780
 RY  = RTIF*SQRT(3)/2
END

esr
end

qtens

atoms
  Ti    0    0   0
  F   RTIF   0   0
  F  -RTIF/2  RY 0
  F  -RTIF/2 -RY 0
end

fragments
  Ti   t21.ti
  F    t21.f
end

xc
  GGA Becke Perdew
end

charge 0 1
unrestricted

relativistic scalar zora
Corepotentials  t12.rel &
  Ti 1
  F 2
end

end input
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.

$ADFBIN/adf << eor
title  TiF3  relativistic spinorbit open shell restricted
noprint sfo,frag,functions

DEFINE
  RTIF = 1.780
  RY  = RTIF*SQRT(3)/2
END

esr
end

qtens

atoms
  Ti    0    0   0
  F   RTIF   0   0
  F  -RTIF/2  RY 0
  F  -RTIF/2 -RY 0
end

fragments
  Ti   t21.ti
  F    t21.f
end

xc
  GGA Becke Perdew
end

relativistic spinorbit zora
Corepotentials  t12.rel &
  Ti 1
  F 2
end

end input
eor

Next a scalar relativistic spin-restricted calculation is performed. The TAPE21 of this calculation is saved as a fragment in the next spin-unrestricted calculation, using only 1 SCF iteration, which is a way to get the scalar relativistic spin-restricted open shell result for the magnetic dipole hyperfine interaction.

$ADFBIN/adf << eor
title  TiF3  scalar relativistic restricted
noprint sfo,frag,functions

DEFINE
 RTIF = 1.780
 RY  = RTIF*SQRT(3)/2
END

atoms
  Ti    0    0   0
  F   RTIF   0   0
  F  -RTIF/2  RY 0
  F  -RTIF/2 -RY 0
end

fragments
  Ti   t21.ti
  F    t21.f
end

xc
  GGA Becke Perdew
end

relativistic scalar zora
Corepotentials  t12.rel &
  Ti 1
  F 2
end

end input
eor

mv TAPE21 t21.TiF3
rm logfile

$ADFBIN/adf << eor
title  TiF3  scalar relativistic open shell restricted
noprint sfo,frag,functions

DEFINE
 RTIF = 1.780
 RY  = RTIF*SQRT(3)/2
END

esr
end

qtens

atoms
  Ti    0    0   0 f=TiF3
  F   RTIF   0   0 f=TiF3
  F  -RTIF/2  RY 0 f=TiF3
  F  -RTIF/2 -RY 0 f=TiF3
end

fragments
  TiF3   t21.TiF3
end

xc
  GGA Becke Perdew
end

charge 0 1
unrestricted

scf
 iter 0
end

relativistic scalar zora
Corepotentials  t12.rel &
  Ti 1
  F 2
end

end input
eor

Finally a spin-orbit coupled spin-unrestricted calculation is performed using the collinear approximation. Note that symmetry NOSYM is used.

$ADFBIN/adf << eor
title  TiF3  relativistic spinorbit open shell unrestricted collinear
noprint sfo,frag,functions

DEFINE
  RTIF = 1.780
  RY  = RTIF*SQRT(3)/2
END

esr
end

qtens

symmetry nosym
unrestricted
collinear

atoms
  Ti    0    0   0
  F   RTIF   0   0
  F  -RTIF/2  RY 0
  F  -RTIF/2 -RY 0
end

fragments
  Ti   t21.ti
  F    t21.f
end

xc
  GGA Becke Perdew
end

relativistic spinorbit zora
Corepotentials  t12.rel &
  Ti 1
  F 2
end

end input
eor