Example: ESR g-tensor, A-tensor, Q-tensor, D-tensor: HfV

Download ESR_HfV.run

For the ESR g-tensor and D-tensor (zero-field splitting, ZFS) the effect of spin-orbit coupling is important. For the ESR A-tensor and Q-tensor (EFG) spin-orbit coupling is less important.

In this example first spin-orbit coupling is taken into account perturbatively. Next spin-orbit coupling is taken into account self-consistent, using the COLLINEAR keyword.

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 this plays a minor role. However, for the g-tensor calculation that includes spin-orbit coupling perturbatively, all electron basis sets are necessary.

In the first ADF calculation the A-tensor (block key ESR) is calculated without the effect of spin-orbit coupling included. The zero-field splitting (key ZFS) is calculated by including spin-orbit coupling perturbatively.

$ADFBIN/adf << eor
Atoms
  Hf        0.0 0.0 0.0
  V         0.0 0.0 2.033
End
ESR
END
Unrestricted
Symmetry NoSym
Charge 0 3
Basis
  Type TZ2P
  Core None
End
ZFS
QTENS
BeckeGrid
 Quality good
End
Relativistic Scalar ZORA
SAVE  TAPE21 TAPE10
end input
eor
cp TAPE21 hfv.t21
cp TAPE10 hfv.t10

In the next calculation the module nmr calculates the g-tensor (subkey GFACTORS) using spin-orbit coupling and the external magnetic field as perturbation.

$ADFBIN/nmr << eor
nmr
 gfactors
 u1k best
 out iso tens
end
end input

The module cpl can calculate the A-tensor (key HYPERFINE) using spin-orbit coupling and the nuclear magnetic field as perturbation. Note that one needs to set the SCF convergence criterium to a small value.

$ADFBIN/cpl << eor
hyperfine
 atoms 1 2 :: calculates A-tensor for atom 1 and 2, input order
 SCF Converge 1e-7
end
end input
eor

ADF can calculate the g-tensor and A-tensor (block key ESR) using only the nuclear or external magnetic field as perturbation, since spin-orbit coupling can be taken into account self-consistently. However, in this case, degenerate perturbation theory is used. The collinear approximation is used (and symmetry NOSYM) to account for spin-polarization effects.

$ADFBIN/adf << eor
Atoms
  Hf 0.0 0.0 0.0
  V  0.0 0.0 2.033
End
ESR
END
QTENS
collinear
Unrestricted
Symmetry NoSym
Basis
  Type TZ2P
  Core None
End
BeckeGrid
  Quality good
End
Relativistic Spinorbit ZORA
end input