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