The ZORA equation is the zeroth order regular approximation to the Dirac equation, for some details see also ZORA details. The regular expansion, which leads to the ZORA Hamiltonian, remains valid even for a Coulombic potential. This is in contrast with the expansion that leads to the Pauli Hamiltonian, which is divergent for a Coulombic potential. A scalar relativistic Hamiltonian is a relativistic Hamiltonian without spin-orbit coupling.
Spin-orbit coupling results from the interaction of the electron magnetic moments with the magnetic field generated by their own orbital motion. The computation is more involved than for scalar relativistic or non-relativistic calculations because spin-orbit coupling does not have the ordinary molecular symmetry. Instead, it is invariant under the molecular point double group, which affects both spin and spatial coordinates. One of its effects is to split energies of the molecule that would otherwise be identical in energy. This interaction is responsible for many of the details of spectroscopic properties.
ADF User Documentation: relativistic effects,
ADF-GUI: model Hamiltonians, Tutorial: spin-orbit coupling
Examples: relativistic effects
Related: ZORA details, symmetry
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