Spin-orbit coupling screened nuclear

A different approach is chosen when the screening of nuclear potential due to the electrons is incorporated in /z . Transformation to the eigenspinor basis is then only possible after the DHF equation is solved which makes it more difficult to isolate the spin-orbit coupling parts of the Hamiltonian. Still, it is also in this case possible to define a scalar relativistic formalism if the so-called restricted kinetic balance scheme is used to relate the upper and lower component expansion sets. The modified Dirac formalism of Dyall [24] formalizes this procedure and makes it possible to identify and eliminate the spin-orbit coupling terms in the selfconsistent field calculations. The resulting 4-spinors remain complex functions, but the matrix elements of the DCB Hamiltonian exhibit the non-relativistic symmetry and algebra. 

The nuclear-only DKH (nDKH) approximation described above may be trivially extended to include spin-orbit coupling (SOC) effects. Unfortunately, the nDKH approximation systematically overestimates the spin-orbit splittings of the one-electron energies (in some cases by as much as 100%) due to the neglect of compensating two-electron SOC terms.[78] This error can be corrected through the use of the screened-nuclear-spin-oibit (SNSO) approximation, developed by Boettger [78] see discussion below. 

Fig. 9 Nuclear spin-spin coupling constants J(195Pt-205Tl) for complexes I-V (see Fig. 8), from ZORA DFT computations. Data taken from Autschbach and Le Guennic [126]. Different computational models were applied Model A includes explicit water molecules. In Model B, a continuum model (conductor-like screening model, COSMO) is applied in addition to the explicit solvent molecules of model A. Model C differs from model B in that instead of the VWN functional the statistical averaging of orbital potentials (SAOP) XC potential was used, which allows more accurate computations of NMR parameters [32]. The NMR measurements were carried out in aqueous solution [99,130]...

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