Scalar-Quasirelativistic

Both scalar-quasirelativistic (one-component) and quasirelativistic (two-component) ECPs use a formally nonrelativistic model Hamiltonian... 

For scalar-quasirelativistic calculations, i.e. when spin-orbit coupling is neglected, a one-component form may be obtained by averaging over the spin... 

Bauschlicher [48] compared a number of approximate approaches for scalar relativistic effects to Douglas-Kroll quasirelativistic CCSD(T) calculations. He found that the ACPF/MTsmall level of theory faithfully reproduces his more rigorous calculations, while the use of non-size extensive approaches like CISD leads to serious errors. For third-row main group systems, studies by the same author [49] indicate that more rigorous approaches may be in order. 

Relativistic effects in heavy atoms are most important for inner-shell electrons. In ab initio and DFT calculations these electrons are often treated through relativistic effective core potentials (RECP), also known as pseudopotentials. This approach is sometimes called quasirelativistic, because it accounts for relativity effects in a rather simplified scalar way. The use of pseudopotentials not only takes into account a significant part of the relativistic corrections, but also diminishes the computational cost. 

In a quasirelativistic Hartree-Fock study of Te shifts in a number of tellurium compounds [47], SFR effects were relatively small even for the absolute shieldings and further cancelled out in the relative shifts. The same was foxuid in scalar relativistic DFT calculations [5,42,118]. Third-order SO effects, which were also considered in [47], were significant for shieldings but again largely cancelled for relative shifts. This confirms that HAHA SO effects on... 

A single lanthanide (IV) metallocene, i.e. bis(cyclooctatetraene)cerium(IV) Ce(C8Hg)2 or cerocene, has been studied theoretically. Rosch and Streitwieser (1978,1983) reported the results of nonrelativistic and quasirelativistic scattered-wave Xa calculations taking into account the scalar relativistic effects for cerocene, thorocene and uranocene at fixed idealized Dgh geometries (fig. 13). The authors discuss the participation of metal d and f... 

The first approach used to include scalar relativistic effects has been the replacement of the core orbitals of the heavy atoms by a quasirelativistic ECP. " This has been shown to be a good approximation if only the NMR properties of the neighboring, usually lighter atoms are considered (for which all electrons are treated explicitly), and if the ECP core sizes are chosen to be sufficiently small. Many of the results... 

A third approach to include scalar relativistic effects in chemical shift calculations has been suggested, namely a combination of a first-order quasirelativistic approach with the frozen-core approximation. These authors have shown that the frozen-core approximation is valid if implemented properly. First results suggest good accuracy for this approach. ... 

Figure 1 Scalar relativistic effects on absolute shielding constants in 0X0 complexes. UDFT-IGLO results at DFT-optimized structures. QRJ/QR = quasirelativistic metal ECP in the shift calculations and in the structure optimization. QR//NR = quasirelativistic metal ECP in the shift calculations and nonrelativistic ECP in the structure optimization. NR//NR = nonrelativistic metal ECP in the shift calculations and in the structure optimization. QR//expt. = quasirelativistic metal ECP in the shift calculations, at experimental M-O distances. Experimental absolute shieldings were obtained by converting relative shifts with an absolute shielding value of -1-290.9 ppm for liquid water...

In ECP theory an effective model Hamiltonian only acting on the explicitly treated valence electrons is searched. There are several choices for the formulation of such a valence-only model Hamiltonian, i.e., four-, two-, or one-component approaches and explicit or implicit relativistic treatment [20], Nonrelativistic, scalar-relativistic, and quasirelativistic ECPs use a formally nonrelativistic valence-only model Hamiltonian implicitly including relativistic effects [19]... 

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