Scalar and spin orbit, relativistic effects

L. Visscher, E. van Lenthe. On the distinction between scalar and spin-orbit relativistic effects. Chem. Phys. Lett., 306 (1999) 357- 65. 

In this chapter, we use exclusively relativistically optimized or experimental geometries. Hence, we concentrate on direct relativistic effects only. They can be separated into scalar and spin-orbit/Fermi contact effects. In addition, there are, in both cases, core and valence contributions. 

Except for the efforts mentioned above, relativistic calculations of shielding evaluate the main relativistic effects using one or two component limits of the four-component formalism, quasi-relativistic approaches. These avoid the variational collapse in the calculation of the scalar relativistic terms by employing frozen cores, or effective core potentials. Some include the one-electron spin-orbit terms, and sometimes the higher order spin-orbit terms too. Others include both scalar and spin-orbit terms. Ziegler... 

Relativistic Ab Initio Model Potential embedded cluster calculations on the structure and spectroscopy of local defects created by actinide impurity ions in solid hosts are the focus of attention here. They are molecular like calculations which include host embedding effects and electron correlation effects, but also scalar and spin-orbit coupling relativistic effects, all of them compulsory for a detailed understanding of the large manifolds of states of the 5f" the 5f" 6d configurations. The results are aimed at showing the potentiality of Relativistic Quantum Chemistry as a tool for prediction and interpretation in the field of solids doped with heavy element impurities. 

The CCSD energies were obtained at the fc-CCSD(F12)/cc-pVQZ-F12 level. The corrections for connected triple excitations (T) were obtained at the fc-CCSD(T)/aug-cc-pwCVQZ level. The correction (Q) for connected quadruples contains the difference CCSDT-CCSD(T) calculated at the fc-CCSDT/aug-cc-pVDZ level and the (Q) term obtained at the fc-CCSDT(Q)/cc-pVDZ level. The correction for core valence correlation (CV) was obtained at the ae-CCSD(T)/aug-cc-pwCVQZ level. The harmonic zero-point vibrational energy (ZPVE) correction is supplemented by a zero-point-energy correction for hindered rotation (HR), and both scalar relativistic (MVD) and spin-orbit (SO) effects are taken into account. 

Since especially diatomics built from atoms with large nuclear charge number Z and an open p shell are significantly affected by scalar and spin-orbit effects, molecules containing thallium became perfect test cases for relativistic electronic structure methods. Some representative results for TIH are collected in a later section. 

J. E. Peralta, G. E. Scuseria. Relativistic all-electron two-component self-consistent density functional calculations including one-electron scalar and spin-orbit effects. 

However, the more recent EMS experiments by K. Liu et al. [45] on W(CO)6 at electron impact energies of 1.2 and 2.4 keV gave at first glance quite similar momentum profiles for the HOMO and led thus on the contrary to the conclusion that distorted wave and post-collision effects are too weak to explain the experimentally observed turnups at low electron momenta. Since the target compounds contain relatively heavy metal atoms, this discrepancy between theory and experiment was then also thought to be the outcome of the limitations inherent to a non-relativistic depiction. Further investigations of scalar relativistic and spin-orbit coupling effects indicated, however, a very... 

Four-component relativistic molecular calculations are based directly on the Dirac equation. They include both scalar relativistic effects and spin-orbit... 

In compounds containing heavy main group elements, electron correlation depends on the particular spin-orbit component. The jj coupled 6p j2 and 6/73/2 orbitals of thallium, for example, exhibit very different radial amplitudes (Figure 13). As a consequence, electron correlation in the p shell, which has been computed at the spin-free level, is not transferable to the spin-orbit coupled case. This feature is named spin-polarization. It is best recovered in spin-orbit Cl procedures where electron correlation and spin-orbit interaction can be treated on the same footing—in principle at least. As illustrated below, complications arise when configuration selection is necessary to reduce the size of the Cl space. The relativistic contraction of the thallium 6s orbital, on the other hand, is mainly covered by scalar relativistic effects. 

Because the convenience of the one-electron formalism is retained, DFT methods can easily take into account the scalar relativistic effects and spin-orbit effects, via either perturbation or variational methods. The retention of the one-electron picture provides a convenient means of analyzing the effects of relativity on specific orbitals of a molecule. Spin-unrestricted Hartree-Fock (UHF) calculations usually suffer from spin contamination, particularly in systems that have low-lying excited states (such as metal-containing systems). By contrast, in spin-unrestricted Kohn-Sham (UKS) DFT calculations the spin-contamination problem is generally less significant for many open-shell systems (39). For example, for transition metal methyl complexes, the deviation of the calculated UKS expectation values S (S = spin angular momentum operator) from the contamination-free theoretical values are all less than 5% (32). 

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