The ZORA approximation and other regularized two-component methods can be used to treat all of the electrons (core + valence) in the system. However, all-electron calculations are not always necessary, since the most significant relativistic effects on valence shells of heavy elements can be encapsulated using effective core potentials. These approaches yield accurate stmctures, frequencies, and other properties that depend primarily on the valence electronic structure. However, for properties like XAS, XPS, NMR, EPR, etc., all-electron relativistic approaches are needed. [Pg.300]

Effective core potential (ECP) or pseudo-potential approximation, has been proved to be very useful for modeling of heavy atoms in the ab initio methods (Hay and Wadt 1985). In this approximation, core electrons are replaced by an effective potential, thereby reducing the number of electrons to be considered and hence requiring fewer basis functions. The ECP method takes into account the relativistic effect on valence electrons, thus making it applicable to heavy atoms (e.g., second- and third-row transition metals, lanthanides and actinides). It is relatively cheap, works very well, and has very little loss in reliability. [Pg.18]

An important advantage of ECP basis sets is their ability to incorporate approximately the physical effects of relativistic core contraction and associated changes in screening on valence orbitals, by suitable adjustments of the radius of the effective core potential. Thus, the ECP valence atomic orbitals can approximately mimic those of a fully relativistic (spinor) atomic calculation, rather than the non-relativistic all-electron orbitals they are nominally serving to replace. The partial inclusion of relativistic effects is an important physical correction for heavier atoms, particularly of the second transition series and beyond. Thus, an ECP-like treatment of heavy atoms is necessary in the non-relativistic framework of standard electronic-structure packages, even if the reduction in number of [Pg.713]

The transition metal atom has a possibility to possess a magnetic moment in metaUic material, then an investigation of the spin polarization of the cluster from a microscopic point of view is very important in understanding the magnetism of the metallic materials. We try to explain the spin polarization and the magnetic interactions of the cluster in terms of the molecular orbital. For the heavy element in the periodic table whose atomic number is beyond 50, it is mentioned that the relativistic effects become very important even in the valence electronic state. We perform the relativistic DV-Dirac-Slater calculation in addition to the nonrelativistic DV-Xa calculation for the small clusters of the 3d, 4d and 5d transition elements to clarify the importance of the relativistic effects on the valence state especially for the 5d elements. [Pg.51]

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