Spin-Orbit Effects on Heavy Elements

Spin-orbit effects are in general important to account for in excited-states calculations and in chemical reactions involving trans-uranium actinides and in many cases also uranium complexes. In fact, the only uranium state in which spin-orbit effects are unimportant are complexes where only the ground states of U(VI) is involved, the most known of which is the uranyl ion, UO2+. 

Spin-orbit calculations were at the time hampered by the calculation of the spin-orbit integrals over the three spin operators, Sx,Sy, and S, although a number of applications were done during the 1990s, including studies by Wahlgren et al. [25] and Rakowitz et al. [26] on the spin-orbit splitting in the 6p-shell of thallium and by Teichteil et al. on iodine [27]. 

At the time both LS-based methods (one component calculations followed by a separate calculation of the spin-orbit contributions), two- and four-component methods were developed. Despite the increase in computer power the high computational cost of four-component methods restricts their applicability to relatively small molecular systems. However, different flavors of two-component Hamiltonian have matured in the past years and are now approaching the computational efficiency of one-component methods (ZORA, X2C, etc.). (See for instance references [1,28-35]). As a result, for chemical reactions or spectroscopic studies, one-component approaches treating spin-orbit coupling a posteriori are preferred. 

In these approaches, the spin-orbit part can be done either at the variation-perturbation level where only a few spin-free states are included in the spin-orbit Hamiltonian, or in a spin-orbit Cl, typically including all single excitations from the reference states as in the spin-orbit Cl method EPCISO [36].Fromager etflZ. [37] has shown that the two methods are essentially equivalent provided that the orbitals are relaxed separately in all of the spin-free reference configurations. 

Of course, other approaches to the spin-orbit problem have also been developed. This includes the spin-orbit Cl suggested by Yabushita et al [46], and ECPs describing the spin-orbit interaction explicitly, like Dolg et al. [47], and Seijo and Barandiaran [48] using the AIMP approach. 

---