Heavy spin-orbit splitting

Z, as determined from spin-orbit splittings in atomic spectra (5). The Jtf is small relativistic correction, important mainly for heavy atoms (Z > 50). The values for the elements with the p configuration (N, P, As, Sb) were obtained by interpolation. (Taken from Barnes and Smith (5), appeared also in Jameson and Gutowsky (35)]. 

For heavy atoms, like Re(IV), the spin-orbit splitting parameter increases tremendously k/hc = 1000 cm x. This will be reflected massively in the magnetism because the Ag-factors are proportional to k and the D-value... 

It was not until the 1970s that the full relevance of relativistic effects in heavy-element chemistry was discovered. However, for the sixth row (W---Bi), relativistic effects are comparable to usual shell-structure effects and therefore provide an explanation for many unusual properties of gold chemistry155-159. The main effects on atomic orbitals are (i) the relativistic radial contraction and energetic stabilization of the s and p shells, (ii) the spin-orbit splitting and (iii) the relativistic radial expansion and energetic destabilization of the outer d and f shells. 

Core-non-penetrating Rydberg states of molecules that contain heavy atoms and have a 1 + ion-core ground state, such as HgF or BaF, are likely to exhibit a level pattern closer to case (b+, e) than (b+, d). The 2F7/2 — 2F5/2 spin-orbit splitting in Ba+ is 225 cm-1 for 4/ and 16 cm-1 for 11/, which is in reasonable agreement with the n 3-scaling prediction of 225(4/ll)3 = 11 cm-1. 

The first prerequisite for measurement of photoelectron spin-polarization is the ability to separately detect the photoelectrons ejected from the different fine-structure levels (e.g., 2n3/2 and 2n1/2 for HX+ X2n). When the molecule contains a heavy atom (e.g., large spin-orbit splitting), it becomes easier to use the electron kinetic energy to distinguish the photoelectrons ejected from the different fine structure channels. For spin-polarization analysis, the accelerated electron beam (20-120 keV) can be scattered by a thin gold foil in a Mott-detector. The spin-polarization is determined from the left-right (or up-down) asymmetry in the intensities of the scattered electrons (Heinzmann, 1978). Spin polarization experiments, however, are difficult because the differential spin-up/spin-down flux of photoelectrons is typically one thousandth that obtained when recording a total photoionization spectrum. 

At the moment the number of true four-component molecular EFG calculations is still rather limited due to the considerable computational effort especially in the post-DHF steps. Just five years ago Pj kko expressed the need for fully relativistic benchmark calculations in order to abandon perturbative corrections for considerable relativistic effects and to establish reference results. Furthermore spin-orbit effects can cause an EFG e.g. in atoms with Z > 0 and half-filled shells where according to nonrelativistic theory the EFG should vanish. This is the case for e.g. a system leading to a Pij2P f2 spin-orbit-split configuration. Also in closed-shell molecules with heavy halogen nuclei the spin-orbit effect is not completely quenched [88]. 

Since electrons in p orbitals come much closer to the nucleus than d and f electrons which feel a higher centrifugal barrier, p orbitals in heavy elements are expected to show the largest spin-orbit splittings. 

The accuracy of DK KS wave functions for the description of g values can be illustrated by switching off the relativistic form of the Hartree interaction [19,35]. The commonly used DKnuc restriction (neglecting the two-electron contribution to the spin-orbit interaction) [14,16] notably overestimates the spin-orbit splitting (Section 3.1) [33]. For molecules without very heavy atoms, this approximation does not significantly change common observables [19]. However, g tensor values are much more sensitive to the proper relativistic form of... 

Another recent development is the implementation of DK Hamiltonians which include spin-orbit interaction. An early implementation shared the restriction of the relativistic transformation to the kinetic energy and the nuclear potential with the efficient scalar relativistic variant electron-electron interaction terms were treated in nonrelativistic fashion. Further development of the DKH approach succeeded in including also the Hartree potential in the relativistic treatment. This resulted in considerable improvements for spin-orbit splitting, g tensors and molecular binding energies of small molecules of heavy main group and transition elements. Application of Hamiltonians which include spin-orbit interaction is still computationally demanding. On the other hand, the SNSO method is an approximation which seems to afford a satisfactory level of accuracy for a rather limited computational effort. 

The Hamiltonian of the electron-photon interaction will be used in a very simplified form taking into account only the simplest band structure of a semiconductor with parabolic electron and hole bands without complications related to heavy and light holes, spin-orbit splitted hole band or with the Dirac model of the band structure in the case of small band gap semiconductors. In the case of simple parabolic band after their size quantization in a spherical symmetry quantum dots the electrons and holes are characterized by envelope wave functions with the quantum numbers I, n, m. An essential simplification of the future calculations is the fact that in the selected simple model the band-to-band transitions under the influence of the electron-photon interaction Hamiltonian take place with the creation of an e-h pair with exactly the same quantum numbers for electron and for hole as follows e l,n,m), h l,n,m). ... 

Whilst there have been several theoretical investigations of the effect of hybridisation on the crystal-field excitations within the ground multiplet (Maekawa et al. 1985, Lopes and Coqblin 1986), there have been relatively few in which the spin-orbit level is explicitly included. Cox et al. (1986) have shown, in the context of the Anderson impurity model, that when is comparable to the spin-orbit splitting, the inelastic peak is broadened and shifted to lower energies. Given that the cross-section is weak, at about half the intensity of the praseodymium spin-orbit cross-section, they concluded that the transition was unlikely to be seen except in heavy-fermion compounds with low values of This appears to be confirmed by the failure to observe such a transition in CePdj in recent measurements on HET (Osborn, unpublished). On the other hand, the... 

---