Spin-orbit effects light atoms

The so-called heavy-atom chemical shift of light nuclei in nuclear magnetic resonance (NMR) had been identified as a spin-orbit effect early on by Nomura etal. (1969). The theory had been formulated by Pyykktt (1983) and Pyper (1983), and was previously treated in the framework of semi-empirical MO studies (PyykktJ et al. 1987). The basis for the interpretation of these spin-orbit effects in analogy to the Fermi contact mechanism of spin-spin coupling has been discussed by Kaupp et al. (1998b). 

This last example shows that larger splittings as they occur in heavy atoms can also be treated by the theoretical methods. In such cases, first-order corrections, which have often been found to be sufficient to describe spin-orbit effects in the area of potential minima in light molecules, have to be... 

These Ba reactions fall into a class of kinematically constrained reactions H + H L HH + L, where H and L denote heavy and light atoms, respectively [116,117], One consequence is that initial orbital angular momentum is channelled into rotational angular momentum of the diatomic product. With the assumption of constant product recoil energy, which can be used to interpret the dynamics of a number of Ba(lS) reactions [118], the formation of low and high v product vibrational levels is associated with large and small impact parameters, respectively. Thus, the variation of the spin-orbit effect with product vibrational level for the Ba( D) reactions provides information on the dependence of the reaction dynamics on incident impact parameter. 

For molecules such as these, the spin-orbit effect is essentially quenched in the molecule, because to exist it must form a strong bond, and the spin-orbit splitting is not so large that the quenching cannot be achieved. This is obvious for light atoms such as C and Si, but even Pb(C2H5)4 has four equivalent sp hybridized bonds. We can... 

The information obtainable from photoelectron polarization measurements is reviewed, for both atoms and molecules, by Heinzmann and Cherepkov (1996). Even at non-relativistic excitation energy, photoelectrons can be spin-polarized (Fano, 1969). For l / 0 atoms, due to the spin-orbit splitting of the initial atomic and/or the final ionic state, photoelectrons are in most cases highly spin-polarized (up to 100%) when photoexcited with circularly polarized light. Analogous effects occur in molecular photoionization, but systematic studies have only been made for hydrogen halide molecules, HX. The electronic ground state of HX+ is X2n. 

An even simpler but less well-justified approximation avoids the calculation of the matrix elements of the two-electron part of the operator altogether. Only the matrix elements of the one-electron part of are computed, and in the sum over nuclei a in Equation 3.3, contributions from each atom are not multiplied by Z but by the effective spin-orbit coupling nuclear charge of atom a, which has been optimized empirically to represent the partial compensation of the one-electron part by the two-electron part of the operator. Recommended values of for atoms of main-group and transition metal elements are listed in Table 3.1. This method is generally acceptable in molecules containing heavy atoms but is not very accurate in those composed of light atoms only. 

Theory can now provide much valuable guidance and interpretive assistance to the mechanistic photochemist, and the evaluation of spin-orbit coupling matrix elements has become relatively routine. For the fairly large molecules of common interest, the level of calculation cannot be very high. In molecides composed of light atoms, the use of effective charges is, however, probably best avoided, and a case is pointed out in which its results are incorrect. It seems that the mean-field approximation is a superior way to simplify the computational effort. The use of at least a double zeta basis set with a method of wave function computation that includes electron correlation, such as CASSCF, appears to be imperative even for calculations that are meant to provide only semiquantitative results. The once-prevalent degenerate perturbation theory is now obsolete for quantitative work but will presumably remain in use for qualitative interpretations. 

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