Spin step operators

From the final expression for above, it is clear that operators of the type at aj that move electrons from to a orbitals destroy the structure that made it possible to vectorize the construction of the a vectors for the nonrelativistic Cl. However, the ( ,7)2 operator has the required stmcture, and so at least the calculations of the contributions to Saa from the (W° )z component should be vectorizable. To transform the expressions for the X and y components into a similar form to the z components, we note that if we introduce the overall spin step operators 5+ and S- defined by... 

This contribution is calculated twice, in fact once for the original Cl vector, after which the spin step operators are applied, and once for the Cl vector after application of the spin step operators. 

The action of the spin step operators on a vector b can be evaluated with the following expressions ... 

However, there also exists a third possibility. By using a famous relation due to Dirac, the relativistic effects can be (in a nonunique way) divided into spin-independent and spin-dependent terms. The former are collectively called scalar relativistic effects and the latter are subsumed under the name spin-orbit coupling (SOC). The scalar relativistic effects can be straightforwardly included in the one-electron Hamiltonian operator h. Unless the investigated elements are very heavy, this recovers the major part of the distortion of the orbitals due to relativity. The SOC terms may be treated in a second step by perturbation theory. This is the preferred way of approaching molecular properties and only breaks down in the presence of very heavy elements or near degeneracy of the investigated electronic state. 

From the discussion of the Marcus theory above and equations (20) and (21), we see that the experimental data needed to judge the feasibility of ET steps involving spin traps and spin adducts are the redox potentials and A values of the ST +/ST and ST/ST - couples, as well as those for hydroxylamine derivatives related to the operation of reactions (4) or (5). The electroactivity of the spin adducts themselves is also of interest since it must somehow be related to their lifetimes in a redox-active environment. Moreover, the excited-state redox potentials (of ST /ST and ST,+/ST ) are also necessary for the understanding of photo-ET processes of spin traps. 

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