Intermediate coupling states

An accurate procedure for performing calculations that incorporate spin-orbit and other relativistic effects, and that represents intermediate coupling states for molecules containing heavy atoms, is based on A-S coupling in conjunction with the use of the ab initio REP-based spin-orbit operator and extended configuration interaction. The coupling scheme is more familiar than co-co coupling to chemists and physicists. In addition, the complexity of calculations necessary to achieve reliable results is computationally tractable. 

Table I. g-values and Ueff of ground states In Russell-Saunders and intermediate coupling for different configurations.

Due to the intermediate coupling the sign of the crystal field matrix element 6 is reversed compared to the pure Russell-Saunders state. Thus for 8-fold cubic coordination a F7 ground state was found. From EPR measurements on Pu3"1" diluted in fluorite host lattices, a magnetic moment at T=0 K can be calculated, ranging from li ff = 1.333 (in Ce02) to y ff = 0.942 (in SrCl2) (24,... 

An intermediate spin state (a quartet 4A2) similarly is feasible for five-coordinate iron(III) though, as pointed out by Kahn [118], the situation may be more complex. If the states are close in energy then they can interact through spin-orbit coupling to give a so-called spin-admixed ground state. 

The X coupling parameter defines a set of intermediate hybrid states between the unperturbed and the fully perturbed states. Then, the total change in the free energy is... 

Hamiltonian quantum states. Two situations can be envisaged. In the first one, the system moves stepwise from the APC states to the interconversion complex. We assume that the i-th state of the active precursor is populated i f > at a given time to, and if f> is intermediate Hamiltonian state that are coupled by the electro-magnetic field. 

A suitable comparison of the Os(VI)/ Os(III) couple is the well-studied three-electron oxidant HCr04, where the intermediate oxidation states Cr(V)/Cr(IV) appear to be unstable with respect to disproportionation. However, the Os system shows a dramatically enhanced electrochemical reversibihty compared to Cr(IV). This feature may play an important role in the ability of related systems that act as redox catalysts. 

We take as an example the case of plutonium monopnictides PuP, PuAs, PuSb, the susceptibility of which is well fitted by Eq, (17). Results are given in Table 8 while bare data are in agreement with the full J multiplet value ( 1 pP in the intermediate coupling), the corrected value is substantially smaller and points towards a Fg ground state (see Table 8) in agreement with more detailed discussions ... 

Due to the localization of the 5 f electrons in the oxides a final state multiplet structure is expected. Therefore, these spectra have been compared with final state intensities calculated in an intermediate coupling scheme which accoimts for the strong spin-orbit... 

Even AS = 2 transitions in excited states can be rapid. In ground state spin equilibria these transitions can be nonadiabatic due to the requirement of mixing through spin-orbit coupling with excited intermediate spin states. In photophysical processes these excited states can actually be populated. Again this conclusion follows from the success of photoperturbation methods applied to AS = 2 spin equilibria. For example, excitation of the singlet state of iron(II) results in detectable population of the quintet spin-equilibrium state more rapidly than... 

The solution is summarized in Figure 8.1. The4F state has L 3, and so (from Tabic 7.1) it is split by an intermediate field into three states which belong to the IRs A2 Ti T2 =r2 r4 r5. To examine the effect of spin—orbit coupling on these intermediate-field states, we use the fact that if -tp fi"fi, where fi forms a basis for T and x1 forms a basis for F, then ip = fix forms a basis for the direct product (DP) representation F F. Here S=3/2, and the representation 1 / is Tg (Table 8.2). Take the DPs of Tg with 1 2, T4, and P to obtain... 

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