Double groups order

For the calculation of the g values only the latter second-order term and the first order spin term, which contain j3H, are significant, and in the former either OMg and nMg, or n Mg and 0 Ms must belong to the same double group irreducible representation for the contribution to be non-vanishing. 

In order to illustrate the utility of double groups let us consider several examples. Suppose that we have an ion with one d electron in a planar complex. Real examples of this case are represented by complexes of Ou(II) and Ag(II) (where we virtually have one positron, but this behaves as one electron except in the signs of the energies). In each case there will be two states with / values l i = 2 i, namely, J — i and / = . Using 9.3-2, we find that these form bases for the following representations ... 

The double group G was introduced in Chapter 8 in order to deal with irreducible representations (IRs) that correspond to half-integral values of j. Because... 

As is outlined in Appendix A, the U can straightforwardly be determined, making use of the determinantal form (10) of Hso- In particular, an associated unitary 2x2 matrix can be found for each of the 12 elements of D3. The resulting group of order 24, the so-called spin double group is the symmetry group of the SO operator (10). 

Using the methods discussed in the tutorial (Sect. 2), the group of symmetry operations of Hso can be constructed explicitly. As is shown in Appendix B, the symmetry group of Hso of (53) is T, the spin double group of the tetrahedral rotation group, is of order 48. T also is the symmetry group of the total Hamiltonian H = Hes + Hso-... 

Inclusion of spin-orbit effects at zero magnetic field is critical primarily in two arenas, structure determination of light actinides (notably Pu) [48] and certain spectroscopic characterizations. At non-zero field their inclusion is clearly more important. Calculating spin-orbit effects however raises the computational requirements by approximately an order of magnitude because one must use double-group symmetries (complex-valued KS orbitals are already possible in GTOFF, which works with Hermitian matrices rather than real-symmetric ones). Therefore, a rapid, high-accuracy approximate scheme for inclusion of spin-orbit effects has been developed [48]. 

The mean average steady-state blood levels of ciclosporin (adjusted for dose) in a group of 3 children with kidney transplants taking carbamazepine were 50% lower than in 3 other matched patients not taking carbamazepine. Four other individual patients have also shown this interaction. One needed her ciclosporin dosage to be doubled in order to maintain adequate blood levels while taking carbamazepine 800 mg daily. When the carbamazepine was replaced by sodium valproate in 3 patients, the ciclosporin dosages could be reduced to their previous level. 

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