Term splitting

Indeed, in. some cases it is probable that V2 is not ob.served at all, but that the fine. structure arises from term splitting due to spin-orbit coupling or to distortions from regular octahedral symmetry. 

Split-Phase Motor. A split-phase motor is a single-phase induction motor equipped with an auxiliary winding, displaced in magnetic position from, and connected in parallel with, the main winding. Note Unless otherwise specified, the auxiliary circuit is assumed to be opened when the motor has attained a predetermined speed. The term split-phase motor, used without qualification, described a motor to be used without impedance other than that offered by the motor windings themselves, other types being separately defined. 

In an octahedral crystal field, for example, these electron densities acquire different energies in exactly the same way as do those of the J-orbital densities. We find, therefore, that a free-ion D term splits into T2, and Eg terms in an octahedral environment. The symbols T2, and Eg have the same meanings as t2g and eg, discussed in Section 3.2, except that we use upper-case letters to indicate that, like their parent free-ion D term, they are generally many-electron wavefunctions. Of course we must remember that a term is properly described by both orbital- and spin-quantum numbers. So we more properly conclude that a free-ion term splits into -I- T 2gin octahedral symmetry. Notice that the crystal-field splitting has no effect upon the spin-degeneracy. This is because the crystal field is defined completely by its ordinary (x, y, z) spatial functionality the crystal field has no spin properties. 

The ground term of the cP configuration is F. That of is also F. Those of and d are " F. We shall discuss these patterns in Section 3.10. For the moment, we only note the common occurrence of F terms and ask how they split in an octahedral crystal field. As for the case of the D term above, which splits like the d orbitals because the angular parts of their electron distributions are related, an F term splits up like a set of / orbital electron densities. A set of real / orbitals is shown in Fig. 3-13. Note how they comprise three subsets. One set of three orbitals has major lobes directed along the cartesian x or y or z axes. Another set comprises three orbitals, each formed by a pair of clover-leaf shapes, concentrated about two of the three cartesian planes. The third set comprises just one member, with lobes directed equally to all eight corners of an inscribing cube. In the free ion, of course, all seven / orbitals are degenerate. In an octahedral crystal field, however, the... 

Figure 3-20. The symmetrical pattern of ground term splittings in octahedral symmetry.

In octahedral symmetry, the F term splits into Aig + T2g + Tig crystal-field terms. Suppose we take the case for an octahedral nickel(ii) complex. The ground term is 2g. The total degeneracy of this term is 3 from the spin-multiplicity. Since an A term is orbitally (spatially) non-degenerate, we can assign a fictitious Leff value for this of 0 because 2Leff+l = 1. We might employ Van Vleck s formula now in the form... 

It is instructive to analyze the effect of the interaction terms (Majorana operators) in Eq. (6.24). These terms split the degeneracies of the multiplets of Figure 6.1, as shown in Figure 6.3. Thus, the Majorana terms remove the degeneracies of the local modes and bring the behavior of the molecule towards the normal limit, precisely in the same way as in tri- or tetratomic molecules. 

Cyclicity of administration is vital in the use of 5-FU as a radiosensitizer. The concept of cyclical treatment has been well established in cancer chemotherapy and alien to classical radiation therapy (where it is termed split-course therapy). 5-FU radio-sensitizes tumor tissue as well as normal cells. However, this normal tissue radio-sensitizationis limited to the irradiated field. Suitable fractionation (i.e., cyclical therapy) can permit rapid normal tissue recovery (23). The results of infused 5-FU and radiation in head and neck cancer supports the principle that cyclical treatment with 5-FU does not suffer from the limitations apparent in split-course radiation treatments. 

After determination of the quahtative schemes for the term splitting in the crystal fields, it is possible to go to a quantitative estimation of separation between the crystal field levels. All the electronic interaction stages can be represented quantitatively by means of the few parameters ... 

If the small magnitude of the OMC shell (5/ here) relaxation is taken into account, there is another way out that can be optimal for the low-lying states. It was suggested in [19] to add the Term-Splitting (TS) correction (see also [24]) to the (G)RECP operator... 

To obtain the left (weak interaction) side we look up each of the free-ion terms in Table 9.3 and find that these terms split as follows ... 

In principle, it is possible to relate the excited term splittings Ae, the ground term splitting Ag, and to express the ZFS value of D in terms of A and Ae. For example, for tetragonal symmetry one can deduce Ae = 3Ag/4 and D = 412(AX 1 - A 1), where Ax = A + /2Ag - /3Ae and Ap = A + VjAg + 2/3Ae. However, in practice, as is known from spectral studies, these relationships do not hold well, particularly for the calculation of D, to which many excited terms including those of different multiplicity contribute. To evaluate D with any accuracy from the ligand field parameters it appears to be necessary to use the entire relevant dh manifold.89,90... 

Figure 10. Term splitting diagrams for the Cu(II) ion in a C3, site with Jahn-Teller and spin orbit splitting and band assignments for experimentally observed transitions (Figure 9b) drawn to scale.

The C3V symmetry at the SI site imposes on the Cu ion term splitting (21) shown in Fig. 10. The relative separations A2 between the E-states and A3 between the lower E-state and the A-state depend on the angle between the Cu-0 bond and the threefold symmetry axis (22) and, conversely, from measured A2 and A3 one can determine 3. The E-states are split further by the Jahn-Teller effect and spin orbit coupling into E+ and E components, the energies of which are given by (21)... 

For a weaker (stronger) axial CF the excited 4Tig term splits into a 4A2g and 4 g pair, and we need to return to the Weissbluth-Griffith approach. The ZFS interaction matrix of the form... 

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