Tetragonal fields

This hamiltonian has cylindrical symmetry around the axis of quantization. It lifts the degeneracy of the spherical 2P and 2D terms to yield the following 

Note that we have chosen to use primed symbols to emphasize the shell-theoretical nature of these labels, as opposed to true spatial symmetry assignments. The corresponding tetragonal symmetries can easily be found from the standard D h j D4k subduction relations, keeping in mind that the results must be multiplied by the pseudoscalar Blg representation of D4h, One thus obtains  

These levels may be related to the doublet states in the unperturbed octahedron according to the following branching scheme  

In the perspective of shell-theoretic selection rules the two types of emission clearly expose a difference in quasi-spin characteristics. The -emitting levels 

From the point of view of technological applications [58], complexes with a quadrate field in the border zone between 2E and 2 T emitters are perhaps of particular interest. Indeed for such complexes very slight changes in the environment may easily lead to dramatic changes in the emission spectra. This effect has indeed been demonstrated by Fucaloro et al. [55] for the cis-dihydroxo complexes ds-[Cr(NH3)4(OH)2]+ and cis-[Cr(en)2(OH)2]+. 

---

Lower Symmetry Crystal Fields There are two common types of distortion from an octahedral symmetry. One distortion alters the charges along the z axis, giving rise to what is called a tetragonal field in which the... 

Zeeman Interaction. We now wish to find the effect of applying a magnetic field upon the doubly degenerate ground state of c/1 in a tetragonal field. The perturbation operator for this can be written... 

Pd(I) ion has a 4d9 electronic configuration. Consequently, this ion behaves in a tetragonal field in the same manner as Cu(II) ion. The g values calculated from the crystal field theory (12) are ... 

Fig. 4. The energy of the T2g multiplet as a function of the tetragonal field and the spin-orbit coupling, A. The negative and positive values of AJA correspond to a tetragonal compression and elongation respectively. The energy separations indicated on the left and right hand sides of the figure are the limiting values...

Fig. 5. a The calculated gy values for the Eg, Fj (Eg) excited and rg( Aig) ground electronic states as a function of the tetragonal field Aj. The perturbation expressions of [ 13] have been used with the AOM parameters A, = 7000 cm and A = 0.85 x 830 cm, b The allowed magnetic dipole transitions for circularly polarized light (k c) in an applied magnetic field c for a tetragonally compressed Cu(II)Lg complex... 

Tg state means that a new MCD signal will develop to lower energy and opposite sign as the temperature is increased. The temperature dependence of the MCD spectrum shown in Fig. 6 displays this behavior and allows the tetragonal field to be quantified as At 1900 cm" [11]. 

Transition energies (Equation 15) were calculated from Table III of Reference 18 after noting that the ground state energy of nickel in a tetragonal field, relative to the spherically perturbed free ion, is ... 

In addition to the 72 and states, the T, state lies some 500cm above in pseudo-octahedral complexes. In lower symmetry complexes both E and Tj are split, and in strong tetragonal fields, one of the Tj components is below E [32] as evidenced by the markedly broader emission spectrum [33]. There appears to be good thermalization between the Ti and E states. As a result of the thermalization, all of the photophysical rates for steps originating in E/ T, are population weighted averages of the rate constants for the individual states. If all reaction occurs in doublet states, the same conclusion applies to calculated from Eq. (21). 

If we have the analysis of a large number of low-spin ferric compounds, they may be conveniently summarized on a crystal field diagram such as Figure 8. Here we have plotted the tetragonal field (A/A) as abscissa and V/A, which we have termed the rhombicity, as ordinate. All of these compounds, with the exception of the ones labelled with... 

If the crystal field is rigorously cubic both D and E arc zero and there is no zero field splitting however, there may be small contributions from a spin Hamiltonian containing quartic terms. For a tetragonal field E = 0. In the present case < < 1 (37). 

It is seen that the tetragonal field does not contribute to rj while the rhombic field does not contribute to q. 

---