Trigonal crystal field

On a theoretical basis, Pd(III) and Pd(I) ions are probably located in a distorted octahedral or trigonal crystal field (Si or Si/, Sir sites) rather than in a square planar environment. The ESR spectra of adsorbed CO CO /... 

In equation (4) A is the parameter of the trigonal crystal field. This crystal field splits the 7 2-state into an orbital singlet and a doublet, the parameter A is defined in such a way that for positive A the ground state is the orbital singlet. 

Fig. 1. Splitting of the 2T2(t ) term by the spin-orbital interaction and trigonal crystal field.

Macfarlane,.R. M. (1963) Analysis of the spectrum of ions in trigonal crystal fields. J. Chem. Phys., 39, 3118-26. 

Figure 18 Crystal field splitting of the t2g manifold by the quasi-trigonal crystal field in LnTi03 perovskites. (Ref 16. Reproduced by permission of Physical Society of Japan)...

The multiplet structures of ruby calculated by the DV-ME method with and without the correlation correction are shown in Fig. 4. The experimental values are also shown together. In this case, the multiplet structures are calculated directly using the molecular orbitals of the impurity states obtained by the cluster calculation. In the calculated results, each level is broadened by the presence of the trigonal crystal field. Although the split of each peak seems to be somewhat overestimated due to the computational errors, it can be improved by increasing the number of sampling points (2). 

Table I. The calculated Coulomb integrals (eV). AO(p), AO(c), MO, MO(CC) denote the values calculated by the Cr-3d AOs in the point charge model (p), by the Cr-3d AOs in the cluster model (c), by the MOs of the impurity states and by the MOs of the impurity states with the correlation correction (CC), respectively, e and t represent the 6g and tag states in the octahedral notation, while (a) and (e) specify the states split by the trigonal crystal field.

Fiq. 26. Energy level diagram of Cr + in an octahedral and in an octahedral plus a trigonal crystal field environment. The two upper levels and Ti F) are... 

It is not easy to extract the 5 parameters for trigonal crystal fields directly from experimental data. It is therefore advisable to restrict 53/5 to the PCEM ratio. If all the crystal-field levels of the 7 = 2 multiplet are known, so that the experimental barycenter can be obtained, it is possible to determine the 5g parameter by the shift of the 0) state from the barycenter. The 5 parameter can be extracted from the splitting of a 7 = 1 level. 

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