Orbitally degenerate metal ions

The extension of the theory of the double exchange to systems containing orbitally degenerate metal ions with unquenched orbital angular momenta is given in [109-111]. As an example we will consider the corner-shared bioctahedral dimer... 

Mechanisms of the Interactions Between Two Orbitally Non Degenerate Metal Ions. . 92... 

TPP (45, 46), as well as data for octaalkyl and octathioalkyl porphyrazines. As with the phthalocyanines and porphyrins, the electronic spectra of porphyrazines can be rationalized using Gouterman s four-orbital model, shown in Fig. 5 (47, 48). All of these macrocycles, when symmetrically substituted and with a metal ion incorporated in the central hole, for example, the M[pz(A4)] or B4, have D4h symmetry, with a doubly degenerate lowest unoccupied molecular orbital (LUMO) (eg) and two highest lying highest occupied molecular orbitals (HOMOs) that complete the four Gouterman orbitals with alM and a2u symmetry. 

Hund s rule establishes that all orbitals of a given sublevel must have been occupied by single electrons with parallel spins before two electrons of opposite spins can occupy a single sublevel. Let us consider, for instance, a metallic ion with configuration. Based on Hund s rule, the first three electrons occupy the l2g degenerate orbitals with parallel spins. The remaining two electrons then have two possibilities ... 

For later discussions it is important to consider what happens if one of the d-orbitals (eg or t2g) is not full (e.g. CoO with seven electrons per atom or TiCl3 with one). The d-orbital is now degenerate, and the orbital motion is no longer quenched. Consider the case of a transitional-metal ion in the d1 state. Suppose that the spins are parallel to the z-axis the spin-orbit coupling will separate the orbitals into functions of the forms... 

The five d orbitals in an isolated, gaseous metal ion are degenerate. If a spherically symmetric field of negative charges is placed around the metal, the orbitals will remain degenerate, but all of them will be raised in energy as a result of the repulsion between... 

Thus, for a transition metal ion in a simple cubic lattice, crystal field theory predicts that the (/-orbitals are split into two types, one consisting of two members, henceforth referred to as the eg set, of higher energy than the remaining three, which are also degenerate and referred to as the t2g set. The labels eg and t2g are given because of their transformation properties in the group Of, which describes the site symmetry of an ion in a simple cubic lattice.19... 

The metal ions which form Square planar complexes with simple ligands have a -electronic configuration. The five degenerate d-orbitals of the uncomplexed metal ion split into four different levels in a square planar complex. Thus three orbital parameters are needed. to describe the ligand field d-sputtings. 

Many inorganic ions are not readily detected because they have orbitally degenerate ground states. Spin relaxation in these states is so rapid that the EPR spectrum cannot be observed at typical temperatures where electrochemical experiments are carried out. Temperatures of 4 K or lower are required to observe these ions. Table 29.1 lists transition metal ions that occur in nondegenerate ground states due to crystal field splittings and as such are amenable to observation. 

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