Effective d-orbital set

Earlandite structure, 6,849 Edge-coalesced icosahedra eleven-coordinate compounds, 1, 99 repulsion energy coefficients, 1,33,34 Edta — see Acetic acid, ethylenediaminetetra-Effective atomic number concept, 1,16 Effective bond length ratios non-bonding electron pairs, 1,37 Effective d-orbital set, 1,222 Egta — see Acetic acid,... 

The examination takes place in two stages, one corresponding to the formal interelectronic repulsion component of the Hamiltonian HER and the second to the spin-orbit coupling term Hes. As will be pointed out, in principle, and in certain cases in practice, it is not proper to separate the two components. However, the conventional procedure is to develop HLS as a perturbation following the application of Her. That suffices for most purposes, and simplifies the procedures. Any interaction between the d- or/-electron set and any other set is ignored. It is assumed that it is negligible or can be taken up within the concept of an effective d-orbital set. 

Of course, the effective d-orbital sets cannot be expected to be eigenfunctions of the proper quantum mechanical operators for various physical properties of the complex, including the energy. It is presumed that effective operators, related to the proper ones, can be set up, of which the effective d-orbitals are eigenvalues. 

In symmetries lower than cubic the (/-orbitals mix with the donor atom s—p hybrid orbitals to varying extents in molecular orbitals of appropriate symmetry. However, the mixing is believed to be small and the ligand field treatment of the problem proceeds upon the basis that the effective d-orbitals still follow the symmetry requirements as (/-orbitals should. There will be separations between the MOs which can be reproduced using the formal parameters appropriate to free-ion d-orbitals. That is, the separations may be parameterized using the crystal field scheme. Of course, the values that appear for the parameters may be quite different to those expected for a free ion (/-orbital set. Nevertheless, the formalism of the CFT approach can be used. For example, for axially distorted octahedral or tetrahedral complexes we expect to be able to parameterize the energies of the MOs which house the (/-orbitals using the parameter set Dq, Ds and Dt as set out in Section 6.2.1.4 or perhaps one of the schemes defined in equations (11) and (12). 

As is usual, the above expressions for the energies of the two d-orbital sets in the AOM have neglected the 5-bonding interaction which is allowed by synunetry. Its effects are assmned to be small. Expressions for the energies corrected for the 8-bonding by the inclusion of a parameter Ci are given in Appendix 2. 

The effect of configurational mixing of higher-lying s orbitals into the ligand field d-orbital basis set is also likely to favour elongation rather than contraction. ... 

Recall the splitting of the d orbitals in octahedral environments. The energies of the t2g and g subsets are shown in Fig. 8-4 with respect to their mean energy. We have used the conventional barycentre formalism. In effect, we express the energy of an electron in the t2g or orbitals with respect to the total energy possessed by a set of five electrons equally distributed amongst the five d functions. Alternatively, we say that our reference energy is that of 2l d electron within the equivalent spherical mean field. 

In Appendix A2, we have formally applied the perturbation method to find the energy levels of a d ion in an octahedral environment, considering the ligand ions as point charges. However, in order to understand the effect of the crystalline field over d ions, it is very illustrative to consider another set of basis functions, the d orbitals displayed in Figure 5.2. These orbitals are real functions that are derived from the following linear combinations of the spherical harmonics ... 

The interesting feature of 20 is that the Si-H interaction occurs for the set of electron-donating ancillary ligands Cp2/PMe3. Thus, the only factor that can, in principle, account for the different behavior of titanium and its heavier analogs in these reactions is the contracted nature of the titanium d-orbitals and hence the less effective backdonation from metal as discussed in Section II.B. The nonclassical nature of the zirconium complex 19 compared with neutral 18 can be then attributed to the presence of a positive charge. 

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