Covalency effect

Theoretical modeling of the effect of pressure on nearest neighbor covalency in lanthanide systems has focused on the central field covalency and symmetry restricted covalency models (see Sect. 3.2.1.1) [144,167,191,192]. In the central 

The central field covalency model predicts that the spin-orbit coupling constant is three times more sensitive to increased covalency than the interelectronic repulsion parameter Fk. 

The symmetry restricted covalency model attributes covalency to bonding interactions and molecular orbital formation between ligand orbitals and the 4f valence orbitals. The participation of free ion 4f orbitals cp in molecular orbital formation leads to 4f radial expansion and enhanced covalency. Molecular orbital formation is directional (non-spherical) and is determined by the symmetry of the ligand distribution around the lanthanide. The lanthanide centered mole- 

Shen and Holzapfel [190] and Wang and Bulou [191,192] have considered a covalency model that combines the central field and symmetry restricted covalency models. The approach incorporates the effects of nuclear screening and hybridization of ligand orbitals with 4f orbitals. When the radial 4f wavefunc-tions of the central field covalency model (instead of the free ion 4f wavefunc-tions) are used in the formation of lanthanide centered molecular orbitals, we obtain 

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Many of the spinel-type compounds mentioned above do not have the normal structure in which A are in tetrahedral sites (t) and B are in octahedral sites (o) instead they adopt the inverse spinel structure in which half the B cations occupy the tetrahedral sites whilst the other half of the B cations and all the A cations are distributed on the octahedral sites, i.e. (B)t[AB]o04. The occupancy of the octahedral sites may be random or ordered. Several factors influence whether a given spinel will adopt the normal or inverse structure, including (a) the relative sizes of A and B, (b) the Madelung constants for the normal and inverse structures, (c) ligand-field stabilization energies (p. 1131) of cations on tetrahedral and octahedral sites, and (d) polarization or covalency effects. ... 

In conclusion, it might be said that the method gives useful results for crystals with distinct molecules. It shows that the large QS in the five-coordinated complexes XFe(R2C tc)2 is primarily caused by covalency effects and is almost entirely due to the valence iron electrons. 

We have shown in this chapter that the major electronic features that determine the spin dynamics of SIMs based on lanthanides can be directly correlated with the local coordination environment around the 4f metal ions. By using an effective point-charge model that accounts for covalent effects, we have shown that the splitting of the ground state,/, of the lanthanide into Mj sublevels, caused by the influence of the CF created by the surrounding ligands, is consistent with... 

Accounting for electron correlation in a second step, via the mixing of a limited number of Slater determinants in the total wave function. Electron correlation is very important for correct treatment of interelectronic interactions and for a quantitative description of covalence effects and of the structure of multielec-tronic states. Accounting completely for the total electronic correlation is computationally extremely difficult, and is only possible for very small molecules, within a limited basis set. Formally, electron correlation can be divided into static, when all Slater determinants corresponding to all possible electron populations of frontier orbitals are considered, and dynamic correlation, which takes into account the effects of dynamical screening of interelectron interaction. 

The effective CF models, intended to include covalence effects via effective charges and shielding parameters [46] (superposition model [47], effective charge model [48], simple overlap model [49, 50]), keep the radial (M-L distance) dependence of the CF parameters as in the simple (point charge) electrostatic model. Dedicated studies have shown, however, that the radial dependence of these parameters deviates strongly from the latter for the whole series of lanthanide ions [51, 52]. 

The effective ionic radii of Shannon and Prewitt (1969) can frequently be used to predict average interatomic distances and to correlate unit cell volumes of series of isostructural oxides and fluorides. However, some systematic discrepancies were recently found in tetrahedral oxy-anion distances and in the unit cell volumes of certain series of fluoride compounds. It was pointed out by Banks, Greenblatt, and Post (1970) that the observed V—0 distances in Ca2VC>4Cl are smaller than those predicted by the effective ionic radii. Subsequently, the discrepancies in Ca2VC>4Cl and other tetrahedral oxy-anion distances were attributed to covalency effects (Shannon, 1971, and Shannon and Cairo, 1972) in which bonds exhibiting a greater degree of covalency were assumed to shorten. 

Covalency effects on cell dimension vs ionic radii plots manifest themselves in a lowering of the line joining the more covalent ions relative to a line joining the Mg and Ca compounds. Thus, in fluorides, Ni... 

Further evidence for covalency effects comes from a comparison of interatomic distances and Y—0 symmetric stretching frequencies (Table 6) in the MYO4 scheelite compounds where Y =Mo or W. As the covalent character of the M—0 bond increases (as measured by xm in Table 6) and thus that of the Y—0 bond decreases, the mean Y—0 distance increases. This increase in Y—0 distance is accompanied by a decrease in the symmetric stretching frequency of the YO4 group. A similar relationship between M—0 covalency and IO4 stretching frequencies exists for the MIO4 scheelite compounds (Tarte, 1973). 

As the discussion of Chapter 2 and the numerical charges in (3.190) suggest, the extreme ionic picture such as (3.189a) must be modified by donor-acceptor interactions that create partial covalency by delocalizing significant charge ( 0.5e) from bare fluoride ions into acceptor orbitals of the central cation. Such partial-covalency effects can be represented by resonance delocalization of the form... 

While our primary focus has been on stable closed-shell (or low-spin) coordination species in which covalency effects are pronounced, it is also useful to examine the opposite extreme of weak coordinate bonding and free-atom -like spin multiplicities, corresponding to the original assumptions of crystal-field theory. 

The binding energies in Table 4.44 show the expected strong preference for anionic over neutral ligands in complexes of the metal cation. However, the geometries and other properties of these complexes reflect strong covalency effects (albeit enhanced by net ionic attraction) that will principally be considered. 

Some enzymes are controlled by both allosterism and covalent modification often brought about by hormone stimulation of the cell. Allosteric effects will take effect immediately because the enzyme is responding to local intracellular conditions of substrate or coenzyme concentrations, but covalent effects because they are driven by hormonal stimulation may take a little longer to have an impact but will be part of a coordinated response in several tissues of the body sensitive to the hormone. 

The third and final control step is mediated by PK. This enzyme, like HK, exists as a number of isoenzymes in different tissues and, like the PFK reaction, is controlled by both the concentration of metabolites and covalent effects. Furthermore, PK also illustrates two other means of metabolic control, namely enzyme induction and feedforward, regulation. 

The accordance between the experimental and calculated Dq values can be improved slightly if the actual nonpoint charge distribution of B ions and covalence effects are considered. However, the Dq value is usually obtained from experimental measurements, and this value is considered to be an empirical parameter, as the dependency on a (the distance A-B) is explained well. 

With the same anion, unit-cell volumes in isostructural series are proportional (but not necessarily in a hnear fashion) to the cationic volume. Covalence effects on the shortening of metal-oxygen and metal-fluorine distances are not comparable. 

This treatment is based on the inadequate three-parameter theory of the free ion on the one hand and does not account for covalency effects on the other. Indeed, three main absorption bands are found, the third of which is of low intensity (two electron jump) and located in the UV-region. It is only observed in cases where it is not masked by charge-transfer transitions. In addition, some peaks of very weak intensity are found in the visible region around the first two main bands (Fig. 1, 2 Table 2). While A is fixed by the energetic position of the first main band, B may be calculated from the second (or third) main band by the formula ... 

With these configurations it becomes necessary to introduce a second parameter, the Racah B parameter, in order to define the separation (15JB) between the F and P terms. As is well known, by comparison with the free ion the value of B in complexes is considerably reduced (10 to 50%) as a consequence of covalency effects (nephelauxetic effect). 

It allows also to explain, from covalency effects, the anisotropy of transport properties ... 

The important point for bonding is not so much the structural description of the strongly disturbed oxygen sublattice, but (as discussed for U02+x), the required association postulated between ions and oxygen vacancies. Once again, molecularities are formed, strongly hinting at covalent effects. 

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