Central field, covalency

However one can investigate the two extreme possibilities — all central field covalency, or all symmetry restricted covalency. The former limit is obtained either by setting a4 = 1 and finding z6tt from some em-... 

We have though previously expressed our reservations (10, 11) concerning the combination of ft and ft data for the derivation of a2 and (ZjZ0). Thus, whereas the repulsion parameter, B, is essentially an outer radial quantity (82, 83) the spin-orbit coupling constant, , is dominantly an inner orbital function (84). Moreover the (ZjZo) values derived in most cases indicate a rather small measure of central field covalency. Nevertheless, the a2 values obtained tend to parallel the mm rather than the a 0ot values, especially as the extent of covalency increases from the M(IV) to M(V) to M(VI) series, thus suggesting that flroot values may be too large. On the other hand the values are likely... 

The two eflPects above constitute what is called central field covalency since they aflFect both the a and the tt orbitals on the metal to the same extent. There is also, of course, symmetry restricted covalency which acts difiFerently on metal orbitals of diflFerent symmetries. This type of covalency shows up in optical absorption spectra as differences in the values of Ps and p -, as compared with 35. The first two s refer to transitions within a given symmetry subshell while 635 refers to transitions between the two subshells. This evidence of covalency almost of necessity forces one to admit the existence of chemical bonds since it is difficult to explain on a solely electrostatic model. The expansion of the metal orbitals can be caused either by backbonding to vacant ligand orbitals, or it may be a result of more or less extensive overlap of ligand electron density in the bond region. Whether or not this overlap density can properly be assigned metal 3d character is what we questioned above. At any... 

CFCM central-field covalency model L total orbital angular momentum... 

The reduction of the free-ion parameters has been ascribed to different mechanisms, where in general two types of models can be distinguished. On the one hand, one has the most often used wavefunction renormalisation or covalency models, which consider an expansion of the open-shell orbitals in the crystal (Jprgcnscn and Reisfeld, 1977). This expansion follows either from a covalent admixture with ligand orbitals (symmetry-restricted covalency mechanism) or from a modification of the effective nuclear charge Z, due to the penetration of the ligand electron clouds into the metal ion (central-field covalency mechanism). 

Two mechanisms contribute to the decrease of Racah B parameters. First, lone pairs of electrons from the ligand may penetrate the 3d shell of the transition metal and screen its 3d electrons from the nucleus, thereby decreasing the effective nuclear charge experienced by the electrons and expanding the 3d shell. This mechanism is termed central field covalency. In the second mechanism, referred to as symmetry restricted covalency, delocalization of the trans-... 

It is worth emphasizing two aspects of eq. (19) expressing minimum requirements for a plausible L.C.A.O. approximation to the partly filled shell, and which have been neglected recently by several authors. One is the introduction of the central-field covalency in the form of the variable... 

If we accept eq. (19) destroying the validity of / = 2 when 63 and 6s are different from zero, we may make the approximation that only the part of the orbital concentrated on the central ion makes a significant contribution to the interelectronic repulsion. Since the effect of the central-field covalency can be represented by... 

The Lande parameter ni in a system having spherical symmetry is essentially a one-electron operator quantity, as illustrated in Dr. Schmidtke s lecture (49). In a complex, the L. C. A. 0. M. O. description hence suggest that the new value of na (adapted to the lower Z due to central-field covalency) is multiplied by the square b representing the electronic density of the t2g sub-shell in MX6. Empirically, the dependence of ni is roughly a proportionality to Z, and we hence write... 

At present there is consensus on the fact that the observed nephelauxetic effect in the spectra of lanthanide compounds is analogous to the phenomenon observed in the spectra of d-transition metal complexes. The nephelauxetic effect cannot be quantitatively interpreted by excluding the covalent interaction of lanthanide ions with surrounding ligands [34]. Jorgensen has proposed [38] two possible mechanisms of interaction for the observed nephelauxetic effect, namely (i) direct participation of lanthanide 4f orbitals in the formation of molecular orbitals also known as symmetry restricted covalency , (ii) transfer of some part of the ligand electron density to the unfilled 6s and 6p orbitals of the lanthanide also known as central field covalency . 

Gerloch and Woolley reformulated the AOM in a way that resolves some of the difficulties encountered with, for example, square planar CuCLi , but rejects parameter transferability. The LF parameters are determined from both optical and magnetic data, with SO coupling taken fully into account. The five-orbital model, which lies at the heart of LF theory is retained the d orbitals, it is argued, are not significantly involved in covalency and remain pure , albeit with expanded radial functions as a consequence of central-field covalence. 

Fig. 6 Variation of the parameter B across the CrX63 series (nephelauxetic effects due to central field covalency) and Jprgensens B33, B35, and B55 (differential covalency or symmetry restricted covalency B33 (eg-eg), B35 (eg-t2g), B55(t2g-t2g))...

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. 

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... 

The results obtained by use of these various assumptions are collected in Table 4 (vi) and it is seen that for both the MF and the MF series negative values of Zett are encountered when it is assumed that the nephelauxetic effect is due only to central-field covalency. This physically unrealistic result supports the contention that it is unreasonable to ascribe all of p to central-field effects, but the fairly satisfactory parallel between the Zmin values derived from Paz and the Zroot quantities rein-... 

As far as optical spectra are concerned, Jorgensen (19, 20, 22) has rationalized a large body of experimental data in terms of the parameters 10 Dq and B. Two different origins of the nephelauxetic effect have been advanced (19) (i) the central-field covalency is due to screening the nuclear charge of the central ion by electrons of the ligands (ii) the symmetry-restricted covalency is caused by delocalization of metal d electrons onto the ligands (the delocalization is symmetry dependent eg electrons for... 

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