Symmetry-restricted 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-... 

In the 5 d series however it is possible to derive additional information bearing upon the problem of the relative extent of central field and symmetry restricted covalency. For many 5 d complexes reasonable estimates of the effective spin-orbit coupling constant can be derived from the spectra, and thence the relativistic ratio, / (= complex/ gas). When both f) and / are known for a given system, Jorgensen (74) has suggested how estimates of both covalencv contributions may be made. 

Finally, it is of interest to compare the estimates of covalency contributions for Ir(IV) hexahalides deduced by Allen et al. (11) from spectroscopic data, with those obtained by Owen and Thornley (85, 86) from ESR results. These latter authors attributed the reduction of below the free-ion value, entirely to symmetry restricted covalency, deriving the expression 0bsd = N (Cd +s , >), where the normalising constant, N , is equal to (1 —4a S + and [Pg.153]

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... 

SRCM symmetry-restricted covalency model r linewidth... 

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). 

The symmetry-restricted covalency model (SRCM) leads to AFk (x N4 and Af a IV2,... 

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-... 

Z, in the central ion radial function as we saw above, this is nearly a more fundamental effect than the symmetry-restricted covalency represented by positive 63 or 65. Another is the overlap integral S3 and S5 between the appropriate central ion orbitals and ligand orbitals of eq. (20) introducing the normalization conditions... 

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 . 

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))...

Zhao et al. [ 144,166] proposed an approach based on symmetry restricted covalency [167]. Symmetry restricted covalency attributes covalency effects to the delocalization of d electron density onto ligand orbitals through a and rr molecular orbital formation between metal d orbitals and ligand s, p, and/or d orbitals [168]. The formation of molecular orbitals occurs between metal d orbitals and ligand orbitals of the same symmetry and varies with the coordination environment. The delocalization of d electron density that occurs upon molecular orbital formation leads to a reduction in the Racah B and C parameter values from the free ion values Bg and Cg. The reduction can be expressed by... 

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 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-... 

The symmetry restricted covalency model therefore predicts that the interelec-tronic repulsion parameters will be more sensitive to increased covalency than the spin orbit coupling constant Qf. 

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... 

However, these two extreme assumptions do enable us to obtain the limiting possibilities for any given complex. Thus, if we interpret /S as arising solely from central-field effects we can derive the minimum value of Zett for the complex, whilst, conversely, if /S is assumed to be due only to symmetry restricted covalency we shall obtain the minimum value for the coefficient of presence, a, for the metal atom wave function. In this connection it is well to remember that the Stevens coefficients a and b are not strictly normalised by the relationship = since the... 

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... 

---