Ligand cross-terms

Since the shifts produced by the cross-terms between ligand and central ion nuclei are often significant, the strikingly broad ENDOR lines ( 1 MHz) observed for transition metal ions61,62) may be traced back, at least in part, to unresolved splittings due to second order interactions of numerous ligands with the central ion. ENDOR frequencies up to second order for an I = 1 nucleus in the presence of a second ligand nucleus with a spin K = 1 are tabulated in Appendix B, Eqs. (B4). 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

The observed ft . are minimized root mean square values based upon the spectroscopic data reported by Ciampolini et al. [66]. The individual crystal field contributions ft .(CF) are listed for each calculated ft together with the particular ligand polarization contribution ft (LP). The calculated total ft .(tot) sums the crystal field (CF) and ligand field (LF) contributions with the CF-LP cross-term. 

Scheme 10.1 Examples of derivation of descriptors (ordinary terms) for ligands (organic molecules, etc.) and biopolymers and of derivation of cross terms.

Proteo-chemometrics approach was the name proposed for a QSAR approach based on the combined analysis of series of receptors and ligands, wherein description of ligands, proteins, and the so-called ligand-protein cross-terms are correlated with interaction activities [Lapinsh, Pmsis et al, 2003]. 

The + sign in Eq. (25) corresponds to the case where Q represents a real operator (EFG), the sign to the case where Q represents a complex operator (orbital momentum). The matrix elements , representing cross-terms between iron AO s and ligand AO s, can be transformed by introducing a completeness relation of orthogonal terms iF >, which contain the iron AO s V> ... 

In terms of scope and chemoselectivity, hydrozirconation takes its place between hydroboration and hydroaiumination. However, the synthetic applications of organozirconocene complexes have been considerably expanded over these last few decades, and it can be expected that they will become more and more attractive in the future. Beside the direct substitution sequences, indirect reaction pathways involving transmetalation or activation by ligand abstraction have been successfully applied in a number of cross-coupling and C-C bond-forming reactions. 

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