Spin delocalisation

Under spin delocalisation a situation is assumed when, in a magnetic system, an extra electron cannot be attributed to a single centre it behaves as an itinerant. A prototype of this situation is represented by the homo-nuclear d2-dl mixed-valence system (Fig. 10.15). Let the d - r core of the system behave as high-spin. Then the extra electron can be added to either centre A or B and consequently the (determinantal) wave function of the dimer is degenerate 

For the (orbitally) degenerate state a linear combination of two Slater determinants should be taken as the molecular wave function 

The diagonal matrix elements are equal to the relative energies depending on the total spin-spin state 

The corresponding wave functions alter their parity they are either of g- or u-type with respect to the centre of inversion. 

A more complete solution of the spin delocalisation problem for homo-nuclear dn+x — d systems has been given by Anderson [20]. Denoting the total spins S(d ) = 50 and 5(/ +1) = 50 + 1/2, the dimer involves 2S0 + 1 half-integer spin states, namely 

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Figure 1. Induced spin density map for MnCu(pba)(H20)j. 2H20 at 10K under 5 T in projection along the perpendicular to the basal plane. Solid and dashed lines are used respectively for negative and positive spin densities. Contour steps are 5 mpB/A2. The spin delocalisation is more pronounced toward the N atom than the O atoms.

M N(Bu )CH=CHNBu R] [R=TEMPO, OC6H2Bu 2-2,6-Me-4, OC6Me4-2,3,5,6-OH-4, Bu SiMe3, WCp(CO)3, Re(CO)5] together with EPR spectral data, DPT calculations on model compounds showed that spin delocalisation to the five-membered ring decreased in the sequence M = Ge > Si > C, implicating the importance of the zwitterionic structure 64. 

Contact shifts and through-bond spin delocalisation in paramagnetic lanthanide complexes... 

Since the spin delocalisation in lanthanide complexes is small (see sect. 2.1), the unpaired electrons can be considered as spatially confined onto the metal, thus producing an electronic magnetic point dipole which may interact with peripheral nuclear magnetic momenta via dipolar interactions (eq. (23), Bertini and Luchinat (1996)). 

The authors conclude that [JR(L2)3]3+ (R — Ce-Dy) are isostructural in solution and adopt a structure reminiscent to that found in the crystal structure of [Eu(L2)3]3+. The aromatic backbone acts as an efficient relay for spin delocalisation and/or spin polarization which allows contact contributions to operate at long distances. 

Nuclear magnetic resonance (NMR) Chemical shift, nuclear coupling constants, relaxation times For paramagnetic proteins enhanced chemical shift resolution, contact and dipolar shifts, spin delocalisation, magnetic coupling from temperature dependence of shifts. 

Structure 45 for the radical cation of 1 showed significant spin delocalisation to the [3-ring end groups. The potential energy curve for rotation around the C6-C7 and C6 -C7 single bonds and the effect of this rotation on selected bond distances are reproduced in Fig. 21. 

The current picture of the p-carotene radical cation is thus delocalisation of the unpaired spin delocalised over the entire conjugated... 

We have assumed that no angular momentum contribution assists. Then the basis set of spin functions consists of the uncoupled set Sa,Msa) Sb, Msb), or the coupled set SA,SB,S,Ms), its size is N = (2Sa + l)(2Ss + 1). Additionally, the orbital angular momentum can be added and then the basis set becomes a direct product of all orbital and spin functions. In a special case, spin delocalisation (double exchange) operates. 

For example, in the Fe (d ) coordinated phenoxyl-radical complex (Fe -0 -Ph), the formal oxidation state of the metal is classed as +IV, since a closed shell phenolato anion would have to be removed. However, in many cases spectroscopic measurements, amongst others EPR, have proven the presence of a high-spin d electron configuration at the iron and a phenoxyl ligand in such complexes. In this case, the iron ion has a physical oxidation number of +III even though the formal oxidation state would be classed as -I-IV. As a result of these potential confusions, several research groups have prepared numerous examples of metal-coordinated ligand-radical complexes, particularly coordinated phenoxyl radicals, in order to examine the nature of the metal oxidation states and the extent of spin delocalisation in such complexes. 

To obtain electron-spin densities it is necessary to distinguish Fermi contact shifts from the pseudocontact shifts for each compound. This may be done sometimes by comparing two series of complexes differing only in central metal ion, if it can be shown that the modes of spin delocalisation are identical but one member is magnetically isotropic. Alternatively, the shifts for a given nucleus in the paramagnetic species are compared in solution and in the solid. Fermi contact shifts are the same in fixed and mobile phases the ratio of pseudocontact shifts in fixed and mobile environments is related to the g-value anisotropies. (While theoretically generally applicable the method is restricted because of the wide lines obtained with solids.) Discrimination between... 

As has been shown in the NMR spectra of the ferric high-spin complex, the a spin delocalisation contributes predominantly to the value, although the contribution from the n spin delocalisation cannot be neglected. The fact that the shift difference between 3- and 7-F signals is smaller for met-aquo Mb than for met-cyano Mb could be interpreted as indicative of the predominance of the a spin delocalisation contribution to the dc value in the former complex. 

Since the haem methyl proton signals of MbCO were observed in the narrow chemical shift range between 2 and 4 ppm,the spreads of the haem methyl proton signals in the spectra of deoxy Mb (Fig. 10) reflected the hyperfine shift pattern of the haem methyl proton signals. Hence the larger dispersion of the haem methyl proton signals in the spectrum of Mb(7-PF) could be attributed to the significant n spin delocalisation. 

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