Diamagnetic systems

The high sensitivity and selectivity of the EPR response enables diamagnetic systems to be doped with very low concentrations of paramagnetic ions, the fate of which can be followed during the progress of a reaction. The criteria [347] for the use of such tracer ions are that they should give a distinct EPR spectrum, occupy a single coordination site and have the same valency as, and a similar diffusion coefficient to, the host matrix ion. Kinetic data are usually obtained by comparison with standard materials. 

As the essentials of this book are devoted to paramagnetic systems, we shall, for the sake of completeness, conclude this introductory chapter by a related discussion about diamagnetic systems and more precisely about water NMRD in protein solutions. 

Water exchange reaction mechanism 332 Water NMRD in diamagnetic systems 33-9 Water protein relaxation rate 149 Wigner rotation matrices 65, 67 Wild type azurin 122... 

Both mer- and /ac-M(dien)(XYZ)"+ complexes for octahedral metal centers can be formed but the factors determining the relative stabilities have yet to be determined.612 In diamagnetic systems these configurations can be distinguished using NMR.23,613 Table 9 summarizes the available information. 

The information content of nuclear longitudinal relaxation measurements in both paramagnetic and diamagnetic systems can be greatly increased by performing such measurements as a function of the magnetic field. For paramagnetic species, the reason is apparent from the functional form of the equations discussed in Chapter 3 and from the relevant experimental data, reported in Chapter 5. The field dependence of a relaxation rate is called relaxation dispersion, and is abbreviated as NMRD. In principle, NMRD would be helpful for any chemical system, but practical limitations, as will be shown, restrict its use, with a few exceptions, to water protons. 

The f0) in equation 17 vanish identically for any diamagnetic system, e. g., the singlet state considered here. 

NMR provides a powerful tool for the investigation of paramagnetic metal complexes paramagnetism allows the resolution of magnetically non equivalent environments that cannot be resolved in a comparable diamagnetic system. Furthermore the large expansion of the chemical shift range of the observed resonances (the isotropic shift) permits the characterization of fast dynamic processes. 

There are two common features of these two types of hyperfine interactions. First, both 8C and 8pc are inversely dependent on temperature. Second, they both depend on the total electronic spin 5 of the iron atom as shown in Eqs. (1) and (2). The magnitude of the hfs resonances depends on the 5 value of each Hb derivative. For example, met-Hb is a high-spin ferric complex with five unpaired electrons per heme, deoxy-Hb is a high-spin ferrous complex with four unpaired electrons per heme, and both cyanomet- and azidomet-Hb are low-spin ferric complexes, each with one unpaired electron per heme. The hyperfine interactions can shift resonances either upfield or downfield from their diamagnetic counterparts. It should be noted that both HbC>2 and HbCO are low-spin ferrous complexes that are diamagnetic systems (S = 0) and they will not give rise to hyperfine interactions. 

Co(NO)(PR3)3] (R = Ph, alkyl, OEt) can be directly prepared from CoX2-6H20 salts (X = Cl-, N03-) and PR3 under appropriate conditions (Table 34). A tetrahedral structure is inferred from IR and NMR evidence for these CoNO 10 diamagnetic systems, and is indeed found for... 

Three-electron bonds are usually associated with paramagnetic systems. However it is not generally appreciated that three-electron bonds may be incorporated into the VB structures for diamagnetic systems. This incorporation involves the spin-pairing of the unpaired f ab electron of the three-electron bond structure A B with the unpaired electron of a second radical species Y, when the orbitals for the two unpaired electrons overlap [4-6,37,38]. If the odd-electron of Y occupies the AO y, the singlet (S = 0) spin wavefunction for the four electrons is that of eq.(22),... 

Up to now most quantum mechanical studies of the ground and excited states of model heme complexes have focused primarily on diamagnetic systems (36), with less frequent treatment of heme systems with unpaired spins (37-42). With the inclusion of a restricted Hartree-Fock treatment (37, 38) within an INDO formalism parameterized for transition metals (39, 40, ), it is now possible to calculate the relative energies of different spin states of ferric heme complexes in an evenhanded fashion at a semiempirical level. 

Observed linewidths of NMR signals in paramagnetic systems vary enormously and the conditions that govern the observed widths are considerably more complex than in diamagnetic systems. Swift (30) reviewed the problem some years ago. Relaxation times of spin-j nuclei are governed by dipolar and hyperfine exchange (Fermi contact) relaxation processes. The dipolar interaction is normally dominant except in some delocalized systems in which considerable unpaired spin density exists on nuclei far removed from the metal ions (e.g. Ti-radicals). Distinction between the two processes can be made by consideration of the different mathematical expressions involved. For dipolar relaxation when o)fx 1 (t = rate constant for rotation of the species containing the coupled pair and to, = nuclear resonance frequency) ... 

The proton chemical shifts are dominated, in diamagnetic systems, by the electron population pis of the Is orbital. The magnetic shielding constant for a nucleus is mainly expressed in terms of the so-called local... 

Closed-shell (diamagnetic) systems can be investigated using a restricted Hartree-Fock (RHF) calculation, while unrestricted Hartree-Fock (UHF) calculations are able to accommodate open-shell (paramagnetic) systems as well. The Hartree-Fock approximation is also important in serving as a foundation for a variety of more accurate quantum chemical calculations that account for electron correlation. 

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