G-tensor anisotropy

The Florence NMRD program (8) (available at www.postgenomicnmr.net) has been developed to calculate the paramagnetic enhancement to the NMRD profiles due to contact and dipolar nuclear relaxation rate in the slow rotation limit (see Section V.B of Chapter 2). It includes the hyperfine coupling of any rhombicity between electron-spin and metal nuclear-spin, for any metal-nucleus spin quantum number, any electron-spin quantum number and any g tensor anisotropy. In case measurements are available at several temperatures, it includes the possibility to consider an Arrhenius relationship for the electron relaxation time, if the latter is field independent. 

Yonetoni and co-workers (1972) have shown that hemoglobin and myoglobin form nitrosyl complexes with different bond angles at 77 K and at room temperature. The high-temperature species has less g tensor anisotropy (g = 2.03, gy = 1.98-1.99) and poorly resolved hyperfine splitting. Addition of glycerol at high concentrations prevented the transition between these forms. 

In addition to g tensor anisotropy, EPR spectra are often strongly affected by hyperfine interactions between the nuclear spin I and the electron spin S. These interactions take the form T A S, where A is the hyperfine coupling tensor. Like the g tensor, the A tensor is a second-order third-rank tensor that expresses orientation dependence, in this case, of the hyperfine coupling. The A and g tensors need not be colinear in other words, A is not necessarily diagonal in the coordinate systems which diagonalize g. 

This picture can qualitatively account for the g tensor anisotropy of nitrosyl complexes in which g = 2.08, gy = 2.01, and g == 2.00. However, gy is often less than 2 and is as small as 1.95 in proteins such as horseradish peroxidase. To explain the reduction in g from the free electron value along the y axis, it is necessary to postulate delocalization of the electron over the molecule. This can best be done by a complete molecular orbital description, but it is instructive to consider the formation of bonding and antibonding orbitals with dy character from the metal orbital and a p orbital from the nitrogen. The filled orbital would then contribute positively to the g value while admixture of the empty orbital would decrease the g value. Thus, the value of gy could be quite variable. The delocalization of the electron into ligand orbitals reduces the occupancy of the metal d/ orbital. This effectively reduces the coefficients of the wavefunction components which account for the g tensor anisotropy hence, the anisotropy is an order of magnitude less than might be expected for a pure ionic d complex in which the unpaired electron resides in the orbital. 

Bratt et al.96 studied the g-tensor anisotropy of PP 960 in viridis in the temperature range from 5 to 180 K at 24 Tesla (670 GHz) and compared it to that of PPs65 >n R- sphaeroides (and PP o0 in PS I). A slight shift towards a more axial... 

The procedure based on the direct use of the g tensor anisotropy and Eq. (2.24) is quite common for S = xh systems, since g values from frozen solutions are easily obtainable. In this case, both the second order Zeeman contributions and possibly the effects of temperature on the g values are neglected. Furthermore, the directions of the molecular axes are arbitrarily assumed unless single-crystal data are available. Attempts are available in the literature regarding low spin cobalt(II) [77] and copper(II) [61]. 

FIGURE 10.5 Contributions to in the theoretical simulation of spin relaxation in the radical pairs from DCA-POZ and DCA-PSZ evaluated under the assumption of 0 (data points). The full simulations are represented by the curves denoted / -POZ/DQtot.A 0.45 and fc-PSZ/DQtot, respectively. The contribution from the esdi mechanism (k-esdi )=6E-7) corresponds to an effective translational diffusion constant of D = 6 x 10 cm s. The curves indicated as / -POZ/DQ.A represent the contributions of the ahfi mechanism, the indicating the factor by which the theoretical anisotropy parameter A is reduced. The curve indicated hy k-PSZ/DQ.g denotes the contribution due to the g tensor anisotropy in the PSZ radical. The constant values c POZ and c PSZ represent the field-independent contributions to k. For details of the calculation cf. Ref. 23. 

Finally, we address the apparent trend of the kj-values for the DCA-PSZ pair to increase slightly at the high held end. Actually, this trend can be reproduced by the contribution k ta of the g tensor anisotropy mechanism, however, using an orienta-tional correlation time Tc of 8 x 10 s that is only about half the value extracted from a ht of the spin-rotational mechanism, as described above. It is possible that distortional motions of the nonplanar azine ring—which has been invoked to account for the deviation of the isotropic hyperhne constants of the azine radicals... 

Low-spin Fe(iii) porphyrins have been the subject of a number of studies. (638-650) The favourably short electronic spin-lattice relaxation time and appreciable anisotropic magnetic properties of low-spin Fe(iii) make it highly suited for NMR studies. Horrocks and Greenberg (638) have shown that both contact and dipolar shifts vary linearly with inverse temperature and have assessed the importance of second-order Zeeman (SOZ) effects and thermal population of excited states when evaluating the dipolar shifts in such systems. Estimation of dipolar shifts directly from g-tensor anisotropy without allowing for SOZ effects can lead to errors of up to 30% in either direction. Appreciable population of the excited orbital state(s) produces temperature dependent hyperfine splitting parameters. Such an explanation has been used to explain deviations between the measured and calculated shifts in bis-(l-methylimidazole) (641) and pyridine complexes (642) of ferriporphyrins. In the former complexes the contact shifts are considered to involve directly delocalized 7r-spin density... 

The isotropic and anisotropic hyperfine coupling terms in a arise from interactions between electron and nuclear spins, and provide information about the nature of the orbital containing the unpaired electron and the extent to which it overlaps with orbitals on adjacent atoms. The anisotropic term can cause similar difficulties to the g tensor anisotropy in analysing spectra of polycrystalline powders extracting coupling constants from spectra of transition metal ions or radicals in zeolites can be difficult or impossible without computer simulation. 

The time-resolved EPR spectroscopy of photo-excited Rh(III) corroles has been examined at length in two articles [191, 192], Compared with the excited states of main group corroles such as Sn(tpfc)(Cl) [193] and Ga(tpfc)(py) [194], the excited states of Rh(ffl) corroles display broadened signals and greater g tensor anisotropy. This was attributed to spin-orbit coupling effects that effectively admix 3dd and 3jiji excited states. 

For organic aromatic radicals, the EPR spectra at X-band frequencies (9 GHz) are difficult to distinguish, all of them are in resonance approximately at the free electron g value (2.0023), which indicates that the angular momentum is strongly quenched for these molecules, and a typical line-width of 1-2 mT. They can be characterized by ENDOR spectroscopy but also very efficiently distinguished by their g-tensor anisotropy observable by means of high-field EPR spectroscopy. This is demonstrated (Fig. 4) for two radicals created transiently within the photocycle of photosynthetic purple bacteria... 

For a given complex, depends upon certain physical constants of the electron and the proton, the temperature, a function of the g-values and g-tensor anisotropy and a geometric factor which relates the relative orientation of the nucleus with respect to the g-tensor. In the case of proton resonances, and an axially symmetric octahedral Co(II) system, the relationship isKi38.Ki39.Ki4o... 

The experimental procedure of measurements in three crystal planes is also applicable for systems with appreciable g-tensor anisotropy. The technical details to obtain the hyperfine coupling tensors from ENDOR single crystal measurements are discussed in Chapter 3. 

Combined zero-field and g-tensor anisotropy The g-tensor anisotropy can be appreciable for transition metal ion complexes, but also for some triplet state molecules. The Q-band spectrum of an (NO)2 surface complex in zeolite LTA has been analyzed to have rhombic symmetry for the g-tensor and the zero-field splitting, see Fig. 6.5 in Chapter 6. Complications due to overlap with another spectrum (in this example an NO surface complex) are common in practical applications. Variations of the experimental conditions, e.g. the sample composition (amount of nitric oxide in this example) and measurements at different microwave frequencies can then give support for the assignment. Refinement of the visual assignment by simulations as discussed in Section 3.4.1.7 is also frequently employed. 

The ESR spectra of 2 adsorbed on supports sometimes show strong temperature dependency. Such ESR spectral changes are generally accompanied by shifting and/or broadening of certain features due to g-tensor anisotropy and give very rich information about the motional dynamics of the 2 on oxide surface [125]. 

In polycrystalline perdeutero-naphthalene, measurement of hyperfine splitting and g-tensor anisotropy. Radical generated by photoehemical cleavage of dimer. ) Determination of heat of dissoeiation of dimer. 

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