Hyperfine dependence

There have been a number of observations of the LFE in systems where the RP hfetime has been extended through the use of RIPs or microreactors (summarized in a recent review)." Of interest for neutral RPs in solution reactions is the hyperfine dependence of these LFEs. Early experimental and theoretical studies concluded that substantial LFEs are only observed for RPs in which there are substantial HFCs in one pair member and negligible couplings in the other." " In a more recent study, RPs with a wide range of combinations of HFCs and lifetime were screened for LFEs by simulation on a supercomputer." This study concluded that indeed for short-lived RPs, the large small HFC combination is required to produce substantial LFEs, but for long-hved RPs the restriction vanishes. 

The tliree-line spectrum with a 15.6 G hyperfine reflects the interaction of the TEMPO radical with tire nitrogen nucleus (/ = 1) the benzophenone triplet caimot be observed because of its short relaxation times. The spectrum shows strong net emission with weak E/A multiplet polarization. Quantitative analysis of the spectrum was shown to match a theoretical model which described the size of the polarizations and their dependence on diffrision. 

For example, if the molecular structure of one or both members of the RP is unknown, the hyperfine coupling constants and -factors can be measured from the spectrum and used to characterize them, in a fashion similar to steady-state EPR. Sometimes there is a marked difference in spin relaxation times between two radicals, and this can be measured by collecting the time dependence of the CIDEP signal and fitting it to a kinetic model using modified Bloch equations [64]. 

A good correlation with ordinary Hammett a values was based on 16 well-behaved substituents, and p-SOMe conformed well to this. Various other substituents showed deviations which were attributed to enhanced + R effects. These included p-SPh and this was explained in terms of 7t(pd) bonding, which was thus taken to play no part in the effect of p-SOMe on the methyl hyperfine splitting. More recently several 4-substituted benzyl radicals of the type RSO C6H4CH2 (n — 0,1 or 2 R = Me, Ph, Tol, COMe or OMe) have been examined by ESR spectroscopy249. The ability to delocalize spin density onto the substituent decreases in general as n increases and the effect of R depends on the oxidation state of sulfur. These authors have devised a new scale of substituent effects (sigma dot... 

The value of the magnetic hyperfine interaction constant C = 22.00 kHz is supposed to be reliably measured in the molecular beam method [71]. Experimental data for 15N2 are shown in Fig. 1.24, which depicts the density-dependence of T2 = (27tAv1/2)-1 at several temperatures. The fact that the dependences T2(p) are linear until 200 amagat proves that binary estimation of the rotational relaxation rate is valid within these limits and that Eq. (1.124) may be used to estimate cross-section oj from... 

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

The remainder of equation (38) describes the multiplet effect, and it can be seen that whether an individual line in the multiplet corresponds to emission or absor ption depends on the signs of the hyperfine coupling constants but is independent of Hq. The nature of the hyperfine field is such that the integral over the whole multiplet is zero if Ag = 0. 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

Contact shifts give information on the electronic structure of the iron atoms, particularly on the valence distribution and on the magnetic coupling within polymetallic systems. The magnetic coupling scheme, which is considered later, fully accounts for the variety of observed hyperfine shifts and the temperature dependence. Thus, through the analysis of the hyperfine shifts, NMR provides detailed information on the metal site(s) of iron-sulfur proteins, and, thanks to the progress in NMR spectroscopy, also the solution structure 23, 24 ). 

Fig. 4. Top Theoretical temperature dependence of the hyperfine shift of the H/3 protons of reduced spinach [Fe2S2] ferredoxin 151). The solid line corresponds to the situation where only one species exists in solution, whereas the dashed line corresponds to a situation where there is fast equilibrium between two species (in a 20/80 ratio) differing for the location of the extra electron 151). Bottom.-. Experimental temperature dependence of the H NMR shifts. The signals are labeled as in Fig. 2B.

In addition to the standard constraints introduced previously, structural constraints obtainable from the effects of the paramagnetic center(s) on the NMR properties of the nuclei of the protein can be used (24, 103). In iron-sulfur proteins, both nuclear relaxation rates and hyperfine shifts can be employed for this purpose. The paramagnetic enhancement of nuclear relaxation rates [Eqs. (1) and (2)] depends on the sixth power of the nucleus-metal distance (note that this is analogous to the case of NOEs, where there is a dependence on the sixth power of the nucleus-nucleus distance). It is thus possible to estimate such distances from nuclear relaxation rate measurements, which can be converted into upper (and lower) distance limits. When there is more than one metal ion, the individual contributions of all metal ions must be summed up (101, 104-108). If all the metal ions are equivalent (as in reduced HiPIPs), the global paramagnetic contribution to the 7th nuclear relaxation rate is given by... 

Thus, the starting parameters for the computer-simulation of spectrum IB were chosen to agree with the value of hyperfine fields at 613 K as measured by Rlste and Tenzer, using neutron scattering measurements (36). In addition, the magnetic relaxation rate depends on temperature, as discussed in the Theory section of this paper. 

Let us now turn to the second parameter, namely the shape of the "property surface". Around reference configurations, the dependence of the hyperfine coupling constants on the inversion motion is well represented by ... 

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

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