Radical pair theory

Avdievich N I and Forbes M D E 1995 Dynamic effects in spin-correlated radical pair theory J modulation and a new look at the phenomenon of alternating line widths in the EPR spectra of flexible biradicals J. Phys. Chem. 99 9660-7... 

II. The Radical Pair Theory of CIDNP A. Basic Concepts... 

The basic postulates of radical pair theory may be summarized as follows ... 

The principal concern in radical pair theory is not which state is of lower energy but rather the energy difference and its variation as the length of the box or the inter-radical distance in the radical pair changes. Further, AEsi is time-dependent because the inter-radical distance fluctuates with time. As the separation gets larger, decreases... 

With the establishment of the primary phototriplet reduction mechanism we now turn to the explanation for the effect of flow rates and the formation of polarized phenoxy radicals. Since reaction [2] is a relatively fast secondary process it is readily understood that the observation of the primary ketyl radicals will be dependent upon flow rate. The triplet polarization (E) of the secondary phenacyl radical should not have been affected but the increased contribution of the E/A Radical-Pair polarization altered the overall appearance of the polarization pattern. The diffusion model of the Radical-Pair theory relates the E/A polarization magnitude to the radical concentration within the reaction zone. Since the phenacyl radical is considered to be very chemically reactive, and the product phenol "accumulated" within the reaction zone is also a much better hydrogen donor, the following reactions will proceed within the reaction zone ... 

Fig. 13. CIDNP effects observed for the cyclobutane signals of the dimethylindene dimer during the photoinduced electron transfer reaction with chloranil (a), and simulated spectra based on the radical pair theory and assuming a ring-opened (extended) dimer radical cation (b), a ring-closed (localized) dimer radical cation (c) and the consecutive ( cooperative ) involvement of open and closed radical cations (d) [256]...

According to the radical pair theory [54], the CIDNP effect results from the competition between a geminate spin dependent radical (ion) pair reaction and the separation of the radicals (radical ions) by diffusion [55]. The free radicals (radical ions) may react with diamagnetic species (e.g. solvent) and accordingly, the escape products have certain nuclear spin states. overpopulated. An enhanced absorption or an emission line in the NMR spectrum is observed. 

Figure 2 shows the magnetic field dependence of the ratio of the yields of symmetrical (2) and unsymmetrical (1) products for the reaction of benzyl chloride with Et3GeNa in benzene17. As earlier observed in the reactions of alkyllithiums with dichlorodiphenylmethane9, the field dependence pattern qualitatively reflects two basic mechanisms of radical pair theory — HFI and Ag mechanisms. In this particular case, the cage effects in nonviscous media (benzene) create the necessary prerequisites for the... 

If we are to use the radical pair theory to explain the effects of micellization on the cage reaction probability as well as the magnetic field effect, it is mandatory that we be able to observe CIDNP in these systems. In addition, since CIDNP is sensitive to events on the time scale of the radical pair lifetime, detailed analysis of the CIDNP can often lead to mechanistic insight to the dynamics of the radical pair. Below we describe one such result. 

The first discovery of chemically induced dynamic electron polarization (CIDEP) was made by Fessenden and Schuler in 1963 (58). These authors observed the abnormal spectra of the H atoms produced during the irradiation of liquid methane. The low-field line in the esr spectrum was inverted compared to the corresponding high-field line. The related chemically induced dynamic nuclear polarization effect (CIDNP) was reported independently four years later by Bargon et al. (22) and by Ward and Lawler (134). Because of the wider application of nmr in chemistry, the CIDNP effect immediately attracted considerable theoretical and experimental attention, and an elegant theory based on a radical-pair model (RPM) was advanced to explain the effect. The remarkable development of the radical-pair theory has obviously brought cross-fertilization to the then-lesser-known CIDEP phenomenon. 

The current theories of chemically induced magnetic polarization can therefore be summarized into the two basically different mechanisms the photoexcited triplet mechanism (PTM) responsible for the initial electron polarization and the observed Overhauser effect in nuclear polarization, and the radical-pair mechanism which, to date, accounts for almost the remaining bulk of the known polarization systems. We proceed to describe the simple physical models of these two mechanisms by beginning with the more sophisticated radical-pair theory. 

One of the fundamental results of the radical pair theory of ODNP is that it relates the polarizations of products formed by direct combination or disproportionation of the polarizing geminate radical pairs with that of products derived from transfer or coupling reactions of radicals escaping these pairs (Sect. 2, rule. 4 Sect. 3, Eq. (25,27,36,37) Sect. 4.1, Eq. (39)). ( antitati-vely, this relation is given by equations... 

Here, N represents escaped products. We can see from the radical pair theory that reactions (9-1) and (9-2) are independent on nuclear spins inside the RP, but that reaction (9-3) is dependent on the nuclear spins. If a starting molecule contains a magnetic isotope such as x, it will be represented as A. On the other hand, if A contains no such magnetic isotope, it will be represented by A. 

Anomalous (in the sense of radical pair theory) polarization phases and magnetic field dependence were reported for substrates containing 19F nuclei, and were explained by cross-relaxation [67], Azumi and co-workers [68] investigated the photolysis of benzaldehyde. The polarizations could be accounted for by S-T0 mixing at high fields and by S-T mixing at low fields. At a field of 325 mT, however, the authors could not reconcile the CIDNP phase with the predictions of the radical pair mechanism from additional DNP experiments, they concluded that cross-relaxation with... 

The controversy over the mechanism of CIDEP in radical reactions extends also to CIDNP. An elaboration of a theory for CIDNP based upon the radical-pair approach has been offered recently,424 425 and a brief note has been published which questions the need for an alternative to the radical-pair approach to account for CIDNP, and further shows that the same assumptions are necessary in both the radical-pair and Overhauser mechanisms, namely, that nuclear relaxation can occur in the escaping radicals.426 427 It would seem that, whereas in CIDEP the experimental observations require some alternative to the radical-pair treatment for satisfactory explanation, so far, CIDNP observations can be explained on the basis of the radical-pair theory, although this does not preclude the possibility that other mechanisms are also operative. 

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