Chemical Reactions through Radical Pairs

Let us consider chemical reactions through radical pairs as shown in Fig. 3-1. Radical pairs are usually produced from singlet and triplet excited states. These reaction precursors are called S- and T-precursors, respectively. Radical reactions also occur from free radicals, which is called F-precursors. Because the dynamic behavior of radical pairs from F-precursors is similar to that from T-ones, we omit discussion of reactions from F-precursors for simplicity s sake in this book. 

2 Singlet and Triplet States of Radical Pairs and Their Mixing 

A radical pair consists of two weakly coupled radicals and its spin Hamiltonian (Hrp) in solution can be represented by the exchange (Hex) and magnetic (Hmag) terms [1], 

/ is the value of the exchange integral between two electron spins (Si and S2) and the 1/2 term is put for convenience although it is not used in many textbooks. Eq. (3-3) is just the sum of spin Hamiltonian of one radical given by Eq. (2-22), but the nuclear Zeeman terms are omitted in Eq. (3-3) because their magnitude is much smaller than those of the electron Zeeman term and the HFC one. In Eq. (3-3), ga and gb are the isotropic g-values of two component radicals (radicals a and b) in a radical pair, respectively, and A, and A are the isotropic HFC constants with nuclear spins (/, and 4) in radicals a and b, respectively. 

The combination of two electron spins (Si and S2) with Si = S2 = 1/2 in a radical pair generates the singlet (S) and triplet (T n = +1 and 0) states which can be represented by the product of the electron- and nuclear-spin wavefuctions. 

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M. From Eqs (3-11) and (3-13), the S-T conversion of radical pars was found to be influenced by the following terms (a) the Zeeman term which is characterized by AgjUgB, (b) the hyperfine coupling (HFC) terms which are characterized by i4, and At, and (c) the exchange term which is characterized by J. Thus, the MFEs on chemical reactions through radical pairs can be classified by the following typical mechanisms ... 

In 1973, Sagdeev et al. [16] reported MFEs on thermal reactions of substituted benzyl chlorides (ACl) with n-butyl lithium (BLi) in hot hexane and cyclohexane. Although there were many serious misprints in this paper, this was the first report for MFEs on chemical reactions through radical pairs. The reactions occur through the following scheme ... 

Magnetic Field Effects on Chemical Reactions through Radical Pairs Involving Heavy Atom-Centered Radicals... 

Although the low field effects on chemical reactions through radical pairs had been explained by the LCM, Timmel et al. [14] proposed that the so-called low field effects arose also fi om coherent superpositions of degenerate electron-nuclear spin states in a radical pair in zero field. They made some model calculations for their mechanism. At first, let us consider the case of a radical pair with a single spin-1/2 nucleus, e.g., a proton. When the exchange term is not included (J= 0 J), its spin Hamiltonian (H) can be expressed from Eq. (3-3) as... 

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