The Hyperfine Coupling HFC in ESR

In section 2.2, we considered ESR spectra of radicals having one electron spin (S). In this section, we will see how their ESR spectra are changed by nuclear spins in them. At first, let us consider a radical which has only one nuclear spin (I). In this case, its Hamiltonian is written by 

the spin-spin interaction between an electron spin and a nuclear spin can be represented by the isotropic term (AS I ) when the radical rotates very fast in solution. This term is called the hyperfine coupling (HFC) and the coefficient (A) the (isotropic) HFC constant. When it is fixed in a crystal or solid matrix, however, the interaction becomes anisotropic, but the latter case is not considered in this section. 

In the following part of this book, we will write ms and mi as m and M, respectively, for simplicity. 

When the microwave frequency (v) is fixed, the field position (B(M)) where the ESR transition occurs for each M is given as follows  

As shown in Fig. 2-6, the field positions for ESR transitions are split to a doublet for 7=1/2 and a triplet for 1=7, respectively, from the original position (Bo). Such split structures are called HF structures. It is noteworthy that the sign of a can not be determined from ESR measurements at room temperature and even at 77 K. The sign can be obtained experimentally from chemically induced dynamic nuclear polarization (CIDNP) which will be explained in Chapter 4. 

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