Introduction To Dynamic Spin Chemistry: Magnetic Field Effects On Chemical And Biochemical Reactions

5.2: Theoretical Interpretation of CIDEP by the Radical Pair Mechanism

5.2 Theoretical Interpretation of CIDEP by the Radical Pair Mechanism

In this section, we will see how CIDEP can be generated from the radical pair mechanism. The spin polarization ( P) of ESR transition is represented as shown in Fig. 5-1. Here, P is given as follows:


Figure 5-1: ESR signals in (a) absorption and (b) in emission.

The population of the i-th level is denoted by n i( i = ? or ?), which is represented by

In Eqs. (5-2) and (5-3), N is the total number of electron spins and < S z> is the net z-component of the spins. Eqs. (5-2) and (5-3) are reasonable because n a ( n ?) becomes N or 0 (0 or N) when < S z> is 1/2 or ?1/2. From Eqs. (5-1) (5-3), P can be given as follows:

Problem 5-1

Calculate the P values in the thermal equilibrium ( P eq) at room temperature (20 C) for the ESR transitions of an electron at the X-, K-, and Q-bands (9, 25, and 35 GHz). CIDEP is observed for the case of P < P eq (enhanced absorption) or P > 0 (emission) as shown in Fig. 5-1.

Answers

Problem 5-1

From Eq. (2-8), the Zeeman splitting is equal to the energy of an applied microwave ( hv) in the resonance condition of ESR. Thus, the n ?