6 Radical spectra with multiple hyperfine splittings

When a radical present $r$ different groups of equivalent nuclei with spin $I$, it will have different coupling constants, $a_1$, $a_2$, $a_3$, $\ldots$, $a_r$, and it can give a complex hyperfine structure. The values of $a_j$ can be obtained for direct measure on the spectrum.

The position of all lines in the spectrum is given by:

$$H_k = H_0 - \sum_{j=1}^{r} \left ( a_j \sum_{i=1}^{n_j} m_{k,i,j} \right ) \ =\ H_0 - \sum_{j=1}^{r} a_j M_{k,j}$$ (7)

where $j$ indicates the groups of equivalent nuclei and $i$ the nuclei within each group. $m_{k,i,j}$ are the individual Z components of the angular momentum of nuclear spin $i$ of the equivalent group $j$ in the state $k$ and $M_{k, j}$ is the total Z component of the angular momentum of spin of the equivalent nuclei $j$ in the state $k$.

The spectrum of a neutral radical derived from the methanol (obtained by abstraction of an atom of H in the photolysis of a dissolution of $CH_3OH$ and $H_2O_2$) $\cdot CH_2OH$ is shown in Fig. 15. The electron is interacting with three protons, two of which are equivalent. The smallest splitting corresponds to the proton of the OH. Three doublets are obtained with a relation of intensities 1:2:1. The values of the two coupling constants and the reconstruction of the spectrum are also indicate in the Fig. 15.

Figure 15: Successive splittings and EPR spectrum of the $\cdot CH_2OH$.