$T_1$’s of the $^{13}$C spins of the 0.41 M 2-propanol sample solved in acetone d-6 without magnetic impurities were measured to be 20 s (CC) and 8 s (CSs). Therefore, within the time scale much shorter than these $T_1$’s, the $^{13}$C chains in the 2-propanol molecules can be approximated as an isolated system. We added magnetic impurities (Fe(III) acac) and prepared 4 samples, as shown in Table \[FID\_tc\].

  --- ------------- ------- ----------------------- ------------------- -------------------------------- ----------------- ------------
       $C_{\rm m}$   $T_1$   $T_1 \cdot C_{\rm m}$    $T_2^{(\rm f)}$    $T_2^{(\rm f)}\cdot C_{\rm m}$   $T_2^{(\rm s)}$   $T_1$(HSs)
          (mM)        (s)        (mM$\cdot$s)              (ms)                   (M$\cdot$s)                  (ms)            (ms)
   1       12         1.3             15             $3.0\times 10^2$         $3.5 \times 10^{-3}$        $3.0 \times 10$       93
   2       26        0.64             17             $1.0 \times 10^2$        $2.6 \times 10^{-3}$        $3.9\times 10$        43
   3       47        0.36             17              $9.9\times 10$          $4.7 \times 10^{-3}$        $3.8\times 10$        24
   4       94        0.17             16              $6.4\times 10$          $6.0 \times 10^{-3}$        $3.9\times 10$        17
  --- ------------- ------- ----------------------- ------------------- -------------------------------- ----------------- ------------

  : \[FID\_tc\] Measured $T_1$’s, $T_2$’s of CC and $T_1$ of HSs are summarized. $C_{\rm m}$: the concentration of the magnetic impurity (Fe(III)acac), $T_1$: the longitudinal relaxation time constant of CC, $T_2^{(\rm f)}$: the relaxation time constant of the signal in the full-decoupling case, 