In the case of allyl pyruvate, the analytical treatment of the LAC problem becomes impractical for several reasons. First, the spin system in this case includes nine spins, with JHH-couplings being in the same range. This makes the analysis rather cumbersome, since it is impossible to reduce the dimension of the Hamiltonian by omitting spins with weaker couplings. Second, the path of polarization transfer is indirect, since JCH coupling constants between protons derived from pH2 and the C nucleus are negligible. Thus, CH2 group of the allyl moiety acts as a polarization relay since it has significant scalar couplings to both the nascent pH2-protons and the C nuclei of the pyruvate moiety (Table ). As a result, the simulated magnetic field dependence for 13 C1 in allyl pyruvate has two pronounced maxima and many smaller features, in contrast to the smooth field dependence for C-maleic acid. In 13 C2 in allyl pyruvate, the coupling constants with the relaying CH2 group are relatively small, which leads to a low efficiency of polarization transfer and an intricate field dependence. No sharp features of the field dependence are detected in the experiment; however, qualitatively measured data is in good agreement with calculations (Fig. ). Fig. . Field dependence of C polarization for the case of continuous hydrogenation at fixed ultralow field (protocol 1) for maleic acid (a) and allyl pyruvate (b).