It is well known that the association of parahydrogen (pH
2) with an unsaturated molecule or a transient metalorganic complex can enhance the intensity of NMR signals; the effect is known as parahydrogen-induced polarization (PHIP). During recent decades, numerous methods were proposed for converting pH
2-derived nuclear spin order to the observable magnetization of protons or other nuclei of interest, usually
13C or
15N. Here, we analyze the constraints imposed by the topological symmetry of the spin systems on the amplitude of transferred polarization. We find that in asymmetric systems, heteronuclei can be polarized to 100%. However, the amplitude drops to 75% in A
2BX systems and further to 50% in A
3B
2X systems. The latter case is of primary importance for biological applications of PHIP using sidearm hydrogenation (PHIP-SAH). If the polarization is transferred to the same type of nuclei, i.e.,
1H, symmetry constraints impose significant boundaries on the spin-order distribution. For AB, A
2B, A
3B, A
2B
2, AA’(AA’) systems, the maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A’) came from pH
2). Remarkably, if the polarization of all spins in a molecule is summed up, the total polarization grows asymptotically with ~1.27
and can exceed 2 in the absence of symmetry constraints (where
is the number of spins). We also discuss the effect of dipole–dipole-induced pH
2 spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis.
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