  It is well known that the association of parahydrogen (pH2) 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 the last decades, numerous methods were proposed
for converting pH2-derived nuclear spin order to the observable magnetization
of pro-tons 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. In asymmetric systems, heteronuclei can
be polarized to 100%. However, the amplitude drops to 75% in A2BX systems and
further to 50% in A3B2X 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, A2B, A3B, A2B2, AA'(AA') systems, the maxi-mum average polarization for
each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, when A and B (or A')
came from pH2 We also discuss the effect of dipole-dipole induced pH2
spin-order distribution in heterogeneous catalysis or nematic liquid crystals.
Practical examples from the literature illustrate our theoretical analysis.
