Symmetry Constraints on Spin Order Transfer in Parahydrogen-Induced Polarization (PHIP)

Abstract

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 recent decades, numerous methods were proposed for converting pH2-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 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 maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A’) came from pH2). 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 pH2 spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis.

Exceptionally Mild and High-Yielding Synthesis of Vinyl Esters of Alpha-Ketocarboxylic Acids, Including Vinyl Pyruvate, for Parahydrogen-Enhanced Metabolic Spectroscopy and Imaging

“…For the efficient spin-order transfer (SOT) from pH 2 to a nucleus of choice, various approaches are available. ,, The highest polarization so far was achieved using fully deuterated precursors at high magnetic fields for the PHIP-SAH. , The reason is that the symmetry of interactions in the ethyl groups restricts the polarization transfer to 13 C at high fields to 50% and to about 35% at low fields . Up to now, it was not shown that deuteration of the precursor can improve (even theoretically) the polarization transfer in PHIP-SAH at low fields; the opposite was demonstrated .…”

Parahydrogen-induced polarization and spin order transfer in ethyl pyruvate at high magnetic fields

“…RF-SOT at higher magnetic fields appears to be better way to transfer polarization in certain cases because: Heteronuclei are weakly coupled with hydrogens, so there is no efficient spontaneous polarization transfer to 2 H, 13 C and other heteronuclei; The effective spin system can be reduced to two protons and one (third) nucleus of choice, e.g., 13 C using selective deuteration 31 , 32 or selective excitation 50 , 51 . Note that because of the symmetry constraints 45 , 46 , a 100% polarization using only selective excitations in systems like ethyl pyruvate (A 3 B 2 X) is also not possible. …”

“…It is important to note that the low efficiency is not a problem with the particular MFC or molecule. Instead, it is a fundamental property that is bound to the symmetry of the spin system 45,46 . Experimentally, no more than 5% 13 C polarization was achieved with MFC for 40 mM pyruvate in an aqueous solution 35 .…”

Spying on parahydrogen-induced polarization transfer using a half-tesla benchtop MRI and hyperpolarized imaging enabled by automation

“…limit the efficiency of SOT 46 , 47 . As a result, often, 100% polarization can not be achieved (even theoretically) with MFC 40 , 48 , 49 . Pulse sequences and irradiation-based SOTs are more flexible in this regard 50 – 52 , offering higher polarizations but higher hardware demands, too.…”