{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T01:27:04Z","timestamp":1767922024952,"version":"3.49.0"},"reference-count":63,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T00:00:00Z","timestamp":1646352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002347","name":"Federal Ministry of Education and Research","doi-asserted-by":"publisher","award":["01ZX1915C"],"award-info":[{"award-number":["01ZX1915C"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["PR 1868\/3-1"],"award-info":[{"award-number":["PR 1868\/3-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["HO-4602\/2-2"],"award-info":[{"award-number":["HO-4602\/2-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["HO-4602\/3"],"award-info":[{"award-number":["HO-4602\/3"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK2154-2019"],"award-info":[{"award-number":["GRK2154-2019"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC2167"],"award-info":[{"award-number":["EXC2167"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["FOR5042"],"award-info":[{"award-number":["FOR5042"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB1479"],"award-info":[{"award-number":["SFB1479"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["TRR287"],"award-info":[{"award-number":["TRR287"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005156","name":"Alexander von Humboldt Foundation","doi-asserted-by":"publisher","award":["Sofja Kovalevskaja Award"],"award-info":[{"award-number":["Sofja Kovalevskaja Award"]}],"id":[{"id":"10.13039\/100005156","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2020-779"],"award-info":[{"award-number":["075-15-2020-779"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2021-580"],"award-info":[{"award-number":["075-15-2021-580"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2019(AA\u2019) systems, the maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A\u2019) came from pH2). Remarkably, if the polarization of all spins in a molecule is summed up, the total polarization grows asymptotically with ~1.27N and can exceed 2 in the absence of symmetry constraints (where N is the number of spins). We also discuss the effect of dipole\u2013dipole-induced pH2 spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis.<\/jats:p>","DOI":"10.3390\/sym14030530","type":"journal-article","created":{"date-parts":[[2022,3,6]],"date-time":"2022-03-06T20:40:02Z","timestamp":1646599202000},"page":"530","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Symmetry Constraints on Spin Order Transfer in Parahydrogen-Induced Polarization (PHIP)"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8763-617X","authenticated-orcid":false,"given":"Andrey N.","family":"Pravdivtsev","sequence":"first","affiliation":[{"name":"Section Biomedical Imaging, Molecular Imaging North Competence Center (MOIN CC), Department of Radiology and Neuroradiology, University Medical Center Schleswig-Holstein (UKSH), Kiel University, Am Botanischen Garten 14, 24118 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2819-7584","authenticated-orcid":false,"given":"Danila A.","family":"Barskiy","sequence":"additional","affiliation":[{"name":"Helmholtz-Institut Mainz, GSI Helmholtzzentrum fu\u00fcr Schwerionenforschung, 55128 Mainz, Germany"},{"name":"Quantum, Atomic, and Neutron Physics (QUANTUM) Institute of Physics, Johannes Gutenberg University, Mainz, 55099 Mainz, Germany"}]},{"given":"Jan-Bernd","family":"H\u00f6vener","sequence":"additional","affiliation":[{"name":"Section Biomedical Imaging, Molecular Imaging North Competence Center (MOIN CC), Department of Radiology and Neuroradiology, University Medical Center Schleswig-Holstein (UKSH), Kiel University, Am Botanischen Garten 14, 24118 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3480-7649","authenticated-orcid":false,"given":"Igor V.","family":"Koptyug","sequence":"additional","affiliation":[{"name":"International Tomography Center, SB RAS, 3A Institutskaya st., 630090 Novosibirsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/S0079-6565(97)00007-1","article-title":"Parahydrogen Induced Polarization","volume":"31","author":"Natterer","year":"1997","journal-title":"Prog. 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