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The approach is based on our quantum ring\u2010polymer contraction (qRPC) technique, in which the inexpensive Hartree\u2010Fock potential is evaluated on the full ring\u2010polymer, while the expensive coupled\u2010cluster correction is evaluated on the centroid only. This qRPC decomposition is combined with a second\u2010generation Car\u2010Parrinello\u2010like dynamics of the Hartree\u2010Fock reference and a basis\u2010consistent extrapolation of the coupled\u2010cluster and de\u2010excitation amplitudes. The combination of all three acceleration layers is essential for making correlated PIMD calculations feasible. We apply the method to a proton shared by water and formaldehyde. Relative to classical nuclei, nuclear quantum effects broaden covalent X\u2013H bond\u2010length distributions, reduce the bias of the shared proton toward formaldehyde, and shift the mean proton\u2010transfer coordinate from 0.206 to 0.135\u00a0\u00c5. The probability of finding the proton closer to formaldehyde decreases from 81.7% to 61.1%. The corresponding nuclear magnetic shielding tensors show that electron correlation and nuclear quantum effects are of comparable magnitude and can act in opposite directions. These results demonstrate that predictive simulations of asymmetric hydrogen bonds require a simultaneous treatment of correlated electronic structure and nuclear quantum fluctuations.<\/jats:p>","DOI":"10.1002\/jcc.70473","type":"journal-article","created":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T02:01:26Z","timestamp":1785549686000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Accelerated \u201cOn\u2010the\u2010Fly\u201d Coupled\u2010Cluster Path\u2010Integral Molecular Dynamics: Impact of Nuclear Quantum Effects on An Asymmetric Proton"],"prefix":"10.1002","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6246-7103","authenticated-orcid":false,"given":"Thomas","family":"Spura","sequence":"first","affiliation":[{"name":"Department of Chemistry University of Paderborn  Paderborn Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4945-1481","authenticated-orcid":false,"given":"Hossam","family":"Elgabarty","sequence":"additional","affiliation":[{"name":"Department of Chemistry University of Paderborn  Paderborn Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5471-2407","authenticated-orcid":false,"given":"Thomas D.","family":"K\u00fchne","sequence":"additional","affiliation":[{"name":"Center for Advanced Systems Understanding (CASUS)  G\u00f6rlitz Germany"},{"name":"Helmholtz Zentrum Dresden\u2010Rossendorf  Dresden Germany"},{"name":"Institute of Artificial Intelligence, Technische Universit\u00e4t Dresden  Dresden Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,7,31]]},"reference":[{"key":"e_1_2_10_2_1","volume-title":"Quantum Mechanics and Path Integrals","author":"Feynman R. 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