{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T13:19:58Z","timestamp":1785158398907,"version":"3.55.0"},"reference-count":50,"publisher":"AIP Publishing","issue":"19","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,5,21]]},"abstract":"<jats:p>Nuclear magnetic resonance (NMR) spectroscopy is one of the indispensable techniques in chemistry because it enables us to obtain accurate information on the chemical, electronic, and dynamic properties of molecules. Computational simulation of the NMR spectra requires time-consuming density functional theory (DFT) calculations for an ensemble of molecular conformations. For large flexible molecules, it is considered too high-cost since it requires time-averaging of the instantaneous chemical shifts of each nuclear spin across the conformational space of molecules for NMR timescales. Here, we present a Gaussian process\/deep kernel learning-based machine learning (ML) method for enabling us to predict, average in time, and analyze the instantaneous chemical shifts of conformations in the molecular dynamics trajectory. We demonstrate the use of the method by computing the averaged 1H and 13C chemical shifts of each nuclear spin of a trefoil knot molecule consisting of 24 para-connected benzene rings (240 atoms). By training ML model with the chemical shift data obtained from DFT calculations, we predicted chemical shifts for each conformation during dynamics. We were able to observe the merging of the time-averaged chemical shifts of each nuclear spin in a singlet 1H NMR peak and two 13C NMR peaks for the knot molecule, in agreement with experimental measurements. The unique feature of the presented method is the use of the learned low-dimensional deep kernel representation of local spin environments for comparing and analyzing the local chemical environment histories of spins during dynamics. It allowed us to identify two groups of protons in the knot molecule, which implies that the observed singlet 1H NMR peak could be composed of the contributions from protons with two distinct local chemical environments.<\/jats:p>","DOI":"10.1063\/5.0147398","type":"journal-article","created":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T10:11:23Z","timestamp":1684318283000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":10,"title":["NMR spectrum prediction for dynamic molecules by machine learning: A case study of trefoil knot molecule"],"prefix":"10.1063","volume":"158","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3004-1036","authenticated-orcid":false,"given":"Mikhail","family":"Tsitsvero","sequence":"first","affiliation":[{"name":"Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8866-4279","authenticated-orcid":false,"given":"Jenny","family":"Pirillo","sequence":"additional","affiliation":[{"name":"Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4883-5085","authenticated-orcid":false,"given":"Yuh","family":"Hijikata","sequence":"additional","affiliation":[{"name":"Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7175-8474","authenticated-orcid":false,"given":"Tamiki","family":"Komatsuzaki","sequence":"additional","affiliation":[{"name":"Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2023,5,17]]},"reference":[{"key":"2023081108123703300_c1","doi-asserted-by":"publisher","first-page":"136403","DOI":"10.1103\/physrevlett.104.136403","article-title":"Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons","volume":"104","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"2023081108123703300_c2","doi-asserted-by":"crossref","unstructured":"J.\n            Vandermause\n          , Y.Xie, J. S.Lim, C. J.Owen, and B.Kozinsky, \u201cActive learning of reactive Bayesian force fields applied to heterogeneous catalysis dynamics of H\/Pt,\u201d Nat. Commun.13, 5183 (2022).10.1038\/s41467-022-32294-0","DOI":"10.1038\/s41467-022-32294-0"},{"key":"2023081108123703300_c3","doi-asserted-by":"publisher","first-page":"e1603015","DOI":"10.1126\/sciadv.1603015","article-title":"Machine learning of accurate energy-conserving molecular force fields","volume":"3","year":"2017","journal-title":"Sci. Adv."},{"key":"2023081108123703300_c4","doi-asserted-by":"publisher","first-page":"3887","DOI":"10.1038\/s41467-018-06169-2","article-title":"Towards exact molecular dynamics simulations with machine-learned force fields","volume":"9","year":"2018","journal-title":"Nat. Commun."},{"key":"2023081108123703300_c5","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.cpc.2019.02.007","article-title":"sGDML: Constructing accurate and data efficient molecular force fields using machine learning","volume":"240","year":"2019","journal-title":"Comput. Phys. Commun."},{"key":"2023081108123703300_c6","article-title":"Lecture Notes in Physics Vol. 968 (Springer, 2020)","volume-title":"Machine Learning Meets Quantum Physics,"},{"key":"2023081108123703300_c7","doi-asserted-by":"publisher","first-page":"10073","DOI":"10.1021\/acs.chemrev.1c00022","article-title":"Gaussian process regression for materials and molecules","volume":"121","year":"2021","journal-title":"Chem. Rev."},{"key":"2023081108123703300_c8","doi-asserted-by":"publisher","first-page":"144106","DOI":"10.1063\/5.0063534","article-title":"Gaussian process models of potential energy surfaces with boundary optimization","volume":"155","year":"2021","journal-title":"J. Chem. Phys."},{"key":"2023081108123703300_c9","doi-asserted-by":"publisher","first-page":"4501","DOI":"10.1038\/s41467-018-06972-x","article-title":"Chemical shifts in molecular solids by machine learning","volume":"9","year":"2018","journal-title":"Nat. Commun."},{"key":"2023081108123703300_c10","doi-asserted-by":"publisher","first-page":"4558","DOI":"10.1021\/acs.jpclett.9b01570","article-title":"Multiresolution 3D-DenseNet for chemical shift prediction in NMR crystallography","volume":"10","year":"2019","journal-title":"J. Phys. Chem. Lett."},{"key":"2023081108123703300_c11","doi-asserted-by":"publisher","first-page":"2964","DOI":"10.1038\/s41467-021-23208-7","article-title":"Structure determination of an amorphous drug through large-scale NMR predictions","volume":"12","year":"2021","journal-title":"Nat. Commun."},{"key":"2023081108123703300_c12","doi-asserted-by":"publisher","first-page":"74","DOI":"10.3390\/computation10050074","article-title":"Regression machine learning models used to predict DFT-computed NMR parameters of zeolites","volume":"10","year":"2022","journal-title":"Computation"},{"key":"2023081108123703300_c13","doi-asserted-by":"publisher","first-page":"8820","DOI":"10.1039\/d2cp00361a","article-title":"Thermal fluctuation and conformational effects on NMR parameters in \u03b2-O-4 lignin dimers from QM\/MM and machine-learning approaches","volume":"24","year":"2022","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023081108123703300_c14","doi-asserted-by":"crossref","unstructured":"M.\n            Ceriotti\n          , \u201cBeyond potentials: Integrated machine-learning models for materials,\u201d MRS Bull.47, 1045-1053 (2022).10.1557\/s43577-022-00440-0","DOI":"10.1557\/s43577-022-00440-0"},{"key":"2023081108123703300_c15","volume-title":"Applied Theoretical Organic Chemistry","year":"2018"},{"key":"2023081108123703300_c16","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1126\/science.aav5021","article-title":"Topological molecular nanocarbons: All-benzene catenane and trefoil knot","volume":"365","year":"2019","journal-title":"Science"},{"key":"2023081108123703300_c17","doi-asserted-by":"publisher","first-page":"5083","DOI":"10.1021\/acs.jctc.5b00856","article-title":"Enhancing NMR prediction for organic compounds using molecular dynamics","volume":"11","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"2023081108123703300_c18","doi-asserted-by":"publisher","first-page":"14763","DOI":"10.1002\/anie.201708266","article-title":"Fully automated quantum-chemistry-based computation of spin\u2013spin-coupled nuclear magnetic resonance spectra","volume":"56","year":"2017","journal-title":"Angew. Chem., Int. Ed."},{"key":"2023081108123703300_c19","doi-asserted-by":"publisher","first-page":"7863","DOI":"10.1039\/d2sc01306a","article-title":"A machine learning protocol for revealing ion transport mechanisms from dynamic NMR shifts in paramagnetic battery materials","volume":"13","year":"2022","journal-title":"Chem. Sci."},{"key":"2023081108123703300_c20","first-page":"370","volume-title":"Deep Kernel Learning","year":"2016"},{"key":"2023081108123703300_c21","first-page":"3338","article-title":"Manifold Gaussian processes for regression","year":"2016"},{"key":"2023081108123703300_c23","doi-asserted-by":"publisher","first-page":"23551","DOI":"10.1039\/d2cp03205h","article-title":"Impact of solvent interactions on 1H and 13C chemical shifts investigated using DFT and a reference dataset recorded in CDCl3 and CCl4","volume":"24","year":"2022","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023081108123703300_c24","first-page":"1","article-title":"POT: Python optimal transport","volume":"22","year":"2021","journal-title":"J. Mach. Lear. Res."},{"key":"2023081108123703300_c25","doi-asserted-by":"publisher","first-page":"7437","DOI":"10.1039\/C8SC02859A","article-title":"Dihydrogen contacts observed by through-space indirect NMR coupling","volume":"9","year":"2018","journal-title":"Chem. Sci."},{"key":"2023081108123703300_c26","first-page":"421","volume-title":"Gaussian 16 Revision C. 01. 2016","year":"2016"},{"key":"2023081108123703300_c27","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.jmgm.2005.12.005","article-title":"Automatic atom type and bond type perception in molecular mechanical calculations","volume":"25","year":"2006","journal-title":"J. Mol. Graphics Modell."},{"key":"2023081108123703300_c28","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1002\/jcc.20035","article-title":"Development and testing of a general amber force field","volume":"25","year":"2004","journal-title":"J. Comput. Chem."},{"key":"2023081108123703300_c29","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1186\/1756-0500-5-367","article-title":"ACPYPE - AnteChamber PYthon Parser interfacE","volume":"5","year":"2012","journal-title":"BMC Res. Notes"},{"key":"2023081108123703300_c30","doi-asserted-by":"publisher","first-page":"3684","DOI":"10.1063\/1.448118","article-title":"Molecular dynamics with coupling to an external bath","volume":"81","year":"1984","journal-title":"J. Chem. Phys."},{"key":"2023081108123703300_c31","doi-asserted-by":"publisher","first-page":"014101","DOI":"10.1063\/1.2408420","article-title":"Canonical sampling through velocity rescaling","volume":"126","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023081108123703300_c32","doi-asserted-by":"publisher","first-page":"7182","DOI":"10.1063\/1.328693","article-title":"Polymorphic transitions in single crystals: A new molecular dynamics method","volume":"52","year":"1981","journal-title":"J. Appl. Phys."},{"key":"2023081108123703300_c33","doi-asserted-by":"publisher","first-page":"10089","DOI":"10.1063\/1.464397","article-title":"Particle mesh Ewald: An N\u00b7log(N) method for Ewald sums in large systems","volume":"98","year":"1993","journal-title":"J. Chem. Phys."},{"key":"2023081108123703300_c34","doi-asserted-by":"publisher","first-page":"1463","DOI":"10.1002\/(sici)1096-987x(199709)18:12&lt;1463::aid-jcc4&gt;3.0.co;2-h","article-title":"LINCS: A linear constraint solver for molecular simulations","volume":"18","year":"1997","journal-title":"J. Comput. Chem."},{"key":"2023081108123703300_c35","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.softx.2015.06.001","article-title":"GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers","volume":"1","year":"2015","journal-title":"SoftwareX"},{"key":"2023081108123703300_c36","doi-asserted-by":"publisher","first-page":"7260","DOI":"10.1103\/physrevb.58.7260","article-title":"Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties","volume":"58","year":"1998","journal-title":"Phys. Rev. B"},{"key":"2023081108123703300_c37","doi-asserted-by":"publisher","first-page":"10861","DOI":"10.1021\/jp074167r","article-title":"Extension of the self-consistent-charge density-functional tight-binding method: Third-order expansion of the density functional theory total energy and introduction of a modified effective Coulomb interaction","volume":"111","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"2023081108123703300_c38","doi-asserted-by":"publisher","first-page":"5678","DOI":"10.1021\/jp070186p","article-title":"DFTB+, a sparse matrix-based implementation of the DFTB method","volume":"111","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"2023081108123703300_c39","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1021\/ct300849w","article-title":"Parametrization and benchmark of DFTB3 for organic molecules","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023081108123703300_c40","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1021\/ct5009137","article-title":"Parameterization of the DFTB3 method for Br, Ca, Cl, F, I, K, and Na in organic and biological systems","volume":"11","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"2023081108123703300_c41","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1063\/1.447334","article-title":"A unified formulation of the constant temperature molecular dynamics methods","volume":"81","year":"1984","journal-title":"J. Chem. Phys."},{"key":"2023081108123703300_c42","doi-asserted-by":"publisher","first-page":"1695","DOI":"10.1103\/physreva.31.1695","article-title":"Canonical dynamics: Equilibrium phase-space distributions","volume":"31","year":"1985","journal-title":"Phys. Rev. A"},{"key":"2023081108123703300_c43","doi-asserted-by":"publisher","first-page":"154104","DOI":"10.1063\/1.3382344","article-title":"A consistent and accurate ab\u00a0initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu","volume":"132","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023081108123703300_c44","doi-asserted-by":"publisher","first-page":"184115","DOI":"10.1103\/physrevb.87.184115","article-title":"On representing chemical environments","volume":"87","year":"2013","journal-title":"Phys. Rev. B"},{"key":"2023081108123703300_c45","doi-asserted-by":"publisher","first-page":"154110","DOI":"10.1063\/1.5090481","article-title":"Atom-density representations for machine learning","volume":"150","year":"2019","journal-title":"J. Chem. Phys."},{"key":"2023081108123703300_c46","first-page":"95","article-title":"Vol. 1 (MIT Press, Cambridge, MA, 2006),","volume-title":"Gaussian Processes for Machine Learning,"},{"key":"2023081108123703300_c47","doi-asserted-by":"publisher","first-page":"106949","DOI":"10.1016\/j.cpc.2019.106949","article-title":"DScribe: Library of descriptors for machine learning in materials science","volume":"247","year":"2020","journal-title":"Comput. Phys. Commun."},{"key":"2023081108123703300_c48","article-title":"GPyTorch: Blackbox matrix-matrix Gaussian process inference with GPU acceleration","volume-title":"Advances in Neural Information Processing Systems","year":"2018"},{"key":"2023081108123703300_c49","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1561\/2200000073","article-title":"Computational optimal transport: With applications to data science","volume":"11","year":"2019","journal-title":"Found. Trends Mach. Learn."},{"key":"2023081108123703300_c50","volume-title":"Modern Multidimensional Scaling: Theory and Applications","year":"2005"},{"key":"2023081108123703300_c51","first-page":"2825","article-title":"Scikit-learn: Machine learning in Python","volume":"12","year":"2011","journal-title":"J. Mach. Learn. Res."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0147398\/17634741\/194108_1_5.0147398.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0147398\/17634741\/194108_1_5.0147398.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:12:58Z","timestamp":1691741578000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/158\/19\/194108\/2891394\/NMR-spectrum-prediction-for-dynamic-molecules-by"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,17]]},"references-count":50,"journal-issue":{"issue":"19","published-print":{"date-parts":[[2023,5,21]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0147398","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,5,21]]},"published":{"date-parts":[[2023,5,17]]},"article-number":"194108"}}