{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T11:55:21Z","timestamp":1792151721700,"version":"4.4.0"},"reference-count":62,"publisher":"AIP Publishing","issue":"15","funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0025352"],"award-info":[{"award-number":["DE-SC0025352"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0023509"],"award-info":[{"award-number":["DE-SC0023509"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,21]]},"abstract":"<jats:p>Minimum-energy paths and intrinsic reaction coordinates are central tools for analyzing chemical reactions. As one-dimensional objects, however, individual paths do not provide a continuous representation of the surrounding potential energy surface (PES), including the arrangement of adjacent valleys, ridges, and higher-order saddle regions. We introduce the nudged elastic membrane method, which constructs a two-dimensional reduced PES in a selected region of configuration space using energies and forces, without requiring Hessian evaluations. The method is demonstrated for a three-dimensional analytical model and for triplet formaldehyde. In both cases, the membrane recovers known reaction-path and stationary-point regions. For formaldehyde, it also reveals a previously unreported second-order saddle point on the fitted PES. Structures extracted from the membrane provide starting points for subsequent stationary-point refinement.<\/jats:p>","DOI":"10.1063\/5.0346317","type":"journal-article","created":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T11:26:21Z","timestamp":1792149981000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Nudged elastic membranes for constructing reduced two-dimensional potential energy surfaces"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-1147-9797","authenticated-orcid":false,"given":"Uday Sankar","family":"Manoj","sequence":"first","affiliation":[{"name":"Department of Chemistry, Pennsylvania State University 1 , University Park, Pennsylvania 16802,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-4888-2312","authenticated-orcid":false,"given":"Nicole","family":"Drew","sequence":"additional","affiliation":[{"name":"Department of Physics, Pennsylvania State University 2 , University Park, Pennsylvania 16802,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0742-030X","authenticated-orcid":false,"given":"Ismaila","family":"Dabo","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, Carnegie Mellon University 3 , 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0495-6774","authenticated-orcid":false,"given":"Lukas","family":"Muechler","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Pennsylvania State University 1 , University Park, Pennsylvania 16802,","place":["USA"]},{"name":"Department of Physics, Pennsylvania State University 2 , University Park, Pennsylvania 16802,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,16]]},"reference":[{"key":"2026101607261824600_c1","doi-asserted-by":"publisher","first-page":"2800","DOI":"10.1063\/1.442352","volume":"75","year":"1981","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c2","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/bf00549673","volume":"66","year":"1984","journal-title":"Theor. Chim. Acta"},{"key":"2026101607261824600_c3","doi-asserted-by":"publisher","first-page":"4161","DOI":"10.1021\/j100717a029","volume":"74","year":"1970","journal-title":"J.\u00a0Phys. Chem."},{"key":"2026101607261824600_c4","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1142\/9789812839664_0016","volume-title":"Classical and Quantum Dynamics in Condensed Phase Simulations","year":"1998"},{"key":"2026101607261824600_c5","doi-asserted-by":"publisher","first-page":"7010","DOI":"10.1063\/1.480097","volume":"111","year":"1999","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c6","doi-asserted-by":"publisher","first-page":"7877","DOI":"10.1063\/1.1691018","volume":"120","year":"2004","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c7","doi-asserted-by":"publisher","first-page":"1514","DOI":"10.1002\/jcc.10231","volume":"24","year":"2003","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026101607261824600_c8","doi-asserted-by":"publisher","first-page":"e1354","DOI":"10.1002\/wcms.1354","volume":"8","year":"2018","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026101607261824600_c9","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1146\/annurev-physchem-050317-020929","volume":"71","year":"2020","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2026101607261824600_c10","doi-asserted-by":"publisher","first-page":"044303","DOI":"10.1063\/1.2202241","volume":"125","year":"2006","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c11","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1515\/pac-2017-0104","volume":"89","year":"2017","journal-title":"Pure Appl. Chem."},{"key":"2026101607261824600_c12","doi-asserted-by":"publisher","first-page":"8937","DOI":"10.1039\/c8sc02653j","volume":"9","year":"2018","journal-title":"Chem. Sci."},{"key":"2026101607261824600_c13","doi-asserted-by":"publisher","first-page":"12837","DOI":"10.1039\/c9cp02431j","volume":"21","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026101607261824600_c14","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1039\/d2fd00026a","volume":"238","year":"2022","journal-title":"Faraday Discuss."},{"key":"2026101607261824600_c15","doi-asserted-by":"publisher","first-page":"205101","DOI":"10.1088\/1751-8113\/42\/20\/205101","volume":"42","year":"2009","journal-title":"J.\u00a0Phys. A: Math. Theor."},{"key":"2026101607261824600_c16","doi-asserted-by":"publisher","first-page":"20906","DOI":"10.1039\/c1cp22565k","volume":"13","year":"2011","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026101607261824600_c17","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1038\/nchem.1843","volume":"6","year":"2014","journal-title":"Nat. Chem."},{"key":"2026101607261824600_c18","doi-asserted-by":"publisher","first-page":"7592","DOI":"10.1002\/anie.200800918","volume":"47","year":"2008","journal-title":"Angew. Chem., Int. Ed."},{"key":"2026101607261824600_c19","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/bf00532206","volume":"70","year":"1986","journal-title":"Theor. Chim. Acta"},{"key":"2026101607261824600_c20","doi-asserted-by":"publisher","first-page":"6931","DOI":"10.1016\/j.tetlet.2015.10.092","volume":"56","year":"2015","journal-title":"Tetrahedron Lett."},{"key":"2026101607261824600_c21","doi-asserted-by":"publisher","first-page":"e202400786","DOI":"10.1002\/cphc.202400786","volume":"26","year":"2025","journal-title":"ChemPhysChem"},{"key":"2026101607261824600_c22","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1080\/00268970410001703363","volume":"102","year":"2004","journal-title":"Mol. Phys."},{"key":"2026101607261824600_c23","doi-asserted-by":"publisher","first-page":"3285","DOI":"10.1080\/00268970210162691","volume":"100","year":"2002","journal-title":"Mol. Phys."},{"key":"2026101607261824600_c24","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1080\/01442350600676921","volume":"25","year":"2006","journal-title":"Int. Rev. Phys. Chem."},{"key":"2026101607261824600_c25","doi-asserted-by":"publisher","first-page":"2661","DOI":"10.1021\/acs.jctc.9b01211","volume":"16","year":"2020","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026101607261824600_c26","doi-asserted-by":"publisher","first-page":"234901","DOI":"10.1063\/1.2135783","volume":"123","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c27","doi-asserted-by":"publisher","first-page":"234903","DOI":"10.1063\/1.1931587","volume":"122","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c28","doi-asserted-by":"publisher","first-page":"4018","DOI":"10.1021\/jacs.7b12896","volume":"140","year":"2018","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026101607261824600_c29","doi-asserted-by":"publisher","first-page":"16005","DOI":"10.1021\/ja075346p","volume":"129","year":"2007","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026101607261824600_c30","doi-asserted-by":"publisher","first-page":"2082","DOI":"10.1063\/1.1636455","volume":"120","year":"2004","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c31","doi-asserted-by":"publisher","first-page":"7820","DOI":"10.1063\/1.1691408","volume":"120","year":"2004","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c32","doi-asserted-by":"publisher","first-page":"134106","DOI":"10.1063\/1.2841941","volume":"128","year":"2008","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c33","doi-asserted-by":"publisher","first-page":"e1000415","DOI":"10.1371\/journal.pcbi.1000415","volume":"5","year":"2009","journal-title":"PLoS Comput. Biol."},{"key":"2026101607261824600_c34","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1146\/annurev-physchem-050317-021219","volume":"69","year":"2018","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2026101607261824600_c35","doi-asserted-by":"publisher","first-page":"1800175","DOI":"10.1002\/adts.201800175","volume":"2","year":"2019","journal-title":"Adv. Theory Simul."},{"key":"2026101607261824600_c36","doi-asserted-by":"publisher","first-page":"130901","DOI":"10.1063\/1.4916307","volume":"142","year":"2015","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c37","doi-asserted-by":"publisher","first-page":"070902","DOI":"10.1063\/1.5109531","volume":"151","year":"2019","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c38","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1146\/annurev-physchem-083122-125941","volume":"75","year":"2024","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2026101607261824600_c39","doi-asserted-by":"publisher","first-page":"e1398","DOI":"10.1002\/wcms.1398","volume":"9","year":"2019","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026101607261824600_c40","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1039\/d1cy01329g","volume":"12","year":"2022","journal-title":"Catal. Sci. Technol."},{"key":"2026101607261824600_c41","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.checat.2021.04.009","volume":"1","year":"2021","journal-title":"Chem Catal."},{"key":"2026101607261824600_c42","doi-asserted-by":"publisher","first-page":"2735","DOI":"10.1021\/acs.jctc.2c01271","volume":"19","year":"2023","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026101607261824600_c43","doi-asserted-by":"publisher","first-page":"4050","DOI":"10.1021\/acs.jctc.0c00172","volume":"16","year":"2020","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026101607261824600_c44","doi-asserted-by":"publisher","first-page":"e70329","DOI":"10.1002\/jcc.70329","volume":"47","year":"2026","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026101607261824600_c45","doi-asserted-by":"publisher","first-page":"13942","DOI":"10.1039\/d0cp02379e","volume":"22","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026101607261824600_c46","volume-title":"Topics in Current Chemistry","year":"2022"},{"key":"2026101607261824600_c47","doi-asserted-by":"publisher","first-page":"241102","DOI":"10.1063\/1.3457903","volume":"132","year":"2010","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c48","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1246\/bcsj.20140189","volume":"87","year":"2014","journal-title":"Bull. Chem. Soc. Jpn."},{"key":"2026101607261824600_c49","doi-asserted-by":"publisher","first-page":"9978","DOI":"10.1063\/1.1323224","volume":"113","year":"2000","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c50","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1002\/nla.1839","volume":"20","year":"2013","journal-title":"Numer. Linear Algebra Appl."},{"key":"2026101607261824600_c51","doi-asserted-by":"publisher","first-page":"170201","DOI":"10.1103\/physrevlett.97.170201","volume":"97","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"2026101607261824600_c52","doi-asserted-by":"publisher","first-page":"109584","DOI":"10.1016\/j.commatsci.2020.109584","volume":"175","year":"2020","journal-title":"Comput. Mater. Sci."},{"key":"2026101607261824600_c53","doi-asserted-by":"publisher","first-page":"015323","DOI":"10.1063\/5.0082185","volume":"12","year":"2022","journal-title":"AIP Adv."},{"key":"2026101607261824600_c54","doi-asserted-by":"publisher","first-page":"3250","DOI":"10.1021\/acs.jctc.7b00360","volume":"13","year":"2017","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026101607261824600_c55","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.commatsci.2018.09.049","volume":"156","year":"2019","journal-title":"Comput. Mater. Sci."},{"key":"2026101607261824600_c56","doi-asserted-by":"publisher","first-page":"094107","DOI":"10.1063\/1.4961868","volume":"145","year":"2016","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026101607261824600_c57","doi-asserted-by":"publisher","first-page":"9635","DOI":"10.1021\/acs.jpca.3c05899","volume":"127","year":"2023","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2026101607261824600_c58","doi-asserted-by":"publisher","first-page":"4543","DOI":"10.1021\/acs.jpca.9b02298","volume":"123","year":"2019","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2026101607261824600_c59","doi-asserted-by":"publisher","first-page":"23280","DOI":"10.1039\/c7cp04578f","volume":"19","year":"2017","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026101607261824600_c60","doi-asserted-by":"publisher","first-page":"3641","DOI":"10.1021\/acs.jpclett.6b01637","volume":"7","year":"2016","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026101607261824600_c61","doi-asserted-by":"publisher","first-page":"e26390","DOI":"10.1002\/qua.26390","volume":"121","year":"2021","journal-title":"Int. J. Quantum Chem."},{"key":"2026101607261824600_c62","doi-asserted-by":"publisher","first-page":"5281","DOI":"10.1063\/1.476315","volume":"108","year":"1998","journal-title":"J.\u00a0Chem. Phys."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0346317\/21172662\/154105_1_5.0346317.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0346317\/21172662\/154105_1_5.0346317.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T11:26:23Z","timestamp":1792149983000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/165\/15\/154105\/3406670\/Nudged-elastic-membranes-for-constructing-reduced"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,16]]},"references-count":62,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2026,10,21]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0346317","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10,21]]},"published":{"date-parts":[[2026,10,16]]},"article-number":"154105"}}