{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T13:59:02Z","timestamp":1781531942280,"version":"3.54.5"},"reference-count":65,"publisher":"AIP Publishing","issue":"7","funder":[{"name":"Conselleria de Educacion, Ciencia, Universidades e Formacion Profesional","award":["ED431G 2023\/03"],"award-info":[{"award-number":["ED431G 2023\/03"]}]},{"name":"Conselleria de Educacion, Ciencia, Universidades e Formacion Profesional","award":["ED431C 2025\/06"],"award-info":[{"award-number":["ED431C 2025\/06"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,2,21]]},"abstract":"<jats:p>We present a general framework to construct and systematically search for ring conformations based on Cremer\u2013Pople (CP) coordinates. To our knowledge, this is the first algorithm that provides reasonable ring geometries across different ring sizes from arbitrary CP coordinates. A two-stage ring reconstruction algorithm is proposed: (i) projecting the molecule in the xy plane and enforcing ring closure while preserving bond lengths, and (ii) redistributing angular distortions across the ring via constrained minimization to achieve chemically viable conformations. The approach is extended to rings with rigid (multiple) bonds through a rigorous ring-reduction scheme that lowers puckering dimensionality and incorporates local stiffness via adjustable parameters, allowing for straightforward recovery of the full structure. In addition, the positions of the substituents attached to the ring are deduced from invariant local references. To systematically explore the conformational space, we formulate a preconditioned sampling of CP amplitudes as a function of hyperspherical coordinates. In addition, the concept of basis conformations is examined to ensure the unambiguous identification of conformers. Applications to saturated and unsaturated rings with up to eight atoms at the \u03c9B97X-D\/def2-TZVPP level demonstrate accurate recovery and classification of known conformers, including correct symmetry multiplicities. Overall, this framework offers a robust and general route to generate high-quality starting geometries for subsequent electronic structure optimizations, while facilitating efficient exploration of puckering space.<\/jats:p>","DOI":"10.1063\/5.0315467","type":"journal-article","created":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T11:52:37Z","timestamp":1771501957000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["A general method for constructing and searching conformations in molecular rings: From Cremer\u2013Pople coordinates to 3D geometries"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4046-7110","authenticated-orcid":false,"given":"Anxo","family":"Lema-Saavedra","sequence":"first","affiliation":[{"name":"Centro Singular de Investigaci\u00f3n en Qu\u00edmica Biol\u00f3xica e Materiais Moleculares (CIQUS), C\/ Jenaro de la Fuente s\/n, Universidade de Santiago de Compostela 1 , 15782 Santiago de Compostela,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6468-1592","authenticated-orcid":false,"given":"Antonio","family":"Fern\u00e1ndez-Ramos","sequence":"additional","affiliation":[{"name":"Centro Singular de Investigaci\u00f3n en Qu\u00edmica Biol\u00f3xica e Materiais Moleculares (CIQUS), C\/ Jenaro de la Fuente s\/n, Universidade de Santiago de Compostela 1 , 15782 Santiago de Compostela,","place":["Spain"]},{"name":"Departamento de Qu\u00edmica F\u00edsica, Avda. das Ciencias s\/n, Universidade de Santiago de Compostela 2 , 15782 Santiago de Compostela,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,2,19]]},"reference":[{"key":"2026021906523365300_c1","volume-title":"Conformational Analysis","year":"1965"},{"key":"2026021906523365300_c2","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1002\/wcms.96","volume":"2","year":"2012","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2026021906523365300_c3","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1021\/ar2001765","volume":"45","year":"2012","journal-title":"Acc. Chem. Res."},{"key":"2026021906523365300_c4","doi-asserted-by":"publisher","first-page":"1356","DOI":"10.1021\/ct3010722","volume":"9","year":"2013","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026021906523365300_c5","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1007\/s40828-015-0014-0","volume":"1","year":"2015","journal-title":"ChemTexts"},{"key":"2026021906523365300_c6","doi-asserted-by":"publisher","first-page":"7169","DOI":"10.1039\/c9cp06869d","volume":"22","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026021906523365300_c7","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1186\/s13321-021-00578-0","volume":"13","year":"2021","journal-title":"J.\u00a0Cheminform."},{"key":"2026021906523365300_c8","doi-asserted-by":"publisher","first-page":"e1583","DOI":"10.1002\/wcms.1583","volume":"12","year":"2022","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2026021906523365300_c9","doi-asserted-by":"publisher","first-page":"114110","DOI":"10.1063\/5.0197592","volume":"160","year":"2024","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021906523365300_c10","doi-asserted-by":"publisher","first-page":"2483","DOI":"10.1021\/ja01202a069","volume":"69","year":"1947","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c11","doi-asserted-by":"publisher","first-page":"7281","DOI":"10.1021\/ja00728a009","volume":"92","year":"1970","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c12","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1063\/1.1675525","volume":"55","year":"1971","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021906523365300_c13","doi-asserted-by":"publisher","first-page":"1354","DOI":"10.1021\/ja00839a011","volume":"97","year":"1975","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c14","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1107\/S0108768184002391","volume":"40","year":"1984","journal-title":"Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater."},{"key":"2026021906523365300_c15","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1107\/S0108768183003110","volume":"39","year":"1983","journal-title":"Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater."},{"key":"2026021906523365300_c16","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1107\/s0108768184002548","volume":"40","year":"1984","journal-title":"Acta Crystallogr., Sect. B: Struct. Sci."},{"key":"2026021906523365300_c17","doi-asserted-by":"publisher","first-page":"5502","DOI":"10.1021\/j100377a017","volume":"94","year":"1990","journal-title":"J.\u00a0Phys. Chem."},{"key":"2026021906523365300_c18","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.1016\/s0040-4039(00)71589-9","volume":"8","year":"1967","journal-title":"Tetrahedron Lett."},{"key":"2026021906523365300_c19","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/0040-4020(68)89003-9","volume":"24","year":"1968","journal-title":"Tetrahedron"},{"key":"2026021906523365300_c20","doi-asserted-by":"publisher","first-page":"8205","DOI":"10.1021\/ja00778a043","volume":"94","year":"1972","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c21","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1107\/s0108768189008189","volume":"45","year":"1989","journal-title":"Acta Crystallogr., Sect. B: Struct. Sci."},{"key":"2026021906523365300_c22","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1107\/S0108768189008189","volume":"45","year":"1989","journal-title":"Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater."},{"key":"2026021906523365300_c23","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1107\/S0108768189008190","volume":"45","year":"1989","journal-title":"Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater."},{"key":"2026021906523365300_c24","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1002\/poc.610030304","volume":"3","year":"1990","journal-title":"J.\u00a0Phys. Org. Chem."},{"key":"2026021906523365300_c25","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1021\/ci960115f","volume":"37","year":"1997","journal-title":"J.\u00a0Chem. Inf. Comput. Sci."},{"key":"2026021906523365300_c26","doi-asserted-by":"publisher","first-page":"10440","DOI":"10.1021\/j100092a010","volume":"98","year":"1994","journal-title":"J.\u00a0Phys. Chem."},{"key":"2026021906523365300_c27","doi-asserted-by":"publisher","first-page":"1526","DOI":"10.1002\/jcc.26559","volume":"42","year":"2021","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026021906523365300_c28","doi-asserted-by":"publisher","first-page":"4280","DOI":"10.1021\/acs.jctc.9b00363","volume":"15","year":"2019","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026021906523365300_c29","doi-asserted-by":"publisher","first-page":"2646","DOI":"10.1021\/acs.jpca.3c00095","volume":"127","year":"2023","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2026021906523365300_c30","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1021\/acs.jcim.0c01144","volume":"61","year":"2021","journal-title":"J.\u00a0Chem. Inf. Model."},{"key":"2026021906523365300_c31","doi-asserted-by":"publisher","first-page":"154107","DOI":"10.1063\/1.5144278","volume":"152","year":"2020","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021906523365300_c32","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1090\/qam\/10667","volume":"2","year":"1944","journal-title":"Q. Appl. Math."},{"key":"2026021906523365300_c33","unstructured":"S.\n            Ruder\n          , arXiv:1609.04747 (2023)."},{"key":"2026021906523365300_c34","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","volume":"17","year":"2020","journal-title":"Nat. Methods"},{"key":"2026021906523365300_c35","doi-asserted-by":"publisher","first-page":"8190","DOI":"10.1039\/b925388b","volume":"12","year":"2010","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026021906523365300_c36","doi-asserted-by":"publisher","first-page":"2374","DOI":"10.1039\/b718588j","volume":"10","year":"2008","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026021906523365300_c37","doi-asserted-by":"publisher","first-page":"4941","DOI":"10.1063\/1.1701743","volume":"47","year":"1967","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021906523365300_c38","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/s0022-2860(98)00421-9","volume":"445","year":"1998","journal-title":"J.\u00a0Mol. Struct."},{"key":"2026021906523365300_c39","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1002\/ijch.198000048","volume":"20","year":"1980","journal-title":"Isr. J. Chem."},{"key":"2026021906523365300_c40","volume-title":"Nomenclature of Organic Chemistry","year":"1993"},{"key":"2026021906523365300_c41","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1021\/ja00837a001","volume":"97","year":"1975","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c42","doi-asserted-by":"publisher","first-page":"124114","DOI":"10.1063\/5.0287590","volume":"163","year":"2025","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021906523365300_c43","doi-asserted-by":"publisher","first-page":"14084","DOI":"10.1002\/chem.201403379","volume":"20","year":"2014","journal-title":"Chem. Eur. J."},{"key":"2026021906523365300_c44","doi-asserted-by":"publisher","first-page":"6615","DOI":"10.1039\/b810189b","volume":"10","year":"2008","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026021906523365300_c45","doi-asserted-by":"publisher","first-page":"3297","DOI":"10.1039\/b508541a","volume":"7","year":"2005","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026021906523365300_c46","year":"2016"},{"key":"2026021906523365300_c47","unstructured":"A. Lema-Saavedra and A.Fern\u00e1ndez-Ramos (2025). \u201cA general method for constructing and searching conformations in molecular rings: From Cremer\u2013Pople coordinates to 3D geometries,\u201d Zenodo. https:\/\/doi.org\/10.5281\/zenodo.17831714"},{"key":"2026021906523365300_c48","doi-asserted-by":"publisher","first-page":"4570","DOI":"10.1021\/jp811208g","volume":"113","year":"2009","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2026021906523365300_c49","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1002\/jcc.540050405","volume":"5","year":"1984","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026021906523365300_c50","doi-asserted-by":"publisher","first-page":"9322","DOI":"10.1021\/jo030227n","volume":"68","year":"2003","journal-title":"J.\u00a0Org. Chem."},{"key":"2026021906523365300_c51","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/bf02741995","volume":"41","year":"2000","journal-title":"J.\u00a0Struct. Chem."},{"key":"2026021906523365300_c52","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/0166-1280(82)80039-0","volume":"87","year":"1982","journal-title":"J.\u00a0Mol. Struct.: THEOCHEM"},{"key":"2026021906523365300_c53","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/0166-1280(83)80097-9","volume":"93","year":"1983","journal-title":"J.\u00a0Mol. Struct.: THEOCHEM"},{"key":"2026021906523365300_c54","doi-asserted-by":"publisher","first-page":"5774","DOI":"10.1021\/ja01049a013","volume":"91","year":"1969","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c55","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1007\/s11224-011-9921-x","volume":"23","year":"2012","journal-title":"Struct. Chem."},{"key":"2026021906523365300_c56","doi-asserted-by":"publisher","first-page":"7814","DOI":"10.1021\/ja00493a005","volume":"100","year":"1978","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c57","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/s0166-1280(02)00714-5","volume":"623","year":"2003","journal-title":"J.\u00a0Mol. Struct.: THEOCHEM"},{"key":"2026021906523365300_c58","doi-asserted-by":"publisher","first-page":"3964","DOI":"10.1021\/ja00429a036","volume":"98","year":"1976","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026021906523365300_c59","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1002\/(sici)1096-987x(19970130)18:2&lt;254::aid-jcc9&gt;3.0.co;2-u","volume":"18","year":"1997","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026021906523365300_c60","doi-asserted-by":"publisher","first-page":"10236","DOI":"10.1021\/jo202176j","volume":"76","year":"2011","journal-title":"J.\u00a0Org. Chem."},{"key":"2026021906523365300_c61","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/s0166-1280(01)00603-0","volume":"577","year":"2002","journal-title":"J.\u00a0Mol. Struct.: THEOCHEM"},{"key":"2026021906523365300_c62","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1002\/qua.21486","volume":"108","year":"2008","journal-title":"Int. J. Quantum Chem."},{"key":"2026021906523365300_c63","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1007\/bf00807573","volume":"127","year":"1996","journal-title":"Monatsh. Chem."},{"key":"2026021906523365300_c64","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1007\/s11224-012-0192-y","volume":"24","year":"2013","journal-title":"Struct. Chem."},{"key":"2026021906523365300_c65","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1021\/jo00027a051","volume":"57","year":"1992","journal-title":"J.\u00a0Org. Chem."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0315467\/20910001\/074109_1_5.0315467.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0315467\/20910001\/074109_1_5.0315467.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T11:52:39Z","timestamp":1771501959000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/164\/7\/074109\/3380416\/A-general-method-for-constructing-and-searching"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,19]]},"references-count":65,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,2,21]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0315467","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,2,21]]},"published":{"date-parts":[[2026,2,19]]},"article-number":"074109"}}