{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,9]],"date-time":"2024-11-09T05:16:32Z","timestamp":1731129392622,"version":"3.28.0"},"reference-count":73,"publisher":"Wiley","issue":"32","license":[{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["J Comput Chem"],"published-print":{"date-parts":[[2024,12,15]]},"abstract":"Abstract<\/jats:title>Closo<\/jats:italic>\u2010boron hydrides Bn<\/jats:italic><\/jats:sub>Hn<\/jats:italic><\/jats:sub>2\u2212<\/jats:sup> (n<\/jats:italic>\u2009=\u20095\u201312) are a conceptually well understood class of compounds. For these and a few related prototype compounds, both the local and the global picture of 3\u2010center bonding are extracted from position\u2010space quantities based on the electron density and the pair density. For this purpose, three\u2010center delocalization indices between quantum theory of atoms in molecules (QTAIM) atoms in position space are used to develop a consistent set of local bond and triangle, and global cluster delocalization ratios (DRs), which are quantitatively compared with conceptual \u0393 values derived from the styx<\/jats:italic> code for each cluster. Combination of the cluster DRs with associated effective numbers of skeletal electron sharing (SES) for selected cluster surface edges, triangles, or the whole cluster yields effective styx<\/jats:italic> type values describing the trend and even the size of the conceptual styx<\/jats:italic> codes for closo<\/jats:italic>\u2010boranes Bn<\/jats:italic><\/jats:sub>Hn<\/jats:italic><\/jats:sub>2\u2212<\/jats:sup> and related systems with increasing cluster size n<\/jats:italic> reasonably well. For nonuniform cluster topologies, the different vertex degrees are shown to cause systematic 3\u2010center wise bond delocalization effects for the associated edges and triangles of different average vertex degrees. Extension of DR analysis beyond the styx type triangular cluster\u2010surface bonding corresponds to a triangulation of multicentric bonding. The cluster\u2010wise results keep indicating consistency with the mixed 2\u2010 and 3\u2010center bonding approach. The successfully established chemical meaning of the local edge, triangle, and global cluster DR<\/jats:italic>s and their associated SES<\/jats:italic> values constitutes the basis for systematic investigations of mixed 2\u2010 and 3\u2010center bonding scenarios in particular in intermetallic and related (endohedral) cluster compounds in the future.<\/jats:p>","DOI":"10.1002\/jcc.27486","type":"journal-article","created":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T08:39:46Z","timestamp":1725007186000},"page":"2862-2877","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Delocalization\u2010ratio analysis of 3\u2010center bonding in position\u2010space for closo<\/i>\u2010boranes and related systems: Approaching the styx<\/i> picture and beyond"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-2382-2261","authenticated-orcid":false,"given":"Frank R.","family":"Wagner","sequence":"first","affiliation":[{"name":"Chemical Metals Science Max Planck Institute for Chemical Physics of Solids Dresden Germany"}]}],"member":"311","published-online":{"date-parts":[[2024,8,30]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1051\/jcp\/1949460268"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1740320"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1743672"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1021\/ic50103a018"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.196.4294.1047"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1039\/c29710000792"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-6054-4"},{"key":"e_1_2_8_6_3","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2792(08)60027-8"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1021\/ic50198a062"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1021\/ic50095a046"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1954.0162"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1021\/ic50159a034"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1038\/physci236099a0"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1021\/ar00105a003"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1021\/acs.inorgchem.4c01390"},{"key":"e_1_2_8_12_2","volume":"145","author":"Xu S.","year":"2023","journal-title":"J. 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