{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T20:34:44Z","timestamp":1780086884515,"version":"3.54.0"},"reference-count":48,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:00:00Z","timestamp":1777420800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:00:00Z","timestamp":1777420800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["J Comput Chem"],"published-print":{"date-parts":[[2026,4,30]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>\n                    This work establishes partial \u03c3\u2010covalent bonding as a general electronic phenomenon extending from main\u2010group biradicals to d\n                    <jats:sup>8<\/jats:sup>\n                    \u2013d\n                    <jats:sup>8<\/jats:sup>\n                    transition\u2010metal systems (Co(I), Rh(I), Ir(I)). Using dispersion\u2010corrected DFT (B3LYP\u2010D3\/def2\u2010TZVP for transition metals and 6\u201031+G(d) for other elements) in combination with Wiberg bond index and frontier molecular orbital analyses, we show that partial \u03c3\u2010bonding is strongly governed by ligand field and orbital symmetry. While shorter metal\u2013metal distances correlate with larger bond orders, singlet\u2013triplet energetic differences arise from competition between ligand\u2010field splitting and exchange energy and spin\u2010orbit coupling. Compared to isolated metal\u2013metal ion dimers at the same distance, both ligand types in the study modify not only the orbital characters but also the frontier orbital energy levels. Strong field C\u2010donor ligands significantly widen the HOMO\u2013LUMO gap while changing orbital ordering so that the HOMO has d\n                    <jats:sub>z<\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    \u2013d\n                    <jats:sub>z<\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    antibonding character and the LUMO has a bonding p\n                    <jats:sub>z<\/jats:sub>\n                    \u2013p\n                    <jats:sub>z<\/jats:sub>\n                    orbital. Consequently, it leads to triplet\u2010dominant metal\u2013metal bonding, (WBO\n                    <jats:sub>Triplet<\/jats:sub>\n                    \u2009=\u20090.4;\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>M\u2013M<\/jats:sub>\n                    \u2009=\u20092.9\u2009\u00c5). In contrast, N\u2010donor lantern organic frameworks (LOFs) narrow the HOMO\u2013LUMO gap while alternating orbital ordering so that the HOMO becomes the ligand\u2010based bonding \u03c0\u2010orbital and the LUMO corresponds to a d\n                    <jats:sub>z<\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    \u2013d\n                    <jats:sub>z<\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    antibonding orbital, thereby enabling substantial \u03c3\u2010bonding in both spin states (WBO\n                    <jats:sub>Triplet<\/jats:sub>\n                    \u2009=\u20090.3 with\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>M\u2013M<\/jats:sub>\n                    \u2009=\u20093.1\u2009\u00c5; and WBO\n                    <jats:sub>Singlet<\/jats:sub>\n                    \u2009=\u20090.7 with\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>M\u2013M<\/jats:sub>\n                    \u2009=\u20092.7\u2009\u00c5). More importantly, N\u2010donor LOF environments significantly reduce the HOMO\u2013LUMO gap up to 2.00\u2009eV relative to comparable conventional systems, suggests a viable strategy for band gap engineering at the single\u2010unit\u2010cell level, without requiring infinite stacking.\n                  <\/jats:p>","DOI":"10.1002\/jcc.70373","type":"journal-article","created":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:29:37Z","timestamp":1777454977000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Partial Sigma Covalent Bonding in Transition Metals"],"prefix":"10.1002","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3347-4379","authenticated-orcid":false,"given":"Lam H.","family":"Nguyen","sequence":"first","affiliation":[{"name":"Department of Chemistry University of Utah  Salt Lake City Utah USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1832-1526","authenticated-orcid":false,"given":"Thanh N.","family":"Truong","sequence":"additional","affiliation":[{"name":"Department of Chemistry University of Utah  Salt Lake City Utah USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,4,29]]},"reference":[{"issue":"2","key":"e_1_2_10_2_1","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1021\/ja00158a061","article-title":"A Body\u2010Diagonal Bond in Cubane: Can It Be Introduced?","volume":"112","author":"Hassenruck K.","year":"1990","journal-title":"Journal of the American Chemical Society"},{"issue":"8","key":"e_1_2_10_3_1","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1002\/anie.200390241","article-title":"[Ge8{N(SiMe3)2}6]: A Ligand\u2010Stabilized Ge Cluster Compound With Formally Zero\u2010Valent Ge Atoms","volume":"42","author":"Schnepf A.","year":"2003","journal-title":"Angewandte Chemie International Edition"},{"key":"e_1_2_10_4_1","doi-asserted-by":"crossref","first-page":"3277","DOI":"10.1039\/b508379f","article-title":"Ge8R6: The Ligands Define the Bonding Situation Within the Cluster Core","volume":"20","author":"Schnepf A.","year":"2005","journal-title":"Dalton Transactions"},{"issue":"7","key":"e_1_2_10_5_1","doi-asserted-by":"crossref","DOI":"10.1002\/ijch.202300062","article-title":"Bonding Analysis of the Ge\uf8ffGe Bonds in the Octagermacubane Ge8(Sit\u2010butyl2methyl)6","volume":"63","author":"Pan S.","year":"2023","journal-title":"Israel Journal of Chemistry"},{"issue":"5","key":"e_1_2_10_6_1","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/s00214-019-2458-6","article-title":"Nature of Interlayer Carbon\u2013Carbon Covalent Bonding in Graphene\u2010Based Materials","volume":"138","author":"Nguyen H. 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