{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T23:57:36Z","timestamp":1770422256247,"version":"3.49.0"},"reference-count":260,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T00:00:00Z","timestamp":1697414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MEXT KAKENHI","award":["JP22H04916 (KY)"],"award-info":[{"award-number":["JP22H04916 (KY)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Molecules"],"abstract":"<jats:p>This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).<\/jats:p>","DOI":"10.3390\/molecules28207119","type":"journal-article","created":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T08:25:09Z","timestamp":1697531109000},"page":"7119","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Nature of the Chemical Bonds of High-Valent Transition\u2013Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl\u2013Radical Character by the Classical to Quantum Computations"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4411-7425","authenticated-orcid":false,"given":"Kizashi","family":"Yamaguchi","sequence":"first","affiliation":[{"name":"SANKEN, Osaka University, Ibaraki 567-0047, Osaka, Japan"},{"name":"Center for Quantum Information and Quantum Biology (QIQB), Osaka University, Toyonaka 560-0043, Osaka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1990-1904","authenticated-orcid":false,"given":"Hiroshi","family":"Isobe","sequence":"additional","affiliation":[{"name":"Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Okayama, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7465-6326","authenticated-orcid":false,"given":"Mitsuo","family":"Shoji","sequence":"additional","affiliation":[{"name":"Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Ibaraki, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takashi","family":"Kawakami","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka 560-0043, Osaka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7409-3727","authenticated-orcid":false,"given":"Koichi","family":"Miyagawa","sequence":"additional","affiliation":[{"name":"Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Ibaraki, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/0003-9861(58)90436-3","article-title":"Pigments of rat liver microsomes","volume":"75","author":"Klingenberg","year":"1958","journal-title":"Arch. 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