{"id":19472,"date":"2018-03-04T08:36:14","date_gmt":"2018-03-04T08:36:14","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=19472"},"modified":"2018-03-07T20:16:02","modified_gmt":"2018-03-07T20:16:02","slug":"what-are-the-highest-bond-indices-for-main-group-and-transition-group-elements","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472","title":{"rendered":"What are the highest bond indices for main group and transition group elements?"},"content":{"rendered":"
\n

A bond index (BI) approximately measures the totals of the bond orders at any given atom in a molecule. Here I ponder what the maximum values might be for elements with filled valence shells.<\/p>\n

Following Lewis in 1916[1]<\/a><\/span> who proposed that the full valence shell for main group elements should be 2 (for the first two elements) and 8 (the “octet<\/em>“), Bohr (1922[2]<\/a><\/span>), Langmuir (1919-1921[3]<\/a><\/span>) and Bury (1921[4]<\/a><\/span>) extended this rule to include 18 (the transition series) and 32 (the lanthanides and actinides). If we assume no contributions from higher Rydberg shells (thus 3s, 3p, 3d for carbon etc) and an electron pair model for orbital population (which amounts to the single-determinantal model), then the maximum bond index for hydrogen (and helium) would be 1, it would be 4 for main group elements, and then what?<\/p>\n

For the special case of hydrogen, I have previously identified<\/a>\u00a0(for a hypothetical species) a bond index of 1.33, due mostly to a high Rydberg occupancy of 1.19e. The more normal BI is <1.0, as noted for this hexacoordinated hydride<\/a> system.\u00a0My current estimate for the maximum bond index for main group elements is <4.5. Thus for SF6<\/sub>, it has the value of ~4.33 and that includes a modest occupancy of Rydberg shells of 0.36e = 0.18 BI. Exclude these and it is close to 4.<\/p>\n

Move on from group 16 to group 6 and you get compounds such as\u00a0Me4<\/sub>CrCrMe4<\/sub>4-<\/sup> or ReMe8<\/sub>2-\u00a0<\/sup>where the metal bond indices are ~6.5.\u2021<\/sup> Compounds such as Cr(Me)6 <\/sub>(BI = 5.6)\u00a0 <\/b>and\u00a0W(Me)6\u00a0<\/sub>(BI = 6.1) are rather lower.\u00a0This is a long way from 18\/2 = 9. The lanthanides and actinides[5]<\/a><\/span> are unlikely to reveal many large BIs (32\/2= 16 maximum value) since they are often ionic<\/a> and the wavefunctions may be too complex to allow a simple index such as a BI to be safely computed.<\/p>\n

So if we are hunting for record BIs, the transition elements are the place to hunt. Can a BI of 6.5 be beaten? Can it even approach 9, its maximum value? Does anyone know of candidate molecules?\u00a0<\/p>\n

\n

\u2021<\/sup>FAIR Data doi: 10.14469\/hpc\/3352<\/a>.<\/p>\n

References<\/h2>\n
  1. G.N. Lewis, \"THE ATOM AND THE MOLECULE.\", Journal of the American Chemical Society<\/i>, vol. 38, pp. 762-785, 1916. https:\/\/doi.org\/10.1021\/ja02261a002<\/a>\n\n<\/li>\n
  2. N. Bohr, \"Der Bau der Atome und die physikalischen und chemischen Eigenschaften der Elemente\", Zeitschrift f\ufffdr Physik<\/i>, vol. 9, pp. 1-67, 1922. https:\/\/doi.org\/10.1007\/bf01326955<\/a>\n\n<\/li>\n
  3. I. Langmuir, \"Types of Valence\", Science<\/i>, vol. 54, pp. 59-67, 1921. https:\/\/doi.org\/10.1126\/science.54.1386.59<\/a>\n\n<\/li>\n
  4. C.R. Bury, \"LANGMUIR'S THEORY OF THE ARRANGEMENT OF ELECTRONS IN ATOMS AND MOLECULES.\", Journal of the American Chemical Society<\/i>, vol. 43, pp. 1602-1609, 1921. https:\/\/doi.org\/10.1021\/ja01440a023<\/a>\n\n<\/li>\n
  5. P. Pyykk\u00f6, C. Clavagu\u00e9ra, and J. Dognon, \"The 32\u2010Electron Principle\", Computational Methods in Lanthanide and Actinide Chemistry<\/i>, pp. 401-424, 2015. https:\/\/doi.org\/10.1002\/9781118688304.ch15<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    A bond index (BI) approximately measures the totals of the bond orders at any given atom in a molecule. Here I ponder what the maximum values might be for elements with filled valence shells. Following Lewis in 1916 who proposed that the full valence shell for main group elements should be 2 (for the first […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":5,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[4],"tags":[2012,1402,557,558,1395,2386,1966,1871,1512,2385,1559,2384,1634,1851],"ppma_author":[2661],"class_list":["post-19472","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry","tag-atom","tag-chemical-bond","tag-chemical-bonding","tag-chemical-properties","tag-chemistry","tag-metal-bond-indices","tag-molecule","tag-nature","tag-quantum-chemistry","tag-residential-reits","tag-resonance","tag-tennessine","tag-valence","tag-valence-electron"],"yoast_head":"\nWhat are the highest bond indices for main group and transition group elements? - Henry Rzepa's Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What are the highest bond indices for main group and transition group elements? - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"A bond index (BI) approximately measures the totals of the bond orders at any given atom in a molecule. Here I ponder what the maximum values might be for elements with filled valence shells. Following Lewis in 1916 who proposed that the full valence shell for main group elements should be 2 (for the first […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa's Blog\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-04T08:36:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-03-07T20:16:02+00:00\" \/>\n<meta name=\"author\" content=\"Henry Rzepa\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Henry Rzepa\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"What are the highest bond indices for main group and transition group elements? - Henry Rzepa's Blog","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472","og_locale":"en_GB","og_type":"article","og_title":"What are the highest bond indices for main group and transition group elements? - Henry Rzepa's Blog","og_description":"A bond index (BI) approximately measures the totals of the bond orders at any given atom in a molecule. Here I ponder what the maximum values might be for elements with filled valence shells. Following Lewis in 1916 who proposed that the full valence shell for main group elements should be 2 (for the first […]","og_url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472","og_site_name":"Henry Rzepa's Blog","article_published_time":"2018-03-04T08:36:14+00:00","article_modified_time":"2018-03-07T20:16:02+00:00","author":"Henry Rzepa","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Henry Rzepa","Estimated reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472#article","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472"},"author":{"name":"Henry Rzepa","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"headline":"What are the highest bond indices for main group and transition group elements?","datePublished":"2018-03-04T08:36:14+00:00","dateModified":"2018-03-07T20:16:02+00:00","mainEntityOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472"},"wordCount":358,"commentCount":0,"keywords":["Atom","Chemical bond","chemical bonding","chemical properties","Chemistry","metal bond indices","Molecule","Nature","Quantum chemistry","Residential REITs","Resonance","Tennessine","Valence","Valence electron"],"articleSection":["Interesting chemistry"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472#respond"]}]},{"@type":"WebPage","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472","name":"What are the highest bond indices for main group and transition group elements? - Henry Rzepa's Blog","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website"},"datePublished":"2018-03-04T08:36:14+00:00","dateModified":"2018-03-07T20:16:02+00:00","author":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"breadcrumb":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19472#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog"},{"@type":"ListItem","position":2,"name":"What are the highest bond indices for main group and transition group elements?"}]},{"@type":"WebSite","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/","name":"Henry Rzepa's Blog","description":"Chemistry with a twist","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"},{"@type":"Person","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281","name":"Henry Rzepa","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g370be3a7397865e4fd161aefeb0a5a85","url":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g","caption":"Henry Rzepa"},"description":"Henry Rzepa is Emeritus Professor of Computational Chemistry at Imperial College London.","sameAs":["https:\/\/orcid.org\/0000-0002-8635-8390"],"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?author=1"}]}},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pDef7-544","jetpack-related-posts":[{"id":19499,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19499","url_meta":{"origin":19472,"position":0},"title":"Never mind main group “hypervalency”, what about transition metal “hypervalency”?","author":"Henry Rzepa","date":"March 18, 2018","format":false,"excerpt":"I have posted often on the chemical phenomenon known as hypervalency, being careful to state that as defined it applies just to \"octet excess\" in main group elements. But what about the next valence shell, occurring in transition metals and known as the \"18-electron rule\"? You rarely hear the term\u2026","rel":"","context":"In "Hypervalency"","block_context":{"text":"Hypervalency","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=7"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2018\/03\/NiPP-987x1024.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":26601,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=26601","url_meta":{"origin":19472,"position":1},"title":"Molecules of the year: 2023","author":"Henry Rzepa","date":"December 28, 2023","format":false,"excerpt":"The Science education unit at the ACS publication C&EN publishes its list of molecules of the year (as selected by the editors and voted upon by the readers) in December. Here are some observations about three of this year's batch. Diberyllocene with its unusual Be-Be bond has already beeen covered\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2023\/12\/CF.gif?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":16758,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=16758","url_meta":{"origin":19472,"position":2},"title":"What’s in a name? Carbenes: a reality check.","author":"Henry Rzepa","date":"September 11, 2016","format":false,"excerpt":"To quote from Wikipedia: in chemistry, a carbene is a molecule containing a neutral carbon atom with a valence of two and two unshared valence electrons. The most ubiquitous type of carbene of recent times is the one shown below as 1, often referred to as a resonance stabilised or\u2026","rel":"","context":"In "crystal_structure_mining"","block_context":{"text":"crystal_structure_mining","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1745"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":30890,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=30890","url_meta":{"origin":19472,"position":3},"title":"Valence bond representations with +ve charges on adjacent atoms? An odd titanium complex analysed.","author":"Henry Rzepa","date":"March 8, 2026","format":false,"excerpt":"A few posts back, I contemplated the curly arrows appropriate for the formation of nitrosobenzene dimer from nitrosobenzene, and commented on the odd nature of the N=N double bond formed in this process.. Odd, because the valence bond representation of this dimer (1 below) has two formally positive adjacent nitrogen\u2026","rel":"","context":"In "Interesting chemistry"","block_context":{"text":"Interesting chemistry","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=4"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":19307,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19307","url_meta":{"origin":19472,"position":4},"title":"Are diazomethanes hypervalent molecules? An attempt into more insight by more “tuning” with substituents.","author":"Henry Rzepa","date":"December 26, 2017","format":false,"excerpt":"Recollect the suggestion\u00a0that diazomethane has hypervalent character. When I looked into this, I came to the conclusion that it probably was mildly hypervalent, but on carbon and not nitrogen. Here I try some variations with substituents to see what light if any this casts. I have expanded the resonance forms\u2026","rel":"","context":"In "Hypervalency"","block_context":{"text":"Hypervalency","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=7"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2017\/12\/H2CNCCN_ELF-1024x258.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":19279,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19279","url_meta":{"origin":19472,"position":5},"title":"Can any hypervalence in diazomethanes be amplified?","author":"Henry Rzepa","date":"December 23, 2017","format":false,"excerpt":"In the previous post, I referred to a recently published review on hypervalency which introduced a very simple way (the\u00a0valence electron equivalent \u03b3)\u00a0of quantifying the effect.\u00a0Diazomethane was cited as one example of a small molecule exhibiting hypervalency (on nitrogen) by this measure. Here I explore the effect of substituting diazomethane\u2026","rel":"","context":"In "Hypervalency"","block_context":{"text":"Hypervalency","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=7"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_likes_enabled":false,"authors":[{"term_id":2661,"user_id":1,"is_guest":0,"slug":"admin","display_name":"Henry Rzepa","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g","author_category":"1","first_name":"Henry","last_name":"Rzepa","user_url":"https:\/\/orcid.org\/0000-0002-8635-8390","job_title":"","description":"Henry Rzepa is Emeritus Professor of Computational Chemistry at Imperial College London."}],"_links":{"self":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/19472","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=19472"}],"version-history":[{"count":6,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/19472\/revisions"}],"predecessor-version":[{"id":19482,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/19472\/revisions\/19482"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19472"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=19472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}