{"id":27944,"date":"2024-10-09T16:19:23","date_gmt":"2024-10-09T15:19:23","guid":{"rendered":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=27944"},"modified":"2026-03-05T07:59:19","modified_gmt":"2026-03-05T07:59:19","slug":"a-one-electron-bond-in-methyl-%ce%bb1-borane","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=27944","title":{"rendered":"A one-electron bond in methyl-\u03bb1-borane."},"content":{"rendered":"
\n

In exploring one-electron carbon-carbon bonds, I had noted previously[1]<\/a><\/span> that both hexafluoroethane and ethane itself could each lose an electron to produce such species. A discussion developed in which a molecule isoelectronic with ethane radical cation, namely the methyl-\u03bb1-borane radical (H3<\/sub>B-CH3<\/sub>) was proposed by Jacob<\/a>. The optimised structure at the \u03c9B97XD\/6-31G(d) level exhibited a B-C bond length of 1.57\u00c5, with two of the B-H hydrogens forming a a 3c-3e bond with boron and so a one-electron B-C bond was discounted. Here I take a closer look at this system.<\/p>\n

At the \u03c9B97XD\/Def2-TZVPP level, I located an alternative structure with a longer B-C bond of 1.737\u00c5[2]<\/a><\/span> and an “agostic” like interaction between C and one B-H bond.<\/p>\n

\"\"<\/p>\n

The electron density difference maps between methyl-\u03bb1-borane and its mono cation is shown below and following it the density difference map between the corresponding anion and methyl-\u03bb1-borane radical. These are very similar to the maps obtained previously for hexafluoroethand and ethane \u00a0and support the hypothesis that the differences between the two-electron\/zero-electron species and the one-electron radical originates at least in part in the B-C bond.<\/p>\n

\"\"
\n\"\"<\/p>\n

A contour map of the negative region of the electron density Laplacian (-0.04 au) again shows that it lies along the B-C bond, suggesting covalency. Note the -ve Laplacian in the region of the agostic interaction! The NCI (non-covalent-interaction) plot is featureless.<\/p>\n

\"\"<\/p>\n

The computed methyl-\u03bb1-borane radical has a B-C stretching vibration corresponding to 494 cm-1<\/sup>, a Wiberg bond order of 0.660 and Wiberg bond index totals of 3.51 for carbon and 3.28 for boron. These can all be reasonably interpreted as a one-electron “half” bond between C and B. With a computed bond length of 1.737\u00c5, it represents the shortest “one electron” bond thus far identified, and hence extends the length range of such bonds to around 1.16\u00c5.<\/p>\n

\n

Postscript 1<\/b>
\nI also looked at the radical anion of H3<\/sub>B-BH3<\/sub>–<\/sup> which is isoelectronic to methyl-\u03bb1-borane, revealing rB-B<\/sub> 2.124\u00c5 and has a classic “ethane” D3d<\/sub> like structure. The electron density difference map between H3<\/sub>B-BH3<\/sub>–<\/sup> and the neutral H3<\/sub>B-BH3<\/sub> is shown below, revealing in a considerable reorganisation of the electron density, only one aspect being the B-B region and different from the reorganisation of the radical cation of ethane itself. This reveals that simply talking about a two-atom region for this sort of system is very simplistic and misleading. The Wiberg B-B bond index is 0.383 and the B-B stretching vibration is 384 cm-1<\/sup>.<\/p>\n

\"\"<\/p>\n

The electron density Laplacian of H3<\/sub>B-BH3<\/sub>–<\/sup> contoured for a -ve value of -0.04 au, again implying a covalent B-B bond.<\/p>\n

\"\"<\/p>\n

Postscript 2<\/b><\/p>\n

Here I add hexamethylethane radical cation to the list. Firstly the density difference map. Note the longer C-C bond (2.31\u00c5) than for ethane radical cation (1.933\u00c5). In this sense, the hexamethyl radical cation has a weaker C-C bond than does the unsubstituted version (191 cm-1<\/sup>) vs 477 cm-1<\/sup>)<\/p>\n

\"\"<\/p>\n

The Laplacian shows no -ve value in the C-C region (isosurface value -0.01), again placing it in the weak bond category.<\/p>\n

\"\"<\/p>\n

Finally some NCI plots. Here the density cut-off threshold is crucial. Typically a second period element covalent density is taken as 0.05 au, and this is removed from the NCI analysis. The feature seen along the C-C bond at this level is typical of weak covalent interactions however.<\/p>\n

\"\"<\/p>\n

Reducing the density to 0.023 (typical of density in which one atom is of the third period, ie Si) removes the central C-C feature, leaving only NCI effects between the hydrogen atoms of the methyl groups. These in fact form a continuous weakly stabilizing surface between the two halves.<\/p>\n

\"\"<\/p>\n

So with hexamethylethane radical cation, we get messages that the interaction between the two carbons is both weak, but also not a non-covalent interaction. So this is a very weak covalent bond perhaps, but in this strange region, it is difficult to ascribe a single description to it.<\/p>\n

References<\/h2>\n
  1. https:\/\/doi.org\/<\/a>\n\n<\/li>\n
  2. H. Rzepa, \"A one-electron bond in methyl-\u03bb1-borane.\", 2024. https:\/\/doi.org\/10.14469\/hpc\/14662<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    In exploring one-electron carbon-carbon bonds, I had noted previously that both hexafluoroethane and ethane itself could each lose an electron to produce such species. A discussion developed in which a molecule isoelectronic with ethane radical cation, namely the methyl-\u03bb1-borane radical (H3B-CH3) was proposed by Jacob. The optimised structure at the \u03c9B97XD\/6-31G(d) level exhibited a B-C […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":5,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"federated","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}},"categories":[4],"tags":[],"ppma_author":[2661],"class_list":["post-27944","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry"],"yoast_head":"\nA one-electron bond in methyl-\u03bb1-borane. - 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=27944\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A one-electron bond in methyl-\u03bb1-borane. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"In exploring one-electron carbon-carbon bonds, I had noted previously that both hexafluoroethane and ethane itself could each lose an electron to produce such species. 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The measured C-C bond length was ~2.9a\u00c5 and my conclusion was that the C...C region represented more of a weak \"interaction\" than of a bond\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":27788,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=27788","url_meta":{"origin":27944,"position":1},"title":"A carbon-carbon one-electron bond! Or a weak carbon-carbon interaction?","author":"Henry Rzepa","date":"October 1, 2024","format":false,"excerpt":"More than 100 years ago, before the quantum mechanical treatment of molecules had been formulated, G. N. Lewis proposed a simple model for chemical bonding that is still taught today. This is the idea of the three categories of bond we know as single, double and triple, comprising respectively two,\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":11642,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=11642","url_meta":{"origin":27944,"position":2},"title":"Avoided (pericyclic) anti-aromaticity: Reactions of t-butyl-hydroxycarbene.","author":"Henry Rzepa","date":"November 13, 2013","format":false,"excerpt":"Not long ago, I described a cyclic carbene in which elevating the carbene lone pair into a \u03c0-system transformed it from a formally 4n-antiaromatic \u03c0-cycle into a 4n+2 aromatic \u03c0-cycle. From an entirely different area of chemistry, another example of this behaviour emerges; Schreiner's trapping and reactions of t-butyl-hydroxycarbene, as\u2026","rel":"","context":"In "pericyclic"","block_context":{"text":"pericyclic","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=559"},"img":{"alt_text":"H-mig","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/11\/H-mig.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":19347,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19347","url_meta":{"origin":27944,"position":3},"title":"Hypervalent hydrogen?","author":"Henry Rzepa","date":"January 13, 2018","format":false,"excerpt":"I discussed the molecule the molecule CH3F2- a while back. It was a very rare computed example of a system where the added two electrons populate the higher valence shells known as Rydberg orbitals as an alternative to populating the C-F antibonding \u03c3-orbital to produce CH3- and F-. The net\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":[]},{"id":17829,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17829","url_meta":{"origin":27944,"position":4},"title":"First, hexacoordinate carbon – now pentacoordinate nitrogen?","author":"Henry Rzepa","date":"March 25, 2017","format":false,"excerpt":"A few years back I followed a train of thought here which ended with hexacoordinate carbon, then a hypothesis rather than a demonstrated reality. That reality was recently confirmed via a crystal structure,\u00a0DOI:10.5517\/CCDC.CSD.CC1M71QM. Here is a\u00a0similar proposal for\u00a0penta-coordinate nitrogen. First, a search of the CSD (Cambridge structure database) for such\u00a0nitrogen.\u2026","rel":"","context":"In "Bond slam"","block_context":{"text":"Bond slam","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2237"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":24019,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24019","url_meta":{"origin":27944,"position":5},"title":"More record breakers for the anomeric effect involving C-N bonds.","author":"Henry Rzepa","date":"September 4, 2021","format":false,"excerpt":"An earlier post investigated large anomeric effects involving two oxygen atoms attached to a common carbon atom. A variation is to replace one oxygen by a nitrogen atom, as in N-C-O. Shown below is a scatter plot of the two distances to the common carbon atom derived from crystal structures.\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":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2021\/07\/N-C-O-distances-1024x758.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"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","0":null,"1":"","2":"","3":"","4":"","5":"","6":"","7":"","8":""}],"_links":{"self":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/27944","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=27944"}],"version-history":[{"count":58,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/27944\/revisions"}],"predecessor-version":[{"id":30888,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/27944\/revisions\/30888"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=27944"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=27944"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=27944"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=27944"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}