{"id":25550,"date":"2022-09-11T06:14:09","date_gmt":"2022-09-11T05:14:09","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=25550"},"modified":"2022-09-11T13:51:07","modified_gmt":"2022-09-11T12:51:07","slug":"what-is-the-largest-angle-possible-at-4-coordinate-carbon-180","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=25550","title":{"rendered":"What is the largest angle possible at 4-coordinate carbon – 180\u00b0?"},"content":{"rendered":"
\n

Four-coordinate carbon normally adopts a tetrahedral shape, where the four angles at the carbon are all 109.47\u00b0. But how large can that angle get, and can it even get to be 180\u00b0?<\/p>\n

A search of the CSD (crystal structure database) reveals a spiropentane as having the largest such angle, VAJHAP with 164\u00b0[1]<\/a><\/span><\/p>\n

\"\"<\/p>\n

Because crystal structures might have artefacts such as disorder etc, it is always good to check this with a calculation; hence \u03c9B97XD\/Def2-TZVPP (FAIR data DOI: 10.14469\/hpc\/11148<\/a>) for which a calculated angle of 163.8\u00b0 is reassuring. The smallest angle in this system by the way is 58\u00b0, pretty normal for three-membered rings.<\/p>\n

The localised orbitals show the C-C region defining the large angle to be very “bent” (a banana bond) but otherwise fairly normal.<\/p>\n

\"\"<\/p>\n

So can one “engineer” an even larger angle? Replacing the C=C of the benzo group with a shorter CH2\u00a0<\/sub>group produces the following, which is now almost linear (almost a “hemispherical” carbon).<\/p>\n

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

What about the smallest angle at 4-coordinate carbon? Could it be significantly smaller than the 57\u00b0 noted above for a three membered ring? Searching the CSD reveals XAQHIH[2]<\/a><\/span> with an angle of\u00a043\u00b0 but the calculation above now does not confirm this, the angle changing from 43\u00b0 to 59\u00b0 during optimisation. A reminder that when exploring extreme geometric values, always check with a calculation!<\/p>\n

\u00a0\"\"\u00a0<\/p>\n

\"\"<\/p>\n

The next candidate is CAZFUE[3]<\/a><\/span> with an apparent measured angle of 48\u00b0. This appears to have C2<\/sub> symmetry, and a calculation with this gives a value of 46.6\u00b0. But all is not what it seems. This is a classic example of a semibullvalene [3,3] Cope rearrangement, caught in the “middle” so to speak (See this post here<\/a>). In fact this geometry is actually a transition state, and the crystal structure is the thermal average of two positions, making it appear symmetrical. The ground state for this structure as calculated is different! The two angles now emerge as 40 and 57\u00b0 (average 48.6\u00b0). At the “transition state”, one of the four “bonds” to carbon is unusually long (2.07\u00c5), which is the direct cause of the small 48\u00b0 angle. If this is not allowed as a “bond”, the angle at the other true 4-coordinate carbon emerges as normal at 57\u00b0<\/p>\n

\"\"<\/p>\n

So the answer to the smallest angle does seem to be around 57\u00b0, but it could be as small as 47\u00b0 if one allows bonds of 2.07\u00c5 in one’s definition of 4-coordinate. The candidate for the largest bond angle, of almost 180\u00b0, seems a reasonable synthetic target!<\/p>\n

References<\/h2>\n
  1. R. Boese, D. Blaeser, K. Gomann, and U.H. Brinker, \"Spiropentane as a tensile spring\", Journal of the American Chemical Society<\/i>, vol. 111, pp. 1501-1503, 1989. https:\/\/doi.org\/10.1021\/ja00186a058<\/a>\n\n<\/li>\n
  2. M.V. Roux, J.Z. D\u00e1valos, P. Jim\u00e9nez, R. Notario, O. Casta\u00f1o, J.S. Chickos, W. Hanshaw, H. Zhao, N. Rath, J.F. Liebman, B.S. Farivar, and A. Bashir-Hashemi, \"Cubane, Cuneane, and Their Carboxylates:\u2009 A Calorimetric, Crystallographic, Calculational, and Conceptual Coinvestigation\", The Journal of Organic Chemistry<\/i>, vol. 70, pp. 5461-5470, 2005. https:\/\/doi.org\/10.1021\/jo050471+<\/a>\n\n<\/li>\n
  3. H. Quast, Y. G\u00f6rlach, J. Christ, E. Peters, K. Peters, H.G. von Schnering, L.M. Jackman, A. Ibar, and A.J. Freyer, \"Crystal and molecular structure and the cope activation barriers of some dicyano-1,5-dimethylsemibullvalenes\", Tetrahedron Letters<\/i>, vol. 24, pp. 5595-5598, 1983. https:\/\/doi.org\/10.1016\/s0040-4039(00)94150-9<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    Four-coordinate carbon normally adopts a tetrahedral shape, where the four angles at the carbon are all 109.47\u00b0. But how large can that angle get, and can it even get to be 180\u00b0? A search of the CSD (crystal structure database) reveals a spiropentane as having the largest such angle, VAJHAP with 164\u00b0 Because crystal structures […]<\/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":"","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":[],"tags":[2648],"ppma_author":[2661],"class_list":["post-25550","post","type-post","status-publish","format-standard","hentry","tag-interesting-chemistry"],"yoast_head":"\nWhat is the largest angle possible at 4-coordinate carbon - 180\u00b0? - 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=25550\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the largest angle possible at 4-coordinate carbon - 180\u00b0? - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"Four-coordinate carbon normally adopts a tetrahedral shape, where the four angles at the carbon are all 109.47\u00b0. 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But how large can that angle get, and can it even get to be 180\u00b0? 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Let's see if further interesting chemistry can be unearthed. Specifying only angles > 130\u00b0, the following distribution is obtained. Note the maximum at ~138\u00b0. This is\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":"vajhap","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/VAJHAP.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":25581,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=25581","url_meta":{"origin":25550,"position":1},"title":"Examples of inverted or hemispherical carbon?","author":"Henry Rzepa","date":"September 15, 2022","format":false,"excerpt":"In previously asking what the largest angle subtended at four-coordinate carbon might be, I noted that as the angle increases beyond 180\u00b0, the carbon becomes inverted, or hemispherical (all four ligands in one hemisphere). So what does a search for this situation reveal in the CSD? The query can be\u2026","rel":"","context":"With 2 comments","block_context":{"text":"With 2 comments","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=25581#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2022\/09\/111-nbo.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2022\/09\/111-nbo.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2022\/09\/111-nbo.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2022\/09\/111-nbo.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":14560,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=14560","url_meta":{"origin":25550,"position":2},"title":"Deviations from planarity of trigonal carbon and from linearity of digonal carbon.","author":"Henry Rzepa","date":"September 13, 2015","format":false,"excerpt":"Previously, I explored deviation from ideal tetrahedral arrangements of four carbon ligands around a central (sp3) carbon using crystal structures. Now it is the turn of digonal (sp1) and trigonal (sp2) carbons.\u00a0 Firstly, the digonal C\u2261C case. Attached to each carbon of the C\u2261C unit are two saturated carbon ligands;\u2026","rel":"","context":"In "Chemical IT"","block_context":{"text":"Chemical IT","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":14016,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=14016","url_meta":{"origin":25550,"position":3},"title":"The B\u00fcrgi\u2013Dunitz angle revisited: a mystery?","author":"Henry Rzepa","date":"May 12, 2015","format":false,"excerpt":"The B\u00fcrgi\u2013Dunitz angle is one of those memes that most students of organic chemistry remember.\u00a0It hypothesizes the geometry of attack of a\u00a0nucleophile\u00a0on a\u00a0trigonal\u00a0unsaturated (sp2) carbon in a\u00a0molecule\u00a0such as\u00a0ketone, aldehyde,\u00a0ester, and\u00a0amide\u00a0carbonyl. Its value obviously depends on the exact system, but is generally taken to be in the range 105-107\u00b0. A very\u2026","rel":"","context":"In "Chemical IT"","block_context":{"text":"Chemical IT","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":17041,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041","url_meta":{"origin":25550,"position":4},"title":"The smallest C-C-C angle?","author":"Henry Rzepa","date":"October 31, 2016","format":false,"excerpt":"Is asking a question such as \"what is the smallest angle subtended at a chain of three connected 4-coordinate carbon atoms\" just seeking another chemical record, or could it unearth interesting chemistry? A simple search of the Cambridge structure database for a chain of three carbons, each bearing four substituents\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":14548,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=14548","url_meta":{"origin":25550,"position":5},"title":"Deviations from tetrahedral four-coordinate carbon: a statistical exploration.","author":"Henry Rzepa","date":"September 6, 2015","format":false,"excerpt":"An article entitled \"Four Decades of the Chemistry of Planar Hypercoordinate Compounds\" was recently reviewed by Steve Bacharach on his blog, where you can also see comments. Given the recent crystallographic themes here, I thought I might try a search of the CSD (Cambridge structure database) to see whether anything\u2026","rel":"","context":"In "Chemical IT"","block_context":{"text":"Chemical IT","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2"},"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","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\/25550","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=25550"}],"version-history":[{"count":17,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/25550\/revisions"}],"predecessor-version":[{"id":25580,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/25550\/revisions\/25580"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25550"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25550"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25550"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=25550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}