{"id":17041,"date":"2016-10-31T09:08:26","date_gmt":"2016-10-31T09:08:26","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=17041"},"modified":"2016-12-03T10:22:34","modified_gmt":"2016-12-03T10:22:34","slug":"the-smallest-c-c-c-angle","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041","title":{"rendered":"The  smallest  C-C-C angle?"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"17041\">\n<p>Is asking a question such as &#8220;what is the smallest angle subtended at a chain of three connected 4-coordinate carbon atoms&#8221; just seeking another chemical record, or could it unearth interesting chemistry?<\/p>\n<p>A simple search of the Cambridge structure database for a chain of three carbons, each bearing four substituents (sp3 hybridized in normal paralance) reveals the following distribution:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-17042\" src=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CCC.jpg\" alt=\"ccc\" width=\"450\" srcset=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CCC.jpg 923w, https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CCC-300x232.jpg 300w, https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CCC-768x594.jpg 768w\" sizes=\"(max-width: 923px) 100vw, 923px\" \/><\/p>\n<p>The value 60\u00b0 is of course a three-membered cyclopropane ring. The tail of the distribution is very small, and there are a few small outliers with values of &lt; 54\u00b0. Most of the time such outliers are in fact simple errors, but here we see that they are in fact <a href=\"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=7721\">semibullvalenes<\/a>, of the type shown below, with the small angle subtended at the central of the three carbon atoms coloured in red.<\/p>\n<p><a href=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CAZFUE.svg\"><img decoding=\"async\" class=\"aligncenter size-large wp-image-17043\" src=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CAZFUE.svg\" alt=\"cazfue\" width=\"400\" \/><\/a><\/p>\n<p>In this diagram I have added my own semantic interpretation of what is going on. Let me itemise this:<\/p>\n<ul>\n<li>These molecules can undergo very rapid [3,3] sigmatropic rearrangements, shifting a \u03c3-bond away from the 3-ring to create another such ring.<\/li>\n<li>This process elongates one of the C-C bonds and of neccessity this reduces the angle at the associated carbon.<\/li>\n<li>I have drawn two types of arrow connecting the two structures. The first is an equilibrium arrow, which implies a transition state connecting the two species. This transition state will have equal bond lengths for the forming\/breaking C-C bond, and the transition state will have a <a href=\"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=12662\">rate constant <\/a>which is slower than the time taken for one molecular vibration (~10<sup>-15<\/sup>s)<\/li>\n<li>It is also possible however that the second arrow is the correct one, and this implies an electronic resonance rather than a nuclear motion. This would have a rate constant comensurate with <a href=\"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=5405\">electron dynamics<\/a>\u00a0(~10<sup>-18<\/sup> s) rather than nuclear vibrations.<\/li>\n<\/ul>\n<p>What does x-ray crystallography measure? Well the diffraction of photons by electrons. In order to obtain a diffraction pattern, enough photons have to be diffracted to be measured, and even with most modern instruments this\u00a0still\u00a0takes minutes or hours. During this period, all the various nuclear positions encountered as a result of vibrations or equilibria are sampled. So if the rate constant for the [3,3] sigmatropic rearrangement is fast, x-ray diffraction will measure the average of the two sets of nuclear positions, which can be distinguished only with some difficulty (if at all) from the structure implied instead by electronic resonance.<\/p>\n<p>If the equilibrium arrow applies, then the small angles of &lt;54\u00b0 are merely the average of the normal value for a 3-membered ring and a smaller value for a structure where one of the C-C bonds has been removed. In my opening sentence, I noted that the three carbon carbon atoms had to be connected in a chain. This is no longer true; the goalposts have been moved (a lot)!<\/p>\n<p>If its an electron resonance, then the three carbon atoms are still connected, albeit one of the two C-C bonds is no longer a single bond but rather weaker and hence longer. The goalposts have merely been slightly shifted!<\/p>\n<p>A calculation (B3LYP\/Def2-TZVPP+D3 dispersion, doi: <a href=\"https:\/\/doi.org\/10.14469\/hpc\/1850\">10.14469\/hpc\/1850<\/a>, <span id=\"cite_ITEM-17041-0\" name=\"citation\"><a href=\"#ITEM-17041-0\">[1]<\/a><\/span>) of the structure KUZFUE <span id=\"cite_ITEM-17041-1\" name=\"citation\"><a href=\"#ITEM-17041-1\">[2]<\/a><\/span> shows the C<sub>2<\/sub>-symmetric species shown below, with an elongated C-C bond and hence a reduced C-C-C angle, as being a true minimum (a resonance) rather than a transition state (an equilibrium). The vibration which shortens one C-C bond and lengthens the other has the real calculated wavenumber 244 cm<sup>-1<\/sup>.<sup>\u2021<\/sup> But the boundary between the two possibilities (often referred to as the boundary between a single and a double minimum in a potential energy surface) is notoriously difficult to capture using calculations.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-17046\" src=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CAZFUE.jpg\" alt=\"cazfue\" width=\"450\" srcset=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CAZFUE.jpg 664w, https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CAZFUE-300x208.jpg 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><\/p>\n<p>How could experiment definitively settle the issue? Well, the <a href=\"https:\/\/www6.slac.stanford.edu\">SLAC beam<\/a> is a unique instrument. Its source of X-rays is so intense that you can get an analysable diffraction pattern from a crystal on a timescale so short that during this period no nuclear motions occur (not even vibrations). Those nuclear positions capture the true equilibrium positions of the atoms in the molecule. Now, how does one get beam time on the SLAC?<\/p>\n<hr \/>\n<p><sup>\u2021<\/sup> Click on the image above to see an animation of this normal mode. If you are running the macOS Safari browser, make sure <strong>Preferences\/Security\/Plug-in settings\/Java <\/strong>has the site <strong>ch.ic.ac.uk<\/strong> or <strong>ch.imperial.ac.uk<\/strong> set to <strong>on<\/strong>. If you do not do this, the somewhat unhelpful message <em>You do not have Java applets enabled in your web browser, or your browser is blocking this applet.<\/em> will appear. Note also that new system installations might tend to switch these settings to off.<\/p>\n<h2>References<\/h2>\n    <ol class=\"kcite-bibliography csl-bib-body\"><li id=\"ITEM-17041-0\">H. Rzepa, \"CAZFUE\", 2016. <a href=\"https:\/\/doi.org\/10.14469\/hpc\/1850\">https:\/\/doi.org\/10.14469\/hpc\/1850<\/a>\n\n<\/li>\n<li id=\"ITEM-17041-1\">L.M. Jackman, A. Benesi, A. Mayer, H. Quast, E.M. Peters, K. Peters, and H.G. Von Schnering, \"The Cope rearrangement of 1,5-dimethylsemibullvalene-2,6- and 3,7-dicarbonitriles in the solid state\", <i>Journal of the American Chemical Society<\/i>, vol. 111, pp. 1512-1513, 1989. <a href=\"https:\/\/doi.org\/10.1021\/ja00186a064\">https:\/\/doi.org\/10.1021\/ja00186a064<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> <!-- kcite-section 17041 -->","protected":false},"excerpt":{"rendered":"<p>Is asking a question such as &#8220;what is the smallest angle subtended at a chain of three connected 4-coordinate carbon atoms&#8221; 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 (sp3 hybridized in normal paralance) [&hellip;]<\/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":true,"_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},"jetpack_post_was_ever_published":false},"categories":[1745,1086],"tags":[152,1920,1921,1395,1742,1550,1919,487,1630,1410,142,1922,339,42],"ppma_author":[2661],"class_list":["post-17041","post","type-post","status-publish","format-standard","hentry","category-crystal_structure_mining","category-reaction-mechanism-2","tag-animation","tag-bicyclic-molecule","tag-chemical-record","tag-chemistry","tag-city-cambridge","tag-cycloalkane","tag-cyclopropanes","tag-java","tag-molecular-geometry","tag-organic-chemistry","tag-potential-energy-surface","tag-safari","tag-web-browser","tag-x-ray"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The smallest C-C-C angle? - Henry Rzepa&#039;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=17041\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The smallest C-C-C angle? - Henry Rzepa&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"Is asking a question such as &#8220;what is the smallest angle subtended at a chain of three connected 4-coordinate carbon atoms&#8221; 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 (sp3 hybridized in normal paralance) [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa&#039;s Blog\" \/>\n<meta property=\"article:published_time\" content=\"2016-10-31T09:08:26+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2016-12-03T10:22:34+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CCC.jpg\" \/>\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=\"4 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The smallest C-C-C angle? - Henry Rzepa&#039;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=17041","og_locale":"en_GB","og_type":"article","og_title":"The smallest C-C-C angle? - Henry Rzepa&#039;s Blog","og_description":"Is asking a question such as &#8220;what is the smallest angle subtended at a chain of three connected 4-coordinate carbon atoms&#8221; 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 (sp3 hybridized in normal paralance) [&hellip;]","og_url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041","og_site_name":"Henry Rzepa&#039;s Blog","article_published_time":"2016-10-31T09:08:26+00:00","article_modified_time":"2016-12-03T10:22:34+00:00","og_image":[{"url":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CCC.jpg","type":"","width":"","height":""}],"author":"Henry Rzepa","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Henry Rzepa","Estimated reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041#article","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041"},"author":{"name":"Henry Rzepa","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"headline":"The smallest C-C-C angle?","datePublished":"2016-10-31T09:08:26+00:00","dateModified":"2016-12-03T10:22:34+00:00","mainEntityOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041"},"wordCount":765,"commentCount":7,"image":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041#primaryimage"},"thumbnailUrl":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2016\/10\/CCC.jpg","keywords":["animation","Bicyclic molecule","chemical record","Chemistry","City: Cambridge","Cycloalkane","Cyclopropanes","Java","Molecular geometry","Organic chemistry","potential energy surface","Safari","Web browser","X-ray"],"articleSection":["crystal_structure_mining","reaction mechanism"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041#respond"]}]},{"@type":"WebPage","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17041","name":"The smallest C-C-C angle? 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Consider a simple diene: how does the central C-C bond length respond to the torsion angle between the two C=C bonds? The search of the CSD (Cambridge structure database) is constrained to R < 5%, no errors and no\u2026","rel":"","context":"In &quot;Chemical IT&quot;","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":17063,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17063","url_meta":{"origin":17041,"position":1},"title":"The largest  C-C-C angle?","author":"Henry Rzepa","date":"November 1, 2016","format":false,"excerpt":"I am now inverting the previous question by asking what is the largest angle subtended at a chain of three connected 4-coordinate carbon atoms? 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 &quot;crystal_structure_mining&quot;","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":18950,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=18950","url_meta":{"origin":17041,"position":2},"title":"Elongating an N-B single bond  is much easier than stretching a C-C single bond.","author":"Henry Rzepa","date":"October 24, 2017","format":false,"excerpt":"An N-B single bond is iso-electronic to a C-C single bond, as per below. So here is a simple question: what form does the distribution of the lengths of these two bonds take, as obtained from crystal structures?\u00a0 The Conquest search query is very simple (no disorder, no errors). When\u2026","rel":"","context":"In &quot;crystal_structure_mining&quot;","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\/2017\/10\/C-C-1024x804.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":18121,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=18121","url_meta":{"origin":17041,"position":3},"title":"The \u03c0-\u03c0 stacking of aromatic rings: what is their closest parallel approach?","author":"Henry Rzepa","date":"April 13, 2017","format":false,"excerpt":"Layer stacking in structures such as graphite is well-studied. The separation between the \u03c0-\u03c0 planes\u00a0is\u00a0~3.35\u00c5, which is close to twice the estimated van der Waals (vdW) radius of carbon (1.7\u00c5). But how much closer could such layers get, given that many other types of relatively weak interaction such as hydrogen\u2026","rel":"","context":"In &quot;crystal_structure_mining&quot;","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\/2017\/04\/ring-distances-1024x709.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":14548,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=14548","url_meta":{"origin":17041,"position":4},"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 &quot;Chemical IT&quot;","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":17992,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17992","url_meta":{"origin":17041,"position":5},"title":"The conformation of enols: revealed and explained.","author":"Henry Rzepa","date":"April 6, 2017","format":false,"excerpt":"Enols are simple compounds with an OH group as a substituent on a C=C double bond and with a very distinct conformational preference for the OH group. Here I take a look at this preference as revealed by crystal structures, with the theoretical explanation. First, a search of the Cambridge\u2026","rel":"","context":"In &quot;crystal_structure_mining&quot;","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\/2017\/04\/All-1024x948.jpg?resize=350%2C200","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\/17041","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=17041"}],"version-history":[{"count":18,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/17041\/revisions"}],"predecessor-version":[{"id":17139,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/17041\/revisions\/17139"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=17041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=17041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=17041"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=17041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}