{"id":7267,"date":"2012-07-21T08:18:52","date_gmt":"2012-07-21T07:18:52","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=7267"},"modified":"2018-02-05T14:22:58","modified_gmt":"2018-02-05T14:22:58","slug":"the-first-ever-curly-arrows-and-now-for-something-completely-different","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=7267","title":{"rendered":"The first ever curly arrows. And now for something completely different."},"content":{"rendered":"
\n

The discussion appended to the post<\/a> on curly arrows is continued here. Recollect the curly arrow diagram (in modern style) derived from\u00a0Robinson’s original suggestion:<\/p>\n

\"\"<\/p>\n

The pertinent point is that the angle subtended at the nitrogen atom evolves from being bent (~115\u00b0) on the left, to linear (180\u00b0) on the right. The nitrogen hybridisation changes from trigonal (sp2<\/sup>) to digonal (sp). Because of this, the scheme must represent a reaction rather than a resonance. What kind of species is the molecule on the right? A \u03c9B97XD\/6-311G(d,p) solution of the wave equation indicates it is a transition state<\/strong><\/em>. The normal mode indicates that the nitrogen atom is moving out of the plane of the ring, evolving the C=N double bond back into having a nitrogen lone pair, and apparently on the way to a most interesting non-planar valence-bond isomer of nitrosobenzene. You might have noticed a nitro group has appeared in the 4-position. I did this to try to stabilize the negative charge in this position shown on the right above to prevent it from being a transition state; this subterfuge failed!<\/p>\n

\"\"

The linear form is a transition state. Click for 3D<\/p><\/div>\n

What about an IRC<\/a> (intrinsic reaction coordinate)? It starts off downhill from the transition state at IRC = 0.0.\u00a0To quote Monty Python, and now for something completely different<\/a>. At IRC 2.65, something does indeed happen, a most unusual feature in potential energy surfaces; a bifurcation point<\/strong><\/em>.<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

I am going to have to explain this. Normally, a transition state (a saddle point of order 1) connects two minima. But a bifurcation means that one transition state leads directly downhill (without any intervening minima) to another transition state. When the lower energy transition state is reached, the potential bifurcates, since it now has two (equal) directions for it to continue its downhill descent. Our IRC at this point has to somehow chose which of these two to take. In fact the choice is made randomly. To be precise, small so-called round-off errors in computing the derivatives of the path favour by a tiny tiny margin one of the pathways over the other, and so off it heads. As you can see below, this second pathway involves an (anticlockwise) rotation of the nitroso group (it could also have chosen clockwise).<\/p>\n

\"\"<\/p>\n

That rotation can now be represented by the following.<\/p>\n

\"\"<\/p>\n

I continue to be surprised at where we have arrived at from Robinson’s original curly arrows; bifurcated potential energy surfaces. Well, that introductory student tutorial to curly arrow pushing is going to have to cover a lot of ground!\u00a0<\/p>\n

[qrcode content=”Robinson” size=”200″ alt=”QRCode” class=”CLASS_NAME” align=”right”]<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

The discussion appended to the post on curly arrows is continued here. Recollect the curly arrow diagram (in modern style) derived from\u00a0Robinson’s original suggestion: The pertinent point is that the angle subtended at the nitrogen atom evolves from being bent (~115\u00b0) on the left, to linear (180\u00b0) on the right. The nitrogen hybridisation changes from […]<\/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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[2327],"tags":[875,878,877,876,843,373],"ppma_author":[2661],"class_list":["post-7267","post","type-post","status-publish","format-standard","hentry","category-curl-arrows","tag-lower-energy-transition-state","tag-monty-python","tag-nitro","tag-potential-energy-surfaces","tag-reaction-mechanism","tag-tutorial-material"],"yoast_head":"\nThe first ever curly arrows. And now for something completely different. - 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=7267\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The first ever curly arrows. And now for something completely different. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"The discussion appended to the post on curly arrows is continued here. Recollect the curly arrow diagram (in modern style) derived from\u00a0Robinson’s original suggestion: The pertinent point is that the angle subtended at the nitrogen atom evolves from being bent (~115\u00b0) on the left, to linear (180\u00b0) on the right. The nitrogen hybridisation changes from […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=7267\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa's Blog\" \/>\n<meta property=\"article:published_time\" content=\"2012-07-21T07:18:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-02-05T14:22:58+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2012\/07\/robinson11.svg\" \/>\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":"The first ever curly arrows. 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Why? It simply breaks the (it has to be said to some extent informal)\u2026","rel":"","context":"In "Curly arrows"","block_context":{"text":"Curly arrows","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2327"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2012\/07\/NO_dim.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":22153,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=22153","url_meta":{"origin":7267,"position":1},"title":"Choreographing a chemical ballet: a story of the mechanism of 1,4-Michael addition.","author":"Henry Rzepa","date":"April 13, 2020","format":false,"excerpt":"A reaction can be thought of as molecular dancers performing moves. A choreographer is needed to organise the performance into the ballet that is a reaction mechanism. Here I explore another facet of the Michael addition of a nucleophile to a conjugated carbonyl compound. The performers this time are p-toluene\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\/2020\/04\/SC.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":20464,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=20464","url_meta":{"origin":7267,"position":2},"title":"The Graham reaction: Deciding upon a reasonable mechanism and curly arrow representation.","author":"Henry Rzepa","date":"February 18, 2019","format":false,"excerpt":"Students learning organic chemistry are often asked in examinations and tutorials to devise the mechanisms (as represented by curly arrows) for the core corpus of important reactions, with the purpose of learning skills that allow them to go on to improvise mechanisms for new reactions. A common question asked by\u2026","rel":"","context":"In "Curly arrows"","block_context":{"text":"Curly arrows","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2327"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":7344,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=7344","url_meta":{"origin":7267,"position":3},"title":"The first curly arrows. The d\u00e9nouement.","author":"Henry Rzepa","date":"July 23, 2012","format":false,"excerpt":"Recollect, Robinson was trying to explain why the nitroso group appears to be an o\/p director of aromatic electrophilic substitution. Using \u03c3\/\u03c0 orthogonality, I suggested that the (first ever) curly arrows as he drew them could not be the complete story, and that a transition state analysis would be needed.\u2026","rel":"","context":"In "Curly arrows"","block_context":{"text":"Curly arrows","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2327"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2012\/07\/p-wheland.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":28849,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=28849","url_meta":{"origin":7267,"position":4},"title":"Mechanism of the dimerisation of Nitrosobenzene.","author":"Henry Rzepa","date":"June 14, 2025","format":false,"excerpt":"I am in the process of revising my annual lecture to first year university students on the topic of \"curly arrows\". I like to start my story in 1924, when Robert Robinson published the very first example as an illustration of why nitrosobenzene undergoes electrophilic bromination in the para position\u2026","rel":"","context":"In "reaction mechanism"","block_context":{"text":"reaction mechanism","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1086"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2025\/06\/trans.gif?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2025\/06\/trans.gif?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2025\/06\/trans.gif?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":22404,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=22404","url_meta":{"origin":7267,"position":5},"title":"The first ever curly arrows. Revisited with some crystal structure mining.","author":"Henry Rzepa","date":"May 27, 2020","format":false,"excerpt":"With the current global lockdown, and students along with everyone else staying at home, I have noticed some old posts of mine are getting more attention than normal. One of these is an analysis I did in 2012 of Robinson's original curly arrow illustration. That and the fact that I\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\/2020\/05\/Screenshot-52-1024x622.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\/7267","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=7267"}],"version-history":[{"count":10,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7267\/revisions"}],"predecessor-version":[{"id":19404,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7267\/revisions\/19404"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7267"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=7267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}