{"id":1158,"date":"2009-11-18T14:16:58","date_gmt":"2009-11-18T13:16:58","guid":{"rendered":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158"},"modified":"2018-02-05T14:26:17","modified_gmt":"2018-02-05T14:26:17","slug":"mechanistic-menage-a-trois","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158","title":{"rendered":"Mechanistic M\u00e9nage \u00e0 trois"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"1158\">\n<p>Curly arrow pushing is one of the essential tools of a mechanistic chemist. Many a published article will speculate about the arrow pushing in a mechanism, although it is becoming increasingly common for these speculations to be backed up by quantitative quantum mechanical and dynamical calculations. These have the potential of exposing the underlying choreography of the electronic dance (the order in which the steps take place). The basic grammar of describing that choreography tends to be the full-headed<strong> curly arrow<\/strong> for closed shell systems and its half-barbed equivalent for open shell systems. An effectively unstated and hence implicit rule for closed shell systems is that only one curly arrow is used per breaking or forming bond, i.e. electrons move around bonds in pairs. So consider the following reaction (inspired by a posting on \u00a0<a href=\"http:\/\/comporgchem.com\/blog\/?p=487#comments\" target=\"references\">Steve Bachrach&#8217;s blog<\/a>)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1159\" title=\"Oxygen-nitrogen exchange between three nitrosonium cations\" src=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/no-exchange.jpg\" alt=\"Oxygen-nitrogen exchange between three nitrosonium cations\" width=\"522\" height=\"152\" \/><\/p>\n<p>This is very much a hypothetical mechanism, or a thought-experiment if you will. Three nitrosonium cations decide to get together to swap their partners. Each diatomic molecule swaps e.g. one oxygen for another during this exchange reaction (it could easily be studied experimentally of course using isotopic substitution). Three sets of three curly arrows have been used, shown in different colours above. \u00a0One set of these arrows at least has plenty of analogy in the real world; representing a <sub>\u03c0<\/sub>2<sub>s<\/sub>+<sub>\u03c0<\/sub>2<sub>s<\/sub>+<sub>\u03c0<\/sub>2<sub>s<\/sub> cycloaddition reaction. The other two sets represents rotation of the \u00a0in-plane \u03c0-set and the in-plane \u03c3-set. What about the choreography? Can all three sets move at the same time? If so, they would provide an exception to the rule above; three bonds would concurrently change their order from 3 to 0; the other three the reverse of 0 to 3.<\/p>\n<p>What does quantum mechanics say about this? Well, a well defined, synchronous concerted transition state can indeed be found (B3LYP\/6-31G(d), DOI: \u00a0<a href=\"http:\/\/hdl.handle.net\/10042\/to-2905\" target=\"references\">10042\/to-2905<\/a>)\u00a0It has one imaginary frequency (click on the above diagram to view the animation) which does indeed perform the bond transposition function required! It has the form of the so-called Kekule mode (deriving from a mode found in benzene which involves shortening of the lengths of three bonds, and lengthening of the other three, much in the manner of the resonance named after \u00a0Kekule; see e.g. DOI: <a href=\"http:\/\/dx.doi.org\/10.1039\/B911817A\" target=\"references\">10.1039\/B911817A<\/a> for more details). Of course, describing it as a change in the bond orders 3 \u2192 0\/0 \u2192 3 is simplistic; the bond order in the nitrosonium cation itself is almost certainly somewhat less than three. \u00a0But clearly, the implicit rule that \u00a0mechanistic arrow pushing should not involve more than one arrow departing from or arriving at any one bond can be broken. I will leave it to the reader of this blog to see what happens when you try to rearrange the choreography of the above reaction. Try pushing first one set of three arrows, then another and a final third. What do you get? (the why of the dance is almost certainly due to electrostatic repulsions between the three nitrosonium cations).<\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 1158 -->","protected":false},"excerpt":{"rendered":"<p>Curly arrow pushing is one of the essential tools of a mechanistic chemist. Many a published article will speculate about the arrow pushing in a mechanism, although it is becoming increasingly common for these speculations to be backed up by quantitative quantum mechanical and dynamical calculations. These have the potential of exposing the underlying choreography [&hellip;]<\/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":[2327,4],"tags":[152,155,2648,153,154,2650,20],"ppma_author":[2661],"class_list":["post-1158","post","type-post","status-publish","format-standard","hentry","category-curl-arrows","category-interesting-chemistry","tag-animation","tag-closed-shell-systems","tag-interesting-chemistry","tag-mechanistic-chemist","tag-open-shell-systems","tag-pericyclic","tag-steve-bachrach"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mechanistic M\u00e9nage \u00e0 trois - 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=1158\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mechanistic M\u00e9nage \u00e0 trois - Henry Rzepa&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"Curly arrow pushing is one of the essential tools of a mechanistic chemist. Many a published article will speculate about the arrow pushing in a mechanism, although it is becoming increasingly common for these speculations to be backed up by quantitative quantum mechanical and dynamical calculations. These have the potential of exposing the underlying choreography [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa&#039;s Blog\" \/>\n<meta property=\"article:published_time\" content=\"2009-11-18T13:16:58+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-02-05T14:26:17+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/no-exchange.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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Mechanistic M\u00e9nage \u00e0 trois - 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=1158","og_locale":"en_GB","og_type":"article","og_title":"Mechanistic M\u00e9nage \u00e0 trois - Henry Rzepa&#039;s Blog","og_description":"Curly arrow pushing is one of the essential tools of a mechanistic chemist. Many a published article will speculate about the arrow pushing in a mechanism, although it is becoming increasingly common for these speculations to be backed up by quantitative quantum mechanical and dynamical calculations. These have the potential of exposing the underlying choreography [&hellip;]","og_url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158","og_site_name":"Henry Rzepa&#039;s Blog","article_published_time":"2009-11-18T13:16:58+00:00","article_modified_time":"2018-02-05T14:26:17+00:00","og_image":[{"url":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/no-exchange.jpg","type":"","width":"","height":""}],"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=1158#article","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158"},"author":{"name":"Henry Rzepa","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"headline":"Mechanistic M\u00e9nage \u00e0 trois","datePublished":"2009-11-18T13:16:58+00:00","dateModified":"2018-02-05T14:26:17+00:00","mainEntityOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158"},"wordCount":496,"commentCount":10,"image":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158#primaryimage"},"thumbnailUrl":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/no-exchange.jpg","keywords":["animation","closed shell systems","Interesting chemistry","mechanistic chemist","open shell systems","pericyclic","Steve Bachrach"],"articleSection":["Curly arrows","Interesting chemistry"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158#respond"]}]},{"@type":"WebPage","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158","name":"Mechanistic M\u00e9nage \u00e0 trois - Henry Rzepa&#039;s Blog","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158#primaryimage"},"image":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158#primaryimage"},"thumbnailUrl":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/no-exchange.jpg","datePublished":"2009-11-18T13:16:58+00:00","dateModified":"2018-02-05T14:26:17+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=1158#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158#primaryimage","url":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/no-exchange.jpg","contentUrl":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/no-exchange.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1158#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog"},{"@type":"ListItem","position":2,"name":"Mechanistic M\u00e9nage \u00e0 trois"}]},{"@type":"WebSite","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/","name":"Henry Rzepa&#039;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-iG","jetpack-related-posts":[{"id":27114,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=27114","url_meta":{"origin":1158,"position":0},"title":"The 100th Anniversary year of Curly Arrows.","author":"Henry Rzepa","date":"June 14, 2024","format":false,"excerpt":"Chemists now use the term \"curly arrows\" as a language to describe the electronic rearrangements that occur when a (predominately organic) molecule transforms to another - the so called chemical reaction. It is also used to infer, via valence bond or resonance theory, what the mechanistic implications of that reaction\u2026","rel":"","context":"In &quot;Interesting chemistry&quot;","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":26340,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=26340","url_meta":{"origin":1158,"position":1},"title":"The &#8220;double-headed&#8221; curly arrow as used in mechanistic representations.","author":"Henry Rzepa","date":"August 29, 2023","format":false,"excerpt":"The schematic representation of a chemical reaction mechanism is often drawn using a palette of arrows connecting or annotating the various molecular structures involved. These can be selected from a chemical arrows palette, taken for this purpose from the commonly used structure drawing program Chemdraw. Explanations of how to apply\u2026","rel":"","context":"In &quot;Curly arrows&quot;","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.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2023\/08\/IMG_3157-131x300.jpeg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":6035,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=6035","url_meta":{"origin":1158,"position":2},"title":"Shared space (in science).","author":"Henry Rzepa","date":"January 6, 2012","format":false,"excerpt":"I thought I would launch the 2012 edition of this blog by writing about shared space. If you have not come across it before, it is (to quote Wikipedia), \"an\u00a0urban design\u00a0concept aimed at integrated use of public spaces.\" The BBC here in the UK ran a feature on it recently,\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":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/10\/arrow_pushing.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":8000,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8000","url_meta":{"origin":1158,"position":3},"title":"How is the bromination of alkenes best represented?","author":"Henry Rzepa","date":"October 14, 2012","format":false,"excerpt":"I occasionally delve into the past I try to understand how we got to our present understanding of chemistry. Thus curly arrow mechanistic notation can be traced back to around 1924, with style that bifurcated into two common types used nowadays (on which I have\u00a0commented\u00a0and about which further historical light\u2026","rel":"","context":"In &quot;Curly arrows&quot;","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\/10\/ion-pair-QTAIM.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":2737,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2737","url_meta":{"origin":1158,"position":4},"title":"Secrets of a university tutor: (curly) arrow pushing","author":"Henry Rzepa","date":"October 28, 2010","format":false,"excerpt":"Curly arrows are something most students of chemistry meet fairly early on. They rapidly become hard-wired into the chemists brain. They are also uncontroversial! Or are they? Consider the following very simple scheme. It represents protonation of an alkene by an acid. Two products are of course possible, leading to\u2026","rel":"","context":"In &quot;Curly arrows&quot;","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.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/10\/arrow_pushing.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":19807,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19807","url_meta":{"origin":1158,"position":5},"title":"A Theoretical Method for Distinguishing X\u2010H Bond Activation Mechanisms.","author":"Henry Rzepa","date":"July 25, 2018","format":false,"excerpt":"Consider the four reactions. The first two are taught in introductory organic chemistry as (a) a proton transfer,\u00a0often abbreviated PT,\u00a0from X to B (a base) and (b) a hydride transfer from X to A (an acid). The third example is taught as a hydrogen atom transfer or HAT from X\u2026","rel":"","context":"In &quot;Interesting chemistry&quot;","block_context":{"text":"Interesting chemistry","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=4"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2018\/07\/024-1024x350.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\/1158","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=1158"}],"version-history":[{"count":2,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1158\/revisions"}],"predecessor-version":[{"id":19416,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1158\/revisions\/19416"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1158"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1158"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1158"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=1158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}