{"id":1135,"date":"2009-11-11T10:48:36","date_gmt":"2009-11-11T09:48:36","guid":{"rendered":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1135"},"modified":"2011-06-12T09:16:42","modified_gmt":"2011-06-12T09:16:42","slug":"the-sn1-reaction-revisited","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1135","title":{"rendered":"The SN1 Reaction- revisited"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"1135\">\n<p>In an earlier <a href=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=63\">post<\/a> I wrote about the iconic  S<sub>N<\/sub>1 solvolysis reaction, and presented a model for the transition state involving  13 water molecules. Here, I follow this up with an improved molecule containing 16 water molecules, and how the barrier for this model compares with experiment.  This latter is nicely summarized in the following article:  <a href=\"http:\/\/dx.doi.org\/10.1039\/F19736901195\" target=\"references\">Solvolysis of t-butyl chloride in water-rich methanol + water mixtures<\/a>, which  (for pure water) cites the following activation parameters<\/p>\n<ul>\n<li> \u0394H<sup>\u2020<\/sup><sub>283<\/sub> = 23.0 kcal\/mol<\/li>\n<li> \u0394G<sup>\u2020<\/sup><sub>283<\/sub> = 19.7 kcal\/mol<\/li>\n<li> \u0394S<sup>\u2020<\/sup><sub>283<\/sub> = +11.1 cal\/mol\/K<\/li>\n<\/ul>\n<p>But first, a word about how this new transtion state has been obtained.  The DFT treatment used is quite standard (B3LYP\/6-31G(d) ), and one can indeed locate a transition state using just this approach (this is how the previous model was obtained).  One has to work very hard to orient the starting guess for the geometry so that as many hydrogen bonds between the waters themselves, and to the substrate, are created. The previous model took quite a few guesses and attempts!  The solvent in such a model is simulated by the explicit water molecules themselves. Of course, the quality of the  <em>solvent<\/em> then depends on how many water molecules are used.  A proper solvent field using explicit water molecules is thought to require 100s of water molecules!  But a reasonable approximation\/compromise may well be  13.<\/p>\n<p>So how can the model be improved? Well, in many ways, some of which include treating the dynamics of the system.  But I will stick just to two.<\/p>\n<ol>\n<li> Firstly, we assume that the water molecules are used to form a  <strong>bridge<\/strong> between the incoming nucleophile (another water) and the leaving group (the chloride). In the previous model, two such bridges were constructed using the  13 water molecules. But in fact, there is still space between two of the methyl groups to construct a third bridge.  This takes the total solvent molecules to  16.<\/li>\n<li> Solvent can also be modelled as a <em>continuum<\/em>, in which a cavity which the substrate occupies is surrounded by  a field generated by the continuum solvent. The problem with these cavity approaches in the past has been  that  it is not easy to optimize the geometry of the molecule contained within the cavity. Because the cavity was constructed by tesselation, the first derivatives of the energy of the molecule within the cavity were not regular,   and as a result, geometry optimization (and particularly transition state optimization) would frequently meander and fail to converge. Darrin York and Martin Karplus came to the rescue (some time ago, it has to be said, DOI: <a href=\"http:\/\/dx.doi.org\/10.1021\/jp992097l\" target=\"references\">10.1021\/jp992097l<\/a>) by formulating a smoothed out solvation cavity where the first (and second derivatives) are stable and well behaved. This new algorithm has now been implemented in  Gaussian09, and it now allows really easy transition state location within a solvent cavity<\/li>\n<\/ol>\n<p>The result of this optimization is shown below (and can be seen in original form at the following DOI: <a href=\"http:\/\/hdl.handle.net\/10042\/to-2894\" target=\"references\">10042\/to-2894<\/a>).<\/p>\n<p><div id=\"attachment_1138\" style=\"width: 264px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1138\" class=\"size-full wp-image-1138\" title=\"Transition state for  Sn1 solvolysis of  tert-butyl chloride\" onclick=\"jmolInitialize('..\/Jmol\/');jmolSetAppletColor('cyan');jmolApplet([450,450],'load wp-content\/uploads\/2009\/11\/sn1-16-74.xyz; frame 1; zoom 100; connect (atomno=15) (atomno=1) PARTIAL;connect (atomno=1) (atomno=14) PARTIAL;vectors  on;vectors 4;vectors scale 5.0; color vectors black; vibration 20;animation mode loop;measure  17 24;measure 21 26;measure 22 18;measure 15 43;measure 44 30;measure 31 27;');\" src=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/11\/sn1.jpg\" alt=\"Transition state for  Sn1 solvolysis of  tert-butyl chloride\" width=\"254\" height=\"301\" \/><p id=\"caption-attachment-1138\" class=\"wp-caption-text\">Transition state for  Sn1 solvolysis of  tert-butyl chloride. Click for animation.<\/p><\/div>The model has not changed that much compared to before.  The reaction  (imaginary) mode  still clearly shows formation of the  C-O bond and cleavage of the C-Cl bond. Also as before, there is a lot of motion of the methyl groups, as the forming cation induces stereo-electronic alignment with the  adjacent C-H bonds (and which explains the large secondary deuterium isotope effects measured for this reaction, k<sub>H<\/sub>\/k<sub>D<\/sub> (298) = 2.39,  see DOI: <a href=\"http:\/\/dx.doi.org\/10.1021\/ja01080a004\" target=\"references\">10.1021\/ja01080a004<\/a>). The hydrogen bonding pattern is also retained (despite the surrounding solvent field!).  But what of the predicted activation parameters<\/p>\n<ul>\n<li> \u0394H<sup>\u2020<\/sup><sub>298<\/sub> = 17.4 kcal\/mol<\/li>\n<li> \u0394G<sup>\u2020<\/sup><sub>298<\/sub> = 18.7 kcal\/mol<\/li>\n<li> \u0394S<sup>\u2020<\/sup><sub>298<\/sub> = -4.4 cal\/mol\/K<\/li>\n<\/ul>\n<p>The overall free energy is in great agreement with experiment!  But the entropy is the wrong sign!! The calculation is predicting that the transition state is more rigid than the reactant. One can see how this might happen, since the greater ionic character produces very much stronger hydrogen bonds, which strengthen the three solvent bridges.  It may be simply that the rigid-rotor-harmonic-oscillator approximation breaks down horribly for the entropy in this calculation.   But it is encouraging that the activation barrier is reproducing experiment, which suggests the model cannot be completely wrong!<\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 1135 -->","protected":false},"excerpt":{"rendered":"<p>In an earlier post I wrote about the iconic SN1 solvolysis reaction, and presented a model for the transition state involving 13 water molecules. Here, I follow this up with an improved molecule containing 16 water molecules, and how the barrier for this model compares with experiment. This latter is nicely summarized in the following [&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":[4],"tags":[152,150,24,2651,2648,149,14,151],"ppma_author":[2661],"class_list":["post-1135","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry","tag-animation","tag-darrin-york","tag-energy","tag-historical","tag-interesting-chemistry","tag-martin-karplus","tag-organic-reaction-mechanism","tag-overall-free-energy"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The SN1 Reaction- revisited - 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=1135\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The SN1 Reaction- revisited - Henry Rzepa&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"In an earlier post I wrote about the iconic SN1 solvolysis reaction, and presented a model for the transition state involving 13 water molecules. 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Perisolvolysis of a cyclopropyl chloride.","author":"Henry Rzepa","date":"December 13, 2011","format":false,"excerpt":"There are many treasures in Woodward and Hoffmann's (WH)\u00a0classic monograph. One such is acetolysis of \u00a0the endo chloride (green), which is much much faster than that of the exo isomer (red). The explanation given in their article (p 805) confines itself to succinctly stating that only loss of the endo\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.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2011\/12\/cpendo.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":20560,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=20560","url_meta":{"origin":1135,"position":1},"title":"Smoke and mirrors. All is not what it seems with this Sn2 reaction!","author":"Henry Rzepa","date":"April 4, 2019","format":false,"excerpt":"Previously, I explored the Graham reaction to form a diazirine. The second phase of the reaction involved an Sn2' displacement of N-Cl forming C-Cl. Here I ask how facile the simpler displacement of C-Cl by another chlorine might be and whether the mechanism is Sn2 or the alternative Sn1. The\u2026","rel":"","context":"In &quot;reaction mechanism&quot;","block_context":{"text":"reaction mechanism","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1086"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":4002,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=4002","url_meta":{"origin":1135,"position":2},"title":"The Sn1&#8230;Sn2 mechanistic continuum. The special case of neopentyl bromide","author":"Henry Rzepa","date":"May 9, 2011","format":false,"excerpt":"Introductory organic chemistry invariably features the mechanism of haloalkane solvolysis, and introduces both the Sn1 two-step mechanism, and the Sn2 one step mechanism to students. They are taught to balance electronic effects (the stabilization of carbocations) against steric effects in order to predict which mechanism prevails. It was whilst preparing\u2026","rel":"","context":"In \"free energy\"","block_context":{"text":"free energy","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?tag=free-energy"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2011\/05\/neopentyl-ts.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":29626,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=29626","url_meta":{"origin":1135,"position":3},"title":"Hydrogenating the even more mysterious N\u2261N triple bond in a nitric oxide dimer.","author":"Henry Rzepa","date":"August 25, 2025","format":false,"excerpt":"Previously I looked at some of the properties of the mysterious dimer of nitric oxide \u00a01 - not the known weak dimer but a higher energy form with a \"triple\" N\u2261N bond. This valence bond isomer of the weak dimer was some 24 kcal\/mol higher in free energy than the\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":8246,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8246","url_meta":{"origin":1135,"position":4},"title":"Thalidomide. The role of water in the mechanism of its aqueous racemisation.","author":"Henry Rzepa","date":"November 10, 2012","format":false,"excerpt":"Thalidomide is a chiral molecule, which was sold in the 1960s as a sedative in its (S,R)-racemic form. The tragedy was that the (S)-isomer was tetragenic, and only the (R) enantiomer acts as a sedative. What was not appreciated at the time is that interconversion of the (S)- and (R)\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.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2012\/11\/thal1.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":16308,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=16308","url_meta":{"origin":1135,"position":5},"title":"Deuteronium deuteroxide. The why of pD 7.435.","author":"Henry Rzepa","date":"April 22, 2016","format":false,"excerpt":"Earlier, I constructed a possible model of hydronium hydroxide, or H3O+.OH-\u00a0One way of assessing the quality of\u00a0the model is\u00a0to\u00a0calculate\u00a0the free energy difference between it and two normal water molecules\u00a0and compare\u00a0the result to\u00a0the measured\u00a0difference. Here I apply a further test of the model using isotopes. Pure water has pH 7, which\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":[]}],"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\/1135","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=1135"}],"version-history":[{"count":0,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1135\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1135"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=1135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}