{"id":7926,"date":"2012-10-12T14:42:28","date_gmt":"2012-10-12T13:42:28","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=7926"},"modified":"2013-02-14T08:11:34","modified_gmt":"2013-02-14T08:11:34","slug":"ring-flipping-in-cyclohexane-in-a-different-light","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=7926","title":{"rendered":"Ring-flipping in cyclohexane in a different light"},"content":{"rendered":"
\n

The conformational analysis of cyclohexane<\/a> is a mainstay of organic chemistry. Is there anything new that can be said about it? Let us start with the diagram below:<\/p>\n

\"\"<\/p>\n

This identifies the start of the process as a chair conformation of cyclohexane, with D3d<\/sub> symmetry. I have highlighted a pair of hydrogens attached to the left most carbon atom in blue (equatorial) and magenta (axial). On the right hand side of the diagram this pair has transposed position, with the blue now being axial and the magenta equatorial. The same is true of the other five pairs of methylene hydrogens. We need to identify the pathway by which this happens. The pathway shown above proceeds through a half-chair transition state of C2<\/sub> symmetry, falling to the first intermediate twist-boat of D2<\/sub> symmetry before reaching a second transition state of C2v<\/sub> symmetry known as the boat. The whole diagram is mirror-symmetric about this point. The point to note about this diagram is that the species labelled C2<\/sub> and D2<\/sub> are dissymetric (chiral), whereas the ones labelled D3d<\/sub> and C2v<\/sub> are not. This means that there are two enantiomeric half-chair transition states, as there are the two twist-boats. This introduction of (di)symmetry does rather change the way we look at the process!<\/p>\n

Now let me introduce the intrinsic reaction coordinate<\/a> (IRC, \u03c9B97XD\/6-311G(d,p)\/SCRF=cyclohexane), as followed from the half-chair transition state, and connecting the chair and the twist-boat.<\/p>\n\n\n\n\n\n
View 1 (click to see Chair )<\/td>\nView 2 (click to see Twist-boat)<\/td>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

View 1<\/strong> is looking down the C2<\/sub> axis present in the half-chair transition state and both start and end points. View 2<\/strong> rotates this by 90\u00b0 along the y-axis, and is again looking down a C2<\/sub> axis. This axis is present only when the IRC starts at the D3d<\/sub> chair conformation or reaches a D2<\/sub> twist-boat conformation (becoming one of three at this point). The latter conformation is ~6 kcal\/mol higher in energy than the chair. At this twist-boat geometry (shown below), the two hydrogens labelled with blue and magenta appear to be in an identical environment (in other words the axial or equatorial distinction between them is lost at this point). This might appear to be what we need to “flip” the environments of any pair of axial and equatorial hydrogens. But is it sufficient?<\/p>\n

\"\"<\/p>\n

At the twist boat above, whilst the chemical environment of the pair of hydrogens identified with blue and magenta arrows is identical, their (pro)chirality is not. Because they both sit in a chiral molecule, their individual relationship to that chirality is said to be pro-chiral. The path shown above, on its own, does not interconvert the (pro)chirality of this pair of hydrogens. To do this, we need to get to the enantiomeric twist-boat conformation shown below, and this is achieved by passing through an achiral transition state of C2v<\/sub> symmetry, in other words a pure boat <\/strong>(see below).<\/p>\n

\"\"<\/p>\n

Well, now I pose a question. Is the above route the ONLY way of transposing the axial\/equatorial identity of pairs of methylene hydrogens in this molecule? If you check the text books, some will in fact show a different diagram, in which the C2v\u00a0<\/sub>boat is entirely uninvolved\u00a0and only one enantiomer of the\u00a0D2<\/sub>\u00a0twist-boat conformations is shown, as below.<\/p>\n

\"\"<\/p>\n

These two pathways do differ fundamentally. The first (longer) pathway passes through an achiral boat transition state. The second (shorter) one involves two chiral half-chair transition states connecting a single chiral twist-boat, but implies that there must be two such pathways, each the enantiomer of the other. \u00a0I should point out that since these two options share a common transition state, their energies are identical. Which one is the more realistic? \u00a0I think only the technique of molecular dynamics, in which the momentum of the trajectories along the path is factored in, will tell us.\u00a0<\/p>\n

\n

Postscript<\/strong>: The IRC for the enantiomerization of one twist boat into the other<\/a> via<\/em> a boat transition state is shown below. The axial-equatorial transpositions can be clearly seen in this view.<\/p>\n

\"\"<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

The conformational analysis of cyclohexane is a mainstay of organic chemistry. Is there anything new that can be said about it? Let us start with the diagram below: This identifies the start of the process as a chair conformation of cyclohexane, with D3d symmetry. I have highlighted a pair of hydrogens attached to the left […]<\/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":[],"tags":[48,919,17,24,373],"ppma_author":[2661],"class_list":["post-7926","post","type-post","status-publish","format-standard","hentry","tag-chair","tag-chemical-environment","tag-conformational-analysis","tag-energy","tag-tutorial-material"],"yoast_head":"\nRing-flipping in cyclohexane in a different light - 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=7926\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ring-flipping in cyclohexane in a different light - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"The conformational analysis of cyclohexane is a mainstay of organic chemistry. 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The method also gave interesting results for the larger cyclo-octane ring. How about a larger leap into the unknown? Let us proceed as follows. One fun\u2026","rel":"","context":"In "Interesting chemistry"","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\/2010\/02\/B3N3H12.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1587,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1587","url_meta":{"origin":7926,"position":1},"title":"The conformation of cyclohexane","author":"Henry Rzepa","date":"January 28, 2010","format":false,"excerpt":"Like benzene, its fully saturated version cyclohexane represents an icon of organic chemistry. By 1890, the structure of planar benzene was pretty much understood, but organic chemistry was still struggling somewhat to fully embrace three rather than two dimensions. A grand-old-man of organic chemistry at the time, Adolf von Baeyer,\u2026","rel":"","context":"In "General"","block_context":{"text":"General","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1"},"img":{"alt_text":"D6h to C2h for cyclohexane","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/01\/cx-c2h.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":248,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=248","url_meta":{"origin":7926,"position":2},"title":"Conformational analysis and enzyme activity: models for amide hydrolysis.","author":"Henry Rzepa","date":"April 12, 2009","format":false,"excerpt":"The diagram below summarizes an interesting result recently reported by Hanson and co-workers (DOI: 10.1021\/jo800706y. At ~neutral pH, compound 13 hydrolyses with a half life of 21 minutes, whereas 14 takes 840 minutes. Understanding this difference in reactivity may allow us to understand why some enzymes can catalyze the hydrolysis\u2026","rel":"","context":"In "Interesting chemistry"","block_context":{"text":"Interesting chemistry","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=4"},"img":{"alt_text":"Models for peptide cleavage.","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/04\/amide-cleavage.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":20010,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=20010","url_meta":{"origin":7926,"position":3},"title":"Tetrahedral carbon and cyclohexane.","author":"Henry Rzepa","date":"August 22, 2018","format":false,"excerpt":"Following the general recognition of carbon as being tetrahedrally tetravalent in 1869 (Paterno) and 1874 (Van't Hoff and Le Bell), an early seminal exploitation of this to the conformation of cyclohexane was by Hermann Sachse in 1890. This was\u00a0verified when the Braggs in 1913, followed by an oft-cited article by\u2026","rel":"","context":"In "Interesting chemistry"","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\/08\/diamond.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\/2018\/08\/diamond.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2018\/08\/diamond.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2018\/08\/diamond.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2018\/08\/diamond.jpg?resize=1050%2C600&ssl=1 3x"},"classes":[]},{"id":1603,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1603","url_meta":{"origin":7926,"position":4},"title":"The conformational analysis of cyclo-octane","author":"Henry Rzepa","date":"January 31, 2010","format":false,"excerpt":"In the previous post, I suggested that inspecting the imaginary modes of planar cyclohexane might be a fruitful and systematic way in which at least parts of the conformational surface of this ring might be probed. Here, the same process is conducted for cyclo-octane. The ring starts with planar D8h\u2026","rel":"","context":"In "General"","block_context":{"text":"General","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/01\/co-1.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":3276,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=3276","url_meta":{"origin":7926,"position":5},"title":"The melting points from benzene to cyclohexane: a prime example of dispersion forces in action?","author":"Henry Rzepa","date":"December 30, 2010","format":false,"excerpt":"One of the delights of wandering around an undergraduate chemistry laboratory is discussing the unexpected, if not the outright impossible, with students. The >100% yield in a reaction is an example. This is sometimes encountered (albeit only briefly) when students attempt to recrystallise a product from cyclohexane, and get an\u2026","rel":"","context":"In \"antarctic\"","block_context":{"text":"antarctic","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?tag=antarctic"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/12\/benzene.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\/7926","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=7926"}],"version-history":[{"count":23,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7926\/revisions"}],"predecessor-version":[{"id":7951,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7926\/revisions\/7951"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7926"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7926"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7926"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=7926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}