{"id":2084,"date":"2010-06-01T13:14:40","date_gmt":"2010-06-01T12:14:40","guid":{"rendered":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084"},"modified":"2011-07-07T06:05:42","modified_gmt":"2011-07-07T06:05:42","slug":"chemistry-with-a-super-twist-a-molecular-trefoil-knot-part-2","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084","title":{"rendered":"Chemistry with a super-twist: A molecular trefoil knot, part 2."},"content":{"rendered":"
\n

A conjugated, (apparently) aromatic molecular trefoil might be expected to have some unusual, if not extreme properties. Here some of these are explored.<\/p>\n

    \n
  1. The first is the vibrational spectrum. With 144 atoms for this molecule, it has 426 vibrational modes, but one is highlighted below. This is the mode that moves the atoms in accord with the Kekul\u00e9 resonance. If real, this mode resists such alternation. The mode has a value of ~ 1310 cm-1<\/sup> for benzene, although this is accepted as being lower than expected due to the phenomenon of \u03c0-distortivity (DOI: 10.1039\/b911817a<\/a> and also this post<\/a>). The mode shown below has the value of 1650 cm-1<\/sup>, which is a good deal higher than for benzene. The significant coupling of the CH wagging motions with the C-C\/C-N stretching (Duschinsky coupling) makes the interpretation more complex (it also occurs for benzene itself), but the Kekul\u00e9 mode (there are in fact several) is surprisingly large for so many \u03c0-electrons. Perhaps the large degree of writhe noted in the previous post<\/a> might have something to do with it?
    \"\"

    Molecular trefoil: the Kekul\u00e9 mode for bond alternation. Click for animation.<\/p><\/div><\/li>\n

  2. The NICS<\/a> (nucleus independent chemical shift) at the centroid of the trefoil is -16.4 ppm. This is clearly an aromatic<\/strong> value, and confirms our inference that the system is a 4n+2 aromatic molecule. In this example, the aromaticity is not only three-dimensional, but helical as well. The predicted 1<\/sup>H NMR spectrum (below) shows three regions. The upfield region (~ -5 ppm) corresponds to protons pointing directly inwards to the centre, whilst the lowfield region (~ 8ppm) corresponds to protons at the outside edge.\n

  3. Shown below is the calculated<\/a> electronic circular dichroism (ECD) spectrum. It shows a large Cotton effect due to the chiral nature of the trefoil. The electronic transitions extend beyond ~1500nm, approaching the near infra-red. The phase of the Cotton effect at ~600nm calculated for the chiral isomer shown in the 3D model above would certainly suffice to assign the absolute configuration of the system should the experimental spectrum be measurable.\n
    \"\"<\/a>

    Calculated Electronic circular dichroism spectrum for the base trefoil.<\/p><\/div>\n

    The spectrum above shows maximum absorption at ~600nm, which means optical rotation at the sodium D-line (589 nm) cannot be measured (light has to get through to measure its rotation). However, the region of 880nm (the highest value available on commercial spectrometers) is reasonably transparent for such measurement. Calculations may not be much help, since the linear CPHF equations appear unstable. Thus [\u03b1]880<\/sub> shows an enormous dependence on the precise DFT method chosen to compute it (~ +8763\u00b0@CAM-B3LYP but the very different -59898\u00b0@B3LYP).<\/li>\n<\/ol>\n

    \n

    Henry Rzepa. Chemistry with a super-twist: A molecular trefoil knot, part 2.. . 2010-06-02. URL:http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084. Accessed: 2010-06-02. (Archived by WebCite\u00ae at http:\/\/www.webcitation.org\/5qC4NiFsM<\/a>)<\/p>\n

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

    A conjugated, (apparently) aromatic molecular trefoil might be expected to have some unusual, if not extreme properties. Here some of these are explored. The first is the vibrational spectrum. With 144 atoms for this molecule, it has 426 vibrational modes, but one is highlighted below. This is the mode that moves the atoms in accord […]<\/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":[152,237,575,202,2648],"ppma_author":[2661],"class_list":["post-2084","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry","tag-animation","tag-chemical-shift","tag-chiroptical","tag-henry-rzepa","tag-interesting-chemistry"],"yoast_head":"\nChemistry with a super-twist: A molecular trefoil knot, part 2. - 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=2084\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Chemistry with a super-twist: A molecular trefoil knot, part 2. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"A conjugated, (apparently) aromatic molecular trefoil might be expected to have some unusual, if not extreme properties. Here some of these are explored. The first is the vibrational spectrum. With 144 atoms for this molecule, it has 426 vibrational modes, but one is highlighted below. This is the mode that moves the atoms in accord […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa's Blog\" \/>\n<meta property=\"article:published_time\" content=\"2010-06-01T12:14:40+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2011-07-07T06:05:42+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/06\/trefoil-kekule.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":"Chemistry with a super-twist: A molecular trefoil knot, part 2. - Henry Rzepa'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=2084","og_locale":"en_GB","og_type":"article","og_title":"Chemistry with a super-twist: A molecular trefoil knot, part 2. - Henry Rzepa's Blog","og_description":"A conjugated, (apparently) aromatic molecular trefoil might be expected to have some unusual, if not extreme properties. Here some of these are explored. The first is the vibrational spectrum. With 144 atoms for this molecule, it has 426 vibrational modes, but one is highlighted below. This is the mode that moves the atoms in accord […]","og_url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084","og_site_name":"Henry Rzepa's Blog","article_published_time":"2010-06-01T12:14:40+00:00","article_modified_time":"2011-07-07T06:05:42+00:00","og_image":[{"url":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/06\/trefoil-kekule.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=2084#article","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084"},"author":{"name":"Henry Rzepa","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"headline":"Chemistry with a super-twist: A molecular trefoil knot, part 2.","datePublished":"2010-06-01T12:14:40+00:00","dateModified":"2011-07-07T06:05:42+00:00","mainEntityOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084"},"wordCount":501,"commentCount":3,"image":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084#primaryimage"},"thumbnailUrl":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/06\/trefoil-kekule.jpg","keywords":["animation","chemical shift","chiroptical","Henry Rzepa","Interesting chemistry"],"articleSection":["Interesting chemistry"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084#respond"]}]},{"@type":"WebPage","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084","name":"Chemistry with a super-twist: A molecular trefoil knot, part 2. - Henry Rzepa's Blog","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084#primaryimage"},"image":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084#primaryimage"},"thumbnailUrl":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/06\/trefoil-kekule.jpg","datePublished":"2010-06-01T12:14:40+00:00","dateModified":"2011-07-07T06:05:42+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=2084#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084#primaryimage","url":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/06\/trefoil-kekule.jpg","contentUrl":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/06\/trefoil-kekule.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2084#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog"},{"@type":"ListItem","position":2,"name":"Chemistry with a super-twist: A molecular trefoil knot, part 2."}]},{"@type":"WebSite","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/","name":"Henry Rzepa'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-xC","jetpack-related-posts":[{"id":485,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=485","url_meta":{"origin":2084,"position":0},"title":"Longer is stronger.","author":"Henry Rzepa","date":"June 6, 2009","format":false,"excerpt":"The iconic diagram below represents a cornerstone of organic chemistry. Generations of chemists have learnt early on in their studies of the subject that these two representations of where the electron pairs in benzene might be located (formally called electronic resonance or valence bond forms) each contribute ~50% to the\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":"The Kekule structures of benzene.","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/06\/benzene.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":12583,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=12583","url_meta":{"origin":2084,"position":1},"title":"Kekul\u00e9’s vibration: A modern example of its use.","author":"Henry Rzepa","date":"June 6, 2014","format":false,"excerpt":"Following the discussion here of Kekul\u00e9's suggestion of what we now call a vibrational mode (and which in fact now bears his name), I thought I might apply the concept to a recent molecule known as [2.2]paracyclophane. The idea was sparked by Steve Bachrach's latest post, where the \"zero-point\" structure\u2026","rel":"","context":"In "Historical"","block_context":{"text":"Historical","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=565"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2046,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2046","url_meta":{"origin":2084,"position":2},"title":"Chemistry with a super-twist: A molecular trefoil knot, part 1.","author":"Henry Rzepa","date":"May 31, 2010","format":false,"excerpt":"Something important happened in chemistry for the first time about 100 years ago. A molecule was built (nowadays we would say synthesized) specifically for the purpose of investigating a theory. It was cyclo-octatetraene or (CH)8, and it was made by Willst\u00e4tter and Waser to try to find out if benzene,\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\/05\/metallatrefoil.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":2502,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2502","url_meta":{"origin":2084,"position":3},"title":"Secrets of a university admissions interviewer","author":"Henry Rzepa","date":"September 19, 2010","format":false,"excerpt":"Many university chemistry departments, and mine is no exception, like to invite applicants to our courses to show them around. Part of the activities on the day is an \"interview\" in which the candidate is given a chance to shine. Over the years, I have evolved questions about chemistry which\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\/09\/co2-trimer.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":21631,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=21631","url_meta":{"origin":2084,"position":4},"title":"Molecules of the year – 2019: Topological molecular nanocarbons – All-benzene catenane and trefoil knot.","author":"Henry Rzepa","date":"December 15, 2019","format":false,"excerpt":"Here is another molecule of the year, on a topic close to my heart, the catenane systems 1 and the trefoil knot 2 Such topology is closely inter-twinned with three dimensions (literally) and I always find that the flat pages of a journal are simply insufficient to do them justice.\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\/2019\/12\/trefoils-1024x492.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":12329,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=12329","url_meta":{"origin":2084,"position":5},"title":"More (blog) connections spotted. Something new about diphenyl magnesium?","author":"Henry Rzepa","date":"April 17, 2014","format":false,"excerpt":"I have just noticed unexpected links between two old posts, one about benzene, one about diphenyl magnesium\u00a0and\u00a0a link to August Kekul\u00e9.\u2020 The post about benzene dealt with the apparently simple issue of why all the C-C bonds are of equal length. The answer, in brief is purely because of the\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":"","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\/2084","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=2084"}],"version-history":[{"count":0,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/2084\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2084"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=2084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}