{"id":21225,"date":"2019-09-03T13:13:58","date_gmt":"2019-09-03T12:13:58","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=21225"},"modified":"2019-09-22T17:33:23","modified_gmt":"2019-09-22T16:33:23","slug":"cyclo6-and-10carbon-the-kekule-vibrations-compared","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=21225","title":{"rendered":"Cyclo[6] and [10]carbon. The Kekul\u00e9 vibrations compared."},"content":{"rendered":"
\n

In the previous post<\/a>, I looked at the so-called\u00a0Kekul\u00e9 vibration of cyclo[18]carbon using various quantum methods and basis sets. \u00a0Because some of these procedures can take a very long time, \u00a0I could not compare them using the same high-quality consistent atom basis set for the carbon (Def2-TZVPP). Here I try to start to do this using the smaller six and ten carbon rings to see what trends might emerge. FAIR data are at DOI:\u00a010.14469\/hpc\/6069<\/a><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Method<\/th>\nC-C bond length<\/th>\nKekul\u00e9 mode, cm-1<\/sup><\/th>\nNumber of -ve force constants<\/th>\n<\/tr>\n
Cyclo[6]carbon<\/td>\n<\/tr>\n
B3LYP+GD3BJ<\/td>\n1.302<\/td>\n1300<\/td>\n2<\/td>\n<\/tr>\n
wB97XD<\/td>\n1.298<\/td>\n1262<\/td>\n2<\/td>\n<\/tr>\n
PBEQIDH<\/td>\n1.302<\/td>\n1332<\/td>\n1<\/td>\n<\/tr>\n
MP2<\/td>\n1.318<\/td>\n1428<\/td>\n0<\/td>\n<\/tr>\n
MP3<\/td>\n1.303<\/td>\n923<\/td>\n0<\/td>\n<\/tr>\n
MP4(SDQ)<\/td>\n1.308<\/td>\n943<\/td>\n0<\/td>\n<\/tr>\n
CCSD<\/td>\n1.308<\/td>\n1020<\/td>\n2<\/td>\n<\/tr>\n
CCSD(T)<\/td>\n1.320<\/td>\n1189<\/td>\n2<\/td>\n<\/tr>\n
Cyclo[10]carbon<\/td>\n<\/tr>\n
B3LYP+GD3BJ<\/td>\n1.282<\/td>\n1334<\/td>\n1<\/td>\n<\/tr>\n
wB97XD<\/td>\n1.279<\/td>\n975<\/td>\n1<\/td>\n<\/tr>\n
PBEQIDH<\/td>\n1.282<\/td>\n1578<\/td>\n0<\/td>\n<\/tr>\n
MP2<\/td>\n1.295<\/td>\n2829<\/td>\n0<\/td>\n<\/tr>\n
MP3<\/td>\n1.283<\/td>\n-1946<\/td>\n1<\/td>\n<\/tr>\n
MP4(SDQ)<\/td>\n1.285<\/td>\n-1003<\/td>\n2<\/td>\n<\/tr>\n
CCSD<\/td>\n1.286<\/td>\n-781<\/td>\n3<\/td>\n<\/tr>\n
CCSD(T)<\/td>\n1.295<\/td>\n1266<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The conclusions can be summarised as:<\/p>\n

    \n
  1. For six carbons, all the methods agree that the Kekul\u00e9 vibration is real (+ve force constant), but there are distinct signs that the MP expansion may \u00a0not be fully converged, with \u00a0MP2 and MP3 differing significantly<\/li>\n
  2. For ten carbons, we already see that \u00a0MP3 and MP4 differ from \u00a0MP2 in predicting a -ve force constant.<\/li>\n<\/ol>\n

    Multi-configuration calculations are problematic with these species. \u00a0For C10<\/sub> for example, 20 electrons (10\u00a0\u03c0 and 10 \u03c3) in an active orbital space of 20 is required; a CASSCF(20,20) is beyond the scope of most quantum programs. And there is a need to evaluate the second derivatives of such a wavefunction in order to get the force constant for the required vibration.\u00a0<\/p>\n

    So the onset of bond length alternation in these cyclo-carbons could be as early as 10 atoms. But until higher level calculations can be performed in a systematic manner on these rings, the jury should perhaps still remain out as to when bond length alternation starts in terms of ring size.<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    In the previous post, I looked at the so-called\u00a0Kekul\u00e9 vibration of cyclo[18]carbon using various quantum methods and basis sets. \u00a0Because some of these procedures can take a very long time, \u00a0I could not compare them using the same high-quality consistent atom basis set for the carbon (Def2-TZVPP). Here I try to start to do this […]<\/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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4],"tags":[],"ppma_author":[2661],"class_list":["post-21225","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry"],"yoast_head":"\nCyclo[6] and [10]carbon. The Kekul\u00e9 vibrations compared. - 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=21225\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cyclo[6] and [10]carbon. The Kekul\u00e9 vibrations compared. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"In the previous post, I looked at the so-called\u00a0Kekul\u00e9 vibration of cyclo[18]carbon using various quantum methods and basis sets. \u00a0Because some of these procedures can take a very long time, \u00a0I could not compare them using the same high-quality consistent atom basis set for the carbon (Def2-TZVPP). 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The Kekul\u00e9 vibrations compared. - 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=21225","og_locale":"en_GB","og_type":"article","og_title":"Cyclo[6] and [10]carbon. The Kekul\u00e9 vibrations compared. - Henry Rzepa's Blog","og_description":"In the previous post, I looked at the so-called\u00a0Kekul\u00e9 vibration of cyclo[18]carbon using various quantum methods and basis sets. \u00a0Because some of these procedures can take a very long time, \u00a0I could not compare them using the same high-quality consistent atom basis set for the carbon (Def2-TZVPP). 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It is a stretching mode that lengthens three of the bonds in benzene (a [6]-annulene) and shortens the other three, thus leading to a cyclohexatriene\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\/08\/C18.gif?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":21407,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=21407","url_meta":{"origin":21225,"position":1},"title":"Does Kekulene have Kekul\u00e9 vibrational modes? Yes!","author":"Henry Rzepa","date":"October 19, 2019","format":false,"excerpt":"Increasingly, individual small molecules are having their structures imaged using STM, including cyclo[18]carbon that I recently discussed. The latest one receiving such treatment is Kekulene. As with cyclo[18]carbon, the point of interest was which of the two resonance structures shown below most closely resembled the measured structure. The one on\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\/10\/b3-1423-B2u-1024x575.gif?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":21925,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=21925","url_meta":{"origin":21225,"position":2},"title":"The singlet and open shell higher-spin states of [4], [6] and [8]-annulenes and their Kekul\u00e9 vibrational modes","author":"Henry Rzepa","date":"March 11, 2020","format":false,"excerpt":"In 2001, Shaik and co-workers published the first of several famous review articles on the topic\u00a0A Different Story of \u03c0-Delocalization. The Distortivity of \u03c0-Electrons and Its Chemical Manifestations. The main premise was that the delocalized \u03c0-electronic component of benzene is unstable toward a localizing distortion and is at the same\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\/2020\/03\/CBD-Eu.gif?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":30276,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=30276","url_meta":{"origin":21225,"position":3},"title":"Molecules of the year 2025: Cyclo[48]carbon and others – the onset of bond alternation and the Raman Activity Spectrum.","author":"Henry Rzepa","date":"December 29, 2025","format":false,"excerpt":"The annual \"Molecules of the Year\" selections are available for the year 2025. A theme was elemental allotropes and one such was carbon in the form of C48\u00a0stabilised by formation of a catenane C48.M3 (M = red ligand below) - it was not possible however to crystallise C48.M3. When \"unmasked\"\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":[]},{"id":17858,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=17858","url_meta":{"origin":21225,"position":4},"title":"First, hexacoordinate carbon \u2013 now pentacoordinate oxygen?","author":"Henry Rzepa","date":"March 25, 2017","format":false,"excerpt":"The previous post demonstrated the simple iso-electronic progression from six-coordinate carbon to five coordinate nitrogen. Here, a further progression to oxygen is investigated computationally. The systems are formally constructed from a cyclobutadienyl di-anion and firstly the HO5+ cation, giving a tri-cationic complex. There are no examples of the resulting motif\u00a0in\u2026","rel":"","context":"In "Bond slam"","block_context":{"text":"Bond slam","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2237"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":21250,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=21250","url_meta":{"origin":21225,"position":5},"title":"The Kekul\u00e9 vibration as a function of aromatic ring size. A different perspective using lemniscular rings.","author":"Henry Rzepa","date":"September 27, 2019","format":false,"excerpt":"In the previous posts, I tried to track down the onset of bond length alternation (BLA) as a function of ring size in aromatic cyclocarbons, finding the answer varied dramatically depending on the type of method used to calculate it. So here I change the system to an unusual kind\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\/21225","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=21225"}],"version-history":[{"count":25,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/21225\/revisions"}],"predecessor-version":[{"id":21268,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/21225\/revisions\/21268"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21225"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21225"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21225"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=21225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}