{"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":"2019-09-03T13:13:58","modified_gmt":"2019-09-03T12:13:58","slug":"cyclo6-and-10carbon-the-kekule-vibrations-compared","status":"publish","type":"post","link":"https:\/\/www.rzepa.net\/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,"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":[6],"tags":[1526],"class_list":["post-21225","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry","tag-interesting-chemistry"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1gPyz-5wl","jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/21225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=21225"}],"version-history":[{"count":0,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/21225\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21225"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21225"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}