{"id":21250,"date":"2019-09-27T10:58:30","date_gmt":"2019-09-27T09:58:30","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=21250"},"modified":"2019-09-27T10:58:30","modified_gmt":"2019-09-27T09:58:30","slug":"the-kekule-vibration-as-a-function-of-aromatic-ring-size-a-different-perspective-using-lemniscular-rings","status":"publish","type":"post","link":"https:\/\/www.rzepa.net\/blog\/?p=21250","title":{"rendered":"The Kekul\u00e9 vibration as a function of aromatic ring size. A different perspective using lemniscular rings."},"content":{"rendered":"
\n

In the previous posts, I tried to track down the onset of bond length alternation (BLA<\/strong>) 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 of aromatic ring, the leminiscular<\/em> or figure-eight<\/em> annulene series.\u2665<\/sup><\/span>\u00a0I explore the Kekul\u00e9 vibration for such species for which a 4n+2 \u03c0 electron count means they are cyclically M\u00f6bius aromatic.[1]<\/a><\/span><\/p>\n

The advantage of using a lemniscular motif compared to the untwisted annulene is that perturbations due to trans<\/em>-annular steric interactions between inward facing substituents are minimised. Before introducing the results for this type of molecule, I should also explain why the series\u00a0Cn<\/sub>Fn<\/sub> is used rather than Cn<\/sub>Hn<\/sub>. This is because the\u00a0C-C-H bending vibration is very similar in energy to the Kekul\u00e9 C-C stretches, causing them to mix significantly and obscure the results.\u00a0Substitution with\u00a0F produces “clean<\/a>”\u00a0Kekul\u00e9 modes. You can see this below:<\/p>\n

\"\"<\/a> \"\"<\/a> \"\"<\/a><\/p>\n

One consequence of introducing two half-twists into the \u03c0-system is that this topology gets partitioned into true twist (Tw<\/sub>) and into a different property known as writhe (Wr<\/sub>),[2]<\/a><\/span> the overall effect of which is to reduce the\u00a0p-\u03c0\/p-\u03c0 overlaps of adjacent carbon atoms from suffering two twists to about half this. This in turn may affect the distortive tendency of the \u03c0-electrons to induce BLA in the ring.[3]<\/a><\/span>\u00a0\u00a0Let us now see what this change of molecule does to the value (and sign) of the Kekul\u00e9 vibration. Included are conformations for the larger rings which vary in the total number of trans F-CC-F units in the ring. All the FAIR data for these calculations is at DOI: 10.14469\/hpc\/6139<\/a><\/p>\n

Two density functional methods have been used, at opposite ends of the spectrum revealed in the previous posts, together with a reasonable Def2-TZVPP basis set.\u2021<\/sup>\u00a0Each ring size can have different isomers, depending on the total number of transoid motifs present. For smaller rings (n=6, 10), the B3LYP+GD3BJ and \u03c9B97XD functionals give very similar results. By n=18 however, a clear divergence has occurred, with the\u00a0Kekul\u00e9 modes being real (+ve force constant) for the former and almost equally imaginary (-ve force constant) for the latter.\u00a0<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Cn<\/sub>Fn<\/sub>, n=<\/th>\nKekul\u00e9 vibration (cm-1<\/sup>)<\/th>\n<\/tr>\n
B3LYP+GD3BJ<\/th>\n\u03c9B97XD<\/th>\n<\/tr>\n
6 (0 trans)<\/td>\n1305<\/td>\n1293<\/td>\n<\/tr>\n
\n
\n<\/td>\n<\/tr>\n
10 (2 trans)<\/td>\n1270<\/td>\n1067<\/td>\n<\/tr>\n
10 (4 trans)<\/td>\n1279<\/td>\n1222<\/td>\n<\/tr>\n
\n
\n<\/td>\n<\/tr>\n
14 (2 trans)<\/td>\n1235<\/td>\n1012<\/td>\n<\/tr>\n
14 (4 trans)<\/td>\n1128<\/td>\n-513<\/td>\n<\/tr>\n
14 (6 trans)<\/td>\n1197<\/td>\n-592<\/td>\n<\/tr>\n
\n
\n<\/td>\n<\/tr>\n
18 (2 trans)<\/td>\n974<\/td>\n-987<\/td>\n<\/tr>\n
18 (4 trans)<\/td>\n914<\/td>\n-1091<\/td>\n<\/tr>\n
18 (6 trans)<\/td>\n933<\/td>\n-1232<\/td>\n<\/tr>\n
\n
\n<\/td>\n<\/tr>\n
22 (4 trans)<\/td>\n888<\/td>\n-1309<\/td>\n<\/tr>\n
22 (6 trans)<\/td>\n757<\/td>\n-1811<\/td>\n<\/tr>\n
\n
\n<\/td>\n<\/tr>\n
26 (6 trans)<\/td>\n\u2020<\/td>\n-2140<\/td>\n<\/tr>\n
26 (8 trans)<\/td>\n756<\/td>\n-2229<\/td>\n<\/tr>\n
26 (10 trans)<\/td>\n-437<\/td>\n-3296<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Overall, the B3LYP+GD3BJ series shows a slow and reasonably regular decline in the\u00a0value of the Kekul\u00e9 modes. As the ring sizes gets larger, the double bond configurations of the rings start to become unstable, with C=C bond rotations occuring during geometry optimisations. At n=26 using B3LYP, we seen a sudden change from a real Kekul\u00e9 mode mode for the 8-trans isomer to an imaginary one for the 10-trans isomer. As noted above, this abrupt change occurs much earlier with the \u03c9B97XD functional at n=14, with\u00a0a discontinuity between a conformation with two transoid motifs and the ones with four and six.\u00a0I can offer no explanation (yet) for this strange abrupt onset of an imaginary Kekul\u00e9 mode, except perhaps to speculate that it might be related to the Tw<\/sub>\u00a0and Wr <\/sub>partitioning noted above, given that Tw\u00a0<\/sub>and BLA might themselves be related. As with the cyclocarbons<\/a>, the BLA phenomenon seems to be peculiarly sensitive to the method used to compute it, more so than most other molecular properties.<\/p>\n

Something deep and important is clearly happening and the underlying cause does need to be identified. It reminds in one sense also of the discontinuous transition between planar aromatic (bond equal) and \u00a0non-planar non-aromatic (BLA) \u00a0isomers of 10-\u03c0-Dihetero[8]annulenes[4]<\/a><\/span> \u00a0Who might have imagined that simple aromatic rings could be so tantalisingly complex!<\/p>\n

\n

\u2665<\/sup><\/span> The first example of this was identified in 2005[5]<\/a><\/span> and is characterised by a topological chiral property known as a linking number or Lk. For lemniscular molecules, Lk = 2\u03c0, or in plainer english it contains a double half twist in the \u03c0 system around the ring. \u2021<\/sup>This investigation is a perfect example of the benefits of using a data repository. Many of these species were originally included in an article published in 2009[6]<\/a><\/span> with the calculations being deposited in 2007. So all the starting geometries for the present investigation were quickly obtained from that source. \u2020Bonds rotate to 10-trans isomer.<\/p>\n

References<\/h2>\n
  1. P.L. Ayers, R.J. Boyd, P. Bultinck, M. Caffarel, R. Carb\u00f3-Dorca, M. Caus\u00e1, J. Cioslowski, J. Contreras-Garcia, D.L. Cooper, P. Coppens, C. Gatti, S. Grabowsky, P. Lazzeretti, P. Macchi, ?. Mart\u00edn Pend\u00e1s, P.L. Popelier, K. Ruedenberg, H. Rzepa, A. Savin, A. Sax, W.E. Schwarz, S. Shahbazian, B. Silvi, M. Sol\u00e0, and V. Tsirelson, \"Six questions on topology in theoretical chemistry\", Computational and Theoretical Chemistry<\/i>, vol. 1053, pp. 2-16, 2015. https:\/\/doi.org\/10.1016\/j.comptc.2014.09.028<\/a>\n\n<\/li>\n
  2. S.M. Rappaport, and H.S. Rzepa, \"Intrinsically Chiral Aromaticity. Rules Incorporating Linking Number, Twist, and Writhe for Higher-Twist M\u00f6bius Annulenes\", Journal of the American Chemical Society<\/i>, vol. 130, pp. 7613-7619, 2008. https:\/\/doi.org\/10.1021\/ja710438j<\/a>\n\n<\/li>\n
  3. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, \"A Different Story of \u03c0-DelocalizationThe Distortivity of \u03c0-Electrons and Its Chemical Manifestations\", Chemical Reviews<\/i>, vol. 101, pp. 1501-1540, 2001. https:\/\/doi.org\/10.1021\/cr990363l<\/a>\n\n<\/li>\n
  4. H.S. Rzepa, and N. Sanderson, \"Aromaticity on the edge of chaos: An ab initio study of the bimodal balance between aromatic and non-aromatic structures for 10\u03c0-dihetero[8]annulenes\", Phys. Chem. Chem. Phys.<\/i>, vol. 6, pp. 310-313, 2004. https:\/\/doi.org\/10.1039\/b312724a<\/a>\n\n<\/li>\n
  5. H.S. Rzepa, \"A Double-Twist M\u00f6bius-Aromatic Conformation of [14]Annulene\", Organic Letters<\/i>, vol. 7, pp. 4637-4639, 2005. https:\/\/doi.org\/10.1021\/ol0518333<\/a>\n\n<\/li>\n
  6. C.S. Wannere, H.S. Rzepa, B.C. Rinderspacher, A. Paul, C.S.M. Allan, H.F. Schaefer, and P.V.R. Schleyer, \"The Geometry and Electronic Topology of Higher-Order Charged M\u00f6bius Annulenes\", The Journal of Physical Chemistry A<\/i>, vol. 113, pp. 11619-11629, 2009. https:\/\/doi.org\/10.1021\/jp902176a<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    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 of aromatic ring, the leminiscular […]<\/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-21250","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-5wK","jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/21250","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=21250"}],"version-history":[{"count":0,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/21250\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21250"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21250"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}