{"id":28773,"date":"2025-06-01T08:20:34","date_gmt":"2025-06-01T07:20:34","guid":{"rendered":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=28773"},"modified":"2025-06-01T08:20:34","modified_gmt":"2025-06-01T07:20:34","slug":"cyclo-s6-hexathiane-anomeric-effects-again","status":"publish","type":"post","link":"https:\/\/www.rzepa.net\/blog\/?p=28773","title":{"rendered":"Cyclo-S6 (Hexathiane) – anomeric effects again!"},"content":{"rendered":"
\n

I thought I was done with exploring anomeric effects in small sulfur rings. However, I then realised that all the systems\u00a0that I had described had an odd number of atoms and that I had not looked at any even numbered rings. Thus hexasulfur<\/a> is a smaller (known) ring version of S8<\/sub>, the latter by far the best known allotrope of this element of course.<\/p>\n

Its crystal structure[1]<\/a><\/span> shows it has D3d<\/sub> symmetry, with six identical S-S bond lengths of 2.068\u00c5. A MN15-L\/Def2-TZVPP calculation[2]<\/a><\/span> replicates this pretty well.
\n\"\"
\nSince anomeric effects manifest in crystal structures by unequal bond lengths, at first sight it seemed unlikely that this ring could be shown to exhibit them. But wait, another conformation can be found, what in cyclohexane would be called the twist-boat. It is however around 12 kcal\/mol higher in free energy than the stable form.[3]<\/a><\/span> and has lower (chiral) D2<\/sub> symmetry. This now shows two slightly shorter bonds and four slightly longer bonds. The anomeric NBO E(2) perturbation energies are a relatively modest 7.93 kcal\/mol (S1Lp<\/sub>-S2-S6\u03c3*<\/sub>) resulting in modest S1-S2 bond shortening and comensurate S2-S6 lengthening. By symmetry, three other identical effects manifest.
\n\"\"
\nSo these stereoelectronic effects CAN manifest in even-numbered rings, but only in this case as a higher energy conformer.<\/p>\n

I also show O6<\/sub>, with C2<\/sub> symmetry. As with O7<\/sub> and O5<\/sub> discussed previously[4]<\/a><\/span> the anomeric effect promotes (partial) dissociation into three molecules of O2<\/sub>[5]<\/a><\/span>, but this process is not complete (computationally) \u00a0and weak partial bonds of ~1.997 and 2.06\u00c5 remain between the three O2<\/sub> species, which are probably in fact artefacts of using a single-determinantal wavefunction.\u00a0However it is fun to observe that the NBO E(2) terms are now (O1Lp<\/sub>-O5-O6\u03c3*<\/sub>)\u00a0135<\/strong> kcal\/mol and the even larger (O2Lp<\/sub>-O3-O4\u03c3*<\/sub>) 218<\/strong> kcal\/mol (tending to \u221e for a fully broken bond). These absurdly large values are a consequence of the non-converging perturbation expansion, but they are still amusing to see.
\n\"\"
\nIf you want to see the orbital interactions (as shown on the earlier blogs on this topic), why not download the wavefunction (the .fchk file<\/a>) from the repository archive at the\u00a0DOIs shown above and reveal them for yourself using suitable programs (the free Avogadro2 program<\/a> is one that can do this exceedingly well). After this, I hesitate to say I will not find some other aspects of small sulfur and oxygen rings to write about, but other topics call for the time being!<\/p>\n

References<\/h2>\n
  1. J. Steidel, J. Pickardt, and R. Steudel, \"Redetermination of the Crystal and Molecular Structure of Cyclohexasulfur, S<sub>6<\/sub> [1]\", Zeitschrift f\u00fcr Naturforschung B<\/i>, vol. 33, pp. 1554-1555, 1978. https:\/\/doi.org\/10.1515\/znb-1978-1238<\/a>\n\n<\/li>\n
  2. H. Rzepa, \"S6, D3d, NBO7 G =-2388.986031\", 2025. https:\/\/doi.org\/10.14469\/hpc\/15261<\/a>\n\n<\/li>\n
  3. H. Rzepa, \"S6, D2, NBO7 G = -2388.966504 DG = +12.25\", 2025. https:\/\/doi.org\/10.14469\/hpc\/15260<\/a>\n\n<\/li>\n
  4. H. Rzepa, \"Cyclo-Heptasulfur, S<sub>7<\/sub> \u2013 a classic anomeric effect discovered during a pub lunch!\", 2025. https:\/\/doi.org\/10.59350\/rzepa.28407<\/a>\n\n<\/li>\n
  5. H. Rzepa, \"O6 NBO C2, G = -450.664220\", 2025. https:\/\/doi.org\/10.14469\/hpc\/15259<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    I thought I was done with exploring anomeric effects in small sulfur rings. However, I then realised that all the systems\u00a0that I had described had an odd number of atoms and that I had not looked at any even numbered rings. Thus hexasulfur is a smaller (known) ring version of S8, the latter by far […]<\/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":[],"class_list":["post-28773","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1gPyz-7u5","jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/28773","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=28773"}],"version-history":[{"count":0,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/28773\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=28773"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=28773"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=28773"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}