{"id":24881,"date":"2022-03-22T15:11:38","date_gmt":"2022-03-22T15:11:38","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=24881"},"modified":"2022-03-22T16:01:07","modified_gmt":"2022-03-22T16:01:07","slug":"a-four-atom-molecule-exhibiting-simultaneous-compliance-with-huckel-4n2-and-baird-4n-selection-rules-for-ring-aromaticity","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24881","title":{"rendered":"A four-atom molecule exhibiting simultaneous compliance with H\u00fcckel 4n+2 and Baird 4n selection rules for ring aromaticity."},"content":{"rendered":"
\n

Normally, aromaticity is qualitatively assessed using an electron counting rule for cyclic conjugated rings. The best known is the H\u00fcckel 4n+2 rule (n=0,1, etc) for inferring diatropic aromatic ring currents in singlet-state \u03c0-conjugated cyclic molecules\u2021<\/sup> and a counter 4n rule which infers an antiaromatic paratropic ring current for the system. Some complex rings can sustain both types of ring currents in concentric rings or regions within the molecule, i.e.<\/em> both diatropic and paratropic regions. Open shell (triplet state) molecules have their own rule; this time the molecule has a diatropic ring current if it follows a 4n rule, often called Baird’s rule. But has a molecule which simultaneously follows both H\u00fcckel’s AND Baird’s rule ever been suggested? Well, here is one, as indeed\u00a0I promised in the previous post<\/a>.<\/p>\n

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

The species shown above has two carbons and two borons in a ring. These have a total of 14 valence electrons, eight of which occupy the C-B bonds, leaving six contributing to circulating ring currents. These partition into two<\/strong> \u03c0-electrons which then form a H\u00fcckel 4n+2 aromatic (n=0) and four<\/strong> \u03c3-electrons which then form a Baird 4n aromatic (n=1) as a triplet.\u00a0The triplet for this molecule is indeed its lowest state, 38.9 kcal\/mol or\u00a045.4 kcal\/mol in free energy lower than the two lowest energy singlet states. These arise by placing two electrons in either of the two orbitals \u03c32 or \u03c33 each singly occupied in the triplet state (FAIR Data collection: 10.14469\/hpc\/10267<\/a>)<\/p>\n

\n\n\n\n\n\n\n\n\n\n
Bonding MOs for C2<\/sub>B2<\/sub>.
\nClick image to load 3D model<\/th>\n<\/tr>\n
\u03c33<\/th>\n\u03c32<\/th>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n
\u03c31<\/th>\n<\/tr>\n
\"\"<\/td>\n<\/tr>\n
π1<\/th>\n<\/tr>\n
\"\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

So here we see a different sort of doubly aromatic molecule, to add to C4<\/sub>, B4<\/sub> and N4<\/sub>. With two electrons less than C4<\/sub>, it is now doubly aromatic as a triplet state, this time conforming to two different electron counting rules. It would be good to know if any other examples showing this pattern are known.<\/p>\n

\u2021<\/sup>H\u00fcckel’s rule originally applied to p-\u03c0 electrons in a cycle, such as benzene. Nowadays it is also used for \u03c3 in-plane electrons in a cycle.<\/p>\n

\n

This post has DOI: 10.14469\/hpc\/10271.<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

Normally, aromaticity is qualitatively assessed using an electron counting rule for cyclic conjugated rings. The best known is the H\u00fcckel 4n+2 rule (n=0,1, etc) for inferring diatropic aromatic ring currents in singlet-state \u03c0-conjugated cyclic molecules\u2021 and a counter 4n rule which infers an antiaromatic paratropic ring current for the system. Some complex rings can sustain […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_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},"jetpack_post_was_ever_published":false},"categories":[4],"tags":[],"ppma_author":[2661],"class_list":["post-24881","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry"],"yoast_head":"\nA four-atom molecule exhibiting simultaneous compliance with H\u00fcckel 4n+2 and Baird 4n selection rules for ring aromaticity. - 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=24881\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A four-atom molecule exhibiting simultaneous compliance with H\u00fcckel 4n+2 and Baird 4n selection rules for ring aromaticity. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"Normally, aromaticity is qualitatively assessed using an electron counting rule for cyclic conjugated rings. The best known is the H\u00fcckel 4n+2 rule (n=0,1, etc) for inferring diatropic aromatic ring currents in singlet-state \u03c0-conjugated cyclic molecules\u2021 and a counter 4n rule which infers an antiaromatic paratropic ring current for the system. 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The best known is the H\u00fcckel 4n+2 rule (n=0,1, etc) for inferring diatropic aromatic ring currents in singlet-state \u03c0-conjugated cyclic molecules\u2021 and a counter 4n rule which infers an antiaromatic paratropic ring current for the system. 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The diatropic\/paratropic inversion.","author":"Henry Rzepa","date":"October 26, 2013","format":false,"excerpt":"The 1H NMR spectrum of an aromatic molecule such as benzene is iconic; one learns that the unusual chemical shift of the protons (~\u03b4 7-8 ppm) is due to their deshielding by a diatropic ring current resulting from the circulation of six aromatic \u03c0-electrons following the H\u00fcckel 4n+2 rule. But\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":"Click for 3D","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/10\/dianion.jpeg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1903,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=1903","url_meta":{"origin":24881,"position":1},"title":"Carbobenzene: benzene with a difference","author":"Henry Rzepa","date":"April 16, 2010","format":false,"excerpt":"Some molecules, when you first see them, just intrigue. So it was with carbobenzene, the synthesis of a derivative of which was recently achieved by Remi Chauvin and co-workers (DOI: 10.1002\/chem.200601193). Two additional carbon atoms have been inserted into each of the six C-C bonds in benzene. The structure shows\u2026","rel":"","context":"In "General"","block_context":{"text":"General","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2010\/04\/carbobenzene.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":24974,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24974","url_meta":{"origin":24881,"position":2},"title":"C2N2: a 10-electron four-atom molecule displaying both H\u00fcckel 4n+2 and Baird 4n selection rules for ring aromaticity.","author":"Henry Rzepa","date":"April 7, 2022","format":false,"excerpt":"The previous examples of four atom systems displaying two layers of aromaticity illustrated how 4 (B4), 8 (C4) and 12 (N4) valence electrons were partitioned into 4n+2 manifolds (respectively 2+2, 6+2 and 6+6). The triplet state molecule B2C2 with 6 electrons partitioned into 2\u03c0 and 4\u03c3 electrons, with the latter\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\/2022\/04\/CN-np-300x249.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":2973,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=2973","url_meta":{"origin":24881,"position":3},"title":"(anti)aromaticity avoided: a tutorial example","author":"Henry Rzepa","date":"December 7, 2010","format":false,"excerpt":"More inspiration from tutorials. In a lecture on organic aromaticity, the 4n+2\/4n H\u00fcckel rule was introduced (in fact, neither rule appears to have actually been coined in this form by H\u00fcckel himself!). The simplest examples are respectively the cyclopropenyl cation and anion. The former has 2 \u03c0-electrons exhibiting cyclic delocalisation,\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\/12\/cyclopropenium.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":9556,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=9556","url_meta":{"origin":24881,"position":4},"title":"Linking numbers, and twist and writhe components for two extended porphyrins.","author":"Henry Rzepa","date":"February 17, 2013","format":false,"excerpt":"My last comment as\u00a0appended to the previous post\u00a0promised to analyse two so-called extended porphyrins for their topological descriptors. I start with the\u00a0C\u00e3lug\u00e3reanu\/Fuller theorem\u00a0 which decomposes the topology of a space curve into two components, its twist (Tw) and its writhe (Wr, this latter being the extent to which coiling of\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":9218,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=9218","url_meta":{"origin":24881,"position":5},"title":"Aromaticity in the benzidine-like \u03c0-complex formed from PhNHOPh.","author":"Henry Rzepa","date":"January 19, 2013","format":false,"excerpt":"The transient \u03c0-complex formed during the \"[5,5]\" sigmatropic rearrangement of protonated N,O-diphenyl hydroxylamine can be (formally) represented as below, namely the interaction of a six-\u03c0-electron aromatic ring (the phenoxide anion 2) with a\u00a0four-\u03c0-electron phenyl dication-anion pair 1. Can one analyse this interaction in terms of aromaticity? I showed previously that\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":"pi-QTAIM","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/pi-QTAIM.jpg?resize=350%2C200","width":350,"height":200},"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\/24881","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=24881"}],"version-history":[{"count":29,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/24881\/revisions"}],"predecessor-version":[{"id":24927,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/24881\/revisions\/24927"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24881"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24881"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24881"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=24881"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}