{"id":24814,"date":"2022-03-19T15:36:06","date_gmt":"2022-03-19T15:36:06","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=24814"},"modified":"2022-03-19T16:25:20","modified_gmt":"2022-03-19T16:25:20","slug":"more-aromatic-species-with-four-atoms","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24814","title":{"rendered":"More aromatic species with four atoms. B4 and N4."},"content":{"rendered":"
\n

I discussed in the previous post<\/a> the small molecule C4<\/sub> and how of the sixteen valence electrons, eight were left over after forming C-C σ-bonds which partitioned into six σ and two π. So now to consider B4<\/sub>. This has four electrons less, and now the partitioning is two σ and two π (CCSD(T)\/Def2-TZVPPD calculation, FAIR DOI: 10.14469\/hpc\/10157<\/a>). Again both these sets fit the Hückel 4n+2 rule (n=0).
\n\"\"<\/a><\/p>\n

Since B4<\/sub> has only two rather than six delocalized σ-orbitals, the contributions to the central B-B bond are weaker and so the B-B bond is much longer.<\/p>\n\n\n\n\n\n\n\n
Bonding MOs for B4<\/sub>.
\nClick image to load 3D model<\/th>\n<\/tr>\n
σ1, -0.335 au<\/th>\n<\/tr>\n
\"\"<\/td>\n<\/tr>\n
\u03c01, -0.372 au<\/th>\n<\/tr>\n
\"\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Next, N4<\/sub>.
\n\"\"<\/a><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
π-Bonding MOs for N4<\/sub>.
\nClick image to load 3D model<\/th>\n<\/tr>\n
π3<\/th>\nπ2<\/th>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n
π1<\/th>\n<\/tr>\n
\"\"<\/td>\n<\/tr>\n
σ-Bonding MOs for N4<\/sub>.
\nClick image to load 3D model<\/th>\n<\/tr>\n
σ3<\/th>\nσ2<\/th>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n
σ1<\/th>\n<\/tr>\n
\"\"<\/td>\n<\/tr>\n<\/table>\n

The pattern for N4<\/sub> is different in several aspects. Firstly the π-system has six bonding electrons distributed over only four atoms. This makes the electron repulsions too high and the species is no longer stable, having one large imaginary force constant corresponding to an out-of-plane distorsion. Secondly the lowest energy σ orbital is highly localised onto two nitrogens rather than being delocalised around the ring periphery. So all those electrons crammed into a small space have taken their toll.<\/p>\n

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

\nThus far we have identified three species, B4<\/sub>, C4<\/sub> and N4<\/sub> with interesting sets of respectively 4,8 and 12 electrons, all partitioned into 4n+2 collections. But what happens if one cannot do that; lets say 6 and 10 electrons? Hang around to find out!<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

I discussed in the previous post the small molecule C4 and how of the sixteen valence electrons, eight were left over after forming C-C σ-bonds which partitioned into six σ and two π. So now to consider B4. This has four electrons less, and now the partitioning is two σ and two π (CCSD(T)\/Def2-TZVPPD calculation, […]<\/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_feature_clip_id":0,"_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-24814","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry"],"yoast_head":"\nMore aromatic species with four atoms. B4 and N4. - 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=24814\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"More aromatic species with four atoms. B4 and N4. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"I discussed in the previous post the small molecule C4 and how of the sixteen valence electrons, eight were left over after forming C-C σ-bonds which partitioned into six σ and two π. So now to consider B4. This has four electrons less, and now the partitioning is two σ and two π (CCSD(T)\/Def2-TZVPPD calculation, […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24814\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa's Blog\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-19T15:36:06+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-19T16:25:20+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2022\/03\/B4.jpg\" \/>\n<meta name=\"author\" content=\"Henry Rzepa\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Henry Rzepa\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"More aromatic species with four atoms. B4 and N4. - 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=24814","og_locale":"en_GB","og_type":"article","og_title":"More aromatic species with four atoms. B4 and N4. - Henry Rzepa's Blog","og_description":"I discussed in the previous post the small molecule C4 and how of the sixteen valence electrons, eight were left over after forming C-C σ-bonds which partitioned into six σ and two π. So now to consider B4. This has four electrons less, and now the partitioning is two σ and two π (CCSD(T)\/Def2-TZVPPD calculation, […]","og_url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24814","og_site_name":"Henry Rzepa's Blog","article_published_time":"2022-03-19T15:36:06+00:00","article_modified_time":"2022-03-19T16:25:20+00:00","og_image":[{"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2022\/03\/B4.jpg","type":"","width":"","height":""}],"author":"Henry Rzepa","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Henry Rzepa","Estimated reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24814#article","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24814"},"author":{"name":"Henry Rzepa","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"headline":"More aromatic species with four atoms. 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Three words need translation into modern usage. Where he uses the word nuclei the\u2026","rel":"","context":"In "Historical"","block_context":{"text":"Historical","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=565"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":24769,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24769","url_meta":{"origin":24814,"position":1},"title":"An unusually small (doubly) aromatic molecule: C4.","author":"Henry Rzepa","date":"March 15, 2022","format":false,"excerpt":"When you talk \u03c0-aromaticity, benzene is the first molecule that springs to mind.\u00a0But there are smaller molecules that can carry this property; cyclopropenylidene (five atoms) is the smallest in terms of atom count I could think of until now, apart that is from H3+ which is the smallest possible molecule\u2026","rel":"","context":"In "General"","block_context":{"text":"General","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":9186,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=9186","url_meta":{"origin":24814,"position":2},"title":"The \u03c0-complex in the benzidine rearrangement: a molecular orbital analysis.","author":"Henry Rzepa","date":"January 18, 2013","format":false,"excerpt":"Michael Dewar famously implicated a so-called\u00a0\u03c0-complex in the benzidine rearrangement, back in the days when quantum mechanical calculations could not yet provide a quantitatively accurate reality check. Because this\u00a0\u03c0-complex actually remains a relatively unusual species to encounter in day-to-day chemistry, I thought I would try to show in a simple\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":11421,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=11421","url_meta":{"origin":24814,"position":3},"title":"Six vs ten aromatic electrons?","author":"Henry Rzepa","date":"October 20, 2013","format":false,"excerpt":"Homoaromaticity is a special case of\u00a0aromaticity\u00a0in which\u00a0\u03c0-conjugation\u00a0is interrupted by a single sp3\u00a0hybridized\u00a0carbon atom (it is sometimes referred to as a suspended \u03c0-bond with no underlying \u03c3-foundation).\u00a0But consider the carbene shown below. This example comes from a recently published article which was highlighted on Steve Bachrach's blog. Here aromaticity has resulted\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\/B10-sigma.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":24067,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24067","url_meta":{"origin":24814,"position":4},"title":"Dimerisation of cyclopropenylidene: what are the correct “curly arrows” for this process?","author":"Henry Rzepa","date":"July 21, 2021","format":false,"excerpt":"In another post, a discussion arose about whether it might be possible to trap\u00a0cyclopropenylidene to form a small molecule with a large dipole moment. Doing so assumes that cyclopropenylidene has a sufficiently long lifetime to so react, before it does so with itself to e.g. dimerise. That dimerisation has an\u2026","rel":"","context":"In "Curly arrows"","block_context":{"text":"Curly arrows","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2327"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":24974,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=24974","url_meta":{"origin":24814,"position":5},"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":[]}],"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","author_category":"1","first_name":"Henry","last_name":"Rzepa","user_url":"https:\/\/orcid.org\/0000-0002-8635-8390","job_title":"","description":"Henry Rzepa is Emeritus Professor of Computational Chemistry at Imperial College London."}],"_links":{"self":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/24814","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=24814"}],"version-history":[{"count":25,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/24814\/revisions"}],"predecessor-version":[{"id":24874,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/24814\/revisions\/24874"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24814"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24814"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24814"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=24814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}