{"id":3462,"date":"2011-01-21T12:30:46","date_gmt":"2011-01-21T11:30:46","guid":{"rendered":"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=3462"},"modified":"2017-09-16T08:54:07","modified_gmt":"2017-09-16T07:54:07","slug":"shorter-is-higher-the-strange-case-of-diberyllium","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=3462","title":{"rendered":"Shorter is higher: the strange case of diberyllium."},"content":{"rendered":"
\n

Much of chemistry is about bonds, but sometimes it can also be about anti-bonds. It is also true that the simplest of molecules can have quite subtle properties<\/a>. Thus most undergraduate courses in chemistry deal with how to describe the bonding in the diatomics of the first row of the periodic table. Often, only the series C2<\/sub> to F2 <\/sub>is covered,\u00a0so as to take into account the paramagnetism of dioxygen, and the triple bonded nature of dinitrogen (but never mentioning the strongest bond in the universe<\/a>!). Rarely is\u00a0diberyllium<\/a> mentioned,\u00a0\u00a0and yet by its strangeness, it can also teach us a lot of chemistry.<\/p>\n

The diagram below is what many textbooks show. The diagram can vary (and hence confuse) slightly, in regard to the relative ordering of the \u03c3 and \u03c0 energy levels originating from the overlap of the 2p orbitals. It depends on the atom, and for Be, the \u03c3 comes out higher than the \u03c0. The other key ordering is that the \u03c3* antibonding orbital resulting from out of phase overlap of the two 2s orbitals is actually lower in energy than the \u03c0 bonding orbital resulting from in-phase overlap of the 2p orbitals. Yes, an antibonding orbital is more stable than a bonding orbital!<\/p>\n

\"\"<\/a>

Molecular orbital diagram for Be2<\/p><\/div>\n

Well, the diagram shows that the pair of occupied molecular orbitals resulting from the two (symmetric and antisymmetric, or g<\/em> and u<\/em>) combinations of the 1s orbitals cancel each other, as do the 2s combinations, and we conclude the bond order for this molecule is zero! Actually, if a quantum mechanical calculation is performed <\/a>(at the \u03c9B97XD\/6-311G(d,p) level), the bond length emerges as 2.81\u00c5 and a vibrational wavenumber of 167 cm-1<\/sup> is predicted. Despite the zero bond order, a weak bond IS predicted, and this is the van der Waals<\/strong> or dispersion bond<\/strong>.<\/p>\n

Let us now pump this molecule up to a higher energy state by a double excitation of the two electrons in the 2s \u03c3* electrons. We have to split them up, one each, into the next available orbital, which is the \u03c0, to form a triplet state (just like di-oxygen).<\/p>\n

\"\"<\/a>

The doubly excited state of diberyllium<\/p><\/div>\n

Well, this (higher energy) state is certainly shorter (a contrast with my item on longer being stronger<\/a>). The length is now 1.78\u00c5, which is more than 1\u00c5 shorter<\/strong> than the original state, despite being ~ 45 kcal\/mol higher<\/strong> in energy. The Be-Be stretching wavenumber<\/a> goes up to 917 cm-1<\/sup>. With four electrons in bonding orbitals, diberyllium has a double bond! One can also pair the \u03c0 electrons up to form an open shell (excited) singlet, which is ~ 51 kcal\/mol higher<\/a> than the closed shell (unbonded) singlet. This also has a length of 1.78\u00c5 and a marginally lower stretch of 909 cm-1<\/sup>. Read more about the doubly excited state of this molecule[1]<\/a><\/span>.<\/p>\n

One might be tempted to make an analogy between physics, and its particles and antiparticles. Yes, electrons can occupy antibonding as well as bonding orbitals. But the overall bond order will be reduced to zero if the total numbers of each are equal. And one can be pretty certain that there is no molecule at all in which the number of antibonding electrons exceeds the bonding ones! Or, if anyone is aware of such an example, do tell!<\/p>\n

References<\/h2>\n
  1. P.J. Bruna, and J.S. Wright, \"Strongly bound doubly excited states of Be<sub>2<\/sub>\", Canadian Journal of Chemistry<\/i>, vol. 74, pp. 998-1004, 1996. https:\/\/doi.org\/10.1139\/v96-111<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    Much of chemistry is about bonds, but sometimes it can also be about anti-bonds. It is also true that the simplest of molecules can have quite subtle properties. Thus most undergraduate courses in chemistry deal with how to describe the bonding in the diatomics of the first row of the periodic table. Often, only the […]<\/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,"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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4],"tags":[423,24,424,68,434,74,373],"ppma_author":[2661],"class_list":["post-3462","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry","tag-diberyllium","tag-energy","tag-excited-state","tag-higher-energy","tag-higher-energy-state","tag-pence","tag-tutorial-material"],"yoast_head":"\nShorter is higher: the strange case of diberyllium. - 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=3462\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Shorter is higher: the strange case of diberyllium. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"Much of chemistry is about bonds, but sometimes it can also be about anti-bonds. 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Generations of chemists have learnt early on in their studies of the subject that these two representations of where the electron pairs in benzene might be located (formally called electronic resonance or valence bond forms) each contribute ~50% to the\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":"The Kekule structures of benzene.","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2009\/06\/benzene.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":5441,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=5441","url_meta":{"origin":3462,"position":3},"title":"Driving the smallest car ever made: a chemical perspective.","author":"Henry Rzepa","date":"November 10, 2011","format":false,"excerpt":"Fascination with nano-objects, molecules which resemble every day devices, is increasing. 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And chemists are starting to manipulate electrons (and hence chemistry) on this timescale; for example\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":14718,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=14718","url_meta":{"origin":3462,"position":5},"title":"Interactions responsible for the lowest energy structure of the trimer of fluoroethanol.","author":"Henry Rzepa","date":"October 23, 2015","format":false,"excerpt":"Steve Bachrach on his own blog has commented on a recent article discussing the structure of the trimer of fluoroethanol. Rather than the expected triangular form with three OH---O hydrogen bonds, the lowest energy form only had two such bonds, but it matched the microwave data much better. Here I\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":[]}],"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\/3462","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=3462"}],"version-history":[{"count":1,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/3462\/revisions"}],"predecessor-version":[{"id":18803,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/3462\/revisions\/18803"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3462"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3462"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3462"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=3462"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}