{"id":19073,"date":"2017-11-20T15:01:43","date_gmt":"2017-11-20T15:01:43","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=19073"},"modified":"2017-11-21T12:58:33","modified_gmt":"2017-11-21T12:58:33","slug":"hypervalence-and-octet-expansion-in-sulfur-hexafluoride","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19073","title":{"rendered":"Hypervalence and octet-expansion in sulfur hexafluoride."},"content":{"rendered":"
\n

Following on from discussing octet expansion in species such as SeMe6<\/sub>, ClMe3<\/sub> and ClMe5<\/sub>, I felt impelled to return to SF6<\/sub>, often used as an icon for hypervalence.<\/p>\n

With this molecule we have twelve electrons to partition, six from sulfur and one each from six fluorines (the other six electrons on each F are presumed to form three sets of lone pairs). Recollect the two ways of dealing with them:<\/p>\n

    \n
  1. To place them in pairs firstly into bonding MOs formed from using a 3s\/3p valence atomic orbital basis on the S and a 2s\/2p AO basis on F and to place any remaining electron pairs into antibonding orbitals constructed from the same basis. This would tend to reduce individual S-F bond orders.<\/li>\n
  2. To place four pairs into bonding MOs and the remaining two pairs into MOs constructed using higher or Rydberg valence shells on S. This would tend to increase S-F bond orders by forming hyperbonds.<\/li>\n<\/ol>\n

    I will start with (delocalized) molecular orbitals (FAIR data DOI:\u00a010.14469\/hpc\/3283<\/a>). The HOMO (highest occupied MO) and the next 16 are in fact various variations of orbitals which can be regarded as fluorine lone pairs. The first of interest to us is the A1g<\/sub>-symmetric HOMO-17, which certainly looks as if it is antibonding along the six F-S bonds. But the heavy delocalization of the MOs makes it really difficult to comment on bonding\/antibonding character.<\/p>\n

    \"\"<\/p>\n

    So next, the more localized NBO orbitals (FAIR Data DOI:\u00a010.14469\/hpc\/3284<\/a>), which tends to “collect” the wavefunction into localized regions of bonds and lone pairs. There are twelve equivalent F lone pairs of the following type:\"\"<\/p>\n

    Next the remaining six F lone pairs, which are oriented axially along the S-F bonds. They have distinct S-F anti-bonding character.\"\"<\/p>\n

    Finally six S-F bonding pairs (“acorn” orbitals). But note that whilst they are bonding along one S-F bond, they are mildly antibonding along the opposing S-F bond.\u00a0\"\"<\/p>\n

    The Rydberg occupancy is S:[core]3S(0.98)3p(2.13)3d(0.24)4p(0.03)4f(0.01) and F:\u00a0[core]2S(1.91)2p(5.51)3d(0.01), which gives a total \u00a0Rydberg occupancy of\u00a00.35177e. \u00a0Adding up these effects, the NBO analysis tells us that the individual S-F bond orders are 0.7213. Six times this gives the Wiberg bond index at sulfur:\u00a0 4.3276. This is close to the value of 4 expected from utilising an atomic orbital basis of one 2s and three 2p AOs on sulfur. One can think of this in another way.<\/p>\n

      \n
    1. Start with a valence shell of twelve electrons to form six two-electron S-F bonds. The sulfur would have a bond index of six. Then promote either two electrons into fully antibonding orbitals (5-1=4) or four into non-bonding orbitals (F lone pairs) or possibly intermediate solutions, thus reducing the sulfur bond index by ~two bonds to give a bond index of four. Since the antibonding orbitals in this case are not fully antibonding, the bond index emerges a bit higher at 4.3276, a value also augmented by 0.35177\/2 =\u00a00.175885 due to Rydberg occupancy.<\/li>\n
    2. One might usefully then ask if a bond index for sulfur of \u2265 4 can be usefully described as “hypervalent sulfur<\/em>“? As usual in bonding theory, we need a reference state for non-hypervalent sulfur. If this is taken as two valencies, with a bond index of two, then this molecule is definitely hypervalent. If you assume that you can only construct the equivalent of four two-electron bonds using just a 3s1<\/sup>\/3p3<\/sup> atomic orbital basis, then it is merely mildly hypervalent; the four two-electron bonds are then distributed of course across six S-F regions, or 0.667 bonds per S-F region. The value of\u00a00.7213 actually calculated is exalted by contributions in part from Rydberg orbitals.\u00a0<\/li>\n<\/ol>\n

      What about the octet? 6*0.7213*2 = 8.66e, a mildly expanded octet. I am now going to use the ELF method as an alternative counting procedure. This is based not on orbitals but on the electron density (a more direct experimental observable than orbitals). Six disynaptic basins are located totalling 6.5e. The remainder of the electrons populate the F lone pairs shown below as four distinct monosynaptic basins per F. This is an artefact of the resolution of the cube of ELF values and how the basin centroids are located. These are in fact circular and not point ELF attractors, forming a circular ELF torus around each fluorine.<\/p>\n

      \"\"<\/p>\n

      So, ELF suggests that the sulfur “octet” is not exceeded and in this form of analysis the compound is merely hypercoordinate. In contrast the orbital-based approach indicates mild hypervalency in which the total bond index at S modestly exceeds 4. If you regard the normal valency of sulfur to be two, this is clearly hypervalent. But no substantial octet-expansion beyond the modest Rydberg type is needed to rationalise this species and certainly not up to twelve!<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

      Following on from discussing octet expansion in species such as SeMe6, ClMe3 and ClMe5, I felt impelled to return to SF6, often used as an icon for hypervalence. With this molecule we have twelve electrons to partition, six from sulfur and one each from six fluorines (the other six electrons on each F are presumed […]<\/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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[7],"tags":[557,1395,2294,2295,2296],"ppma_author":[2661],"class_list":["post-19073","post","type-post","status-publish","format-standard","hentry","category-hypervalency","tag-chemical-bonding","tag-chemistry","tag-hypervalent-molecules","tag-octet","tag-sulfur-hexafluoride"],"yoast_head":"\nHypervalence and octet-expansion in sulfur hexafluoride. - 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=19073\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hypervalence and octet-expansion in sulfur hexafluoride. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"Following on from discussing octet expansion in species such as SeMe6, ClMe3 and ClMe5, I felt impelled to return to SF6, often used as an icon for hypervalence. With this molecule we have twelve electrons to partition, six from sulfur and one each from six fluorines (the other six electrons on each F are presumed […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19073\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa's Blog\" \/>\n<meta property=\"article:published_time\" content=\"2017-11-20T15:01:43+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2017-11-21T12:58:33+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2017\/11\/SF6-HIOMO-17-1024x885.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=\"4 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Hypervalence and octet-expansion in sulfur hexafluoride. - 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=19073","og_locale":"en_GB","og_type":"article","og_title":"Hypervalence and octet-expansion in sulfur hexafluoride. - Henry Rzepa's Blog","og_description":"Following on from discussing octet expansion in species such as SeMe6, ClMe3 and ClMe5, I felt impelled to return to SF6, often used as an icon for hypervalence. 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Finally now its the turn of S(\u2261CH)2.\u2021 As the triple bonds imply, this seems to represent twelve shared valence electrons surround the sulfur, six from S itself\u2026","rel":"","context":"In "Historical"","block_context":{"text":"Historical","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=565"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2017\/11\/HCSCH-NBO-1024x973.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":19102,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19102","url_meta":{"origin":19073,"position":1},"title":"Hypervalence and octet-expansion in trimethylene-\u03bb6-sulfane and related species.","author":"Henry Rzepa","date":"November 27, 2017","format":false,"excerpt":"Previously: \"Non-polar\" species such as SeMe6, SMe6, ClMe3, ClMe5 all revealed interesting properties for the Se-C, S-C or Cl-C \"single\" bonds. The latter two examples in particular hinted at internal structures for these single bonds, as manifested by two ELF basins for some of the bonds. Here I take a\u2026","rel":"","context":"In "Hypervalency"","block_context":{"text":"Hypervalency","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=7"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":19307,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=19307","url_meta":{"origin":19073,"position":2},"title":"Are diazomethanes hypervalent molecules? An attempt into more insight by more “tuning” with substituents.","author":"Henry Rzepa","date":"December 26, 2017","format":false,"excerpt":"Recollect the suggestion\u00a0that diazomethane has hypervalent character. When I looked into this, I came to the conclusion that it probably was mildly hypervalent, but on carbon and not nitrogen. Here I try some variations with substituents to see what light if any this casts. I have expanded the resonance forms\u2026","rel":"","context":"In "Hypervalency"","block_context":{"text":"Hypervalency","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=7"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2017\/12\/H2CNCCN_ELF-1024x258.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":18993,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=18993","url_meta":{"origin":19073,"position":3},"title":"VSEPR Theory: Octet-busting or not with trimethyl chlorine, ClMe3.","author":"Henry Rzepa","date":"November 12, 2017","format":false,"excerpt":"A few years back, I took a look at the valence-shell electron pair repulsion approach to the geometry of chlorine trifluoride, ClF3 using so-called ELF basins to locate centroids for both the covalent F-Cl bond electrons and the chlorine lone-pair electrons. Whereas the original VSEPR theory talks about five \"electron\u2026","rel":"","context":"In "Chemical IT"","block_context":{"text":"Chemical IT","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=2"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":15552,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=15552","url_meta":{"origin":19073,"position":4},"title":"VSEPR Theory: A closer look at trifluorothionitrile, NSF3.","author":"Henry Rzepa","date":"January 16, 2016","format":false,"excerpt":"The post on applying VSEPR (\"valence shell electron pair repulsion\") theory to the geometry of ClF3\u00a0has proved perennially popular. So here is a follow-up on another little molecue,\u00a0F3SN. As the name implies, it is often represented with an\u00a0S\u2261N bond. Here I take a look at the conventional analysis. This is\u2026","rel":"","context":"In "Hypervalency"","block_context":{"text":"Hypervalency","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=7"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":18975,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=18975","url_meta":{"origin":19073,"position":5},"title":"Hypervalence revisited. The odd case of hexamethyl selenium.","author":"Henry Rzepa","date":"November 7, 2017","format":false,"excerpt":"One thread that runs through this blog is that of hypervalency. It was therefore nice to come across a recent review of the concept which revisits the topic, and where a helpful summary is given of the evolving meanings over time of the term hypervalent. The key phrase \"it soon\u2026","rel":"","context":"In "Hypervalency"","block_context":{"text":"Hypervalency","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=7"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2017\/11\/165-1024x1008.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\/19073","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=19073"}],"version-history":[{"count":14,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/19073\/revisions"}],"predecessor-version":[{"id":19092,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/19073\/revisions\/19092"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19073"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19073"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19073"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=19073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}