{"id":23712,"date":"2021-05-10T10:15:27","date_gmt":"2021-05-10T09:15:27","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=23712"},"modified":"2021-06-02T13:43:43","modified_gmt":"2021-06-02T12:43:43","slug":"what-does-a-double-%cf%83-bond-along-a-bond-axis-look-like","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=23712","title":{"rendered":"What does a double \u03c3-bond along a bond axis look like?"},"content":{"rendered":"
\n

Introductory chemistry will tell us that a triple bond between say two carbon atoms comprises just one bond of \u03c3-axial symmetry and two of π-symmetry. Increasingly mentioned nowadays is the possibility of a quadruple bond between carbon and either itself or a transition metal, as discussed in the previous post.<\/a> Such a bond comprises TWO bonds of \u03c3-axial symmetry. Since most people are unfamiliar with such double bonds and in particular with how that second \u03c3-bond sits with the first, I thought it would be interesting to show such an orbital. This one is a localised orbital 41<\/b>, selected from the previous post<\/a> for the molecule (PH3<\/sub>)2<\/sub>(CN)2<\/sub>Mo\u2a78C. <\/p>\n\n\n\n\n\n\n\n\n
NBO 41, threshold 0.040 au<\/th>\nNBO 41, threshold 0.018<\/th>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n
NBO 41, threshold 0.016<\/th>\nNBO 41, threshold 0.014<\/th>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n
NBO 41, threshold 0.012<\/th>\nNBO 41, threshold 0.007<\/th>\n<\/tr>\n
\"\"<\/td>\n\"\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The above shows how the orbital changes with the isosurface threshold. At high values, it looks very similar to the normal \u03c3-bond but as the threshold gradually decreases, a second “sheath” starts to surround the inner orbital until the latter is entirely enclosed. This orbital has a node not so much along the bond itself, but between the inner and outer layers of the bond, which is how the two σ-bonds are differentiated. This effect was first noted in 2016<\/a> in terms of the compound CH3<\/sub>F2-<\/sup>, in which an expanded carbon valence shell creates a second σ-bond.<\/p>\n

Certainly not a representation that has ever appeared in a text book I think! But perhaps one that chemists may have increasingly to become familiar with.<\/p>\n

\n

Appendix<\/b> Here are some superimposed orbitals to facilitate comparisons. Firstly orbital 41 (the higher energy σ-orbital) with orbital 22 (the lower energy σ-orbital). The first has yellow\/green for the two phases, the second has red\/blue.
\n\"\"<\/p>\n

Next, σ-orbital 22 (yellow\/green) with orbital 42 (red\/blue) surrounding it, revealing the avoided overlaps (Pauli repulsions) between the two by virtue of having orbital 42 unoccupied. <\/p>\n

\"\"<\/p>\n

Next, σ-orbital 41 (yellow\/green) with orbital 42 (red\/blue) surrounding it, revealing the reduced overlap between these two. <\/p>\n

\"\"<\/p>\n

Appendix 2<\/b> A “pure” form of the double-layered σ-bond can be seen with the diatomic molecule Ti2<\/sub>, contoured at 0.0225 au. The red phase is about to join in the middle.<\/p>\n

\"\"<\/p>\n

The electron density from this orbital is shown below and shows clearly the two layers of density comprising the σ-bond, with the outer layer at this isosurface value (0.00052 au) about to join up in the middle to complete the outer sheath. I have left it unjoined so that you can see “inside layer”, since translucency does not always get the message across.<\/p>\n

\"\"<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

Introductory chemistry will tell us that a triple bond between say two carbon atoms comprises just one bond of \u03c3-axial symmetry and two of π-symmetry. Increasingly mentioned nowadays is the possibility of a quadruple bond between carbon and either itself or a transition metal, as discussed in the previous post. Such a bond comprises TWO […]<\/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-23712","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry"],"yoast_head":"\nWhat does a double \u03c3-bond along a bond axis look like? - 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=23712\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What does a double \u03c3-bond along a bond axis look like? - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"Introductory chemistry will tell us that a triple bond between say two carbon atoms comprises just one bond of \u03c3-axial symmetry and two of π-symmetry. 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The rational\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":22971,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=22971","url_meta":{"origin":23712,"position":2},"title":"A new example of a quadruple bond from carbon – to Fe.","author":"Henry Rzepa","date":"November 7, 2020","format":false,"excerpt":"Way back in 2010, I was writing about an experience I had just had during an organic chemistry tutorial, which morphed into speculation as to whether a carbon atom might sustain a quadruple bond to nitrogen. A decade on, and possibly approaching 100 articles by many authors on the topic,\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\/2020\/11\/NMn_33a-1024x839.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":23686,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=23686","url_meta":{"origin":23712,"position":3},"title":"A reality-based suggestion for a molecule with a metal M\u2a78N quadruple bond.","author":"Henry Rzepa","date":"May 13, 2021","format":false,"excerpt":"I noted in an earlier post the hypothesized example of (CO)3Fe\u2a78C as exhibiting a carbon to iron quadruple bond and which might have precedent in known five-coordinate metal complexes where one of the ligands is a \"carbide\" or C ligand. I had previously mooted that the Fe\u2a78C combination might be\u2026","rel":"","context":"In "crystal_structure_mining"","block_context":{"text":"crystal_structure_mining","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1745"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2021\/05\/Screenshot-703-1024x818.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":28773,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=28773","url_meta":{"origin":23712,"position":4},"title":"Cyclo-S6 (Hexathiane) – anomeric effects again!","author":"Henry Rzepa","date":"June 1, 2025","format":false,"excerpt":"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\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":16696,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=16696","url_meta":{"origin":23712,"position":5},"title":"A periodic table for anomeric centres, this time with quantified interactions.","author":"Henry Rzepa","date":"August 8, 2016","format":false,"excerpt":"The previous post contained an exploration of the anomeric effect as it occurs at an atom centre X for which the effect is manifest in crystal structures. Here I\u00a0quantify the effect, by selecting the test molecule MeO-X-OMe, where X is of two types:A two-coordinate atom across the series B-O and\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\/23712","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=23712"}],"version-history":[{"count":42,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/23712\/revisions"}],"predecessor-version":[{"id":23955,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/23712\/revisions\/23955"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23712"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23712"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23712"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=23712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}