{"id":8860,"date":"2013-01-03T16:48:36","date_gmt":"2013-01-03T16:48:36","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=8860"},"modified":"2019-12-29T09:02:48","modified_gmt":"2019-12-29T09:02:48","slug":"hydrogen-bond-strength-as-a-function-of-ring-size","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860","title":{"rendered":"Hydrogen bond strength as a function of ring size."},"content":{"rendered":"
\n

One frequently has to confront the question: will a hydrogen bond form between a suitable donor (lone pair or \u03c0) and an acceptor? One of the factors to be taken into consideration for hydrogen bonds which are part of a cycle is the ring size. Here I explore one way of quantifying the effect for the series below, n=1-5 (4-8 membered rings).\n<\/p>\n

\"h-bond\"<\/p>\n

I will use the NBO approach. To remind, this reduces the wavefunction for a molecule to a set of localised orbitals, referred to as natural bond orbitals. The perturbation interaction energy E(2) between any (doubly occupied, i.e.<\/em> donor) orbital and an (unoccupied) acceptor orbital establishes the strength of that interaction. For a hydrogen bond, this can be expressed as the NBO corresponding to the (in this case oxygen) lone pair (shown in orange and purple below) and the corresponding H-O\u00a0\u03c3*<\/sup> empty orbital (shown as red and blue below). E(2) is a function both of how close in energy this pair of orbitals is (the smaller the energy gap the better) and how well they overlap (the relevant overlap in this case is the positive one between purple and blue). This latter attribute is shown below for the series n=2,3,4,5 (n=1 does not form any discernible hydrogen bond), at the \u03c9B97XD\/6-311G(d,p) computational level.<\/p>\n\n\n\n\n
\n
\"\"

NBO interaction for 5-ring H-bond.<\/p><\/div>\n<\/td>\n

\n
\"\"

NBO interaction for 6-ring H-bond.<\/p><\/div>\n<\/td>\n<\/tr>\n

\n
\"\"

NBO interaction for 7-ring H-bond.<\/p><\/div>\n<\/td>\n

\n
\"\"

NBO interaction for 8-ring H-bond.<\/p><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The interaction energies E(2) are collected below, together with the computed lengths. To put E(2) into context, it is around 16 kcal\/mol for a strong anomeric interaction, and about 6 kcal\/mol for the stereoelectronic influence in di-fluoroethane. One can see that by the time the angle subtended at the hydrogen has increased to ~150\u00b0, the interaction energy has reached a respectable value.<\/p>\n\n\n\n\n\n\n\n\n
n\u00a0<\/th>\nE(2), kcal\/mol\u00a0<\/th>\nO…H length, \u00c5\u00a0<\/th>\nAngle, \u00b0<\/th>\n<\/tr>\n
1<\/td>\n~0.0<\/a><\/td>\n\u00a0–<\/td>\n\u00a081.8<\/td>\n<\/tr>\n
2<\/td>\n0.75<\/a><\/td>\n2.294<\/td>\n\u00a0109.7<\/td>\n<\/tr>\n
3<\/td>\n3.56<\/a><\/td>\n1.984<\/td>\n\u00a0139.6<\/td>\n<\/tr>\n
4<\/td>\n6.24<\/a><\/td>\n2.017<\/td>\n\u00a0146.5<\/td>\n<\/tr>\n
5<\/td>\n8.35<\/a><\/td>\n1.957<\/td>\n\u00a0153.4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

So the simple trick of looking at the donor-acceptor NBO interaction in a cyclic hydrogen bond can give us a straightforward way of quantifying how the size of the ring and hence the orbital overlap (one presumes that the Lp\/C-O \u03c3*<\/sup> energy gap is similar for all the systems) affects the strength of the interaction. One might also explore this by looking at structures in the Cambridge crystal database. But note from the above that whilst the \u00a0E(2) energies follow ring size, this does not appear to happen for the H…O lengths! The analysis reveals that the maximum number of structures for the span 5 to 8-rings occurs at\u00a0~2.15, 1.85,\u00a01.65\u00a0and 1.85\u00c5 respectively.\u00a0<\/p>\n\n\n\n\n
\n
\"Crystal

Crystal data for 5-rings<\/p><\/div>\n<\/td>\n

\n
\"Crystal

Crystal data for 6-rings.<\/p><\/div>\n<\/td>\n<\/tr>\n

\n
\"Crystal

Crystal data for 7-rings<\/p><\/div>\n<\/td>\n

\n
\"Crystal

Crystal data for 8-rings<\/p><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

One frequently has to confront the question: will a hydrogen bond form between a suitable donor (lone pair or \u03c0) and an acceptor? One of the factors to be taken into consideration for hydrogen bonds which are part of a cycle is the ring size. Here I explore one way of quantifying the effect for […]<\/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":[4],"tags":[144,24,212,41,373],"ppma_author":[2661],"class_list":["post-8860","post","type-post","status-publish","format-standard","hentry","category-interesting-chemistry","tag-cambridge","tag-energy","tag-energy-gap","tag-interaction-energy","tag-tutorial-material"],"yoast_head":"\nHydrogen bond strength as a function of ring size. - 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=8860\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hydrogen bond strength as a function of ring size. - Henry Rzepa's Blog\" \/>\n<meta property=\"og:description\" content=\"One frequently has to confront the question: will a hydrogen bond form between a suitable donor (lone pair or \u03c0) and an acceptor? One of the factors to be taken into consideration for hydrogen bonds which are part of a cycle is the ring size. Here I explore one way of quantifying the effect for […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860\" \/>\n<meta property=\"og:site_name\" content=\"Henry Rzepa's Blog\" \/>\n<meta property=\"article:published_time\" content=\"2013-01-03T16:48:36+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-12-29T09:02:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/h-bond.svg\" \/>\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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Hydrogen bond strength as a function of ring size. - 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=8860","og_locale":"en_GB","og_type":"article","og_title":"Hydrogen bond strength as a function of ring size. - Henry Rzepa's Blog","og_description":"One frequently has to confront the question: will a hydrogen bond form between a suitable donor (lone pair or \u03c0) and an acceptor? One of the factors to be taken into consideration for hydrogen bonds which are part of a cycle is the ring size. Here I explore one way of quantifying the effect for […]","og_url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860","og_site_name":"Henry Rzepa's Blog","article_published_time":"2013-01-03T16:48:36+00:00","article_modified_time":"2019-12-29T09:02:48+00:00","og_image":[{"url":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/h-bond.svg","type":"","width":"","height":""}],"author":"Henry Rzepa","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Henry Rzepa","Estimated reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#article","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860"},"author":{"name":"Henry Rzepa","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"headline":"Hydrogen bond strength as a function of ring size.","datePublished":"2013-01-03T16:48:36+00:00","dateModified":"2019-12-29T09:02:48+00:00","mainEntityOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860"},"wordCount":502,"commentCount":2,"image":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#primaryimage"},"thumbnailUrl":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/h-bond.svg","keywords":["Cambridge","energy","energy gap","interaction energy","Tutorial material"],"articleSection":["Interesting chemistry"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#respond"]}]},{"@type":"WebPage","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860","name":"Hydrogen bond strength as a function of ring size. - Henry Rzepa's Blog","isPartOf":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#primaryimage"},"image":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#primaryimage"},"thumbnailUrl":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/h-bond.svg","datePublished":"2013-01-03T16:48:36+00:00","dateModified":"2019-12-29T09:02:48+00:00","author":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281"},"breadcrumb":{"@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#primaryimage","url":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/h-bond.svg","contentUrl":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/h-bond.svg"},{"@type":"BreadcrumbList","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8860#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog"},{"@type":"ListItem","position":2,"name":"Hydrogen bond strength as a function of ring size."}]},{"@type":"WebSite","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#website","url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/","name":"Henry Rzepa's Blog","description":"Chemistry with a twist","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"},{"@type":"Person","@id":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/#\/schema\/person\/2b40f7b9c872a4dc1547e040a11b6281","name":"Henry Rzepa","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g370be3a7397865e4fd161aefeb0a5a85","url":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g","caption":"Henry Rzepa"},"description":"Henry Rzepa is Emeritus Professor of Computational Chemistry at Imperial College London.","sameAs":["https:\/\/orcid.org\/0000-0002-8635-8390"],"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?author=1"}]}},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pDef7-2iU","jetpack-related-posts":[{"id":6401,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=6401","url_meta":{"origin":8860,"position":0},"title":"Spotting the unexpected. The hydration of formaldehyde.","author":"Henry Rzepa","date":"March 12, 2012","format":false,"excerpt":"In my\u00a0previous post\u00a0I speculated why bis(trifluoromethyl) ketone tends to fully form a hydrate when dissolved in water, but acetone does not. Here I turn to asking why\u00a0formaldehyde is also 80% converted to methanediol\u00a0in water? Could it be that again, the diol is somehow preferentially stabilised compared to the carbonyl precursor\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.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2012\/03\/formaldehyde-diol.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":8925,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=8925","url_meta":{"origin":8860,"position":1},"title":"\u03c0-hydrogen bonds as a function of ring size.","author":"Henry Rzepa","date":"January 5, 2013","format":false,"excerpt":"A simple correlation between a ring size and the hydrogen bonding as quantified by the O(Lp)\/H-O \u03c3* NBO interaction in that ring,\u00a0indicated a 7- or 8-membered ring was preferred over smaller ones. Here is the same study, but this time using the \u03c0-electrons of an alkene as the electron donor.\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":"WAK","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/01\/WAK.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":5040,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=5040","url_meta":{"origin":8860,"position":2},"title":"Are close H\u2026H contacts bonds? The d\u00e9nouement!","author":"Henry Rzepa","date":"October 10, 2011","format":false,"excerpt":"I wrote earlier about the strangely close contact between two hydrogen atoms in cis-butene. The topology of the electron density showed characteristics of a bond, but is it a consensual union? The two hydrogens approach closer than their van der Waals radii would suggest is normal, so something is happening,\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.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2011\/10\/cis-butene-C-H.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":9459,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=9459","url_meta":{"origin":8860,"position":3},"title":"The conformational preference of s-cis amides.","author":"Henry Rzepa","date":"February 10, 2013","format":false,"excerpt":"Amides with an H-N group are a component of the peptide linkage\u00a0(O=C-NH). Here I ask what the conformation (it could also be called a configuration) about the C-N bond is. A search of the following type can be defined: The dihedral shown is for H-N-C=O (but this is equivalent to\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":"cis-amide","src":"https:\/\/i0.wp.com\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2013\/02\/cis-amide.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":6205,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=6205","url_meta":{"origin":8860,"position":4},"title":"An orbital analysis of the stereochemistry of the E2 elimination reaction","author":"Henry Rzepa","date":"February 4, 2012","format":false,"excerpt":"The so-called E2 elimination mechanism is another one of those mainstays of organic chemistry. It is important because it introduces the principle that anti-periplanarity of the reacting atoms is favoured over other orientations such as the syn-periplanar form; Barton used this principle to great effect in developing the theory 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":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2012\/02\/E2.svg","width":350,"height":200},"classes":[]},{"id":6361,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=6361","url_meta":{"origin":8860,"position":5},"title":"Spotting the unexpected. The trifluoromeric effect in the hydration of the carbonyl group.","author":"Henry Rzepa","date":"March 9, 2012","format":false,"excerpt":"The equilibrium for the hydration of a ketone to form a gem-diol hydrate is known to be highly sensitive to substituents. Consider the two equilibria: For propanone, it lies almost entirely on the left, whereas for the hexafluoro derivative it is almost entirely on the right. The standard answer to\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.imperial.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2012\/03\/diol.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\/8860","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=8860"}],"version-history":[{"count":39,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/8860\/revisions"}],"predecessor-version":[{"id":21843,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/8860\/revisions\/21843"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8860"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=8860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}