{"id":1447,"date":"2017-10-12T14:20:13","date_gmt":"2017-10-12T14:20:13","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/?post_type=chapter&#038;p=1447"},"modified":"2017-10-12T14:20:13","modified_gmt":"2017-10-12T14:20:13","slug":"applying-the-criteria-for-aromaticity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/chapter\/applying-the-criteria-for-aromaticity\/","title":{"raw":"Applying the Criteria for Aromaticity","rendered":"Applying the Criteria for Aromaticity"},"content":{"raw":"<div class=\"elm-header\">\r\n<div class=\"elm-header-custom\">\u00a0Valence bond theory uses Lewis diagrams to depict structure and bonding of covalent entities, such as molecules and polyatomic ions, henceforth molecules. The Lewis diagram of many a molecule, however, is not consistent with the observed properties of the molecule. \u00a0The Lewis diagram of some molecules suggests a ring bearing a fully conjugated $$\\pi$$-electron system, or loop of $$\\pi$$ electrons, provided each atom in the ring is sp<sup>2<\/sup>- or sp-hybridized.<\/div>\r\n<\/div>\r\n<div id=\"elm-main-content\" class=\"elm-content-container\">\r\n<div>\r\n<ul>\r\n \t<li>cyclobutadiene (1)<\/li>\r\n<\/ul>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151057\/aromatic1.png\" alt=\"\" width=\"263\" height=\"81\" \/>\r\n<ul>\r\n \t<li>benzene (2)<\/li>\r\n<\/ul>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151100\/aromatic2.png\" alt=\"\" width=\"318\" height=\"104\" \/>\r\n<ul>\r\n \t<li>cyclooctatetraene (3)<\/li>\r\n<\/ul>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151103\/aromatic3.png\" alt=\"\" width=\"330\" height=\"90\" \/>\r\n<ul>\r\n \t<li>pyridine (4)<\/li>\r\n<\/ul>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151105\/aromatic4.png\" alt=\"\" width=\"371\" height=\"114\" \/>\r\n<ul>\r\n \t<li>pyrrole\u00a0(5)<\/li>\r\n<\/ul>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151108\/aromatic5.png\" alt=\"\" width=\"388\" height=\"124\" \/>\r\n<ul>\r\n \t<li>cyclopentadienyl cation (6)<\/li>\r\n<\/ul>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151111\/aromatic6.png\" alt=\"\" width=\"382\" height=\"102\" \/>\r\n<ul>\r\n \t<li>cyclopentadienyl anion (7)<\/li>\r\n<\/ul>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151114\/aromatic7.png\" alt=\"\" width=\"375\" height=\"90\" \/>\r\n\r\nAs evident from the stability of $$\\pi$$ electrons however, only some such rings actually have a loop of $$\\pi$$ electrons. Of the above examples, only the rings in 2, 4, 5, and 7 have a loop of $$\\pi$$ electrons. Resonance theory can predict that the rings in 2, 4, 5, and 7 have a loop of $$\\pi$$ electrons.\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151118\/aromatic8.png\" alt=\"\" width=\"520\" height=\"496\" \/>\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151121\/aromatic9.png\" alt=\"\" width=\"520\" height=\"290\" \/>\r\n\r\nAccording to resonance theory, however, the rings in 1, 3, and 6 also should have a loop of $$\\pi$$ electrons.\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151125\/aromatic10.png\" alt=\"\" width=\"519\" height=\"517\" \/>\r\n\r\nEvidently, resonance theory is no more reliable a tool than Lewis diagrams to be used in predicting if a ring has a loop of $$\\pi$$ electrons. Rings whose Lewis diagram implies a loop of $$\\pi$$ electrons can be classified into three classes:\r\n<ol>\r\n \t<li>aromatic rings<\/li>\r\n \t<li>antiaromatic rings<\/li>\r\n \t<li>nonaromatic rings<\/li>\r\n<\/ol>\r\nTo find whether a ring is aromatic, antiaromatic, nonaromatic, or none of the above, use the following flow chart.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"600\"]<img class=\"internal\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151130\/aromatic19.png\" alt=\"\" width=\"600\" height=\"352\" \/> Figure 1.: Flowchart for determining aromatic behavior in cyclic molecules.[\/caption]\r\n\r\n\r\n<div id=\"section_1\">\r\n\r\n\r\n<h3 class=\"editable\">Aromatic rings<\/h3>\r\nA ring that does have a loop of $$\\pi$$ electrons is said to be aromatic. Thus, the rings in 2, 4, 5, and 7 are aromatic. A compound whose molecule contains one or more aromatic rings is called an aromatic compound. Thus,\u00a02, 4, 5, and 7 are aromatic compounds. There are chemical and spectroscopic methods that can be used to experimentally determine whether a ring is aromatic or not. All aromatic rings share two structural features:\r\n\r\n1. \u00a0The ring is planar.\r\n2. The ring obeys the H\u00fcckel\u2019s rule, which states that the number of electrons in the loop of $$\\pi$$ electrons is equal to 4n + 2, where n is zero or a positive whole number.\r\n\r\n<img 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alt=\"\" width=\"488\" height=\"599\" \/>\r\n\r\nAs is evident from the above examples, determining whether a ring obeys the <a title=\"H\u00fcckel's Rule\" href=\"https:\/\/chem.libretexts.org\/Core\/Organic_Chemistry\/Hydrocarbons\/Arenes\/Properties_of_Arenes\/Aromaticity\/H%C3%BCckel's_Rule\" rel=\"internal\">H\u00fcckel\u2019s rule<\/a> or not using the Lewis diagram is straightforward. \u00a0However, determining whether a ring is planar or not requires careful consideration of many factors. A case in point is [10]annulene (10).\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151133\/aromatic12.png\" alt=\"\" width=\"154\" height=\"136\" \/>\r\n\r\nIf the ring in 10, which obeys the H\u00fcckel\u2019s Rule, were planar, the hydrogen atoms on C-2 and C-7, which are inside the ring, would have to occupy the same space, which would be physically impossible. \u00a0To accommodate the hydrogen atoms on C-2 and C-7 inside the ring, the ring is forced to deviate from planarity. Thus, 10 is not aromatic. If [10]annulene were to assume a configuration in which all double bonds were cis double bonds (11), the ring would be planar and, therefore, be aromatic.\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151134\/aromatic13.png\" alt=\"\" width=\"113\" height=\"144\" \/>\r\n\r\nExperimentally, however, [10]annulene exists exclusively as 10, indicating that the stability gained by having a loop of $$\\pi$$ electrons in 11 is outweighed by considerable angle strain.\r\n\r\n<\/div>\r\n<div id=\"section_2\">\r\n\r\n\r\n<h3 class=\"editable\">Antiaromatic rings<\/h3>\r\nA ring that does not have a loop of $$\\pi$$ electrons and is extremely unstable is said to be antiaromatic. A compound whose molecule contains one or more antiaromatic rings is called an antiaromatic compound. \u00a0The rings in 1 and 6 are antiaromatic. 1 can be isolated only in an inert, solid matrix (helium, argon, etc.) at temperatures approaching absolute zero. \u00a0Under all other conditions, it dimerizes rapidly.\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151137\/aromatic14.png\" alt=\"\" width=\"600\" height=\"67\" \/>\r\n\r\nExperiments have shown that the ring in 1 is not a square but a rectangle, which is evidence that the ring in 1 does not have a loop of $$\\pi$$ electrons. According to molecular orbital theory, 1 is a diradical, which is consistent with its extreme reactivity. 6 has never been observed.\r\n\r\nAll antiaromatic rings share two features:\r\n<ol>\r\n \t<li>The ring is planar.<\/li>\r\n \t<li>If the ring had a loop of $$\\pi$$ electrons as implied by the Lewis diagram, the number of electrons in the loop would be equal to 4n, where n is zero or a positive whole number.<\/li>\r\n<\/ol>\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151139\/aromatic15.png\" alt=\"\" width=\"600\" height=\"192\" \/>\r\n\r\nLarge and, therefore, flexible rings whose Lewis structure suggests a loop of $$\\pi$$ electrons containing 4n number of electrons avoid being antiaromatic by deviating from planarity.\r\n\r\neg:\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151143\/aromatic16.png\" alt=\"\" width=\"82\" height=\"162\" \/>\r\n\r\nExperimentally, 3 is about as stable as any typical alkene, meaning 3 is not antiaromatic. There are no antiaromatic rings containing more than five atoms.\r\n\r\n<\/div>\r\n<div id=\"section_3\">\r\n\r\n\r\n<h3 class=\"editable\">Nonaromatic rings<\/h3>\r\nA ring that does not have a loop of $$\\pi$$ electrons but is not antiaromatic is said to be nonaromatic. A compound whose molecule contains one of more nonaromatic rings is called a nonaromatic compound. A ring whose $$\\pi$$ system contains a 4n number of electrons but avoids being antiaromatic by deviating from planarity is nonaromatic. For example,\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151144\/aromatic17.png\" alt=\"\" width=\"90\" height=\"133\" \/>\r\n\r\nExperimentally, 3 exists in the following nonplanar conformation, known as the tub conformation, in which no two adjacent double bonds are on the same plane. Thus, there is no loop of $$\\pi$$ electrons in the ring in 3; 3 is nonaromatic.\r\n\r\n<img class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151146\/aromatic18.png\" alt=\"\" width=\"153\" height=\"50\" \/>\r\n\r\nA ring whose $$\\pi$$ system contains 4n + 2 number of electrons, but is forced to deviate from planarity is also nonaromatic. This is why [10]annulene (10) is nonaromatic.\r\n\r\nsee also\u00a0annulene, heteroaromatic compound\r\n\r\n<\/div>\r\n<div id=\"section_4\">\r\n\r\n\r\n<h3 class=\"editable\">Contributors<\/h3>\r\n\r\n<ul>\r\n \t<li><a class=\"external\" title=\"http:\/\/www.uvu.edu\/profpages\/profiles\/show\/user_id\/1776\" href=\"http:\/\/www.uvu.edu\/profpages\/profiles\/show\/user_id\/1776\" target=\"_blank\" rel=\"external nofollow noopener\"><span class=\"gD\">Gamini Gunawardena<\/span><\/a> from the <a class=\"external\" title=\"http:\/\/science.uvu.edu\/ochem\/\" href=\"http:\/\/science.uvu.edu\/ochem\/\" target=\"_blank\" rel=\"external nofollow noopener\">OChemPal <\/a>site (<a class=\"external\" title=\"http:\/\/www.uvu.edu\/chemistry\/\" href=\"http:\/\/www.uvu.edu\/chemistry\/\" target=\"_blank\" rel=\"external nofollow noopener\">Utah Valley University<\/a>)<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"elm-header\">\n<div class=\"elm-header-custom\">\u00a0Valence bond theory uses Lewis diagrams to depict structure and bonding of covalent entities, such as molecules and polyatomic ions, henceforth molecules. The Lewis diagram of many a molecule, however, is not consistent with the observed properties of the molecule. \u00a0The Lewis diagram of some molecules suggests a ring bearing a fully conjugated $$\\pi$$-electron system, or loop of $$\\pi$$ electrons, provided each atom in the ring is sp<sup>2<\/sup>&#8211; or sp-hybridized.<\/div>\n<\/div>\n<div id=\"elm-main-content\" class=\"elm-content-container\">\n<div>\n<ul>\n<li>cyclobutadiene (1)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151057\/aromatic1.png\" alt=\"\" width=\"263\" height=\"81\" \/><\/p>\n<ul>\n<li>benzene (2)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151100\/aromatic2.png\" alt=\"\" width=\"318\" height=\"104\" \/><\/p>\n<ul>\n<li>cyclooctatetraene (3)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151103\/aromatic3.png\" alt=\"\" width=\"330\" height=\"90\" \/><\/p>\n<ul>\n<li>pyridine (4)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151105\/aromatic4.png\" alt=\"\" width=\"371\" height=\"114\" \/><\/p>\n<ul>\n<li>pyrrole\u00a0(5)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151108\/aromatic5.png\" alt=\"\" width=\"388\" height=\"124\" \/><\/p>\n<ul>\n<li>cyclopentadienyl cation (6)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151111\/aromatic6.png\" alt=\"\" width=\"382\" height=\"102\" \/><\/p>\n<ul>\n<li>cyclopentadienyl anion (7)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151114\/aromatic7.png\" alt=\"\" width=\"375\" height=\"90\" \/><\/p>\n<p>As evident from the stability of $$\\pi$$ electrons however, only some such rings actually have a loop of $$\\pi$$ electrons. Of the above examples, only the rings in 2, 4, 5, and 7 have a loop of $$\\pi$$ electrons. Resonance theory can predict that the rings in 2, 4, 5, and 7 have a loop of $$\\pi$$ electrons.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151118\/aromatic8.png\" alt=\"\" width=\"520\" height=\"496\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151121\/aromatic9.png\" alt=\"\" width=\"520\" height=\"290\" \/><\/p>\n<p>According to resonance theory, however, the rings in 1, 3, and 6 also should have a loop of $$\\pi$$ electrons.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151125\/aromatic10.png\" alt=\"\" width=\"519\" height=\"517\" \/><\/p>\n<p>Evidently, resonance theory is no more reliable a tool than Lewis diagrams to be used in predicting if a ring has a loop of $$\\pi$$ electrons. Rings whose Lewis diagram implies a loop of $$\\pi$$ electrons can be classified into three classes:<\/p>\n<ol>\n<li>aromatic rings<\/li>\n<li>antiaromatic rings<\/li>\n<li>nonaromatic rings<\/li>\n<\/ol>\n<p>To find whether a ring is aromatic, antiaromatic, nonaromatic, or none of the above, use the following flow chart.<\/p>\n<div style=\"width: 610px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"internal\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151130\/aromatic19.png\" alt=\"\" width=\"600\" height=\"352\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 1.: Flowchart for determining aromatic behavior in cyclic molecules.<\/p>\n<\/div>\n<div id=\"section_1\">\n<h3 class=\"editable\">Aromatic rings<\/h3>\n<p>A ring that does have a loop of $$\\pi$$ electrons is said to be aromatic. Thus, the rings in 2, 4, 5, and 7 are aromatic. A compound whose molecule contains one or more aromatic rings is called an aromatic compound. Thus,\u00a02, 4, 5, and 7 are aromatic compounds. There are chemical and spectroscopic methods that can be used to experimentally determine whether a ring is aromatic or not. All aromatic rings share two structural features:<\/p>\n<p>1. \u00a0The ring is planar.<br \/>\n2. The ring obeys the H\u00fcckel\u2019s rule, which states that the number of electrons in the loop of $$\\pi$$ electrons is equal to 4n + 2, where n is zero or a positive whole number.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" 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alt=\"\" width=\"488\" height=\"599\" \/><\/p>\n<p>As is evident from the above examples, determining whether a ring obeys the <a title=\"H\u00fcckel's Rule\" href=\"https:\/\/chem.libretexts.org\/Core\/Organic_Chemistry\/Hydrocarbons\/Arenes\/Properties_of_Arenes\/Aromaticity\/H%C3%BCckel's_Rule\" rel=\"internal\">H\u00fcckel\u2019s rule<\/a> or not using the Lewis diagram is straightforward. \u00a0However, determining whether a ring is planar or not requires careful consideration of many factors. A case in point is [10]annulene (10).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151133\/aromatic12.png\" alt=\"\" width=\"154\" height=\"136\" \/><\/p>\n<p>If the ring in 10, which obeys the H\u00fcckel\u2019s Rule, were planar, the hydrogen atoms on C-2 and C-7, which are inside the ring, would have to occupy the same space, which would be physically impossible. \u00a0To accommodate the hydrogen atoms on C-2 and C-7 inside the ring, the ring is forced to deviate from planarity. Thus, 10 is not aromatic. If [10]annulene were to assume a configuration in which all double bonds were cis double bonds (11), the ring would be planar and, therefore, be aromatic.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151134\/aromatic13.png\" alt=\"\" width=\"113\" height=\"144\" \/><\/p>\n<p>Experimentally, however, [10]annulene exists exclusively as 10, indicating that the stability gained by having a loop of $$\\pi$$ electrons in 11 is outweighed by considerable angle strain.<\/p>\n<\/div>\n<div id=\"section_2\">\n<h3 class=\"editable\">Antiaromatic rings<\/h3>\n<p>A ring that does not have a loop of $$\\pi$$ electrons and is extremely unstable is said to be antiaromatic. A compound whose molecule contains one or more antiaromatic rings is called an antiaromatic compound. \u00a0The rings in 1 and 6 are antiaromatic. 1 can be isolated only in an inert, solid matrix (helium, argon, etc.) at temperatures approaching absolute zero. \u00a0Under all other conditions, it dimerizes rapidly.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151137\/aromatic14.png\" alt=\"\" width=\"600\" height=\"67\" \/><\/p>\n<p>Experiments have shown that the ring in 1 is not a square but a rectangle, which is evidence that the ring in 1 does not have a loop of $$\\pi$$ electrons. According to molecular orbital theory, 1 is a diradical, which is consistent with its extreme reactivity. 6 has never been observed.<\/p>\n<p>All antiaromatic rings share two features:<\/p>\n<ol>\n<li>The ring is planar.<\/li>\n<li>If the ring had a loop of $$\\pi$$ electrons as implied by the Lewis diagram, the number of electrons in the loop would be equal to 4n, where n is zero or a positive whole number.<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151139\/aromatic15.png\" alt=\"\" width=\"600\" height=\"192\" \/><\/p>\n<p>Large and, therefore, flexible rings whose Lewis structure suggests a loop of $$\\pi$$ electrons containing 4n number of electrons avoid being antiaromatic by deviating from planarity.<\/p>\n<p>eg:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151143\/aromatic16.png\" alt=\"\" width=\"82\" height=\"162\" \/><\/p>\n<p>Experimentally, 3 is about as stable as any typical alkene, meaning 3 is not antiaromatic. There are no antiaromatic rings containing more than five atoms.<\/p>\n<\/div>\n<div id=\"section_3\">\n<h3 class=\"editable\">Nonaromatic rings<\/h3>\n<p>A ring that does not have a loop of $$\\pi$$ electrons but is not antiaromatic is said to be nonaromatic. A compound whose molecule contains one of more nonaromatic rings is called a nonaromatic compound. A ring whose $$\\pi$$ system contains a 4n number of electrons but avoids being antiaromatic by deviating from planarity is nonaromatic. For example,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151144\/aromatic17.png\" alt=\"\" width=\"90\" height=\"133\" \/><\/p>\n<p>Experimentally, 3 exists in the following nonplanar conformation, known as the tub conformation, in which no two adjacent double bonds are on the same plane. Thus, there is no loop of $$\\pi$$ electrons in the ring in 3; 3 is nonaromatic.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05151146\/aromatic18.png\" alt=\"\" width=\"153\" height=\"50\" \/><\/p>\n<p>A ring whose $$\\pi$$ system contains 4n + 2 number of electrons, but is forced to deviate from planarity is also nonaromatic. This is why [10]annulene (10) is nonaromatic.<\/p>\n<p>see also\u00a0annulene, heteroaromatic compound<\/p>\n<\/div>\n<div id=\"section_4\">\n<h3 class=\"editable\">Contributors<\/h3>\n<ul>\n<li><a class=\"external\" title=\"http:\/\/www.uvu.edu\/profpages\/profiles\/show\/user_id\/1776\" href=\"http:\/\/www.uvu.edu\/profpages\/profiles\/show\/user_id\/1776\" target=\"_blank\" rel=\"external nofollow noopener\"><span class=\"gD\">Gamini Gunawardena<\/span><\/a> from the <a class=\"external\" title=\"http:\/\/science.uvu.edu\/ochem\/\" href=\"http:\/\/science.uvu.edu\/ochem\/\" target=\"_blank\" rel=\"external nofollow noopener\">OChemPal <\/a>site (<a class=\"external\" title=\"http:\/\/www.uvu.edu\/chemistry\/\" href=\"http:\/\/www.uvu.edu\/chemistry\/\" target=\"_blank\" rel=\"external nofollow noopener\">Utah Valley University<\/a>)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":44985,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1447","chapter","type-chapter","status-publish","hentry"],"part":27,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/users\/44985"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1447\/revisions"}],"predecessor-version":[{"id":1972,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1447\/revisions\/1972"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/parts\/27"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1447\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/media?parent=1447"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapter-type?post=1447"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/contributor?post=1447"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/license?post=1447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}