{"id":2425,"date":"2018-06-19T20:29:37","date_gmt":"2018-06-19T20:29:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-potsdam-organicchemistry\/chapter\/conformational-analysis\/"},"modified":"2018-08-06T07:57:48","modified_gmt":"2018-08-06T07:57:48","slug":"conformational-analysis","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-potsdam-organicchemistry\/chapter\/conformational-analysis\/","title":{"raw":"3.7. Conformational analysis","rendered":"3.7. Conformational analysis"},"content":{"raw":"
Conformational analysis is the study of the energetics between different rotamers and is useful for understanding the stability of different isomers by taking into account the spatial orientation and through-space interactions of substituents. Conformational analysis can be used to predict and explain product(s) selectivity, mechanisms, and rates of reactions.\u00a0 We will not go into such detail, but we will be taking the principles learnt in cases such as butane and methylcyclohexane, and applying them to more complex alkanes.\r\n
\r\n

Open-chain (acyclic) conformations<\/h1>\r\n
\r\n

Ethane and propane<\/h2>\r\nWe have already seen how the eclipsed form of these alkanes is higher in energy than the staggered form, by around 12-14 kJ\/mol (3-3.4 kcal\/mol), which can be considered as the sum of three eclipsed interactions.\r\n\r\n\"\"\r\n\r\n\r\n\r\n\r\n\r\n
Eclipsed interaction<\/strong><\/td>\r\nEnergy (kcal\/mol)<\/strong><\/td>\r\nEnergy (kJ\/mol)<\/strong><\/td>\r\n<\/tr>\r\n
H||H<\/td>\r\n1.0<\/td>\r\n4.0<\/td>\r\n<\/tr>\r\n
H||CH3<\/sub><\/td>\r\n1.4<\/td>\r\n6.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Butane<\/h2>\r\n<\/div>\r\n
Once we examine butane, we have a new eclipsed interaction, CH3<\/sub>||CH3<\/sub>,for which the energy value can be estimated from from the overall energy difference (found experimentally to be 5.1 kcal\/mol).\r\n\"\"Thus we can see that the interaction between eclipsing methyl groups is worth 3.1 kcal\/mol or 13 kJ\/mol - much more than the H||CH3 interaction we saw first in propane.<\/div>\r\n
\r\n

Higher alkanes<\/h2>\r\nButane shows us that the eclipsing of two methyl groups + two H groups destabilizes more than eclipsing of two H||CH3<\/sub> pairs.\u00a0 This indicates a general principle, that Big-Big eclipsing interactions are the most destabilizing<\/strong>. This can be remembered as \"Big-Big is Bad<\/strong>\"! Experimental studies show that this generally applies both when judging the least stable conformations (where big-big eclipsing is most destabilizing) and when judging the most stable conformations (where gauche interactions are destabilizing relative to anti conformations).\r\n\r\nFor example: Consider 2-methylbutane - what is\/are the most stable conformation(s)?\u00a0 What is\/are the least?\r\n\r\nHINT: It can help to make a molecular model of the compound, and draw a Newman projection.\u00a0 Then rotate one end of the bond through 60o<\/sup> intervals until you have get back to where you started.\u00a0 In the figure below, the front end of the bond is rotating clockwise, going from 1<\/strong> to 2<\/strong>, etc.\r\n\r\n\"\"\r\n\r\n<\/div>\r\n
\r\n
\r\n\r\nFor this class, we will always find that the most stable conformation is staggered (i.e., 1<\/strong>, 3<\/strong> or 5<\/strong>), and the least stable is eclipsed (i.e., 2<\/strong>, 4<\/strong> or 6<\/strong>).\u00a0 Comparing 1<\/strong>, 3<\/strong> and 5<\/strong>, we see that 1<\/strong> has two \"bad\" gauche interactions, whereas 3<\/strong> and 5<\/strong> have only one gauche interaction; thus 3<\/strong> and 5<\/strong> are both equally stable, and they are the most stable conformations for 2-methylbutane.\u00a0 Comparing 2<\/strong>, 4<\/strong> and 6<\/strong>, we see that 2<\/strong> and 6<\/strong> both involve one \"Big-Big\" (methyl-methyl) interaction, but 4<\/strong> does not.\u00a0 Thus 4<\/strong> is the least unstable of the eclipsed forms, and 2<\/strong> and 6<\/strong> are equally unstable so they are the least stable conformations.\r\n\r\nIn cases where the big groups are ethyl, propyl, etc., rather than just methyl, these groups will count as bigger than methyl when judging their destabilizing effects.\u00a0 Branched alkyls such as isopropyl (-CH(CH3<\/sub>)2<\/sub>) are more destabilizing, with tertiary groups such as tert<\/em>-butyl (-C(CH3<\/sub>)3<\/sub>) the most destabilizing of all, reflecting their steric bulk.\r\n\r\n<\/div>\r\n
\r\n

Substituted cyclohexanes\u200b<\/h2>\r\n
\r\n

A Values<\/h3>\r\nSubstituents on a cyclohexane prefer to be in the equatorial position. \u00a0When a substituent is in the axial position, there are two gauche butane interactions more than when a substituent is in the equatorial position. We quantify the energy difference between the axial and equatorial conformations as the A-value,\u00a0which is equivalent to the negative of the \u2206G\u00b0, for the equilibrium shown below. Therefore the A-value, or -\u2206G\u00b0, is the preference for the substituent to sit in the equatorial position.\r\n\r\n\"\"\r\n\r\nRecall that the\u00a0equilibrium constant is\u00a0related to the change in Gibbs Energies<\/a>\u00a0for the reaction:\r\n

\u2206G<\/em>\u00b0 = -RT\u00a0<\/em>1nKeq<\/sub><\/em><\/p>\r\nThe balance between reactants and products in a reaction will be determined by the free energy difference between the two sides of the reaction. The greater the free energy difference, the more the reaction will favor one side or the other.\r\n\r\nTable<\/strong>: Below is a table of A-values for some common substituents.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Substituent<\/strong><\/td>\r\n\u2206G\u00b0 (kcal\/mol)<\/strong><\/td>\r\nA-value<\/strong><\/td>\r\n<\/tr>\r\n
-F<\/td>\r\n-0.28-0.24<\/td>\r\n0.24-0.28<\/td>\r\n<\/tr>\r\n
-Cl<\/td>\r\n-0.53<\/td>\r\n0.53<\/td>\r\n<\/tr>\r\n
-Br<\/td>\r\n-0.48<\/td>\r\n0.48<\/td>\r\n<\/tr>\r\n
-I<\/td>\r\n-0.47<\/td>\r\n0.47<\/td>\r\n<\/tr>\r\n
-CH3<\/sub>\u00a0(-Me)<\/td>\r\n-1.8<\/td>\r\n1.8<\/td>\r\n<\/tr>\r\n
-CH2<\/sub>CH3\u00a0<\/sub>(-Et)<\/td>\r\n-1.8<\/td>\r\n1.8<\/td>\r\n<\/tr>\r\n
-CH(CH3<\/sub>)2<\/sub>\u00a0(-i<\/em>-Pr)<\/td>\r\n-2.1<\/td>\r\n2.1<\/td>\r\n<\/tr>\r\n
-C(CH3<\/sub>)3<\/sub>\u00a0(-t<\/em>-Bu)<\/td>\r\n<-4.5<\/td>\r\n>4.5<\/td>\r\n<\/tr>\r\n
-CH=CH2<\/sub><\/td>\r\n-1.7<\/td>\r\n1.7<\/td>\r\n<\/tr>\r\n
-C=<\/span>CH<\/td>\r\n-0.5<\/td>\r\n0.5<\/td>\r\n<\/tr>\r\n
-CN<\/td>\r\n-0.25-0.15<\/td>\r\n0.15-0.25<\/td>\r\n<\/tr>\r\n
-C6<\/sub>H5<\/sub>\u00a0(-Ph)<\/td>\r\n-2.9<\/td>\r\n2.9<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n\r\nThis table allows us to estimate the actual energy differences between conformations with axial vs. equatorial substituents.\u00a0 However, in general, to stablize we simply place bigger groups equatorial.\u00a0 To find the most stable conformation, we choose the form with the least number of large axial groups; the least stable will have the most number of axial groups.\r\n\r\nWhen \"big\" groups come in close proximity (e.g., two methyls on neighboring carbons on a cyclohexane ring), the \"Big-Big is Bad\" principle applies, as it did with open-chain alkanes.\r\n

Polysubstituted cyclohexanes<\/h3>\r\n
\r\n

1,4-disubstitution<\/h4>\r\nThe A-values of the substituents are roughly additive in either the\u00a0cis<\/em>- or\u00a0trans<\/em>-diastereomers.\r\n\r\n\"1,4-disubstitutions.png\"\r\n\r\n<\/div>\r\n
\r\n

1,3-disubstitution<\/h4>\r\n\u200bA-values are only additive in the\u00a0trans<\/em>-diastereomer:\r\n\r\n\"\"\r\n\r\nWhen there are\u00a0cis<\/em>-substituents on the chair, there is a new interaction in the di-axial conformation:\r\n\r\nIn the above example, each methyl group has one 1,3-diaxial interaction with a hydrogen. The methyl groups also interact with each other. \u00a0This new diaxial interaction is extremely unfavorable based on their steric interaction (double-gauche pentane conformation. a \"big-big\" interaction).\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Practice Problems<\/h3>\r\nPractice problems<\/a>\r\n\r\n\"\"\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>","rendered":"
Conformational analysis is the study of the energetics between different rotamers and is useful for understanding the stability of different isomers by taking into account the spatial orientation and through-space interactions of substituents. Conformational analysis can be used to predict and explain product(s) selectivity, mechanisms, and rates of reactions.\u00a0 We will not go into such detail, but we will be taking the principles learnt in cases such as butane and methylcyclohexane, and applying them to more complex alkanes.<\/p>\n
\n

Open-chain (acyclic) conformations<\/h1>\n
\n

Ethane and propane<\/h2>\n

We have already seen how the eclipsed form of these alkanes is higher in energy than the staggered form, by around 12-14 kJ\/mol (3-3.4 kcal\/mol), which can be considered as the sum of three eclipsed interactions.<\/p>\n

\"\"<\/p>\n\n\n\n\n\n
Eclipsed interaction<\/strong><\/td>\nEnergy (kcal\/mol)<\/strong><\/td>\nEnergy (kJ\/mol)<\/strong><\/td>\n<\/tr>\n
H||H<\/td>\n1.0<\/td>\n4.0<\/td>\n<\/tr>\n
H||CH3<\/sub><\/td>\n1.4<\/td>\n6.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Butane<\/h2>\n<\/div>\n
Once we examine butane, we have a new eclipsed interaction, CH3<\/sub>||CH3<\/sub>,for which the energy value can be estimated from from the overall energy difference (found experimentally to be 5.1 kcal\/mol).
\n\"\"Thus we can see that the interaction between eclipsing methyl groups is worth 3.1 kcal\/mol or 13 kJ\/mol – much more than the H||CH3 interaction we saw first in propane.<\/div>\n
\n

Higher alkanes<\/h2>\n

Butane shows us that the eclipsing of two methyl groups + two H groups destabilizes more than eclipsing of two H||CH3<\/sub> pairs.\u00a0 This indicates a general principle, that Big-Big eclipsing interactions are the most destabilizing<\/strong>. This can be remembered as “Big-Big is Bad<\/strong>“! Experimental studies show that this generally applies both when judging the least stable conformations (where big-big eclipsing is most destabilizing) and when judging the most stable conformations (where gauche interactions are destabilizing relative to anti conformations).<\/p>\n

For example: Consider 2-methylbutane – what is\/are the most stable conformation(s)?\u00a0 What is\/are the least?<\/p>\n

HINT: It can help to make a molecular model of the compound, and draw a Newman projection.\u00a0 Then rotate one end of the bond through 60o<\/sup> intervals until you have get back to where you started.\u00a0 In the figure below, the front end of the bond is rotating clockwise, going from 1<\/strong> to 2<\/strong>, etc.<\/p>\n

\"\"<\/p>\n<\/div>\n

\n
\n

For this class, we will always find that the most stable conformation is staggered (i.e., 1<\/strong>, 3<\/strong> or 5<\/strong>), and the least stable is eclipsed (i.e., 2<\/strong>, 4<\/strong> or 6<\/strong>).\u00a0 Comparing 1<\/strong>, 3<\/strong> and 5<\/strong>, we see that 1<\/strong> has two “bad” gauche interactions, whereas 3<\/strong> and 5<\/strong> have only one gauche interaction; thus 3<\/strong> and 5<\/strong> are both equally stable, and they are the most stable conformations for 2-methylbutane.\u00a0 Comparing 2<\/strong>, 4<\/strong> and 6<\/strong>, we see that 2<\/strong> and 6<\/strong> both involve one “Big-Big” (methyl-methyl) interaction, but 4<\/strong> does not.\u00a0 Thus 4<\/strong> is the least unstable of the eclipsed forms, and 2<\/strong> and 6<\/strong> are equally unstable so they are the least stable conformations.<\/p>\n

In cases where the big groups are ethyl, propyl, etc., rather than just methyl, these groups will count as bigger than methyl when judging their destabilizing effects.\u00a0 Branched alkyls such as isopropyl (-CH(CH3<\/sub>)2<\/sub>) are more destabilizing, with tertiary groups such as tert<\/em>-butyl (-C(CH3<\/sub>)3<\/sub>) the most destabilizing of all, reflecting their steric bulk.<\/p>\n<\/div>\n

\n

Substituted cyclohexanes\u200b<\/h2>\n
\n

A Values<\/h3>\n

Substituents on a cyclohexane prefer to be in the equatorial position. \u00a0When a substituent is in the axial position, there are two gauche butane interactions more than when a substituent is in the equatorial position. We quantify the energy difference between the axial and equatorial conformations as the A-value,\u00a0which is equivalent to the negative of the \u2206G\u00b0, for the equilibrium shown below. Therefore the A-value, or -\u2206G\u00b0, is the preference for the substituent to sit in the equatorial position.<\/p>\n

\"\"<\/p>\n

Recall that the\u00a0equilibrium constant is\u00a0related to the change in Gibbs Energies<\/a>\u00a0for the reaction:<\/p>\n

\u2206G<\/em>\u00b0 = –RT\u00a0<\/em>1nKeq<\/sub><\/em><\/p>\n

The balance between reactants and products in a reaction will be determined by the free energy difference between the two sides of the reaction. The greater the free energy difference, the more the reaction will favor one side or the other.<\/p>\n

Table<\/strong>: Below is a table of A-values for some common substituents.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Substituent<\/strong><\/td>\n\u2206G\u00b0 (kcal\/mol)<\/strong><\/td>\nA-value<\/strong><\/td>\n<\/tr>\n
-F<\/td>\n-0.28-0.24<\/td>\n0.24-0.28<\/td>\n<\/tr>\n
-Cl<\/td>\n-0.53<\/td>\n0.53<\/td>\n<\/tr>\n
-Br<\/td>\n-0.48<\/td>\n0.48<\/td>\n<\/tr>\n
-I<\/td>\n-0.47<\/td>\n0.47<\/td>\n<\/tr>\n
-CH3<\/sub>\u00a0(-Me)<\/td>\n-1.8<\/td>\n1.8<\/td>\n<\/tr>\n
-CH2<\/sub>CH3\u00a0<\/sub>(-Et)<\/td>\n-1.8<\/td>\n1.8<\/td>\n<\/tr>\n
-CH(CH3<\/sub>)2<\/sub>\u00a0(-i<\/em>-Pr)<\/td>\n-2.1<\/td>\n2.1<\/td>\n<\/tr>\n
-C(CH3<\/sub>)3<\/sub>\u00a0(-t<\/em>-Bu)<\/td>\n<-4.5<\/td>\n>4.5<\/td>\n<\/tr>\n
-CH=CH2<\/sub><\/td>\n-1.7<\/td>\n1.7<\/td>\n<\/tr>\n
-C=<\/span>CH<\/td>\n-0.5<\/td>\n0.5<\/td>\n<\/tr>\n
-CN<\/td>\n-0.25-0.15<\/td>\n0.15-0.25<\/td>\n<\/tr>\n
-C6<\/sub>H5<\/sub>\u00a0(-Ph)<\/td>\n-2.9<\/td>\n2.9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n

This table allows us to estimate the actual energy differences between conformations with axial vs. equatorial substituents.\u00a0 However, in general, to stablize we simply place bigger groups equatorial.\u00a0 To find the most stable conformation, we choose the form with the least number of large axial groups; the least stable will have the most number of axial groups.<\/p>\n

When “big” groups come in close proximity (e.g., two methyls on neighboring carbons on a cyclohexane ring), the “Big-Big is Bad” principle applies, as it did with open-chain alkanes.<\/p>\n

Polysubstituted cyclohexanes<\/h3>\n
\n

1,4-disubstitution<\/h4>\n

The A-values of the substituents are roughly additive in either the\u00a0cis<\/em>– or\u00a0trans<\/em>-diastereomers.<\/p>\n

\"1,4-disubstitutions.png\"<\/p>\n<\/div>\n

\n

1,3-disubstitution<\/h4>\n

\u200bA-values are only additive in the\u00a0trans<\/em>-diastereomer:<\/p>\n

\"\"<\/p>\n

When there are\u00a0cis<\/em>-substituents on the chair, there is a new interaction in the di-axial conformation:<\/p>\n

In the above example, each methyl group has one 1,3-diaxial interaction with a hydrogen. The methyl groups also interact with each other. \u00a0This new diaxial interaction is extremely unfavorable based on their steric interaction (double-gauche pentane conformation. a “big-big” interaction).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n

Practice Problems<\/h3>\n

Practice problems<\/a><\/p>\n

\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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