(How to manipulate JSmol structures)

 trans- and cis-Decalin are fused ring analogs of cyclohexane. They are non-interconvertible stereoisomers of one another. Let's consider the JSmol structures above and define some terms. There are four carbon atoms of interest colored blue, green, red and magenta. The blue and green carbons are in ring A and they are directly attached to ring B, which bears the red and magenta carbon atoms, also attached directly to ring A.

Now we shall consider trans-decalin itself. The most stable conformation of this isomer has both rings in chair conformations. While there is some mobility for each ring to undergo subtle conformational change, it is not possible for either ring to undergo conformational inversion to the alternate chair. Note that the blue and green carbon atoms are both trans diequatorial to ring B while the red and magenta carbons bear the same relationship to ring A. If one were to imagine removing the gray -CH₂CH₂- moiety from ring A, the blue and green carbon atoms would be akin to the two methyl groups of trans-1,2- dimethylcyclohexane in its more stable diequatorial chair conformation. trans-1,2-Dimethylcyclohexane can undergo chair-chair interconversion with both methyl groups diaxial. The -CH₂CH₂- chain prohibits the chair-chair interconversion in trans-decalin. The same conclusion can be made for ring B because it is the mirror of ring A.

 To convert trans-decalin into its cis-stereoisomer requires a configurational change. Imagine switching the position of the blue carbon with the methine hydrogen attached to the gray fusion carbon (the one to which the blue and magenta carbons are attached). This conceptual exercise produces the JSmol structure of cis-decalin 1. Not surprisingly, both rings are preferentially in chair conformations. Unlike trans-decalin, cis-decalin 1, just like cis-1,2-dimethylcyclohexane, is free to undergo chair-chair interconversion. Chair-chair conformational inversion of cis-decalin 1 provides cis-decalin 2. [Manipulate the blue axial to ring B; green equatorial to ring B; red axial to ring A; magenta equatorial to ring A. In cis-decalin 2: blue equatorial to ring B; green axial to ring B; red equatorial to ring A; magenta axial to ring A. cis-Decalins 1 and 2 are mirror images of one another (exclude the four colors).

 Just like cyclohexane, trans-decalin has no unfavorable interactions when compared to other decalins. for cis-decalin (using cis-decalin 1 for the sake of discussion) clearly has 1,3-diaxial interactions (gauche butane interactions). Let's analyze cis-decalin 1 via 1,3-diaxial interactions. An axial methyl group is equivalent to an axial methyl group/hydrogen interaction (0.9 kcal/mol; see A values). The axial blue carbon in ring A is 1,3 diaxial to two axial hydrogens in ring B and the axial red carbon in ring B is 1,3-diaxial to two axial hydrogens in ring A. This leads to the conclusion that there are four interactions or 4 x 0.9 kcal/mol = 3.6 kcal/mol more energy in cis-decalin than in trans-decalin. Alternatively, let's count by gauche butane interactions. For the axial blue carbon in ring A we have counting the colors of four carbons: a) blue-gray-gray-red. Just like cyclohexane, trans-decalin has no unfavorable interactions when compared to other decalins. for cis-decalin (using cis-decalin 1 for the sake of discussion) clearly has 1,3-diaxial interactions (gauche butane interactions). Let's analyze cis-decalin 1 via 1,3-diaxial interactions. An axial methyl group is equivalent to an axial methyl group/hydrogen interaction (0.9 kcal/mol; see A values). The axial blue carbon in ring A is 1,3 diaxial to two axial hydrogens in ring B and the axial red carbon in ring B is 1,3-diaxial to two axial hydrogens in ring A. This leads to the conclusion that there are four interactions or 4 x 0.9 kcal/mol = 3.6 kcal/mol more energy in cis-decalin than in trans-decalin. Alternatively, let's count by gauche butane interactions. For the axial blue carbon in ring A we have counting the colors of four carbons: a) blue-gray-gray-red, and b) blue-gray-magenta-gray. For the axial red carbon of ring B we have: c) red-gray-gray-blue, and d) red-gray-green-gray. Clearly, a) and c) are identical, which means that there are three gauche interactions, not four. The energy difference between trans- and cis-decalin should be 2.7 kcal/mol. How can this difference be confirmed experimentally? The heats of combustion of the two isomers gives the answer. trans-Decalin's heat of combustion is ΔH^o_(comb) = -1500.22 kcal/mol while cis-decalin has ΔH^o_(comb) = -1502.92 kcal/mol. Therefore, |Δ(ΔH^o_(comb) )| = 2.7 kcal/mol. There is more heat liberated during the combustion of cis-decalin. These data are reflected in the respective heats of formation: trans-decalin, ΔH_f^{o =} -55.14 kcal/mol; cis-decalin, ΔH_f^{o =} -52.45 kcal/mol. Therefore, |Δ(ΔH_f^o )| = 2.7 kcal/mol).