Let , which is conserved for this closed one-to-one isomerization at fixed volume. Substitute into the equilibrium ratio:ThereforeThe equilibrium split is independent of having started with pure cis, provided equilibration is complete and no side reaction changes the total concentration.
React pentaborane with an alkyne under relatively mild conditions to obtain a nido framework, conventionally nido-2,3-dicarbahexaborane(8) for acetylene. The two entering carbon atoms initially retain their adjacency. A specific mild example uses 2-butyne with triethylamine-assisted at or below room temperature to give nido-. This is a practical route to an explicitly nido carborane, rather than an assumption that an alkyne supplies a closo cage under every condition.[ref]
Improved Synthetic Routes to Small Carboranes: Bench-Scale Preparation of nido-2,3-C2B4H8 Derivatives from B5H9 and from B3H8- Salts by Narayan S. Hosmane and Russell N. Grimes. 1979, abstract and preparation discussion: amine-assisted substituted-alkyne reaction under mild conditions
More energetic gas-phase reaction or pyrolysis promotes hydrogen loss, boron-fragment loss and cage rearrangement, giving closo carboranes, for example - and -, with other cage sizes possible in the mixture. Thermolysis of a previously formed nido carborane is an alternative route to this stage. The point is not a clean same-composition nido-to-closo isomerization: the change of hydrogen content and sometimes cage size must be retained in the formulas.
Milder conditions favour kinetically trapped adjacent-carbon products; higher temperatures permit migration to carbon-separated arrangements, often increasing favourable B–C contacts relative to adjacent C–C/B–B contacts. Conditions and Lewis bases also influence which separated-carbon cage is isolated; temperature alone does not prescribe a single quantitative isomer distribution. Primary thermolysis studies and the small-carborane literature document both cage rearrangement and reagent-dependent product mixtures.[ref]
Synthesis of Carboranes from Dihydrocarboranes by Thomas P. Onak and others. 1963, printed p. 3378, introduction and product summary