3× Axial vs 3× Equatorial: The ΔG_GA Value Is a Robust Computational Measure of Substituent Steric Effects

We define ΔG_GA as the free energy change for the formal equilibrium: [13]G-H + 1-X-adamantane → [13]G-X + adamantane, where [13]G-H is the C₁₃H₂₂ fragment of all-trans graphane with 3-fold symmetry. This compares with a situation where the group X is equatorial to three cyclohexane rings with one where it is axial to three rings. ΔG_GA values vary from 2.9 (CN) to 145.7 kJ mol^-1 (CCl₃), and this wide range means that ΔG can be calculated with confidence. ΔG_GA values for Me, Et, i-Pr, and t-Bu form a regular series, 34.9, 63.3, 101.6, and 142.0, and clearly reflect the steric size of the groups. We propose a model where the six axial hydrogens surrounding X on [13]G-X provide a nearly circular constriction on the substituent close to its point of attachment but which does not extend far above this. We compare these results with A values and with calculations on 2- and 7-substituted [1(2,3)4]pentamantanes. We show that electronic effects on ΔG_GA values are negligible but that they correlate well with computed cone and solid angles subtended by the substituent.