To the Editor

In a 2011 Article, Shaik, Alvarez and co-authors reported a computational study of dihydrogen C–H···H–C interactions in dimers of linear, branched and polyhedral alkanes1. They found that the intermolecular interactions between isolated pairs of polyhedral alkanes are significantly stronger than those between linear alkanes with the same number of carbon atoms, and the discussion of these results included the question “Why do polyhedranes have higher melting points than linear alkanes of similar size?” The purpose of this Correspondence is to mention that the melting point of a solid is also influenced by the entropy change on melting, according to Tm = ΔHm / ΔSm. The reported discussion based on calculated intermolecular interaction energies and the expected number of nearest neighbours in a crystal structure addresses only ΔHm, which cannot alone account for trends in melting points.

It is suggested here that Fig. 1b in the Article from Shaik, Alvarez and co-authors (which shows the melting points of n-alkanes, cycloalkanes and polyhedranes as a function of the number of carbon atoms) is substantially influenced by entropic factors. One contribution to ΔSm is the change in rotational freedom as molecules are released from the solid to the liquid. According to statistical thermodynamics, rotational entropy is dependent on the number of distinguishable molecular orientations, which is governed by the molecular symmetry. Molecules with higher symmetry number (σ) have fewer distinguishable orientations, and their rotational entropy in the liquid is reduced by Rlnσ compared with an equivalent asymmetrical case2. Thus, ΔSm is smaller for a more symmetrical molecule, and the melting point is increased compared with an asymmetrical molecule with comparable ΔHm. The point symmetry groups of the linear alkanes (CnH2n+2) are C2h or C2v for even and odd n, respectively, both giving σ = 2. The polyhedranes considered are cubane (Oh, σ = 24), adamantane (Td, σ = 12), octahedrane (D3d, σ = 6), congressane (D3d, σ = 6), pagodane (D2h, σ = 4), dodecahedrane (Ih, σ = 60) and cyclohexamantane (D3d, σ = 6), all of which have σ > 2. It is notable that the molecule with the highest symmetry number, dodecahedrane (C20H20), has by far the highest melting point.

It is also possible for entropy to be increased in the solid prior to melting through molecular motion. Again, this reduces ΔSm and contributes to an increased melting point. Molecular motion in the solid state has been studied for the alkanes, and plastic phases (where the molecules are essentially free to rotate around fixed lattice points) are experimentally established for the high-symmetry molecules cubane3, adamantane4 and dodecahedrane5. These dynamic effects can also be expected to contribute to the differences in melting points seen for the polyhedranes compared with the linear alkanes.