A yet another theory post, h/t Steven Bachrach.
Everyone remembers the two fundamental chemical bond types: covalent and ionic. Recently, a third one has been proposed, which is called "charge-shift bonding". The valence bond wavefunction that describes the system, e.g., a fluorine molecule, is a linear combination of different charge shift states, e.g.:
Ψ(F2) = C1*φ(F-F) + C2*φ(F+F-) + C3*φ(F-F+)
Now, the fluorine molecule stands here as an example because the energy contribution of the covalent term is positive, meaning that the system exists in a "superposition" of two resonant states, F+F- and F-F+, while the covalent contribution actually destabilizes the molecule. This is a very interesting phenomenon, particularly because it is reminiscent of the Mott transition. For more details on charge-shift bonding, see the review in Nature Chemistry, and the blog post for a more strict explanation of the concept.
While this is an interesting explanation of why the fluorine molecule falls apart so happily, it has been suggested that a similar mechanism can be behind the differences in energy of linear vs. branched alkanes. Basically, the latter have more available options for second-atom "resonances" (C+CC- and C-CC+). Here's the paper and the blog post
Now, this is a very interesting explanation of a long-standing problem. On the other hand, though, the fact that even such seemingly simple and familiar systems as alkanes sometimes have to be treated using multi-reference methods is, in my view, somewhat disencouraging...