What Can We Learn about Dispersion from the Conformer Surface of n-Pentane?

In earlier work [Gruzman, D.; Karton, A.; Martin, J. M. L. J. Phys. Chem. A 2009, 113, 11974], we showed that conformer energies in alkanes (and other systems) are highly dispersion-driven and that uncorrected DFT functionals fail badly at reproducing them, while simple empirical dispersion corrections tend to overcorrect. To gain greater insight into the nature of the phenomenon, we have mapped the torsional surface of n-pentane to 10-degree resolution at the CCSD(T)-F12 level near the basis set limit. The data obtained have been decomposed by order of perturbation theory, excitation level, and same-spin vs opposite-spin character. A large number of approximate electronic structure methods have been considered, as well as several empirical dispersion corrections. Our chief conclusions are as follows: (a) the effect of dispersion is dominated by same-spin correlation (or triplet-pair correlation, from a different perspective); (b) singlet-pair correlation is important for the surface, but qualitatively very dissimilar to the dispersion component; (c) single and double excitations beyond third order are essentially unimportant for this surface; (d) connected triple excitations do play a role but are statistically very similar to the MP2 singlet-pair correlation; (e) the form of the damping function is crucial for good performance of empirical dispersion corrections; (0 at least in the lower-energy regions, SCS-MP2 and especially MP2.5 perform very well; (g) novel spin-component scaled double hybrid functionals such as DSD-PBEP86-D2 acquit themselves very well for this problem.