At What Chain Length Do Unbranched Alkanes Prefer Folded Conformations?

Short unbranched alkanes are known
to prefer linear conformations,
whereas long unbranched alkanes are folded. It is not known with certainty
at what chain length the linear conformation is no longer the global
minimum. To clarify this point, we use ab initio and density functional
methods to compute the relative energies of the linear and hairpin
alkane conformers for increasing chain lengths. Extensive electronic
structure calculations are performed to obtain optimized geometries,
harmonic frequencies, and accurate single point energies for the selected
alkane conformers from octane through octadecane. Benchmark CCSD­(T)/cc-pVTZ
single point calculations are performed for chains through tetradecane,
whereas approximate methods are required for the longer chains up
to octadecane. Using frozen natural orbitals to unambiguously truncate
the virtual orbital space, we are able to compute composite CCSD FNO­(T)
single point energies for all the chain lengths. This approximate
composite method has significant computational savings compared to
full CCSD­(T) while retaining ∼0.15 kcal/mol accuracy compared
to the benchmark results. More approximate dual-basis resolution-of-the-identity
double-hybrid DFT calculations are also performed and shown to have
reasonable 0.2–0.4 kcal/mol errors compared with our benchmark
values. After including contributions from temperature dependent internal
energy shifts, we find the preference for folded conformations to
lie between hexadecane and octadecane, in excellent agreement with
recent experiments [Lüttschwager, N. O.; Wassermann, T. N.; Mata, R. A.; Suhm, M. A. Angew. Chem. Int. Ed. 2013, 52, 463].