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Short unbranched alkanes are known to prefer linear conformations, while longunbranched alkanes are folded. It is not known with certainty at what chainlength the linear conformation is no longer the global minimum. To clarify thispoint, we use {\it ab initio} and density functional methods to compute therelative energies of the linear and hairpin alkane conformers for increasingchain lengths. Extensive electronic structure calculations are performed toobtain optimized geometries, harmonic frequencies and accurate single pointenergies for the selected alkane conformers from octane through octadecane.Benchmark CCSD(T)/cc-pVTZ single point calculations are performed for chainsthrough tetradecane, while approximate methods are required for the longerchains up to octadecane. Using frozen natural orbitals to unambiguouslytruncate the virtual orbital space, we are able to compute composite CCSDFNO(T) single point energies for all the chain lengths. This approximatecomposite method has significant computational savings compared to full CCSD(T)while retaining $\sim0.15$ kcal/mol accuracy compared to the benchmark results.More approximate dual-basis resolution-of-the-identity double-hybrid DFTcalculations are also performed and shown to have reasonable $0.2-0.4$ kcal/molerrors compared with our benchmark values. After including contributions fromtemperature dependent internal energy shifts, we find the preference for foldedconformations to lie between hexadecane and octadecane, in excellent agreementwith recent experiments [L\"{u}ttschwager, N. O.; Wassermann, T. N.; Mata, R.A.; Suhm, M. A. {\it Angew. Chem. Int. Ed.} 2013, 52, 463].

At what chain length do unbranched alkanes prefer folded conformations?