Calculation of conformational energies and optical rotation of the most simple chiral alkane

Quantum chemical calculations have been performed to investigate the conformer distribution of 4-ethyl-4-methyloctane and its optical rotation. With the reference methods MP2 and SCS-MP2, the energies of seven conformers are found within a range of about 1.5 kcal mol(-1). It is demonstrated that the relative energies cannot be reliably predicted with conventional GGA or hybrid density functionals, Hartree-Fock, semiempirical AM1, and classical force field (MM3) calculations. An empirical dispersion correction to GGA (PBE-D), hybrid (B3LYP-D), or double hybrid (B2PLYP-D) functionals corrects these errors and results in very good agreement with the reference energies. Optical rotations have been calculated for all seven conformers at the TDDFT(BHLYP/aTZV2P) level. The computed macroscopic rotation is derived from a classical Boltzmann average. The result (1.9-3.2 deg dm(-1) (g/mL)(-1)) is very close to the experimental value of 0.2 deg dm(-1) (g/mL)(-1) for the (R)-enantiomer and has the right sign. Because six conformers are significantly populated at room temperature and the rotations of individual conformers differ in sign and magnitude, the calculated average rotation is rather sensitive to the conformer population used. From the electronic structure point of view, this example emphasizes the effect of long-range dispersion effects for the evaluation of population averaged quantities in large molecules. Computations based on free enthalpies are in worse agreement with experiment that is attributed to artefacts of the harmonic approximation used to compute the vibrational entropy terms.