Optical activity in conformationally flexible molecules: a theoretical study of large-amplitude vibrational averaging in (R)-3-chloro-1-butene

The simple Boltzmann averaging procedure that is commonly used for computing chiroptical properties of conformationally flexible molecules has been tested against a more rigorous approach involving explicitly computed vibrational wave functions for large-amplitude motion. A one-dimensional, carbon-backbone torsional potential function of the paradigmatic chiral molecule (R)-3-chloro-1-butene was constructed by mapping out the intrinsic reaction coordinate connecting the three relevant transition states and minimum-energy structures. The corresponding one-dimensional vibrational Schrodinger equation was solved using both numerical and algebraic methods to obtain torsional vibrational wave functions, over which averaged coupled-cluster and density-functional specific rotations were computed. The rigorous vibrational Boltzmann approach was then compared systematically with the simpler method based solely on the relative energies of the zero-point vibrational levels of each conformer. By analysis of scaled torsional potentials, the limits of the simple Boltzmann method were probed in terms of the temperature and the barrier heights separating the relevant conformers, revealing a surprising resilience of this scheme. Large deviations between the two averaging methods were observed only after the conformer barriers fell to well under 500 cm(-1). Even for temperatures approaching 1000 K, deviations between the two averaging models are small (less than 10%) for this test case. However, direct analysis of the approximations underlying the simple Boltzmann approach reveals that its success is greatly aided by a favorable cancellation of errors.