An improved method for density functional calculations of the frequency-dependent optical rotation

Density functional theory calculations of the frequency-dependent optical rotation (OR) provide a simple and effective way to determine the absolute configuration of chiral molecules. We report two major improvements of the method here. Firstly, the dipole velocity form of the OR is introduced. In contrast to the commonly employed dipole length form, the dipole velocity form is gauge-origin invariant in any basis set. We present a basis set convergence study which shows that basis sets of augmented double zeta quality yield sufficiently accurate results in most cases. The deviation between the length and velocity forms provides a convenient measure of the basis set error. Secondly, we extend the resolution of the identity (RI) approximation to frequency-dependent OR calculations. Using the Coulomb norm and auxiliary basis sets optimized for ground-state calculations, we obtain RI errors that are negligible compared to errors due to the basis set and the density functional. Total computation times are reduced by a up to a factor of 10, as is demonstrated for a benchmark set of eight different molecules.