Calculation of Optical Rotation Using Density Functional Theory

Abstract

We report calculations of the frequency-dependent electric dipole−magnetic dipole polarizability tensor, β αβ (ν), using ab initio density functional theory (DFT). Gauge invariant (including) atomic orbitals (GIAOs) are used to guarantee origin-independent values of β = ( 1 / 3 )Tr [β αβ ]. Calculations of β at the sodium D line frequency, β(D), for 30 rigid chiral molecules are used to predict their specific rotations, [α] D . Calculations have been carried out using the B3LYP functional and the 6-31G*, DZP, 6-311++G(2d,2p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets. Comparison to experimental [α] D values for 28 of the 30 molecules yields average absolute deviations of calculated and experimental [α] D values in the range 20−25° for the three large basis sets, all of which include diffuse functions. The accuracies of [α] D values calculated using the 6-31G* and DZP basis sets, which do not include diffuse functions, are significantly lower: average deviations from experiment are 33° and 43°, respectively. Hartree−Fock/Self-Consistent Field (HF/SCF) calculations have been carried out in parallel. HF/SCF [α] D values are substantially lower in accuracy than corresponding B3LYP values; at the aug-cc-pVDZ basis set level, the average deviation from experiment is 63°. [α] D values obtained using β values calculated in the static limit (ν = 0) are also of lower accuracy than values obtained using β(D). Absolute Configurations of chiral molecules can be assigned by comparison of predicted and experimental optical rotations. Our results demonstrate that DFT provides substantially more accurate rotations than HF/SCF methodologies employed heretofore and therefore constitutes the current method of choice for stereochemical applications.