Polarizable continuum model (PCM) calculations of solvent effects on optical rotations of chiral molecules

A new theory of solvent effects on the optical rotations of chiral molecules is presented. The frequency-dependent electric dipole-magnetic dipole polarizability, beta(alphabeta)(nu), is calculated using density functional theory (DFT). Solvent effects are included using the polarizable continuum model (PCM). DFT/PCM calculations of sodium D line specific rotations, [alpha](D), have been carried out for seven conformationally rigid chiral organic molecules (fenchone, camphor, alpha-pinene, beta-pinene, camphorquinone, verbenone, and methyloxirane) for a diverse set of seven solvents (cyclohexane, carbon tetrachloride, benzene, chloroform, acetone, methanol, and acetonitrile). The predicted variation in [alpha](D) for the solvents cyclohexane, acetone, methanol, and acetonitrile are in excellent agreement with experiment for all seven molecules. For the solvents carbon tetrachloride, benzene, and chloroform, agreement is much poorer. Since only electrostatic solute-solvent interactions are included in the PCM, our results lead to the conclusion that, for the seven molecules studied, in cyclohexane, acetone, methanol, and acetonitrile electrostatic effects are dominant while in carbon tetrachloride, benzene, and chloroform other nonelectrostatic effects are more important. The observed variations in [alpha](D) with solvent are inconsistent, both qualitatively and quantitatively, with the variations predicted by the equation [alpha](D)(solvent) = {[alpha](D)(gas)}(n(D)(2) + 2)/3.