Compact Basis Sets for Optical Rotation Calculations.

Abstract

In this work, we present two compact basis sets optimized for the calculation of specific rotation: augD-3-21G and augT3-3-21G. They are obtained by combining the standard 3-21G basis set with the diffuse functions of aug-cc-pVDZ and aug-cc-pVTZ, respectively, followed by a reoptimization of the exponents of the diffuse functions. The exponent optimization is based on minimization of the root-mean-square relative error (RMSE) of the specific rotation computed at 589.3 nm (the sodium D line, [α]D) with CAM-B3LYP compared with the corresponding calculations using the full correlation-consistent basis sets. The training set comprises 21 chiral molecules with |[α]D| > 50 deg dm-1 (g/mL)-1. For augT3-3-21G, the functions with the highest angular momentum are neglected, so that augD-3-21G and augT3-3-21G are of the same size. The exponents are optimized for four common elements in chiral organic molecules (H, C, N, and O), while the original exponents are maintained for other elements. Tests are conducted on the training set with CAM-B3LYP at 450 and 633 nm and with B3LYP at 589.3 nm; furthermore, a similar comparison is performed on a control set containing 30 more chiral molecules. A comparison with the optical rotatory prediction (ORP) basis set is also presented. The results show that the new compact basis sets are able to reproduce the calculations with the full Dunning basis sets remarkably well, and definitely better than before reoptimization of the exponents, with relative mean unsigned errors of around 4%. More significantly, augT3-3-21G is either of similar quality or better than aug-cc-pVDZ in reproducing the values obtained with aug-cc-pVTZ, even though augT3-3-21G is smaller than aug-cc-pVDZ. The larger ORP basis set outperforms both augT3-3-21G and aug-cc-pVDZ, but it requires a considerably larger computational effort. In summary, augT3-3-21G provides results that are in very good agreement with those obtained using aug-cc-pVTZ, but approximately 20 times faster, and it may be used for quick and reliable calculations of specific rotation of large chiral molecules.