A hybrid quantum mechanical and empirical model for the prediction of isotropic 13C shielding constants of organic molecules

A method is presented that combines quantum mechanical shift calculations with empirical corrections to yield isotropic C-13 nuclear magnetic resonance (NMR) shifts for organic molecules in good agreement with experiment. A comparison is made between shifts calculated using Hartree-Fock (HF), Moller-Plesset perturbation theory (MP2), and density functional theory (DFT). The absolute shifts calculated by these methods are translated into shifts relative to tetramethylsilane (TMS) using a simple empirical formula with parameters determined over a set of 37 small organic compounds. It is shown that DFT calculations using small basis sets correlate with experiments well enough that the empirical correction allows experimental shifts to be reproduced to within an RMS error of 4-5 parts per million (ppm). Carbons attached to chlorine, bromine, and iodine are treated with the same empirical corrections but with parameters of different values because of the lack of spin orbit corrections in the calculations; however, these carbons are predicted as accurately as other carbons in the data set. Two models are presented; one is applicable to very large molecules. The empirical corrections developed for these models can be used to predict shifts in a wide variety of organic molecules. One of the models is applied to a moderately sized dye molecule that contains an intramolecular hydrogen bond to demonstrate the utility of using an inexpensive quantum mechanics-based method over an empirical fragment-based method.