Experimental and Theoretical <i>ab </i><i>I</i><i>nitio</i> Study of the ¹³C−¹³C Spin−Spin Coupling and ¹H and ¹³C Shielding Tensors in Ethane, Ethene, and Ethyne

Abstract

Experimentally and theoretically (ab initio) determined CC spin−spin coupling tensors and 1H and 13C nuclear shielding tensors are reported for ethane (13C2H6), ethene (13C2H4), and ethyne (13C2H2). The experimental anisotropies of the CC coupling tensors, ΔJCC, for all these molecules, and also the combination JCC,xx − JCC,yy for ethene, were derived from sets of anisotropic couplings (Dexp) analyzed from the 1H and 13C NMR spectra of molecules partially oriented in liquid−crystalline environments. Both harmonic vibrations and structural deformations arising from the correlation of vibrational and reorientational motions were taken into account in the D couplings. The ab initio calculations of all the J tensors were performed using MCSCF linear response theory. The best calculated and experimental ΔJCC values (along with JCC,xx − JCC,yy for ethene) are found to be in good mutual agreement. Together with earlier work on the nJCC tensors in benzene, this study shows that the indirect contribution, 1/2JCCaniso, to experimental couplings between differently hybridized carbons is small and can generally be omitted. This means that the use of experimental DCC couplings in the determination of molecular order tensors and/or conformation does not introduce serious errors. The experimental determination of the 1H and 13C shielding tensors was based on the liquid crystal director rotation by 90° in mixtures of thermotropic nematogens with opposite anisotropy of diamagnetic susceptibility. Ab initio SCF and MCSCF calculations utilizing gauge-including atomic orbitals produce results in good agreement with experiments.