Modeling the 13C chemical-shift tensor in organic single crystals by quantum mechanical methods: finite basis set effects


  • Dedicated to Professor David M. Grant of the University of Utah on the occasion of his 75th birthday, in recognition of the outstanding contributions he has made to the methodology of nuclear magnetic resonance and its application to a wide range of chemical topics over a long period of time.


The influence of using finite basis sets to calculate 13C magnetic shieldings were explored using the Hartree-Fock and the B3LYP hybrid density functional methods. The shielding values were compared in a linear least-squares fashion for a test group of 102 13C complete chemical-shift tensors determined from 14 organic single crystals. Pople's basis sets allow for the addition of polarization and diffuse functions in a straightforward way, allowing the examination of 81 combinations at the double and triple zeta level. Dunning's correlation-consistent basis sets were explored as well. The errors associated with predicting the shielding values were found to be largely systematic as revealed by the analysis of the determined regression parameters between calculated chemical shieldings and experimental chemical shifts. Expansion of the basis set leads to a convergence of these regression parameters to their ideal values. The random errors, however, do not decrease by employing larger basis sets; therefore, given the appropriate regression parameters, a small basis description such as 3-21G can be adequate in predicting the relative magnetic-shielding values, i.e. the chemical shifts. Furthermore, in certain cases the inclusion of unbalanced diffuse and polarization functions can significantly degrade the predicted shielding rmsd. Unless employed carefully, these functions do not justify their computational expense. The chemical-shift distance is used to evaluate shielding predictions in individual tensor components. The analysis of the chemical-shift's distance between calculated and experimental data indicates an orientational dependence on the magnitude of errors and suggests the use of the shift anisotropy as a useful fiduciary mark to optimize model chemistries for magnetic-shielding calculations. Copyright © 2006 John Wiley & Sons, Ltd.