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

Abstract

The influence of using finite basis sets to calculate (13)C 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 (13)C 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.

Intermolecular shielding contributions studied by modeling the C13 chemical-shift tensors of organic single crystals with plane waves

“…While it is known that a significantly large basis set is required for accurate shielding calculations, 47 the effect of finite basis is compensated for by the regression parameters and good agreement can be achieved with a modest basis. 7 In this case, we used 6-31G͑d͒ for the GIAO calculations, which previously provided good agreement with experiment. Basis sets as large as 6-311G͑d , p͒ showed no further improvement in terms of RMSD.…”

“…These corrections explain the difference between the regression parameters reported here using B3LYP/ 6-31G͑d͒ methods and those previously reported in the literature. 6,7 …”

“…9,57 The discrepancy in the theory has been shown to depend on both the basis set and functional employed. 6,7 Even the KT functionals, considered to be the most accurate for shielding calculations, show significant deviations from Ϫ1 for these organic molecules. With the level of precision obtained by GIPAW, the discrepancy is shown here to be also heavily dependent on the type of molecule.…”

“…3, have been used previously, 3 but only recently have methods been developed to perform NMR calculations using periodic boundary conditions. 4,5 It has been shown [6][7][8] that comparing calculated shielding and experimental shift tensors from single-crystal measurements provides the most stringent test of theoretical and computational approaches. Moreover, the crystal tensor data allow exploration of lattice effects, a topic that has not previously been explored with both complete chemical-shift tensors and accurate shielding calculations that incorporate periodic boundary conditions.…”

“…11 An experimental data set of 13 C chemical-shift tensors from all carbon atom locations in 14 organic single crystals [12][13][14][15][16][17][18][19] has been compiled by Grant and co-worker; due to the high precision of these measurements, this data set is of great value for testing theoretical and computational approaches. [6][7][8] Typically, new methodologies to predict the chemical shift focus on collections of shifts from small gas phase molecules. 20 These gas-phase databases provide a diversity of local environments to predict accurate 13 C isotropic shift values where rotational and vibrational effects have been accounted for and include molecules with known electron correlation issues.…”