The direct (recomputation of two-electron integrals) implementation of the gauge-including atomic orbital (GIAO) and the CSGT (continuous set of gauge transformations) methods for calculating nuclear magnetic shielding tensors at both the Hartree-Fock and density functional levels of theory are presented. Isotropic 13C, 15N, and 17O magnetic shielding constants for several molecules, including taxol (C47H51NO14 using 1032 basis functions) are reported. Shielding tensor components determined using the GIAO and CSGT methods are found to converge to the same value at sufficiently large basis sets; however, GIAO shielding tensor components for atoms other than carbon are found to converge faster with respect to basis set size than those determined using the CSGT method for both Hartree-Fock and DFT. For molecules where electron correlation effects are significant, shielding constants determined using (gradient-corrected) pure DFT or hybrid methods (including a mixture of Hartree-Fock exchange and DFT exchange-correlation) are closer to experiment than those determined at the Hartree-Fock level of theory. For the series of molecules studied here, the RMS error for 13C chemical shifts relative to TMS determined using the B3LYP hybrid functional with the 6-311+G(2d,p) basis is nearly three times smaller than the RMS error for shifts determined using Hartree-Fock at this same basis. Hartree-Fock 13C chemical shifts calculated using the 6-31G* basis set give nearly the same RMS error as compared to experiment as chemical shifts obtained using Hartree-Fock with the bigger 6-311+G(2d,p) basis set for the range of molecules studied here. The RMS error for chemical shifts relative to TMS calculated at the Hartree-Fock 6-31G* level of theory for taxol (C47H51NO14) is 6.4 ppm, indicating that for large systems, this level of theory is sufficient to determine accurate 13C chemical shifts.

We describe several improvements to the reaction field model for the ab initio determination of solvation effects. First, the simple spherical cavity model is expanded to include higher-order electrostatic interactions. Second, two new and efficient implementations of the polarizable continuum model (PCM) are described, which allow a more realistic specification of the solute cavity as well as infinite-order electrostatics. Electron correlation effects are evaluated using the B3LYP density functional and Möller−Plesset perturbation theory to second order. An assessment of the importance of these various factors is made by comparing theoretical results to the experimentally known conformational equilibrium between syn and anti forms of furfuraldehyde and the C−C rotational barrier of (2-nitrovinyl)amine. Comparisons are also made with calculations that employ an ellipsoidal cavity with sixth-order electrostatics. Optimization using a simple Onsager model appears to be sufficient to evaluate the important geometry changes in solution. Energies obtained from the spherical and ellipsoidal cavity models often exhibit poor convergence in the truncated electrostatic series. Correlation to experiment is much improved when an infinite-order PCM method is used.

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The rotational barriers for N,N-dimethylformamide and N,N-dimethylacetamide have been investigated theoretically and experimentally. Calculations at the G2(MP2) theoretical level followed by correction to 25 "C reproduced the experimental gas-phase barriers. An examination of the geometries of these amides showed that the lower barrier for the acetamide resulted mainly from a ground state methyl-methyl repulsive interaction. The rotational barriers for the amides were measured in several solvents using NMR selective inversion-recovery experiments. The effect of solvent on the C-N rotational barriers was examined computationally using reaction field theory. This approach was found to give barriers that are in good agreement with experiment for aprotic, non-aromatic solvents which do not engage in specific interactions with the amides. The effect of a hydrogen bonding solvent, water, was studied via incorporating a water molecule hydrogen bonded to the oxygen and examining this ensemble using reaction field theory.

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