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.

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A new theory of solvent effects on the optical rotations of chiral molecules is presented. The frequencydependent electric dipole-magnetic dipole polarizability, β Rβ (ν), is calculated using density functional theory (DFT). Solvent effects are included using the polarizable continuum model (PCM). DFT/PCM calculations of sodium D line specific rotations, [R] D , have been carried out for seven conformationally rigid chiral organic molecules (fenchone, camphor, R-pinene, β-pinene, camphorquinone, verbenone, and methyloxirane) for a diverse set of seven solvents (cyclohexane, carbon tetrachloride, benzene, chloroform, acetone, methanol, and acetonitrile). The predicted variation in [R] D for the solvents cyclohexane, acetone, methanol, and acetonitrile are in excellent agreement with experiment for all seven molecules. For the solvents carbon tetrachloride, benzene, and chloroform, agreement is much poorer. Since only electrostatic solute-solvent interactions are included in the PCM, our results lead to the conclusion that, for the seven molecules studied, in cyclohexane, acetone, methanol, and acetonitrile electrostatic effects are dominant while in carbon tetrachloride, benzene, and chloroform other nonelectrostatic effects are more important. The observed variations in [R] D with solvent are inconsistent, both qualitatively and quantitatively, with the variations predicted by the equation [R] D (solvent) ) {[R] D (gas)}(n D 2 + 2)/3.

We report calculations of the frequency-dependent electric dipole-magnetic dipole polarizability tensor, β Rβ (ν), using ab initio density functional theory (DFT). Gauge invariant (including) atomic orbitals (GIAOs) are used to guarantee origin-independent values of β ) ( 1 / 3 )Tr [β Rβ ]. Calculations of β at the sodium D line frequency, β(D), for 30 rigid chiral molecules are used to predict their specific rotations, [R] D . Calculations have been carried out using the B3LYP functional and the 6-31G*, DZP, 6-311++G(2d,2p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets. Comparison to experimental [R] D values for 28 of the 30 molecules yields average absolute deviations of calculated and experimental [R] D values in the range 20-25°for the three large basis sets, all of which include diffuse functions. The accuracies of [R] D values calculated using the 6-31G* and DZP basis sets, which do not include diffuse functions, are significantly lower: average deviations from experiment are 33°and 43°, respectively. Hartree-Fock/Self-Consistent Field (HF/SCF) calculations have been carried out in parallel. HF/SCF [R] D values are substantially lower in accuracy than corresponding B3LYP values; at the aug-cc-pVDZ basis set level, the average deviation from experiment is 63°. [R] D values obtained using β values calculated in the static limit (ν ) 0) are also of lower accuracy than values obtained using β(D). Absolute Configurations of chiral molecules can be assigned by comparison of predicted and experimental optical rotations. Our results demonstrate that DFT provides substantially more accurate rotations than HF/ SCF methodologies employed heretofore and therefore constitutes the current method of choice for stereochemical applications.

Ab initio Hartree-Fock (HF) and density functional theory (DFT) calculations of the electric dipole-magnetic dipole polarizability β Rβ are reported for the chiral molecules methyloxirane (1) and trans-dimethylthiirane (2) in the static limit. Values of β ) 1 / 3 Tr[β Rβ ] obtained thence are used to predict the specific optical rotations [R] D of 1 and 2. Gauge-including atomic orbitals (GIAOs) are used to ensure origin independence of β and [R] D . β and [R] D values converge slowly to the complete basis set limit. Basis sets including diffuse functions are required to achieve reliable results. HF and DFT values of β Rβ differ generally by 10-30%. Calculated [R] D values for 1 and 2 obtained using large basis sets agree well with experimental values in sign and magnitude. The deviations can be attributed in part to the neglect of the frequency dependence of β and of solvent effects.