James R. Cheeseman

A comparison of models for calculating nuclear magnetic resonance shielding tensors

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...

Ab initio calculation of atomic axial tensors and vibrational rotational strengths using density functional theory

Abstract The first application of the density functional theory (DFT) to the calculation of atomic axial tensors (AATs) is reported. Analytical derivative methods and gauge-invariant atomic orbitals (GIAOs) are employed. DFT/GIAO AATs for trans-2,3 d 2 -oxirane calculated using a [8s6p3d/6s3p] basis set and the Becke 3-Lee-Yang-Parr hybrid density functional, in combination with a DFT harmonic force field and atomic polar tensors (APTs), yield vibrational rotational strengths in better agreement with experiment than comparable calculations at the Hartree-Fock level. The largest remaining deviations between theory and experiment are attributed to experimental error.

Basis set dependence of NMR spin–spin couplings in density functional theory calculations: first row and hydrogen atoms

Abstract We analyze the basis set dependence of NMR spin–spin coupling constants calculated using density functional theory in a set of benchmark molecules containing first row and hydrogen atoms. We find that similarly to calculations based on wavefunction theory, the flexibility of core gaussian basis functions plays a key role. For the set of molecules under consideration, we have analyzed the basis set limit and studied basis set of triple-ζ quality, which may be useful for practical applications.

Calculation of Nuclear Spin−Spin Coupling Constants of Molecules with First and Second Row Atoms in Study of Basis Set Dependence

This paper proposes a systematic way to modify standard basis sets for use in NMR spin-spin coupling calculations, which allows the high sensitivity of this property to the basis set to be handled in a manner which remains computationally feasible. The new basis set series is derived by uncontracting a standard basis set, such as correlation-consistent aug-cc-pVTZ, and extending it by systematically adding tight s and d functions. For elements in different rows of the periodic table, different progressions of functions are added. The new basis sets are shown to approach the basis set limit for calculations on a range of molecules containing hydrogen and first and second row atoms.

Coupled-cluster calculations of optical rotation

Abstract CC2 and CCSD coupled-cluster calculations of the sodium D line specific rotations of 13 chiral organic molecules are compared to HF and DFT/B3LYP calculations and to experiment. For 12 of the molecules, whose [ α ] D values are in the range 0–200, CCSD and B3LYP [ α ] D values are in very similar agreement with experiment: average deviations are 19.8 and 19.4, respectively. CC2 and HF values are less accurate: average deviations are 24.7 and 32.2, respectively. For one molecule, norbornenone, the CCSD [ α ] D value (741) is very different from the B3LYP value (1216) and in much worse agreement with experiment (1146).

Calculation of Raman optical activity spectra of methyl-β-d-glucose incorporating a full molecular dynamics simulation of hydration effects

We report calculations of the Raman and Raman optical activity (ROA) spectra of methyl-β-D-glucose utilizing density functional theory combined with molecular dynamics (MD) simulations to provide an explicit hydration environment. This is the first report of such combination of MD simulations with ROA ab initio calculations. We achieve a significant improvement in accuracy over the more commonly used gas phase and polarizable continuum model (PCM) approaches, resulting in an excellent level of agreement with the experimental spectrum. Modeling the ROA spectra of carbohydrates has until now proven a notoriously difficult challenge due to their sensitivity to the effects of hydration on the molecular vibrations involving each of the chiral centers. The details of the ROA spectrum of methyl-β-D-glucose are found to be highly sensitive to solvation effects, and these are correctly predicted for the first time including those originating from the highly sensitive low frequency vibrational modes. This work shows that a thorough consideration of the role of water is pivotal for understanding the vibrational structure of carbohydrates and presents a new and powerful tool for characterizing carbohydrate structure and conformational dynamics in solution.

Basis Set Dependence of Vibrational Raman and Raman Optical Activity Intensities.

We present a systematic study of the basis set dependence of the backscattering vibrational Raman intensities and Raman Optical Activity (ROA) intensity differences. The accuracies of computed Raman intensities and ROA intensity differences for a series of commonly used basis sets are reported, relative to large reference basis sets, using the B3LYP density functional. This study attempts to separately quantify the relative accuracies obtained from particular basis set combinations: one for the geometry optimization and force field computation and the other for the computation of Raman and ROA tensors. We demonstrate here that the basis set requirements for the geometry and force fields are not similar to those of the Raman and ROA tensors. The Raman and ROA tensors require basis sets with diffuse functions, while geometry optimizations and force field computations typically do not. Eleven molecules were examined: (S)-methyloxirane, (S)-methylthirane, (R)-epichlorhydrin, (S)-CHFClBr, (1S,5S)-α-pinene, (1S,5S)-β-pinene, (1S,4S)-norborneneone, (M)-σ-[4]-helicene, an enone precursor to a cytotoxic sesquiterpene, the gauche-gauche conformer of the monosaccharide methyl-β-d-glucopyranose, and the dipeptide Ac-(alanine)2-NH2. For the molecules examined here, intensities and intensity differences obtained from Raman and ROA tensors computed using the aug-cc-pVDZ basis set are nearly equivalent to those computed with the larger aug-cc-pVTZ basis set. We find that modifying the aug-cc-pVDZ basis set by removing the set of diffuse d functions on all atoms (while keeping the diffuse s and p sets), denoted as aug(sp)-cc-pVDZ, results in a basis set which is significantly faster without much reduction in the overall accuracy. In addition, the popular rDPS basis set introduced by Zuber and Hug offers a good compromise between accuracy and efficiency. The combination of either the aug(sp)-pVDZ or rDPS basis for the computation of the Raman and ROA tensors with the 6-31G* basis set for the geometry optimization and force field calculation is a reliable and cost-effective method for obtaining Raman intensities and ROA intensity differences.

Determination of the Absolute Configurations of Natural Products Using TDDFT Optical Rotation Calculations: The Iridoid Oruwacin

We report the determination of the absolute configuration (AC) of the iridoid natural product oruwacin by comparison of the optical rotations, [alpha] D, of its two enantiomers, calculated using time-dependent density functional theory (TDDFT), to the experimental [alpha] D value, +193. Conformational analysis of oruwacin using density functional theory (DFT) identifies eight conformations which are significantly populated at room temperature. [alpha] D values of these eight conformations are calculated using TDDFT at the B3LYP/aug-cc-pVDZ//B3LYP/6-31G* level, leading to the conformationally averaged [alpha] D values of -193 for the (1 R,5 S,8 S,9 S,10 S)-enantiomer and +193 for the (1 S,5 R,8 R,9 R,10 R)-enantiomer. Comparison of the calculated [alpha] D values to the value of the natural product proves that naturally occurring oruwacin has the AC 1 S,5 R,8 R,9 R,10 R. This AC is opposite to that assigned by Adesogan by comparison of the [alpha] D of oruwacin to that of the iridoid plumericin. Our results show that the assignment of the AC of a natural product by comparison of its [alpha] D to that of a chemically related molecule can be unreliable and should not be assumed to be definitive.

Conformational effects on optical rotation. 2-Substituted butanes.

The specific rotations of 2-substituted butanes (X = F, Cl, CN, and HCC) were calculated at the B3LYP/aug-cc-pVDZ level as a function of the C-C-C-C torsion angle. The results for the four compounds are remarkably similar, despite large differences in the electronic transition energies. The temperature dependence of the specific rotations for 2-methylbutyronitrile and for 2-chlorobutane was studied to give experimental information about the effect of the torsion angle on the specific rotation. The results were in good accord with B3LYP/aug-cc-pVDZ calculations. The specific rotations derived from the study of 2-chlorobutane are similar to those previously obtained for 3-chloro-1-butene, indicating that the double bond does not have a large effect on the optical rotations, but it did lead to a large difference between calculated and observed specific rotations.

Optical rotatory dispersion of 2,3-hexadiene and 2,3-pentadiene.

The specific rotation of (P)-2,3-hexadiene (1) was measured as a function of wavelength for the gas phase, the neat liquid, and solutions. There was a surprisingly large difference between the gas phase and condensed phase values. The specific rotation was calculated using B3LYP and CCSD, and the difference in energy between the three low energy conformers was estimated at the G3 level. The Boltzmann-averaged CCSD-calculated rotations using the gauge independent velocity gauge representation, as well as the B3LYP values, are in agreement with the gas-phase experimental values. In order to avoid possible problems associated with the conformers of 1, 2,3-pentadiene (2) also was examined. Here again, there was a large difference between the gas-phase and condensed-phase specific rotations, with the CCSD velocity gauge (and B3LYP) results being close to the gas-phase experimental values. The possibility that 2,3-pentadiene could be distorted on going from the gas to liquid phase, thereby accounting for the effect of phase on the specific rotation, was examined via a Monte Carlo statistical mechanics simulation. No effect on the geometry was found. Specific rotations of 1 found in solutions were similar to those for the liquid phase, indicating that the phase difference was not due to association.