The components of nucleus-independent chemical shift (NICS) tensors for D_nhn-annulenes are discussed as indexes of the aromatic character of electronic π systems. The component corresponding to the principal axis perpendicular to the ring plane, NICS_zz, is found to be a good measure for the characterisation of the π system of the ring. Isotropic NICS values at ring centres contain large influences from the σ system and from all three principal components of the NICS tensor. At large distances away from the ring center, NICS_zz, which is dominated by contributions from the π system, characterizes NICS well.

Entirely unlike the aromatic closo B_nH_n^2- borane dianions, isoelectronic Si₆^2- and Si₁₂^2- are antiaromatic. Their O_h and I_h symmetries are responsible, as the other deltahedral silicon dianion clusters do not exhibit this behavior. These high symmetries prevent mixing among the degenerate lone pair and skeletal orbitals, leading to paratropic behavior.

Individual molecular orbital (MO) contributions to the magnetic shielding of atoms as well as to the nucleus-independent chemical shifts (NICS) of aromatic compounds can be computed by the widely used gauge-including atomic orbital (GIAO) method. Detailed analyses of magnetic shielding MO-NICS contributions provide interpretive insights that complement and extend those given by the localized MO (“dissected NICSâ€�, LMO-NICS) method. Applications to (4n + 2) Ï€-electron systems, ranging from [n] annulenes to D_nh S₃, S₅, and N₆H₆²⁺ rings as well as to D_2h cyclobutadiene, show the extent to which their diatropic character results from the σ framework and from the Ï€ orbitals. The diatropicity of both these contributions decreases with the number of nodes of the wave function around the ring. The highest-energy orbitals can become paratropic. This is generally the case with the σ orbitals, but is found only for “electron-richâ€� Ï€ systems such as sulfur rings. MO-NICS contributions, which can be interpreted using London−Hückel theory, correlate with inverse ring size.

As shown by detailed nucleus-independent chemical shift (NICS) analyses of the contributions of each molecular orbital, the very recently reported gas-phase all-metal Al₄Li₃^- anion and its relatives (Kuznetsov, A.E.; Birch, K.A.; Boldyrev, A.I.; Li, X.; Zhai, A.I.; Wang, L.S. Science 2003, 300, 622) are aromatic rather than antiaromatic. The paratropic (antiaromatic) four-Ï€-electron contribution is overcome by the predominating diatropic effects of σ aromaticity. However, true antiaromatic all-metal clusters, such as Sn₆^2- (Schiemenz, B.; Huttner, G. Angew. Chem., Int. Ed. Engl. 1993, 32, 297), do exist.

The electronic structure of La₂CuO₄ has been investigated using first-principles cluster calculations and the chemical shieldings at the copper nucleus have been determined with several state-of-the-art quantum chemical methods. We have also calculated the copper shieldings for CuCl, which is often used as a reference substance for copper nuclear magnetic resonance shifts measurements, and found an appreciable paramagnetic contribution in agreement with precise measurements. The calculated chemical shift at the copper nucleus in La₂CuO₄ for an applied field parallel to the CuO₂ planes is generally smaller than, but still in reasonable agreement with, the values derived from experiment with the assumption that the spin susceptibility vanishes at zero temperature. For the field perpendicular to the planes, the quantum chemical result is substantially smaller than the experimental data but in accord with a perturbation theoretical estimate. Inconsistencies in previous representations and interpretations of the copper magnetic shift data are pointed out and corrected.

Quinodimethanes are highly reactive toward dienophiles since Diels−Alder cycloaddition results in an aromatic product. Density functional-based ¹³C, ¹H NMR, NICS, and MO-NICS calculations indicate that the increase of aromatic character of the developing benzenoid ring along the reaction path is especially pronounced after the transition state is reached, even though the number of Ï€ orbitals decreases. The forming aliphatic ring exhibits large ring current effects during the reaction.

Several methods to address aromaticity in terms of nucleus-independent chemical shifts (NICS) are compared. These include NICS at the ring centre NICS(0), NICS 1 Ã… above the ring plane NICS(1), aromatic ring current shielding (ARCS), and dissected NICS, i.e. NICS calculated from selected Ï€ orbitals NICS_Ï€, again in the ring plane and 1 Ã… above. The methods are tested on the basis of density-functional theory (DFT) and the individual gauge for local orbitals (IGLO) technique. Applications include simple organic rings (C₄H₄, C₄H₄²⁺, C₆H₆, C₅H₅^–, C₇H₇⁺) and transition metal carbonyl complexed molecules Fe(CO)₃C₄H₄ and Cr(CO)₃C₆H₆.

Quantum-chemical calculations, at the self-consistent-charge density-functional-based non-orthogonal tight binding (SCC-DFTB) level, are used to provide the input for unimolecular reaction rate theory calculations to predict the temperatures at which rapid, i.e., microsecond timescale, equilibration between mono-cyclic and bi-cyclic carbon clusters can occur. The computational results are discussed in the form of a set of trends for their variation with the size of the cluster, the length of the carbon–carbon bond broken or formed, the vibrational frequencies, the energy differences and the rate constants. The temperatures used experimentally to prepare fullerenes and nanotubes are compatible with the rapid equilibration of rings and bi-cyclic rings, a factor that explains the lack of defects in these higher forms of carbon clusters and the general trend towards the formation of the most stable fullerene for a given nuclearity.

Geometries and ²⁹Si NMR chemical shifts are calculated for silanes Si_nH_2n+2, n=1,…,5, methylsilanes SiH_nMe_4−n, methoxysilanes SiH_n(OMe)_4−n, and methylmethoxysilanes SiMe_n(OMe)_4−n, n=0,…,4. Geometries and ²⁹Si NMR chemical shifts are in satisfying agreement with experiment within LCGTO-DFT at the DZVP/LDA level for geometries and IGLO-III/GGA (GGA=PW91,PBE) level for shielding constants, which is an improvement to B88PW86, P86PW86 and B3LYP results. If an auxiliary basis is applied to express the Coulomb potential, g-functions have to be included to reproduce SiOSi angles and ²⁹Si NMR chemical shifts correctly.

Calculations of ¹³C nuclear shieldings for low-energy isomers of C₃₆H_2x (x=2,3) suggest that it should be possible to use experimental¹³C shifts, when these become available, to distinguish the isomeric form of the underlying fullerene cage and, in the case of isomers based on the six-fold symmetrical cylindrical fullerene cage 36:15, the degree of polar hydrogenation.

Calculated binding energies and spectroscopic properties of C₇₀ dimers are presented. The two most stable isomers of the set of conceivable [2 + 2] cycloaddition products are isoenergetic, and both are compatible with NMR, infrared, and Raman data on the product recently synthesized by Lebedkin et al.

The predictive power of DFT, HF, and MP2 ²⁹Si NMR chemical shift calculations for silane molecules, including fluoro- and methylsilanes (Si_nH_2n+2 (n = 1, ..., 5), Si_nF_2n+2 (n = 1, ..., 3), and SiH_mX_4-m (X = F, CH₃)) is compared. A systematic accumulation of error proportional to the number of hydrogen neighbors to silicon sites is observed for DFT for all applied exchange-correlation functionals, whereas MP2 is not affected by this problem. A proposed empirical correction scheme for DFT provides excellent agreement with experiment with any exchange-correlation functional employed in this study.