A method for calculating the various components of the magnetically induced current-density tensor using gauge-including atomic orbitals is described. The method is formulated in the framework of analytical derivative theory, thus enabling implementation at the Hartree-Fock self-consistent-field (HF-SCF) as well as at electron-correlated levels. First-order induced current densities have been computed up to the coupled-cluster singles and doubles level (CCSD) augmented by a perturbative treatment of triple excitations [CCSD(T)] for carbon dioxide and benzene and up to the full coupled-cluster singles, doubles, and triples (CCSDT) level in the case of ozone. The applicability of the gauge including magnetically induced current method to larger molecules is demonstrated by computing first-order current densities for porphin and hexabenzocoronene at the HF-SCF and density-functional theory level. Furthermore, a scheme for obtaining quantitative values for the induced currents in a molecule via numerical integration over the current flow is presented. For benzene, a perpendicular magnetic field induces a (field dependent) ring current of 12.8 nA T(-1) at the HF-SCF level using a triple-zeta basis set augmented with polarization functions (TZP). At the CCSD(T)/TZP level the induced current was found to be 11.4 nA T(-1). Gauge invariance and its relation to charge-current conservation is discussed.

A review of computational studies of magnetically induced current density susceptibilities in molecules and their relation to experiments is presented. The history of the investigation of magnetically induced current densities and ring currents in molecules is briefly covered. The theoretical development of relativistic and nonrelativistic computational approaches for computing current densities in closed-shell and open-shell molecules is discussed and different state of the art methods to interpret calculated current densities are reviewed. Numerical integration approaches to assess global, semilocal, and local aromatic properties of multiring molecules are presented and demonstrated on free-base trans-porphyrin. We show that numerical integration of the current density combined with guiding visualization techniques of the current flow is a powerful tool for studies of the aromatic character of complicated molecular structures such as annelated aromatic and antiaromatic rings. Representative applications are reported illustrating the importance of careful current density studies for organic and inorganic chemistry. The applications include calculations of current densities and current strengths for aromatic, antiaromatic, and nonaromatic molecules of different kind. Current densities in spherical, cylindrical, tetrahedral, toroidal, and Möbius-twisted molecules are discussed. The aromatic character, current pathways, and current strengths of porphyrins are briefly highlighted. Aromatic properties of inorganic molecules are assessed based on current density calculations. Current strengths as a noninvasive tool to determine strengths of hydrogen bonds are discussed.

An overview of applications of the recently developed gauge including magnetically induced current method (GIMIC) is presented. The GIMIC method is used to obtain magnetically induced current densities in molecules. It provides detailed information about electron delocalization, aromatic character, and current pathways in molecules. The method has been employed in aromaticity studies on hydrocarbons, complex multi-ring organic nanorings, Möbius twisted molecules, inorganic and all-metal molecular rings and open-shell species. Recent studies on hydrogen-bonded molecules indicate that GIMIC can also be used to estimate hydrogen-bond strengths without fragmentation of the system. Preliminary results are presented on the applicability of GIMIC for investigating current transport in molecules attached to clusters simulating molecular conductivity measurements. Advantages and limitations of the GIMIC method are reviewed and discussed.

The magnetically induced current densities for ring-shaped hydrocarbons are studied at the density functional theory (DFT) and second-order Møller-Plesset (MP2) levels using gauge-including atomic orbitals. The current densities are calculated using the gauge-including magnetically induced current approach. The calculations show that all studied hydrocarbon rings sustain strong diatropic and paratropic ring currents when exposed to an external magnetic field, regardless whether they are unsaturated or not. For nonaromatic rings, the strength of the paratropic current flowing inside the ring is as large as the diatropic one circling outside it, yielding a vanishing net ring current. For aromatic molecules, the diatropic current on the outside of the ring is much stronger than the paratropic one inside, giving rise to the net diatropic ring current that is typical for aromatic molecules. For antiaromatic molecules, the paratropic ring-current contribution inside the ring dominates. For homoaromatic molecules, the diatropic current circles at the periphery of the ring. The ring current is split at the CH(2) moiety; the main fraction of the current flow passes outside the CH(2) at the hydrogens, and some current flows inside the carbon atom. The diatropic current does not take the through-space short-cut pathway, whereas the paratropic current does take that route. Calculations of the ring-current profile show that the ring current of benzene is not transported by the pi electrons on both sides of the molecular ring. The strongest diatropic ring current flows on the outside of the ring and in the ring plane. A weaker paratropic current circles inside the ring with the largest current density in the ring plane. Due to the ring strain, small unconjugated and saturated hydrocarbon rings sustain a strong ring current which could be called ring-strain current. Nuclear magnetic shieldings calculated for 1,3,5-cycloheptatriene and homotropylium at the DFT and MP2 levels agree well with experimental values.

For more than a decade, gold nanostructures have attracted the attention of experimentalists and theoreticians alike. Recent years have witnessed increased interest in goldcontaining structures, as several fields of application have found the metal to be not only aesthetical, but also of practical use.[1] In contrast to carbon where the familiar buckminsterfullerene [2] came first, later to be followed by carbon nanotubes, gold research started in reverse; gold nanotubes are already a synthetic reality.[3] Au 32 has to date been considered a moderately uninteresting molecule, just one among the many gold clusters. The most stable structure has been suggested to be space-filling, [4,5] like the majority of all metal clusters studied to date. Using relativistic quantum chemical calculations, we show the existence of another stable isomer: the icosahedral "golden" fullerene Au 32 , the first all-gold fullerenic species. It is spherical and hollow (with a diameter of % 0.9 nm) and structurally very similar to C 60 . Au 32 has a record value of magnetic shielding at its center, and appears to be aromatic.Considering its place in the periodic table, gold is an unusually relativistic element.[6] Among other things, this is expressed in its bonding properties. The element manifests aurophilicity, which further enhances the strong gold-gold interactions.[7] Relativistic effects make many interesting pure gold species such as clusters and nanotubes possible. In addition, heterogenic species are also studied with great interest. The bimetallic icosahedron WAu 12 , first predicted by Pyykkö and Runeberg [8] and later synthesized by Li et al., [9] is representative of these. Recently, images of multiwalled gold nanowires were published.[3] No reports of pure "golden" fullerenes exist, however. The closest match is WAu 12 , where the Au 12 shell engulfs a tungsten atom. The icosahedral form of Au 12 is itself, however, unstable. [10] Few studies of Au 32 exist. Work with empirical potentials suggest that the global energy minimum for the molecule is a low-symmetry, lumplike structure of either C 2[4] or D 2 symmetry.[5] The scalar relativistic density functional theory (DFT) calculations presented here show that Au 32 has another minimum: the icosahedral fullerenic form. To determine the stability of the Au 32 fullerene, we first optimized its structure. Two different functionals, the popular generalized gradient approximation (GGA) functional BP86 [11] and the nonempirical hybrid GGA functional PBE0, [12] were used throughout this work. Au 32 is composed of triangles in icosahedral symmetry, making a near perfect rhombic triacontahedron. Each atom binds to either five or six neighboring gold atoms. Thus, the symmetry is the same as for the truncated icosahedron C 60 , with the vertices and planes interchanged. Figure 1 shows the structure of Au 32 , compared with C 60 .Au 32 is a closed-shell molecule with an appreciable energy gap between the frontier orbitals, factors important for stability. The gap between the highest oc...