Heike Fliegl

The Dalton quantum chemistry program system

Dalton is a powerful general‐purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self‐consistent‐field, Møller–Plesset, configuration‐interaction, and coupled‐cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic‐structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge‐origin‐invariant manner. Frequency‐dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one‐, two‐, and three‐photon processes. Environmental effects may be included using various dielectric‐medium and quantum‐mechanics/molecular‐mechanics models. Large molecules may be studied using linear‐scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Coupled-cluster theory with simplified linear-r12 corrections: The CCSD(R12) model

A simplified singles-and-doubles linear-r(12) corrected coupled-cluster model, denoted CCSD(R12), is proposed and compared with the complete singles-and-doubles linear-r(12) coupled-cluster method CCSD-R12. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation to calculate three-electron integrals needed in the linear-r(12) Ansatz. Basis-set convergence is investigated for a selected set of atoms and small molecules. In a large basis, the CCSD(R12) model provides an excellent approximation to the full linear-r(12) energy contribution, whereas the magnitude of this contribution is significantly overestimated at the level of second-order perturbation theory.

The gauge including magnetically induced current method

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.

Magnetically Induced Current Densities in Aromatic, Antiaromatic, Homoaromatic, and Nonaromatic Hydrocarbons

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.

Expanding the Coordination Cage: A Ruthenium(II)−Polypyridine Complex Exhibiting High Quantum Yields under Ambient Conditions

A mononuclear ruthenium(II) polypyridyl complex with an enlarged terpyridyl coordination cage was synthesized by the formal introduction of a carbon bridge between the coordinating pyridine rings. Structurally, the ruthenium(II) complex shows an almost perfect octahedral N6 coordination around the central Ru(II) metal ion. The investigation of the photophysical properties reveals a triplet metal-to-ligand charge transfer emission with an unprecedented quantum yield of 13% and a lifetime of 1.36 mus at room temperature and in the presence of air oxygen. An exceptional small energy gap between light absorption and light emission, or Stokes shift, was detected. Additionally, time-dependent density functional theory calculations were carried out in order to characterize the ground state and both the singlet and triplet excited states. The exceptional properties of the new compound open the perspective of exploiting terpyridyl-like ruthenium complexes in photochemical devices under ambient conditions.

All-Metal Aromaticity: Revisiting the Ring Current Model among Transition Metal Clusters

We present new insight into the nature of aromaticity in metal clusters. We give computational arguments in favor of using the ring-current model over local indices, such as nucleus independent chemical shifts, for the determination of the magnetic aromaticity. Two approaches for estimating magnetically induced ring currents are employed for this purpose, one based on the quantum theory of atoms in molecules (QTAIM) and the other where magnetically induced current densities (MICD) are explicitly calculated. We show that the two-zone aromaticity/antiaromaticity of a number of 3d metallic clusters (Sc3(-), Cu3(+), and Cu4(2-)) can be explained using the QTAIM-based magnetizabilities. The reliability of the calculated atomic and bond magnetizabilities of the metallic clusters are verified by comparison with MICD computed at the multiconfiguration self-consistent field (MCSCF) and density functional levels of theory. Integrated MCSCF current strength susceptibilities as well as a visual analysis of the calculated current densities confirm the interpretations based on the QTAIM magnetizabilities. In view of the new findings, we suggest a simple explanation based on classical electromagnetic theory to explain the anomalous magnetic shielding in different transition metal clusters. Our results suggest that the nature of magnetic aromaticity/antiaromaticity in transition-metal clusters should be assessed more carefully based on global indices.

Aromatic pathways of porphins, chlorins, and bacteriochlorins.

Magnetically induced current densities have been calculated for free-base porphynoids using the gauge including magnetically induce current (GIMIC) method. Numerical integration of the current density passing selected chemical bonds yields current pathways and the degree of aromaticity according to the magnetic criterion. The ring-current strengths of the porphins, chlorins, and bacteriochlorins are 1.5-2.5 times stronger than for benzene. The calculations show that the 18π [16]annulene inner cross is not the correct picture of the aromatic pathway for porphyrins. All conjugated chemical bonds participate in the current transport independently of the formal number of π electrons. The ring current branches at the pyrrolic rings taking both the outer and the inner route. The NH unit of the pyrrolic rings has a larger resistance and a weaker current strength than the pyrroles without inner hydrogens. The traditional 18π [18]annulene with inactive NH bridges is not how the ring-current flows around the macroring. The porphins have the strongest ring current of ca. 27 nA/T among the investigated porphynoids. The current strengths of the chlorins and bacteriochlorins are 19-24 nA/T depending on whether the ring current is forced to pass an NH unit or not. The current strengths of the 3-fold and 4-fold β-saturated porphynoids are 13-17 nA/T, showing that the inner-cross 18π [16]annulene pathway is not a preferred current route.

Aromatic pathways in twisted hexaphyrins.

The aromatic pathways and the degree of aromaticity of expanded porphyrins have been determined by explicit calculations of the routes and strengths of the magnetically induced currents using the gauge-including magnetically induced current (GIMIC) approach. Density functional theory calculations show that the doubly twisted hexaphyrins fulfilling Hückels (4n + 2) pi-electron rule for aromaticity and those obeying the 4n pi-electron rule for antiaromaticity are aromatic and antiaromatic, respectively. The investigated [26]hexaphyrin (2) and (3) and [30]hexaphyrin (5) isomers are aromatic, and [28]hexaphyrin (4) is antiaromatic. The formally antiaromatic [24]hexaphyrin (1) does not sustain any strong ring current and must be considered nonaromatic. A detailed analysis of the current pathways of the hexaphyrins is presented. It was found that the current pathways of the investigated aromatic hexaphyrins are not always dominated by the flow along the inner route through the non-hydrogenated C-N-C moieties, as previously proposed. The current flow is often split into two branches at the pyrrole rings, but sometimes it takes the outer route via the C=C bond of the pyrrole. The current pathway of the weak paratropic ring current of [24]hexaphyrin is dominated by the outer C=C route. The calculations show that the routes of the current transport cannot be assessed merely by inspection or from nucleus independent chemical shifts; explicit calculations of the current pathways are compulsory. The current-density studies also show that the pyrrole rings do not sustain any strong ring currents of their own.

Calculations of magnetically induced current densities: theory and applications

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. WIREs Comput Mol Sci 2016, 6:639–678. doi: 10.1002/wcms.1270

Effect of Fluorine Substitution on the Aromaticity of Polycyclic Hydrocarbons

The effect of fluorine substitution on the aromaticity of polycyclic hydrocarbons (PAH) is investigated. Magnetically induced current densities, current pathways, and current strengths, which can be used to assess molecular aromaticity, are calculated using the gauge-including magnetically induced current method (GIMIC). The degree of aromaticity of the individual rings is compared to those obtained using calculated nucleus-independent chemical shifts at the ring centers (NICS(0) and NICS(0)(zz)). Calculations of explicitly integrated current strengths for selected bonds show that the aromatic character of the investigated polycyclic hydrocarbons is weakened upon fluorination. In contrast, the NICS(0) values for the fluorinated benzenes increase noteworthy upon fluorination, predicting a strong strengthening of the aromatic character of the arene rings. The integrated current strengths also yield explicit current pathways for the studied molecules. The current pathways of the investigated linear polyacenes, pyrene, anthanthrene, coronene, ovalene, and phenanthro-ovalene are not significantly affected by fluorination. NISC(0) and NICS(0)(zz) calculations provide contradictory degrees of aromaticity of the fused individual ring. Obtained NICS values do not correlate with the current strengths circling around the individual rings.