Stijn Fias

Critical thoughts on computing atom condensed Fukui functions.

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory.

Electrostatic Potentials from Self-Consistent Hirshfeld Atomic Charges

It is shown that molecular electrostatic potentials obtained from iterative or self-consistent Hirshfeld atomic point charges agree remarkably well with the ab initio computed electrostatic potentials. The iterative Hirshfeld scheme performs nearly as well as electrostatic potential derived atomic charges, having the advantage of allowing the definition of the atom in the molecule, rather than just yielding charges. The quality of the iterative Hirshfeld charges for computing electrostatic potentials is examined for a large set of molecules and compared to other commonly used techniques for population analysis.

Multidimensionality of delocalization indices and nucleus independent chemical shifts in polycyclic aromatic hydrocarbons

The aromaticity and local‐aromaticity of a large set of polycyclic aromatic hydrocarbons (PAHs) is studied using multicenter delocalization indices from generalized population analysis and the popular nucleus independent chemical shift (NICS) index. A method for the fast computation of the NICS values is introduced, using the so‐called pseudo‐π‐method. A detailed examination is made of the multidimensional nature of aromaticity. The lack of a good correlation between the NICS and the multicenter delocalization indices is reported and the grounds discussed. It is shown through a thorough statistical analysis that the NICS values arise not only from local aromaticity of the benzenoid rings, but also from other circuits. It is shown that the NICS indices do not reveal the individual aromatic nature of a specific ring, contrary to the delocalization indices.

Woodward-Hoffmann rules in density functional theory : Initial hardness response

The Woodward-Hoffmann rules for pericyclic reactions, a fundamental set of reactivity rules in organic chemistry, are formulated in the language of conceptual density functional theory (DFT). DFT provides an elegant framework to introduce chemical concepts and principles in a quantitative manner, partly because it is formulated without explicit reference to a wave function, on whose symmetry properties the Woodward-Hoffmann [J. Am. Chem. Soc. 87, 395 (1965)] rules are based. We have studied the initial chemical hardness response using a model reaction profile for two prototypical pericyclic reactions, the Diels-Alder cycloaddition of 1,3-butadiene to ethylene and the addition of ethylene to ethylene, both in the singlet ground state and in the first triplet excited state. For the reaction that is thermally allowed but photochemically forbidden, the initial hardness response is positive along the singlet reaction profile. (By contrast, for the triplet reaction profile, a negative hardness response is observed.) For the photochemically allowed, thermally forbidden reaction, the behavior of the chemical hardness along the initial stages of the singlet and triplet reaction profiles is reversed. This constitutes a first step in showing that chemical concepts from DFT can be invoked to explain results that would otherwise require invoking the phase of the wave function.

Electronic structure and aromaticity of graphene nanoribbons.

We analyse the electronic structure and aromaticity of graphene nanoribbons and carbon nanotubes through a series of delocalisation and geometry analysis methods. In particular, the six-centre index (SCI) is found to be in good agreement with the mean bond length (MBL) and ring bond dispersion (RBD) geometry descriptors. Based on DFT periodic calculations, three distinct classes of aromaticity patterns have been found for armchair graphene nanoribbons, appearing periodically as the width of the ribbon is increased. The periodicity in the band gap is found to be related to these aromaticity patterns. Also, the appearance of such distinct aromaticity distribution is explained within the framework of the Clars sextet theory. Both delocalisation and geometry analysis methods are shown to be very fast and reliable tools for easily analysing the aromaticity in carbon nanosystems.

Multidimensionality of delocalization indices and nucleus-independent chemical shifts in polycyclic aromatic hydrocarbons II: proof of further nonlocality.

In a recent contribution, we examined the effect of 10‐ and 14‐center circuits on the nucleus‐independent chemical shifts NICSs using multicenter bond indices (MCBIs) (Fias et al., J Comput Chem 2008, 29, 358). In this study, the nonlocal contributions to the NICS are further investigated for a larger set of polycyclic aromatic hydrocarbons (PAHs). To achieve this, the NICSs are predicted using the MCBI and compared with ab initio results. The NICSs of the central ring of perylene‐ and benzo‐[ghi]perylene‐like fragments and of coronene appear to have other nonlocal contributions than the ones previously studied. It is shown that a model based on the MCBI‐ring current maps and the inclusion of new circuits proves the existence and shows the nature of these new nonlocal effects on the NICS. This new model leads to a better understanding of the differences between the NICSs and delocalization indices. The results show that the NICS value is not only significantly influenced by the higher order circuits encircling the ring at which it is evaluated but also by the local aromaticity of the surrounding rings, and occasionally, like in the case of coronene, the NICSs are even influenced by currents farther away in the molecule.

σ, π aromaticity and anti-aromaticity as retrieved by the linear response kernel

The chemical importance of the linear response kernel from conceptual Density Functional Theory (DFT) is investigated for some σ and π aromatic and anti-aromatic systems. The effect of the ring size is studied by looking at some well known aromatic and anti-aromatic molecules of different sizes, showing that the linear response is capable of correctly classifying and quantifying the aromaticity for five- to eight-membered aromatic and anti-aromatic molecules. The splitting of the linear response in σ and π contributions is introduced and its significance is illustrated using some σ-aromatic molecules. The linear response also correctly predicts the aromatic transition states of the Diels-Alder reaction and the acetylene trimerisation and shows the expected behavior along the reaction coordinate, proving that the method is accurate not only at the minimum of the potential energy surface, but also in non-equilibrium states. Finally, the reason for the close correlation between the linear response and the Para Delocalisation Index (PDI), found in previous and the present study, is proven mathematically. These results show the linear response to be a reliable DFT-index to probe the σ and π aromaticity or anti-aromaticity of a broad range of molecules.

Analysis of Aromaticity in Planar Metal Systems using the Linear Response Kernel.

The linear response kernel is used to gain insight into the aromatic behavior of the less classical metal aromatic E4(2-) and CE4(2-) (E = Al, Ga) clusters. The effect of the systematic replacement of the aluminum atoms in Al4(2-) and CAl4(2-) by germanium atoms is studied using, Al3Ge-, Al2Ge2, AlGe3+, Ge4(2+), CAl3Ge-, CAl2Ge2, CAlGe3+, and CGe4(2+). The results are compared with the values of the delocalization index (δ(1,3)) and nucleus independent chemical shifts (NICS(zz)). Unintegrated plots of the linear response, computed for the first time on molecules, are used to analyze the delocalization in these clusters. All aromaticity indices studied, the linear response, δ(1,3), and NICS(zz), predict that the systems with a central carbon are less aromatic than the systems without a central carbon atom. Also, the linear response is more pronounced in the σ-electron density than in the π-density, pointing out that the systems are mainly σ-aromatic.

How does aromaticity rule the thermodynamic stability of hydroporphyrins

Several measures of aromaticity including energetic, magnetic, and electron density criteria are employed to show how aromatic stabilization can explain the stability sequence of hydroporphyrins, ranging from porphin to octahydroporphin, and their preferred hydrogenation paths. The methods employed involve topological resonance energies and their circuit energy effects, bond resonance energies, multicenter delocalization indices, ring current maps, magnetic susceptibilities, and nuclear-independent chemical shifts. To compare the information obtained by the different methods, the results have been put in the same scale by using recently proposed approaches. It is found that all of them provide essentially the same information and lead to similar conclusions. Also, hydrogenation energies along different hydrogenation paths connecting porphin with octahydroporphin have been calculated with density functional theory. It is shown by using the methods mentioned above that the relative stability of different hydroporphyrin isomers and the observed inaccessibility of octahydroporphin both synthetically and in nature can be perfectly rationalized in terms of aromaticity.

Conduction of molecular electronic devices: Qualitative insights through atom-atom polarizabilities

The atom-atom polarizability and the transmission probability at the Fermi level, as obtained through the source-and-sink-potential method for every possible configuration of contacts simultaneously, are compared for polycyclic aromatic compounds. This comparison leads to the conjecture that a positive atom-atom polarizability is a necessary condition for transmission to take place in alternant hydrocarbons without non-bonding orbitals and that the relative transmission probability for different configurations of the contacts can be predicted by analyzing the corresponding atom-atom polarizability. A theoretical link between the two considered properties is derived, leading to a mathematical explanation for the observed trends for transmission based on the atom-atom polarizability.