QTAIM N-center delocalization indices as descriptors of aromaticity in mono and poly heterocycles

The implementation of the n-center electron delocalization indices, n-DIs, and n-order electron localization indices, n-LIs, within the framework of the quantum theory of atoms in molecules, QTAIM, is performed. n-DIs are shown to be very useful to study the local aromaticity in monocyclic and polycyclic compounds. Total and pi n-DIs from n=4 to 7 were computed for a series of typical 4, 5, 6, and 7-center aromatic and antiaromatic rings. For n>or=5 the pi n-DI accounts for the 95% of the total n-DI and can be employed alone to measure the aromaticity. A scaling factor on the n-DIs is required in order to compare the aromaticity of [5c-6e] and [6c-6e] rings, the same correction allows to estimate the relative aromatic stabilization of polycyclic compounds using the sum of its values for individual rings. This is called Effective Scaled Electron Delocalization, ESED. The comparison with other aromaticity indices reflects a good correlation between ESED and both resonance energies, and HOMA indices. The most important differences between scaled pi n-DIs and NICS(0) indices are found for compounds that contain rings with different number of centers or pi electrons.     

A DFT study of isomeric conjugated,cross-conjugated and semi-conjugated six-membered heterocyclic mesomeric betaines

The structures and electronic properties of seven isomeric six-membered heterocyclic mesomeric betaines (HMBs) and four fully-covalent isomers have been calculated using B3LYP/6-311++G(p,d) methodology. The aromaticity indexes Bird I₆, HOMA, NICS(1) and aromatic stabilisation energy (ASE) have been calculated and compared. In agreement with an earlier study employing connectivity-matrix analysis, the previously unrecognised and little known semi-conjugated HMBs (Class 3) have calculated properties that are quite distinct from the isomeric conjugated HMBs (Class 1) and cross-conjugated HMBs (Class 2). In particular semi-conjugated systems have a higher degree of both classical and magnetic aromaticity than the isomers. In agreement with the calculated vertical ionisation potentials and electron affinities, the six-membered semi-conjugated species have high energy HOMOs and low energy LUMOs and these observations are consistent with the limited experimental data available. The results support the view that semi-conjugated rings should be recognised as a discrete class of dipolar heterocycle.     

Aromaticity of benzenoid hydrocarbons with inserted –B=B– and –BH–BH– groups: a comparison

Structures of selected polycyclic conjugated hydrocarbons with –B=B– and –BH–BH– moieties inserted in different places were calculated at the B3LYP/6-311++G** level and their aromatic properties evaluated. HOMA, NICS(0), NICS(1)zz, Λ and PDI indices were used for studying their aromatic properties. Both optimized planar (as in parent hydrocarbons) and non-planar structures were taken into account. It is shown that insertion of both types of boron groups disturbs and decreases the aromaticity of the corresponding hydrocarbons. The decreasing effect of the –BH–BH– group is much stronger. What is quite intriguing is that it appears that non-planar structures of the studied compounds have a little higher aromaticity than the strictly planar ones. Mutual correlations between results obtained by different aromaticity indices are calculated and thoroughly discussed.     

Reactivity indices as a measure of rate constants for protonation of radical anions and dianions

The DFT-based reactivity indices were used to describe protonation reactions of radical anions (RA) and dianions (DA) of aromatic compounds. A correlation between the experimental rate constants for protonation and the global reactivity indices was found. The indices were expressed through the electron affinities and ionization energies computed at the B3LYP level of theory. The protonation reactions of RA and DA of aromatic compounds are correctly described by the reactivity indices calculated as the inverse of the difference between the formal formation potential of RA (or DA) and the formal reduction potential of the proton donor.     

Control of kinetics and thermodynamics of [1,5]-shifts by aromaticity: a view through the prism of Marcus theory

The effects of aromatic stabilization on the rates of [1,5]-hydrogen shifts in a series of carbo- and heterocyclic dihydroaromatic compounds were estimated by B3LYP/6-31G computations. The aromatic stabilization energy of the product is directly translated into increased exothermicity of these reactions. Relative trends for a significant range of endothermic and exothermic [1,5]-shifts with different intrinsic activation energies are reliably described by Marcus theory. The effects of aromaticity or antiaromaticity are very large and can lead to dramatic acceleration or deceleration of [1,5]-hydrogen shifts and even to complete disappearance of the reaction barrier. Not only the activation energy but the shape and position of the reaction barrier can be efficiently controlled by changes in the aromaticity of the products, making these systems interesting models for studying hydrogen tunneling. Marcus theory can also be applied successfully to other pericyclic shifts such as [1,5]-shifts which involve chlorine and methyl transfer.     

Aromaticity and electronic delocalization in all-metal clusters with single, double, and triple aromatic character

A series of monocyclic planar inorganic compounds with single, double, and triple (anti)aromatic character has been studied. The electron delocalization and aromaticity of these compounds have been assessed by means of two-center and multicenter electronic delocalization indices and their ??-, ??-, and ??-components. Results show that these indices are excellent predictors of the ??-, ??-, and ??-aromatic character of all-metal and semimetal clusters.     

To what extent can aromaticity be defined uniquely?

Statistical analyses of quantitative definitions of aromaticity, ASE (aromatic stabilization energies), RE (resonance energies), Lambda (magnetic susceptibility exaltation), NICS, HOMA, I5, and A(J), evaluated for a set of 75 five-membered pi-electron systems: aza and phospha derivatives of furan, thiophene, pyrrole, and phosphole (aromatic systems), and a set of 30 ring-monosubstituted compounds (aromatic, nonaromatic, and antiaromatic systems) revealed statistically significant correlations among the various aromaticity criteria, provided the whole set of compounds is involved. Hence, broadly considered, the various manifestations of aromaticity are related and aromaticity can be regarded statistically as a one-dimensional phenomenon. In contrast, when comparisons are restricted to some regions or groups of compounds, e.g., aromatic compounds with ASE > 5 kcal/mol or polyhetero-five-membered rings, the quality of the correlations can deteriorate or even vanish. In practical applications, energetic, geometric, and magnetic desriptors of aromaticity do not speak with the same voice. Thus, in this sense, the phenomenon of aromaticity is regarded as being statistically multidimensional.     

Calculation of the HOMA model parameters for the carbon–boron bond

An extension of the harmonic oscillator model of aromaticity (HOMA) model to systems with carbon–boron bonds is presented. Model parameters were estimated using experimental and theoretical bond lengths. It is shown that both approaches produce very similar HOMA models. In the second part of the article, the aromaticity levels of several model compounds containing carbon–boron bonds are calculated using the previously obtained parameters. The results of these calculations are compared with those provided by other aromaticity indices. The aromaticity of boron-containing compounds is also compared with the aromaticity of analogous compounds containing carbon and nitrogen.     

Aromaticity of giant polycyclic aromatic hydrocarbons with hollow sites: super ring currents in super-rings

We present a systematic theoretical study based on semi-empirical, Hartree-Fock (HF), and density functional theory (DFT) models of a series of polycyclic aromatic hydrocarbons (PAHs) that exhibit hollow sites. In this study we focus particularly on the magnetic criteria of aromaticity, namely (1)H NMR and nucleus-independent chemical shifts (NICS), and on their relationships with other electronic properties. The computed shifts and NICS indices indicate that an external magnetic field induces exceptionally strong ring currents in even-layered PAH doughnuts, in particular in the layer directly adjacent to the central hole of double-layered compounds. These exceptionally strong ring currents also correlate with particularly small HOMO-LUMO gaps and electronic excitation energies and to abnormally high polarizabilities, indicating in turn that these compounds have a more pronounced metallic character. Comparison is made with further depictions of aromaticity in these systems and in [18]-[66]annulene rings by employing topological, structural, and energetic criteria.     

Magnetic resonance energies of heterocyclic conjugated molecules

Magnetic resonance energy (MRE), derived from ring-current diamagnetic susceptibility, can be interpreted as a kind of aromatic stabilization energy. For polycyclic conjugated hydrocarbons, this quantity correlates well with topological resonance energy (TRE). MREs for typical heterocyclic conjugated molecules were then calculated and analyzed. It was found that even for heterocycles MRE highly correlates with TRE. Thus, the MRE concept has been firmly established as a reliable indicator of aromaticity, which mediates magnetic criteria of aromaticity with energetic ones. The conformity of heterocycles to the rule of topological charge stabilization can be checked using not only TRE but also MRE.     

Electron affinities of Al(n) clusters and multiple-fold aromaticity of the square Al4(2-) structure

The concept of aromaticity was first invented to account for the unusual stability of planar organic molecules with 4n + 2 delocalized pi electrons. Recent photoelectron spectroscopy experiments on all-metal MAl(4)(-) systems with an approximate square planar Al(4)(2-) unit and an alkali metal led to the suggestion that Al(4)(2-) is aromatic. The square Al(4)(2-) structure was recognized as the prototype of a new family of aromatic molecules. High-level ab initio calculations based on extrapolating CCSD(T)/aug-cc-pVxZ (x = D, T, and Q) to the complete basis set limit were used to calculate the first electron affinities of Al(n)(), n = 0-4. The calculated electron affinities, 0.41 eV (n = 0), 1.51 eV (n = 1), 1.89 eV (n = 3), and 2.18 eV (n = 4), are all in excellent agreement with available experimental data. On the basis of the high-level ab initio quantum chemical calculations, we can estimate the resonance energy and show that it is quite large, large enough to stabilize Al(4)(2-) with respect to Al(4). Analysis of the calculated results shows that the aromaticity of Al(4)(2-) is unusual and different from that of C(6)H(6). Particularly, compared to the usual (1-fold) pi aromaticity in C(6)H(6), which may be represented by two Kekulé structures sharing a common sigma bond framework, the square Al(4)(2-) structure has an unusual "multiple-fold" aromaticity determined by three independent delocalized (pi and sigma) bonding systems, each of which satisfies the 4n + 2 electron counting rule, leading to a total of 4 x 4 x 4 = 64 potential resonating Kekulé-like structures without a common sigma frame. We also discuss the 2-fold aromaticity (pi plus sigma) of the Al(3)(-) anion, which can be represented by 3 x 3 = 9 potential resonating Kekulé-like structures, each with two localized chemical bonds. These results lead us to suggest a general approach (applicable to both organic and inorganic molecules) for examining delocalized chemical bonding. The possible electronic contribution to the aromaticity of a molecule should not be limited to only one particular delocalized bonding system satisfying a certain electron counting rule of aromaticity. More than one independent delocalized bonding system can simultaneously satisfy the electron counting rule of aromaticity, and therefore, a molecular structure could have multiple-fold aromaticity.     

Does the concept of Clar's aromatic sextet work for dicationic forms of polycyclic aromatic hydrocarbons?--testing the model against charged systems in singlet and triplet states

The concept of Clar's π-electron aromatic sextet was tested against a set of polycyclic aromatic hydrocarbons in neutral and doubly charged forms. Systems containing different types of rings (in the context of Clar's concept) were chosen, including benzene, naphthalene, anthracene, phenanthrene and triphenylene. In the case of dicationic structures both singlet and triplet states were considered. It was found that for singlet state dicationic structures the concept of aromatic sextet could be applied and the local aromaticity could be discussed in the context of that model, whereas in the case of triplet state dicationic structures Clar's model rather failed. Different aromaticity indices based on various properties of molecular systems were applied for the purpose of the studies. The discussion about the interdependence between the values of different aromaticity indices applied to neutral and charged systems in singlet and triplet states is also included.     

Thiophene 1-oxides. V. Comparison of the crystal structures and thiophene ring aromaticity of 2,5-diphenylthiophene,its sulfoxide and sulfone

The detailed preparation of 2,5-diphenylthiophene 1-oxide (2) is reported as well as the comparative study of the crystal structures of 2,5-diphenylthiophene, 1 , its sulfoxide 2 and sulfone 3 obtained by X-ray diffraction. This work represents the first experimental study of a complete heterocyclic series, including a thiophene derivative, and the corresponding sulfoxide and sulfone. On the basis of the geometrical parameters, the first unequivocal experimental parameters obtained for a thiophene 1-oxide derivative, we have also examined the evolution of the aromatic character of the thiophene ring when oxidizing the sulfur atom to the sulfoxide and the sulfone. Paolini's bond orders and Julg and Francois's aromaticity indices have also been calculated for the three compounds and compared to those previously calculated for related thiophene derivatives by semi-empirical or ab initio methods [6], [7]. All the data examined showed that, in spite of its non planarity, the thiophene ring of 2,5-diphenylthiophene 1-oxide 2 could still exhibit some de localization of its p electrons indicating a certain degree of aromaticity lower than in thiophene 1 but higher than in the sulfone 3 .     

Benzene fused five-membered heterocycles. A theoretical approach

The Nuclear Independent Chemical Shift of each ring, as a criterion of aromaticity, is used to explain the stability order of benzopyrrole, benzofuran and benzothiophene, and their isomers. The results indicate that the benzene ring is aromatic in all the systems. The five-membered rings of benzopyrrole, benzofuran and benzothiophene are also aromatic, whereas those of isobenzopyrrole, isobenzofuran and isobenzothiophene are non-aromatic. This could be an explanation of the stability of the former molecules. The molecular orbitals and the condensed Fukui functions derived from the electronic structure calculations are also reported. These reactivity indices explain the expected electrophilic substitution of these compounds. The theoretical structure, ionization energies, order of aromaticity, stability and reactivity are in good agreement with the experimental results. The usefulness of this approach to determine the reactivity is discussed since their stability and reactivity may be understood. The reactivity indices are useful to explain and confirm the experimental information, and for molecules with unknown reactive behavior, this approach could help to predict some of the reactions.     

Tuning the Structure and Properties of N-doped Positively Charged Polycyclic Aromatic Hydrocarbons

A detailed study of the geometry, aromatic character, electronic and magnetic properties for a series of positively charged N-doped polycyclic aromatic hydrocarbons (PAHs) was performed. Magnetic properties of the examined molecules were analyzed by means of the magnetically induced current density calculated using the diamagnetic-zero version of the continuous transformation of origin of current density (CTOCD-DZ) method. The comparative study of the local aromaticity of the studied molecules was performed using several different indices: energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six centre delocalization index (SCI) and nucleus independent chemical shifts (NICS). The presence of N-atoms in the inner rings was found to cause a planarity distortion in the studied N-doped systems. The geometric changes and charged nature of the studied N-doped systems do not significantly influence the current density and the local aromaticity distribution in comparison with the corresponding parent benzenoid hydrocarbons. The present study demonstrates how quantum chemical calculations can be used for rational design of novel PAHs and for fine tuning of their properties.     

Application of natural bond orbital analysis to delocalization and aromaticity in C-substituted tetrazoles.

Energies of two tautomeric forms of 10 tetrazole derivatives substituted at C5 were established by DFT/B3LYP calculations carried out at the 6-311++G level. In each case the calculated energy of the 2H-tautomer was lower than that of the 1H. Furthermore, three geometric aromaticity indices of both forms were calculated, as were the values of nuclear independent nuclear shift and aromatic stabilization energy. The electronic properties were evaluated with the help of the natural bonding orbital theory. Following this a new pi-delocalization parameter, the root-mean square of pi-electron density localized on the atoms of the five-membered tetrazole ring, SDn, was introduced. It was concluded that the electronic delocalization can be described equally well by three different parameters: SDn, the extent of the transfer of electron density from the p(z) orbital of one nitrogen to the rest of the pi electron system, and population of two antibonding pi orbitals. Arguably, the information provided by the electronic parameters is similar to that contained in the geometric (structural) aromaticity indices except for tetrazole substituted by -BH(2).