Aromaticity and Diatropicity of Polyacenequinododimethides

Typical polyacenequinododimethides exist only in a single classical structure. These hydrocarbons are moderately aromatic and diatropic, although they have no aromatic conjugated circuits. This apparent dichotomy was resolved with our graph theory of aromaticity and magnetotropicity. Many nonconjugated circuits were found to contribute collectively to aromaticity and diatropicity. For individual molecules, local aromaticity increases with distance from the exo‐methylene groups. This fact indicates that the conjugated‐circuit model is not always applicable to semibenzenoid hydrocarbons such as polyacenequinododimethides.     

Aromaticity and diatropicity of <Emphasis Type="Italic">p</Emphasis>-polyphenyl-α,ω-quinododimethides

p-Polyphenyl-α,ω-quinododimethides were predicted to be moderately aromatic and diatropic, although they exist only in a single classical resonance structure with no aromatic conjugated circuits. Such a dichotomy was resolved using our graph theory of aromaticity and ring-current diamagnetism. Six-site non-conjugated circuits were found to contribute appreciably to aromaticity and ring-current diamagnetism. Within each quinododimethide molecule, local aromaticity increases on going from the outermost to inner phenylene rings.     

Local aromaticities in large polyacene molecules

There has been controversy on the relative aromaticities of individual rings in a large polyacene molecule. Nucleus-independent chemical shift (NICS) values suggest that the highly reactive inner rings might be more aromatic than the outer ones and even more aromatic than benzene. We evaluated the bond resonance energies (BREs) and hypothetical geometry-independent pi-electron currents for a series of linear polyacenes and noticed that for large polyacene molecules the inner rings are never more aromatic than the outer ones. Global HOMA (harmonic oscillator model of aromaticity) values are highly correlative with percentage topological resonance energies (% TREs) but not with average NICS values. Magnetic properties, such as NICS and ring-current intensity, are highly dependent on molecular geometry and so must be carefully related to aromaticity.     

Resonance energy in graphite

According to Zhu et al. the resonance energy/electron (REPE) in infinite graphite sheets is equal to 0.17 eV. In the present work the REPE was calculated for parallelogram-shaped graphite sheets (PSGSs). The number of Kekulé structures and contributions of benzene-like and naphthalene-like conjugated circuits were taken into account. Analogously to polyacenes, it was found that REPE = 0.00 eV in PSGSs. The convergence is slow. These results indicate that PSGS is less "aromatic" than its infinite counterpart. Therefore addition reactions are expected to be less difficult to carry out in PSGSs than in infinite or rectangular graphite sheets.     

Aromaticity in linear polyacenes: generalized population analysis and molecular quantum similarity approach

The relative aromaticity of benzenoid rings in the linear polyacenes is investigated using two novel aromaticity approaches. According to the first, the aromaticity of individual benzene rings was gauged by the values of six-center bond indices (SCI) calculated within the so-called Generalized Population Analysis (GPA). In the second approach, the same goal is addressed using the theory of Molecular Quantum Similarity (MQS). Both independent approaches are found to correlate very well, and both point toward decreasing aromaticity in any linear polyacenes upon going from the outer to inner rings.     

Local aromaticity in polyacenes manifested by individual proton and carbon shieldings: DFT mapping of aromaticity

Exponential dependencies between locally calculated geometric and magnetic indexes of aromaticity, harmonic oscillator model of aromaticity (HOMA) and nucleus independent chemical shifts (NICS)(0), NICS(1) and NICS(1)zz, and the number of conjugated benzene rings in linear acenes, from benzene to decacene were observed at B3LYP/6-311+G** level of theory. Correlations between HOMA and NICS indexes showed exponential dependencies and were fitted with simple three-parameter function. Similar correlations between both indexes of aromaticity and proton and carbon nuclear isotropic shieldings of individual acene rings were observed. Contrary to proton data, the predicted ¹³C nuclear isotropic shieldings of carbon atoms belonging to inner rings in polyacenes were less shielded, indicating lower aromaticity and therefore, higher reactivity.     

Electron delocalization and aromaticity in linear polyacenes: atoms in molecules multicenter delocalization index

Molecular aromaticity in the linear polyacenes is investigated using an atoms in molecules based six center index (SCI-AIM) which measures the electron delocalization. SCI-AIM values for the linear polyacenes indicate decreasing aromaticity going from outer to inner rings in the polyacene series. The SCI-AIM approach is compared to a Mulliken-like approach, and a critical comparison to the PDI index is made.     

A Triply [5]Helicene-Bridged (1,3,5)Cyclophane

A rigid propeller-shaped conjugated triple macrocycle consisting of two nearly perfectly stacked benzene rings and three linking [5]helicene moieties has been synthesized using a glyoxylic Perkin approach. Analysis of the electron delocalization in this atypical aromatic molecule revealed global aromaticity and a 78 π-electron circuit along the edge of its triple loop, to the detriment of the two 6 π-electron circuits in the two stacked benzene rings.     

Visualizing electron delocalization in contorted polycyclic aromatic hydrocarbons

Electron delocalization in contorted polycyclic aromatic hydrocarbon (PAH) molecules was examined through 3D isotropic magnetic shielding (IMS) contour maps built around the molecules using pseudo-van der Waals surfaces. The resulting maps of electron delocalization provided an intuitive, yet detailed and quantitative evaluation of the aromatic, non aromatic, and antiaromatic character of the local and global conjugated cyclic circuits distributed over the molecules. An attractive pictural feature of the 3D IMS contour maps is that they are reminiscent of the Clar π-sextet model of aromaticity. The difference in delocalization patterns between the two faces of the electron circuits in contorted PAHs was clearly visualized. For π-extended contorted PAHs, some splits of the π system resulted in recognizable patterns typical of smaller PAHs. The differences between the delocalization patterns of diastereomeric chiral PAHs could also be visualized. Mapping IMS on pseudo-van der Waals surfaces around contorted PAHs allowed visualization of their superimposed preferred circuits for electron delocalization and hence their local and global aromaticity patterns.

Electron delocalization in contorted polycyclic aromatic hydrocarbon (PAH) molecules was examined through 3D isotropic magnetic shielding (IMS) contour maps built around the molecules using pseudo-van der Waals surfaces.     

Applying the conjugated circuits method to Clar structures of [n]phenylenes for determining resonance energies

We consider the aromaticity of biphenylene and structurally related linear or angular [n]phenylenes for which the direct application of the model of conjugated circuits does not offer valid expressions for resonance energy and aromaticity. We located the cause of this problem as being due to Kekulé valence structures in which neighboring benzenoid rings are connected by two CC double bonds. By restricting the selection of Kekulé valence structures to those that contribute to Clar structures of such systems, we were able to show that linear and angular [n]phenylenes have approximately similar resonance energies, with angular [n]phenylenes being slightly more stable due to second order contributions arising from disjoint conjugated circuits. Expressions for resonance energies of [n]phenylenes up to n = 8 are listed and recursion expressions for higher n values are outlined.     

An investigation of the aromaticity of transition metal heterocyclic complexes by conventional criteria and indices of aromaticity

Conventional criteria and indices of aromaticity, including electronic, geometric, energetic and magnetic aspects have been applied to examine the aromaticity of five typical transition metal heterocyclic complexes, i.e. six-membered osmabezene 1 and iridabenzene 2, five-membered cobaltacyclopentadiene 3 and iridacyclopentadiene 4, and four-membered tungstacyclobutadiene 5. The results show that the cyclic, planar, conjugated and Hückel 4n+2 rule’s criteria in the transition-metal-containing heterocycles of the five complexes studied are all met. Five quantitative aromaticity indices, including Bird aromatic index (I_n), homodesmotic reaction aromatic stabilization energy (HASE), absolute hardness (η), diamagnetic susceptibility exaltation (Λ) and NMR chemical shift (δH), qualitatively lead to a consistent and affirmative conclusion that all of them are aromatic. However, they fail to draw a common conclusion for their relative magnitudes of aromaticity, which proves once again the multidimensional character of aromaticity.     

meso‐Aryl [20]π Homoporphyrin: The Simplest Expanded Porphyrin with the Smallest Möbius Topology

An unstable conjugated homoporphyrin was successfully stabilized by introducing meso ‐aryl substitutents. It was evident from the moderate diatropic ring current found by NMR analysis that the newly formed 20π conjugated free base and its protonated form exhibited Möbius aromatic character. Furthermore, complexation as a ligand with an Rh^I ion afforded a unique binding mode and retained the Möbius aromaticity. Overall, these compounds are the smallest Möbius aromatic molecules, as confirmed by spectral and crystal‐structure analysis and supported by theoretical studies.     

A statistical approach to resonance energies of large molecules

For large conjugated molecules, resonance energies of SCF MO quality are not available. Here we outline a method of determining molecular resonance energies by combining a graph theoretical approach to aromaticity with a statistical analysis of random Kekule valence structures. The approach involves construction of random Kekule valence forms and subsequent enumeration of conjugated circuits within each such structure.     

Comparison of Thiophene–Pyrrole Oligomers with Oligothiophenes: A Joint Experimental and Theoretical Investigation of Their Structural and Spectroscopic Properties

We have prepared a new series of mixed thiophene–pyrrole oligomers to investigate the electronic benefits arising from the combination of these two heterocycles. The oligomers are functionalized with several hexyl and aryl groups to improve both processability and chemical robustness. An analysis of their spectroscopic (absorption and emission), photophysical, electrochemical, solid state, and vibrational properties is performed in combination with quantum‐chemical calculations. This analysis provides relevant information regarding the use of these materials as organic semiconductors. The balance between the high aromatic character of pyrrole and the moderate aromaticity of thiophene allows us to address the impact of the coupling of these heterocycles in conjugated systems. The data are interpreted on the basis of the aromaticity, molecular conformations, ground and excited electronic state structures, frontier orbital topologies and energies, oxidative states, and quinoidal versus aromatic competition.     

Circuit resonance energy: a key quantity that links energetic and magnetic criteria of aromaticity

Energetic and magnetic criteria of aromaticity are different in nature and sometimes make different predictions as to the aromaticity of a polycyclic pi-system. Thus, some charged polycyclic pi-systems are aromatic but paratropic. We derived the individual circuit contributions to aromaticity from the magnetic response of a polycyclic pi-system and named them circuit resonance energies (CREs). Each CRE has the same sign and essentially the same magnitude as the corresponding cyclic conjugation energy (CCE) defined by Bosanac and Gutman. Such CREs were found to play a crucial role in associating the energetic criteria for determining the degree of aromaticity with the magnetic ones. We can now interpret both energetic and magnetic criteria of aromaticity consistently in terms of CREs. Ring-current diamagnetism proved to be the tendency of a cyclic pi-system to retain aromatic stabilization energy (ASE) at the level of individual circuits.     

Sigma-pi energy separation in homodesmotic reactions.

A well-established quantity for specifying the aromaticity or antiaromaticity of cyclic conjugated molecules is the so-called aromatic stabilization energy (ASE), which can be derived-either experimentally or theoretically-from appropriate homodesmotic reactions. To gain further insight into the origin of aromaticity, several schemes have been devised to partition ASE into nuclear and electronic as well as sigma and pi contributions, some of which have resulted in contradictory statements about the driving force of aromatic stabilization. Currently, these contradictions have not been resolved and have resulted in a confusing distinction between two different types of aromaticity: extrinsic and intrinsic aromaticity. By investigating different homodesmotic reactions we show that, in contrast to ASE itself, the individual contributions that enter the ASE can strongly depend on the type of reaction. Caution is therefore advised if conclusions or physical interpretations are derived from the individual components. The contradictions result from the fact that some reactions suffer from an imbalance in the number of interaction terms at the two sides of the reaction equation. The concept of isointeractional reactions is introduced and results in the elimination of the imbalance. For these reactions, the contradictions disappear and the distinction between intrinsic and extrinsic aromaticity becomes unnecessary. As far as the sigma-pi partitioning is concerned, several schemes proposed in the literature are compared. Contradictory results are obtained depending on the partitioning scheme and reaction used. In this context, it is demonstrated that for the partitioning of the electron-electron interaction, the scheme introduced by Jug and K?ster is the one that is most theoretically grounded.     

Chemical graph theory and n-center electron delocalization indices: a study on polycyclic aromatic hydrocarbons

Relations between aromaticity indices derived from chemical graph theory and those based on 6-center electron delocalization are investigated for a series of polybenzenoid hydrocarbons. Aromatic stabilization obtained by means of the effective scaled electron delocalization is highly correlated to the resonance energy, RE, obtained both from SCF MO calculations and conjugated ring circuits model. Local aromaticity of benzene rings is discussed using two different criteria, in one of them aromaticity is just given by the cyclic pi-electron conjugation of the ring, whereas terms involving more than one ring are also considered in the other one. Indices derived from chemical graph theory and those obtained from the 6-center electron delocalization give rise to the same local aromaticity. Moreover, 6-center electron delocalization provides more quantitative information.     

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.     

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.     

Electronic Properties of Vinylene-Linked Heterocyclic Conducting Polymers: Predictive Design and Rational Guidance from DFT Calculations

The band structure and electronic properties in a series of vinylene-linked heterocyclic conducting polymers are investigated using density functional theory (DFT). In order to accurately calculate electronic band gaps, we utilize hybrid functionals with fully periodic boundary conditions to understand the effect of chemical functionalization on the electronic structure of these materials. The use of predictive first-principles calculations coupled with simple chemical arguments highlights the critical role that aromaticity plays in obtaining a low band gap polymer. Contrary to some approaches which erroneously attempt to lower the band gap by increasing the aromaticity of the polymer backbone, we show that being aromatic (or quinoidal) in itself does not ensure a low band gap. Rather, an iterative approach which destabilizes the ground state of the parent polymer toward the aromatic ? quinoidal level crossing on the potential energy surface is a more effective way of lowering the band gap in these conjugated systems. Our results highlight the use of predictive calculations guided by rational chemical intuition for designing low band gap polymers in photovoltaic materials.