Bond Resonance Energy Verification of σ-Aromaticity in Cycloalkanes.

The Klein-Larson bonding model is best suited for describing σ-conjugation and σ-aromaticity of cycloalkanes. Methylene groups (-CH-) in cycloalkanes are isoconjugates with ethylene groups (-CH═CH-) in annulenes, both contributing two electrons to cyclic conjugation and aromaticity. As in the case of π-aromatic stabilization, σ-aromatic stabilization must be associated with ring-current diamagnetism.

Excited-State Intramolecular Proton Transfer and Global Aromaticity.

A general survey of excited-state intramolecular proton transfer (ESIPT) processes was made from the viewpoint of global aromaticity. For most ESIPT processes studied, a tautomeric product in the first excited electronic state was found to have a larger topological resonance energy (TRE) than the reactant in the same excited state. Conversely, if a transient tautomer is much less aromatic in the excited state than the reactant, an appreciable aromaticity-imposed energy barrier to the reaction will result.

Aromatic Character of Irregular-Shaped Nanographenes.

We found that the Clar sextet formula with the maximum number of sextet rings cannot always be defined meaningfully for large irregular-shaped PAHs. It is true that edge structure is always a primary determinant of the PAH aromaticity pattern. In large PAH molecules, every edge structure modifies the aromaticity pattern near the edge, but its influence fades on going away from the edge.

Magnetic resonance energy and topological resonance energy.

Ring-current diamagnetism of a polycyclic π-system is closely associated with thermodynamic stability due to the individual circuits. Magnetic resonance energy (MRE), derived from the ring-current diamagnetic susceptibility, was explored in conjunction with graph-theoretically defined topological resonance energy (TRE). For many aromatic molecules, MRE is highly correlative with TRE with a correlation coefficient of 0.

Kinetic Stability of Non-IPR Fullerene Molecular Ions.

Many fullerenes that violate the isolated pentagon rule (IPR) form stable metallofullerenes. In general, a fullerene cage is kinetically stabilized by acquiring a given number of electrons. Kinetic stability of negatively charged non-IPR fullerenes, including the recently isolated endohedral metallofullerene with a heptagonal face, was rationalized in terms of bond resonance energy (BRE).

Origin of kinetic instability of fullerenes that violate the isolated pentagon rule.

The isolated pentagon rule (IPR) holds without exceptions for neutral fullerene molecules. Unlike those in non-IPR fullerenes, 5/5 bonds (i.e.

Aromatic character of nanographene model compounds.

Superaromatic stabilization energy (SSE) defined to estimate the degree of macrocyclic aromaticity can be used as a local aromaticity index for individual benzene rings in very large polycyclic aromatic hydrocarbons (PAHs) and finite-length graphene nanoribbons. Aromaticity patterns estimated using SSEs indicate that the locations of both highly aromatic and reactive rings in such carbon materials are determined primarily by the edge structures. Aromatic sextets are first placed on the jutting benzene rings on armchair edges, if any, and then on inner nonadjacent benzene rings.

Constrained Clar formulas of coronoid hydrocarbons.

Aromatic character of coronoid hydrocarbons is greatly influenced by the shapes of outer and inner peripheries. The most aromatic rings in coronoids are jutting benzene rings on the armchair edges, if any. Clar formulas of many coronoids conform to the aromaticity patterns.

Superaromatic stabilization energy as a novel local aromaticity index for polycyclic aromatic hydrocarbons.

Superaromatic stabilization energy (SSE), previously proposed by us, can be used as a novel local aromaticity index for benzene rings in polycyclic aromatic hydrocarbons (PAHs). SSE can be interpreted as the first local aromaticity index explicitly related to all relevant circuits in a polycyclic π-system, an origin of local aromaticity, being free of local aromaticity arising from adjacent six-site circuits. Therefore, this quantity is best suited for characterizing the electronic structure of large pericondensed PAHs and graphene nanoflakes.

Analytical study of superaromaticity in cycloarenes and related coronoid hydrocarbons.

Recently synthesized septulene is a unique cycloarene molecule in that no macrocyclic conjugation circuits can be chosen from the π-system. This molecule has essentially no superaromatic stabilization energy (SSE) and can be viewed as an ideal nonsuperaromatic macrocycle. SSEs for kekulene and other cycloarenes are also very small.

Validity and limitations of the bridged annulene model for porphyrins.

According to the bridged annulene model, macrocyclic aromaticity of a porphyrinoid species can be attributed to the annulene-like main macrocyclic conjugation pathway (MMCP). Macrocyclic aromaticity, however, is given theoretically as a sum of contributions from all macrocyclic circuits. We found that the aromaticity due to each macrocyclic circuit is determined formally but broadly by Hückel's [4n + 2] rule of aromaticity.

Macrocyclic aromaticity of porphyrin units in fully conjugated oligoporphyrins.

Individual porphyrin macrocycles in fully conjugated oligoporphyrins exhibit different degrees of macrocyclic aromaticity. We proposed a theoretical method for estimating the degrees of macrocyclic aromaticity of these porphyrin units. This method, based on the concept of bond resonance energy, is applicable to all types of porphyrin oligomers.

The origin of global and macrocyclic aromaticity in porphyrinoids.

The global and macrocyclic aromaticity of porphyrinoids was characterized using our graph theory of aromaticity. The sequential line plots of topological resonance energy (TRE) against the number of π-electrons (N(π)) for different porphyrinoids are similar with four major extrema to those for five-membered heterocycles. This supports the view that five-membered rings are the main origin of global aromaticity in porphyrinoids.

Electronic and magnetic characteristics of polycyclic aromatic hydrocarbons with factorizable Kekulé structure counts.

The Kekulé structure count (K) for some types of polycyclic aromatic hydrocarbons (PAHs), such as fluoranthene and perylene, can be factorized into the product of those for two or more aromatic subunits. The ring-current map for these PAHs placed in a perpendicular magnetic field exhibits a substantial localization on aromatic subunits. We found that such localization of π circulation is a characteristic of fairly small K-factorizable species in the neutral electronic state.

Aromatic character of polycyclic π systems formed by fusion of two or more rings of the same size.

The sequential line plot of topological resonance energy (TRE) against the number of π electrons (N(π)) for any polycyclic aromatic hydrocarbon (PAH) is very similar with the same number of extrema to that for benzene. Thus, global aromaticity of a PAH molecular ion strongly reflects that of a benzene molecular ion. Likewise, the N(π) dependence of TRE for any polycyclic π system formed by fusion of two or more rings of the same size reflects that for a monocyclic species of the same ring size.

Unusually high aromaticity and diatropicity of bond-alternate benzene.

Enormous effort has been devoted to the elucidation of possible effects of bond-length alternation on the benzene pi-system. Benzene tends to stay highly aromatic and highly diatropic even if strong bond-length alternation is introduced artificially into the pi-system. Such peculiar aromatic and magnetic characters of benzene were justified consistently and unambiguously within a single theoretical framework.

Graph-topological approach to magnetic properties of benzenoid hydrocarbons.

Application of topological properties and graph theory to benzenoid hydrocarbons allowed us to construct an effective approach interpreting ring current formation in molecules when exposed to an external magnetic field. Transformation of unexcited canonical structures for molecules of 34 benzenoid hydrocarbons into circuit structures and then to directed circuit structures allowed us to define global magnetic characteristics (GMC). GMC/n(2) values correlate very well with exaltation of magnetic susceptibility DeltaLambda/n(2) (computed at the CSGT/B3LYP/6-311G** level of theory by using optimized geometries at the B3LYP/6-311G** DFT level) with cc = 0.

Prediction of the main macrocyclic conjugation pathway for porphyrinoids from the ring current distribution.

For some porphyrinoids, such as orangarin and amethyrin, the main route of macrocyclic pi-circulation is different from the main macrocyclic conjugation pathway predicted by porphyrin chemists. Our analytical theory of ring-current diamagnetism allows us to predict the main macrocyclic conjugation pathway from the ring current distribution. We can now interpret macrocyclic aromaticity and macrocyclic circulation consistently within the same theoretical framework.

Aromaticity of neutral and doubly charged polyacenes.

The aromatic character of neutral and doubly charged polyacenes was explored in terms of the harmonic oscillator model of aromaticity (HOMA) and bond resonance energy (BRE). Doubly charged species of polyacenes are different in global and local aromaticity from the neutral species. Neutral species are fairly uniform in local aromaticity, whereas doubly charged species are more aromatic in the edge rings than in the central rings.

Macrocyclic aromaticity in Hückel and Möbius conformers of porphyrinoids.

Macrocyclic aromaticity is one of the key concepts in porphyrin chemistry. The degree of macrocyclic aromaticity and the associated main macrocyclic conjugation pathway in Hückel- and Möbius-type porphyrinoids were determined using our recently proposed procedure based on bond resonance energy (BRE). All porphyrinoids with diatropic and paratropic macrocycles were found to have positive and negative superaromatic stabilization energies (SSEs), respectively.

Origin of stacked-ring aromaticity.

Although strong diatropic currents run in the pi-stacked dimers of 4n pi annulenes, they are still antiaromatic with negative topological resonance energies (TREs). The TRE difference between two annulene molecules and the pi-stacked annulene dimer can be used as a practical measure of stacked-ring aromaticity. As predicted by Corminboeuf et al.

Macrocyclic conjugation in N-fused porphyrins and related species.

Macrocyclic aromaticity is the most important concept in porphyrin chemistry. We propose a general graph-theoretical procedure for predicting the main macrocyclic conjugation pathway in porphyrinoids. This procedure, based on calculated bond resonance energies (BREs), can be applied not only to natural and expanded porphyrins but also to porphyrinoids with fused rings.

Macrocyclic conjugation pathways in porphyrins.

Macrocyclic aromaticity is the most important concept in porphyrinoid chemistry. Bond resonance energy (BRE) for any pi-bond linking adjacent pyrrolic or other rings represents the stabilization energy due to macrocyclic aromaticity. We found that a main conjugation pathway associated with macrocyclic aromaticity can be traced by choosing a pi-bond with a larger BRE at every bifurcation of the pi-network.

A simple method for estimating the superaromatic stabilization energy of a super-ring molecule.

A simple graph-theoretical method is proposed for readily estimating the degree of extra stabilization due to macrocyclic conjugation (superaromaticity). This method is based theoretically on the concept of circuit resonance energy previously defined for cyclic pi systems. We confirmed that kekulene and related super-ring molecules are essentially nonsuperaromatic, with very small superaromatic stabilization energies.

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.