Recursion Equations in Polycyclic Hydrocarbon Series and the Number of Dewar Long-Bond Resonance Structures with Applications

Basic recursion equations for characteristic and matching polynomials and the number of Dewar resonance structures for polycyclic polyene series are derived. Fibonacci-like series of numbers frequently appear in recursion and analytical expressions for determining resonance energy terms for polycyclic polyene series successively built up by given Aufbau units. Linear polycyclic polyene series built up from given Aufbau units usually give analytical expressions for determining their resonance energy terms. Polycyclic polyene series with all fixed pπ bonds (K = 1) have some aromatic stabilization energy as measured by topological resonance energy (TRE), which is explained by the appearance of sextet and larger aromatic circuits in some of their Dewar resonance structures (DS); note that DS can be read as singular (Dewar structure) or plural (Dewar structures) depending on the context. It is demonstrated that a finer evaluation of relative resonance energy and aromaticity requires the inclusion of both Dewar structures (DS) and Kekulé structures (K). In the valence-bond determination of bond lengths and aromaticity of polycyclic conjugated systems with fixed single and double bonds, the inclusion of Dewar resonance structures is required. Topological conjugation energy (TCE) for all series, whether they have all fixed pπ double bonds (K = 1) or numerous Kekulé resonance structures (K > 1), is very similar.

Endowing Polycyclic Aromatic Hydrocarbons with Induced Supramolecular Chirality by Engineering Cation-π Interaction

The cation-π interaction is a crucial noncovalent binding force prevalent in many biological and chemical systems, however, are rarely reported in chiral supramolecular systems. Here, a supramolecular chiral system is reported, wherein cation-π interaction play significant roles. The interaction involves a chiral cationic palladium complex (R-Pd) co-assembling with 12 different polycyclic aromatic hydrocarbons (PAHs), resulting in the formation of supramolecular gels in mixed solvents. This co-assembly induces supramolecular chirality in the PAHs, with cation-π interaction identified as the primary driving force. The confirmation of this interaction is supported by high-resolution mass, 1H NMR, nuclear overhauser effect spectroscopy (NOESY), XRD and CD. Most importantly, with the synergy of hydrogen bonds, the cation-π interaction can be stabilized in a mixed solvent containing water, leading the co-assembly to form supramolecular gel, as well as enhanced chiral induction of PAHs. This discovery serves as a proof-of-principle example showing how the weak cation-π interaction could be a powerful guide in attaining induced chirality of PAHs.

Comparison of Various Theoretical Measures of Aromaticity within Monosubstituted Benzene

The effects of monosubstitution on the aromaticity of benzene are assessed using a number of different quantitative schemes. The ability of the mobile π-electrons to respond to an external magnetic field is evaluated using several variants of the NICS scheme which calculate the shielding of points along the axis perpendicular to the molecule. Another class of measures is related to the drive toward the uniformity of C-C bond lengths and strengths. Several energetic quantities are devised to approximate an aromatic stabilization energy and the tendency of the molecule to maintain planarity. There is a lack of consistency in that the various measures of aromaticity lead to differing conclusions as to the effects of substituents on the aromaticity of the ring.

Aromaticity in the Electronic Ground and Lowest Triplet States of Molecules with Fused Thiophene Rings

Analysis of the variations of the off-nucleus isotropic magnetic shielding, σiso(r), around thiophene, thienothiophenes, dithienothiophenes and sulflowers in their electronic ground (S0) and lowest triplet (T1) states reveals that some of the features of aromaticity and bonding in these molecules do not fit in with predictions based on the popular Hückel's and Baird's rules. Despite having 4n π electrons, the S0 states of the sulflowers are shown to be aromatic, due to the local aromaticities of the individual thiophene rings. To reduce its T1 antiaromaticity, the geometry of thiophene changes considerably between S0 and T1: In addition to losing planarity, the carbon-carbon two 'double' and one 'single' bonds in S0 turn into two 'single' and one 'double' bonds in T1. Well-defined Baird-style aromaticity reversals are observed between the S0 and T1 states of only three of the twelve thiophene-based compounds investigated in this work, in contrast, the sulflower with six thiophene rings which is weakly aromatic in S0 becomes more aromatic in T1. The results suggest that the change in aromaticity between the S0 and T1 states in longer chains of fused rings is likely to affect mostly the central ring (or the pair of central rings); rings sufficiently far away from the central ring(s) can retain aromatic character.

Predicting a New Δ-Proton Sponge-Base of 4,12-Dihydrogen-4,8,12-triazatriangulene through Proton Affinity, Aromatic Stabilization Energy, and Aromatic Magnetism

Herein, we report designing a new Δ (delta-shaped) proton sponge base of 4,12-dihydrogen-4,8,12-triazatriangulene (compound 1) and calculating its proton affinity (PA), aromatic stabilization, natural bond orbital (NBO), electron density ρ(r), Laplacian of electron density ∇2 ρ(r), (2D-3D) multidimensional off-nucleus magnetic shielding (σzz (r) and σiso (r)), and scanning nucleus-independent chemical shift (NICSzz and NICS). Density functional theory (DFT) at B3LYP/6-311+G(d,p), ωB97XD/6-311+G(d,p), and PW91/def2TZVP were used to compute the magnetic shielding variables. In addition, relevant bases like pyridine, quinoline, and acridine were also studied and compared. The protonation of compound 1 yields a highly symmetric carbocation of three Hückel benzenic rings. Comparing our findings of the studied molecules showed that compound 1 precedes others in PA, aromatic isomerization stabilization energy, and basicity. Therefore, the basicity may be enhanced when a conjugate acid gains higher aromatic features than its unprotonated base. Both multidimensional σzz (r) and σiso (r) off-nucleus magnetic shieldings outperformed electron-based techniques and can visually monitor changes in aromaticity that occur by protonation. The B3LYP/6-311+G(d,p), ωB97XD/6-311+G(d,p), and PW91/def2TZVP levels showed no significant differences in detailing isochemical shielding surfaces.

On Integral INICS Aromaticity of Pyridodiazepine Constitutional Isomers and Tautomers

The structure, energetics, and aromaticity of c.a. 100 constitutional isomers and tautomers of pyrido[m,n]diazepines (m = 1, 2; n = 2, 3, 4, 5; m ≠ n) were studied at the B3LYP/cc-pVTZ level. The pyrido[1,3]diazepines appear the most, while pyrido[2,4]diazepines are the least stable (ca. 26 kcal/mol). In the pyrido[1,n]diazepine group (n = 2-5), the [1,5] isomers are higher in energy by ca. 4.5 kcal/mol and the [1,4] ones by ca. 7 kcal/mol, and the pyrido[1,2]diazepines are the least stable (ca. 20 kcal/mol). All the most stable pyrido[1,n]diazepines have N-atoms near the ring's junction bond but on opposite sites. The most stable [2,n]-forms are also those with the pyridine ring N6-atom near the junction bond. Surprisingly, for the [1,2]-, [1,3]-, and [1,4]-isomer condensation types of pyridine and diazepine rings, the same N9 > N7 > N6 > N8 stability pattern obeys. The stability remains similar in a water medium simulated with the Polarizable Continuum Model of the solvent and is conserved when calculated using the CAM-B3LYP or BHandHlyp functionals. The ring's aromaticity in the pyridine[m,n]diazepines was established based on the integral INICS index resulting from the NICSzz-scan curves' integration. The integral INICS index is physically justified through its relation to the ringcurrent as demonstrated by Berger, R.J.F., et al. Phys. Chem. Chem. Phys. 2022, 24, 624. The six-membered pyrido rings have negative INICSZZ indices and can be aromatic only if they are not protonated at the N-atom. All protonated pyrido and seven-membered rings exhibit meaningful positive INICSZZ values and can be assigned as antiaromatic. However, some non-protonated pyrido rings also have substantial positive INICSZZ indices and are antiaromatic. A weak linear correlation (R2 = 0.72) between the INICSZZ values of the pyridine I(6) and diazepine I(7) rings exists and is a consequence of the communication between the π-electron systems of the two rings. The juxtaposition of the INICS descriptor of the six- and seven-membered rings and diverse electron density parameters at the Ring Critical Points (RCP) revealed good correlations only with the Electrostatic Potentials from the electrons and nuclei (ESPe and ESPn). The relationships with other RCP parameters like electron density and its Laplacian, total energy, and the Hamiltonian form of kinetic energy density were split into two parts: one nearly constant for the six-membered rings and one linearly correlating for the seven-membered rings. Thus, most of the electron density parameters at the RCP of the six-membered rings of pyridodiazepines practically do not change with the diazepine type and the labile proton position. In contrast, those of the seven-membered rings display aromaticity changes in the antiaromatic diazepine with its ring structural modifications.

Interpretable Deep-Learning Unveils Structure-Property Relationships in Polybenzenoid Hydrocarbons

In this work, interpretable deep learning was used to identify structure-property relationships governing the HOMO-LUMO gap and the relative stability of polybenzenoid hydrocarbons (PBHs) using a ring-based graph representation. This representation was combined with a subunit-based perception of PBHs, allowing chemical insights to be presented in terms of intuitive and simple structural motifs. The resulting insights agree with conventional organic chemistry knowledge and electronic structure-based analyses and also reveal new behaviors and identify influential structural motifs. In particular, we evaluated and compared the effects of linear, angular, and branching motifs on these two molecular properties and explored the role of dispersion in mitigating the torsional strain inherent in nonplanar PBHs. Hence, the observed regularities and the proposed analysis contribute to a deeper understanding of the behavior of PBHs and form the foundation for design strategies for new functional PBHs.

Frontier Orbital Views of Stacked Aromaticity

Recent studies have theoretically and experimentally demonstrated that antiaromatic molecules with 4n π electrons exhibit stacked aromaticity according to π-π stacking when arranged in a face-to-face manner. However, the mechanism of its occurrence has not been clearly studied. In this study, we investigated the mechanism of stacked aromaticity using cyclobutadiene. When the antiaromatic molecules are stacked in a face-to-face manner, the orbital interactions between the degenerate singly occupied molecular orbitals (SOMOs) of the monomer unit cause a larger energy gap between the degenerate highest-occupied molecular orbitals (HOMOs) and the lowest-unoccupied molecular orbitals (LUMOs) of the dimer. However, the antiaromatic molecules are more stable in less symmetric conformations, mainly because of pseudo-Jahn-Teller distortions. In the case of cyclobutadiene, the two SOMOs of the monomer unit split into HOMO and LUMO because of the bond alternation. When the molecules are stacked in a face-to-face manner, the HOMO-LUMO gap of the dimer is smaller than that of the monomer due to the interactions between the HOMOs and LUMOs of the two monomer units. When the monomer units are within a specific distance of each other, the HOMO and LUMO of the dimer, which correspond to antibonding and bonding between the units, respectively, are interchanged. This alternation of molecular orbitals may result in an increase in the bond strength between the monomer units, exhibiting stacked aromaticity. We demonstrated that it is possible to control the distance exhibited by stacked aromaticity by engineering the HOMO-LUMO gap of the monomer units.

Synthesis of Defective Nanographenes Containing Joined Pentagons and Heptagons

Defective nanographenes containing joined pentagons and heptagons exhibit striking physicochemical properties from both experimental and theoretical perspectives compared with their pure hexagonal counterparts. Thus, the synthesis and characterization of these unique polyarenes with well-defined defective topologies have attracted increasing attention. Despite extensive research on nonalternant molecules since the last century, most studies focused on the corresponding mutagenic and carcinogenic activities. Recently, researchers have realized that the defective domain induces geometric bending and causes electronic perturbation, thus leading to significant alteration of the photophysical properties. This review discusses the synthesis and characterization of small nonalternant polycyclic hydrocarbons in the early stage and recent developments in embedding pentagon-heptagon (5-7) pairs into large carbon skeletons through in-solution chemistry.

Aromaticity Concepts Derived from Experiments

Aromaticity, a very important term in organic chemistry, has never been defined unambiguously. Various ways to describe it come from different phenomena that have been experimentally observed. The most important examples related to some theoretical concepts are presented here.

On Aromaticity of the Aromatic α-Amino Acids and Tuning of the NICS Indices to Find the Aromaticity Order

The NICS aromaticity indices of the rings in flexible phenylalanine (Phe), tryptophan (Trp), tyrosine (Tyr), and histidine (His) chiral molecules were analyzed. These molecules have several dozens of conformers, and their rings are slightly non-planar. Therefore, the population-averaged NICS_pav index was defined, and the NICS scans had to be performed with respect to planes found by the least-squares routine. A rule differentiating an obverse and a reverse ring face in aromatic amino acids was formulated. The NICS scan minima corresponding to the obverse and reverse face were unequal, which prompted us to use the term ring face aromaticity/ring face tropicity. It appeared that for Phe, Trp, Tyr, and His, the reverse face has always had higher ring face aromaticity/ring face tropicity than the obverse one. Despite the NICS modifications, uncertainty about the amino acid aromaticity order remained. This motivated us to use the integral INICS index newly proposed by Stanger as well. Then, the following sequence was obtained: Trp(phenyl) > Phe > Trp(pyrrole) > His > Tyr. The juxtaposition of the INICS indices of amino acids with that of some model rings revealed a fair transferability of the values. Finally, analysis of the substituent effect on INICS demonstrated that the aromaticity of Tyr is the lowest due to the strength of the OH group π-electron-donating effect able to perturb enough the ring charge distribution and its magnetic aromaticity. The NICS calculations were executed using the ARONICS program written within the project.

Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D?

Several fully π-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored hitherto should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for tetrahedral or octahedral molecules, an aromatic closed-shell electronic structure with 6n + 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel’s 4n + 2 rule for each macrocyclic path, yet their π-electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., with π-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic π-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite the fact that these molecules show substantial π-electron delocalization, they cannot be classified as true 3D-aromatics.

Quantitative Resonance Theory Based on the Clar Sextet Model

Despite its great explanatory power in understanding the chemistry of polycyclic aromatic hydrocarbons (PAHs) and related systems, the Clar sextet rule still remains an intuitive and qualitative model with notable exceptions in some cases. Here we develop a quantitative theory of chemical resonance based on semilocalized Clar-type resonance structures (named the Clar resonators) consisting of variable numbers of Clar sextets and C═C bonds. The constructed wave functions of the Clar resonators are used to expand the actual wave function of the π-conjugated system obtained from a DFT or Hartree-Fock calculation. The resultant weights and one-electron energies of the Clar resonators can serve as a quantitative measure of the importance of these resonators. Implementing the theory in our open-source python code EzReson and applying it to over a thousand PAH molecules of different sizes and shapes, we show that the weight of the Clar resonators increases exponentially with increasing number of sextets and that their energy decreases linearly with the latter, thus confirming the general validity of the Clar rule. On the basis of such a large-scale resonance analysis, we propose three extended Clar rules, along with a unified quantitative model, that are able to evaluate the importance of all Clar resonators and the ring aromaticity for PAHs. Using the present theories, we uncover the essential role that the minor Clar resonators may play in correctly understanding the resonance stabilization and local aromaticity of rings, which was totally overlooked in the original Clar model.

Symmetry and Combinatorial Concepts for Cyclopolyarenes, Nanotubes and 2D-Sheets: Enumerations, Isomers, Structures Spectra & Properties

This review article highlights recent developments in symmetry, combinatorics, topology, entropy, chirality, spectroscopy and thermochemistry pertinent to 2D and 1D nanomaterials such as circumscribed-cyclopolyarenes and their heterocyclic analogs, carbon and heteronanotubes and heteronano wires, as well as tessellations of cyclopolyarenes, for example, kekulenes, septulenes and octulenes. We establish that the generalization of Sheehan’s modification of Pólya’s theorem to all irreducible representations of point groups yields robust generating functions for the enumeration of chiral, achiral, position isomers, NMR, multiple quantum NMR and ESR hyperfine patterns. We also show distance, degree and graph entropy based topological measures combined with techniques for distance degree vector sequences, edge and vertex partitions of nanomaterials yield robust and powerful techniques for thermochemistry, bond energies and spectroscopic computations of these species. We have demonstrated the existence of isentropic tessellations of kekulenes which were further studied using combinatorial, topological and spectral techniques. The combinatorial generating functions obtained not only enumerate the chiral and achiral isomers but also aid in the machine construction of various spectroscopic and ESR hyperfine patterns of the nanomaterials that were considered in this review. Combinatorial and topological tools can become an integral part of robust machine learning techniques for rapid computation of the combinatorial library of isomers and their properties of nanomaterials. Future applications to metal organic frameworks and fullerene polymers are pointed out.

Aromaticity of Heterocirculenes

This review summarizes the results on the aromaticity of a series of synthesized and hypothetical neutral heterocirculene molecules and their double charged ions. The aromaticity of heterocirculenes is a direct reflection of their electronic structure responsible for the specific optoelectronic and photophysical properties. We show how the presence of a heteroatom in the outer macrocycle affects the aromaticity of hetero[8]circulenes. In addition, we also describe the change in aromaticity and strain energy for a series of the “lower” (n < 8) and “higher” (n > 8) hetero[n]circulenes. It was demonstrated that the loss of planarity with increased strain leads to an increased antiaromaticity of the lower hetero[n]circulenes, whereas higher hetero[n]circulenes demonstrate a more pronounced aromatic nature because of the small departure from planarity of each heteroarene ring in hetero[n]circulene molecule. Finally, we discuss the aromatic nature of the first examples of π-extended hetero[8]circulenes.

Assessment of the Performance of the Bond Resonance Energy, Circuit Resonance Energy, Magnetic Resonance Energy, Ring Currents, and Aromaticity of Anthracene, Biphenylene, Phenalenyl, and p-Terphenyl

This paper contributes to the further understanding of bond resonance energy (BRE), circuit resonance energy (CRE), and ring currents (RC = I) as indices for the measure of local ring aromaticity and topological resonance energy (TRE) and magnetic resonance energy (MRE) as indices for the measure of global molecular aromaticity. Calculations of ring currents in the 3-ring polycyclic hydrocarbons of anthracene, biphenylene, phenalenyl, and p-terphenyl are demonstrated. This comparative study provides new molecular insights. A number of shortcut techniques are briefly illustrated. p-Terphenyl is a benzenoid total resonant sextet (TRS) and biphenylene is shown to be a nonbenzenoid TRS, i.e., both obey Clar's sextet principle. p-Terphenyl has only ring circuits, whereas anthracene, biphenylene, and phenalenyl have ring circuits and larger circuits engulfing the ring circuits. The perimeter circuits of anthracene, biphenylene, and phenalenyl engulf all other circuits, thus leading to the definition of MRE. By these several aromatic indices, the monocation, monoanion, and monoradical of phenalenyl are equally aromatic. The agreement in the prediction of local ring aromaticity between the three indices of m-BRE, t-BRE, and CRE is evaluated.

Topology Effects in Molecular Organic Electronic Materials: Pyrene and Azupyrene*

Pyrene derivatives play a prominent role in organic electronic devices, including field effect transistors, light emitting diodes, and solar cells. The flexibility in the desired properties has previously been achieved by variation of substituents at the periphery of the pyrene backbone. In contrast, the influence of the topology of the central π‐electron system on the relevant properties such as the band gap or the fluorescence behavior has not yet been addressed. In this work, pyrene is compared with its structural isomer azupyrene, which has a π‐electron system with non‐alternant topology. Using photoelectron spectroscopy, near edge X‐ray absorption fine structure spectroscopy, and other methods, it is shown that the electronic band gap of azupyrene is by 0.72 eV smaller than that of pyrene. The difference of the optical band gaps is even larger with 1.09 eV, as determined by ultraviolet–visible absorption spectroscopy. The non‐alternant nature of azupyrene is also associated with a more localized charge distribution. Further insight is provided by density functional theory (DFT) calculations of the molecular properties and ab initio coupled cluster calculations of the optical transitions. The concept of aromaticity is used to interpret the major topology‐related differences.

Triplet State Baird Aromaticity in Macrocycles: Scope, Limitations, and Complications

The aromaticity of cyclic 4nπ-electron molecules in their first ππ* triplet state (T1), labeled Baird aromaticity, has gained growing attention in the past decade. Here we explore computationally the limitations of T1 state Baird aromaticity in macrocyclic compounds, [n]CM's, which are cyclic oligomers of four different monocycles (M = p-phenylene (PP), 2,5-linked furan (FU), 1,4-linked cyclohexa-1,3-diene (CHD), and 1,4-linked cyclopentadiene (CPD)). We strive for conclusions that are general for various DFT functionals, although for macrocycles with up to 20 π-electrons in their main conjugation paths we find that for their T1 states single-point energies at both canonical UCCSD(T) and approximative DLPNO-UCCSD(T) levels are lowest when based on UB3LYP over UM06-2X and UCAM-B3LYP geometries. This finding is in contrast to what has earlier been observed for the electronic ground state of expanded porphyrins. Yet, irrespective of functional, macrocycles with 2,5-linked furans ([n]CFU's) retain Baird aromaticity until larger n than those composed of the other three monocycles. Also, when based on geometric, electronic and energetic aspects of aromaticity, a 3[n]CFU with a specific n is more strongly Baird-aromatic than the analogous 3[n]CPP while the magnetic indices tell the opposite. To construct large T1 state Baird-aromatic [n]CM's, the design should be such that the T1 state Baird aromaticity of the macrocyclic perimeter dominates over a situation with local closed-shell Hückel aromaticity of one or a few monocycles and semilocalized triplet diradical character. Monomers with lower Hückel aromaticity in S0 than benzene (e.g., furan) that do not impose steric congestion are preferred. Structural confinement imposed by, e.g., methylene bridges is also an approach to larger Baird-aromatic macrocycles. Finally, by using the Zilberg-Haas description of T1 state aromaticity, we reveal the analogy to the Hückel aromaticity of the corresponding closed-shell dications yet observe stronger Hückel aromaticity in the macrocyclic dications than Baird aromaticity in the T1 states of the neutral macrocycles.

A study on the aromaticity and magnetic properties of N-confused porphyrins

In this paper, topological resonance energy (TRE) methods were used to describe the global aromaticity of nitrogen confused porphyrin (NCP) isomers. The TRE results show that all NCP isomers exhibit lower aromaticity than the normal porphyrins, and their aromaticity decreases as the number of confused pyrrole rings in the molecule increases. In the NCPs, global aromaticity decreases as the distance between the nitrogen atoms increases. The bond resonance energy (BRE) and circuit resonance energy (CRE) indices were applied to study local aromaticity and conjugated pathways. Both the BRE and CRE indices revealed that individual pyrrolic subunits maintain their strong aromatic character and are the main source of global aromaticity. Ring currents (RC) were analysed using the Hückel-London model. RC results revealed that the macrocyclic electron conjugation pathway is the main source of diatropicity. As the number of confused pyrrole rings in the molecule increases, its diatropicity gradually decreases. In the confused pyrrole rings of the NCP isomers, the diatropic RC passing through the β-positions is always weaker than that passing through the inner sections. This is unrelated to the location of the protonated or non-protonated nitrogen atom at the periphery of the molecule and must be ascribed to the unique properties of the confused pyrrole rings.

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 (-CH₂-) 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. Both nucleus-independent chemical shift (NICS) and bond resonance energy (BRE) values support this interpretation. Bond resonance energy has been used to determine local ring aromaticity in nonalternant hydrocarbons, alternant hydrocarbons, heterocyclic conjugated molecules, fullerenes, pure boron clusters, and porphyrins. This contribution represents the first application of bond resonance energy toward the evaluation of σ-aromaticity/σ-antiaromaticity of polycyclic alkanes.

A study on the aromatic conjugation pathways and the ring currents of bridged [18]annulenes

In this article, the topological resonance energy (TRE) method was used to investigate the global aromaticity of a set of [18]annulene-derived compounds which were obtained by replacing either two, four, or all six of the inner hydrogen atoms of [18]annulene with bridges (oxygen, imino-, sulfur, or combinations of the three). Our TRE results show that all the mono-bridged, di-bridged, and tri-bridged [18]annulenes are globally aromatic systems with positive TREs and show relatively larger aromaticity in comparison with the [18]annulene. The aromaticity of each compound was explained using the topological charge stabilization (TCS) rule. The bond resonance energy (BRE) and circuit resonance energy (CRE) methods were used to evaluate local aromaticity. Our BRE and CRE results show that incorporation of five-membered heterocyclic rings changes the main conjugation pathway of the bridged [18]-annulenes. The local aromaticities arising from the five-membered heterocyclic rings (6π) contribute strongly to global aromaticity. However, the ring current (RC), which arises from the 18π annulene-like pathway structures, is the primary determinant of the magnetic properties of the molecule. Our RC results are in good agreement with available ¹H-NMR chemical shift data.

The topological resonance energy method was used to investigate the global aromaticity of a set of [18]annulene-derived compounds obtained by replacing two, four, or all six of the inner hydrogen atoms with bridges (oxygen, imino-, sulfur, or combinations of the three).

Combinatorial Enumeration of Isomers of Superaromatic Polysubstituted Cycloarenes and Coronoid Hydrocarbons with Applications to NMR

We have employed combinatorial techniques based on character cycle indices, Pólya's theory, and Euler totem function to enumerate isomers of polysubstituted cycloarenes and coronoid hydrocarbons which have been receiving considerable attention because of their superaromaticity, ring currents, and interesting magnetic properties. Systematic enumeration and construction of tables of polysubstituted isomers such as fluoro-chloro superaromatic hydrocarbons are considered as they are of interest in the study of environmental pollutants and toxicity. Isomers of fluoro-chloro polysubstituted donut shaped circumkekulenes, circumseptulenes, circumoctulenes, etc., are enumerated in addition to other cycloarenes, polycyclic circumcoronaphenes and coronoids. Applications to ¹³C NMR, proton NMR and multiple quantum NMR spectroscopies of these superaromatic species are considered.

Practical Tight-Binding Hückel-Like Modeling of Electronic Properties of Saturated Hydrocarbons: On σ-Aromaticity of Cyclopropane and Correlations of Alkane Ionization Energies and Enthalpies of Formation Corrected for Protobranching

This testing of σ-aromaticity in cyclopropane and protobranching in alkanes via a Hückel-like model proposed by Klein and Larson is expedited by mirror-plane fragmentation per the method of McClelland originally developed for conjugated polyenes. Alkane carbon sp³ orbitals are represented by edge weighted tetrahedral stellate graphs connected to hydrogen orbitals.

The predictive power of aromaticity: quantitative correlation between aromaticity and ionization potentials and HOMO–LUMO gaps in oligomers of benzene, pyrrole, furan, and thiophene

The aromaticity of oligomers predicts their HOMO–LUMO gaps and ionization potentials.

The role of the long-range exchange corrections in the description of electron delocalization in aromatic species

In this article, we address the role of the long-range exchange corrections in description of the cyclic delocalization of electrons in aromatic systems at the density functional theory level. A test set of diversified monocyclic and polycyclic aromatics is used in benchmark calculations involving various exchange-correlation functionals. A special emphasis is given to the problem of local aromaticity in acenes, which has been a subject of long-standing debate in the literature. The presented results indicate that the noncorrected exchange-correlation functionals significantly overestimate cyclic delocalization of electrons in heteroaromatics and aromatic systems with fused rings, which in the case of acenes leads to conflicting local aromaticity predictions from different criteria. © 2017 Wiley Periodicals, Inc.