Three Queries about the HOMA Index

A Negatively Curved Nanographene with Four Embedded Heptagons

Negatively curved nanographenes are considered as cutouts of three-dimensional fully sp2-hybridized carbon allotropes such as Schwarzites. Here we present the synthesis of a C76 cut-out of the Schwarzite 8-4-1-p proposed by Lenosky et al. and investigate its optical as well as electrochemical properties. Furthermore, supramolecular interactions with fullerenes C60 and C70 were studied.

Excited-state aromaticity reversals in norcorrole

Aromaticity reversals between the electronic ground state (S0) and the lowest triplet (T1) and singlet (S1) excited states of NiII norcorrole (NiNc) and norcorrole (H2Nc) are investigated by comparing the HOMA (harmonic oscillator model of aromaticity) values at the optimized S0, T1 and S1 geometries, and by analysing the changes in the nucleus-independent chemical shift (NICS) values and in the isotropic magnetic shielding distributions between the S0 and T1 states. The results strongly suggest that the antiaromatic features of the S0 states of the NiNc and H2Nc molecules, two very similar antiaromatic "internal crosses", undergo aromaticity reversals upon excitation to T1 or S1 and merge with the aromatic peripheries to produce Baird-aromatic systems with 24 π electrons each. Somewhat counterintuitively, the geometries of the fully aromatic T1 and S1 states of NiNc and H2Nc turn out to have larger bowl depths and so are more non-planar than the corresponding S0 geometries at which both molecules display antiaromatic features.

Unveiling Carbon Cluster Coating in Graphene CVD on MgO: Combining Machine Learning Force field and DFT Modeling

In this study, we investigate the behavior of carbon clusters (Cn, where n ranges from 16 to 26) supported on the surface of MgO. We consider the impact of doping with common impurities (such as Si, Mn, Ca, Fe, and Al) that are typically found in ores. Our approach combines density functional theory calculations with machine learning force field molecular dynamics simulations. It is found that the C21 cluster, featuring a core-shell structure composed of three pentagons isolated by three hexagons, demonstrates exceptional stability on the MgO surface and behaves as an "enhanced binding agent" on MgO-doped surfaces. The molecular dynamics trajectories reveal that the stable C21 coating on the MgO surface exhibits less mobility compared to other sizes Cn clusters and the flexible graphene layer on MgO. Furthermore, this stability persists even at temperatures up to 1100K. The analysis of the electron localization function and potential function of Cn on MgO reveals the high localization electron density between the central carbon of the C21 ring and the MgO surface. This work proposes that the C21 island serves as a superstable and less mobile precursor coating on MgO surfaces. This explanation sheds light on the experimental defects observed in graphene products, which can be attributed to the reduced mobility of carbon islands on a substrate that remains frozen and unchanged.

Rational Design of Cyclopentadiene-Based Super- and Hyperacids Based on Aromaticity

The design and synthesis of neutral organic superacids have been of interest recently due to their vast applications in chemistry and material sciences, for example, olefinic polymerization, isolation of highly reactive short-lived cations, etc. Cyclopentadiene behaves as a mild organic acid, producing a stable conjugate base by gaining aromaticity and conjugation after deprotonation. To stabilize conjugate bases of organic acids to show superacidities and hyperacidities, we considered aromatic phenyl substituents with cyclopentadiene (mono-, di-, and triphenyl-substituted cyclopentadiene and their cyano derivatives). The MP2, DFT (B3LYP, M06-2X), and CBS-QB3 methods were used to calculate the gas-phase proton affinities of the parent cyclopentadiene, and the DFT methods were chosen for the substituted cyclopentadiene as they yield an experimental proton affinity of cyclopentadiene of 253.66 kcal/mol (Expt. 253.6 ± 1.3 kcal/mol). The stable trisubstituted cyclopentadiene derivative shows gas-phase enthalpies of deprotonation (ΔHacid) of 245 and 239 kcal/mol with DFT B3LYP and M06-2X methods, respectively, with values in the range of hyperacidity. Some of the tautomers of cyclopentadiene derivatives show hyperacidity, with proton affinity values of 205-240 kcal/mol. Triphenyl-substituted cyclopentadiene behaves as a moderate acid but transforms into a superacid after replacing the phenyl group with nitrobenzene, which is a stronger acid than H2SO4 (ΔHacid = 298 kcal/mol). The nucleus-independent chemical shift (NICS) shows the extent of conjugation in the derivatives of cyclopentadienyl anions after deprotonation, which affects the stabilities of conjugate bases, i.e., the acidities of the protonated species. The calculated harmonic oscillator model of aromaticity and NICS indices reveal that the stability of conjugate bases as well as their acidities increase with increasing aromaticity of cyclopentadiene rings after deprotonation in all molecules.

Electronic Current Density Induced by Uniform Magnetic Fields in Clarenes

Some planar and non-planar clarenes have been studied using maps of magnetically induced quantum-mechanical current density and tools from differential topology to assess their magnetic response in connection with recent results by Du and Wang. Bond current strengths have been computed to estimate quantitative measures. Isosurfaces of the divergence of induced Lorentz force density have been shown to provide useful additional criteria, especially in the case of non-planar clarenes.

Width effects on bilayer graphene nanoribbon polarons

Recent progress in nanoelectronics suggests that stacking armchair graphene nanoribbons (AGNRs) into bilayer systems can generate materials with emergent quasiparticle properties. In this context, the impact of width changes is especially relevant. However, its effect on charged carriers remains elusive. In this work, we investigate the effect of width and interlayer interaction changes on polaron states via a hybrid Hamiltonian that couples the electronic and lattice interactions. Results show the rising of two interlayer polarons: the non-symmetric and the symmetric. The coupling strength needed to induce the transition between states depends on the nanoribbon width, being at the most extreme case of ≈174 meV. Electronic properties such as the coupling strength threshold, carrier size, and gap are shown to respect the AGNR width family 3p, 3p + 1, and 3p + 2 rule. The findings demonstrate that strong interlayer interaction simultaneously delocalizes the carriers and reduces the gap up to 0.6 eV. Additionally, it is found that some layers are more prone to share charge, indicating a potential heterogeneous stacking where a particular electronic pathway is favored. The results present an encouraging prospect for integrating AGNR bilayers in future flexible electronics.

Unraveling the effect of aromaticity for the dynamics of excited states of single benzene fluorophores

The photophysical properties of a series of recently synthesized single benzene fluorophores were investigated using ensemble density functional theory calculations. The energetic stability of the ground and excited state species were counterposed against the aromaticity index derived from local vibrational modes. It was found that the large Stokes shift of the fluorophores (up to ca. 5800 cm  - 1 ) originates from the effect of electron donating and electron withdrawing substituents rather than π -delocalization and related (anti-)aromaticity. On the basis of nonadiabatic molecular dynamics simulations, the absence of fluorescence from one of the regioisomers was explained by the occurrence of easily accessible S  1 /S  0 conical intersections below the vertical excitation energy level. It is demonstrated in the manuscript that the analysis of local mode force constants and the related aromaticity index represent a useful tool for the characterization of π -delocalization effects in π -conjugated compounds.

A multi-descriptor analysis of substituent effects on the structure and aromaticity of benzene derivatives: π-Conjugation versus charge effects

This work provides a detailed multi-component analysis of aromaticity in monosubstituted (X = CH3, CH 2 - , CH 2 + , NH2, NH-, NH+, OH, O-, and O+) and para-homodisubstituted (X = CH3, CH2, NH2, NH, OH, and O) benzene derivatives. We investigate the effects of substituents using single-reference (B3LYP/DFT) and multireference (CASSCF/MRCI) methods, focusing on structural (HOMA), vibrational (AI(vib)), topological (ELFπ), electronic (MCI), magnetic (NICS), and stability (S0-T1 splitting) properties. The findings reveal that appropriate π-electron-donating and π-electron-accepting substituents with suitable size and symmetry can interact with the π-system of the ring, significantly influencing π-electron delocalization. While the charge factor has a minimal impact on π-electron delocalization, the presence of a pz orbital capable of interacting with the π-electron delocalization is the primary factor leading to a deviation from the typical aromaticity characteristics observed in benzene.

Switchable Design of Redox-Enhanced Nonaromatic Quinones Enabled by Conjugation Recovery

An innovative switchable design strategy for modulating the electronic structures of quinones is proposed herein, leading to remarkably enhanced intrinsic redox potentials by restoring conjugated but nonaromatic backbone architectures. Computational validation of two fundamental hypotheses confirms the recovery of backbone conjugation and optimal utilization of the inductive effect in switched quinones, which affords significantly improved redox chemistry and overall performance compared to reference quinones. Geometric and electronic analyses provide strong evidence for the restored backbone conjugation and nonaromaticity in the switched quinones, while highlighting the reinforcement of the inductive effect and suppression of the resonance effect. This strategic approach facilitates the development of an exceptional quinone, viz. 2,6-naphthoquinone, with outstanding performance parameters (338.9 mAh g-1 and 912.9 mWh g-1). Furthermore, 2,6-anthraquinone with superior cyclic stability, demonstrates comparable performance (257.4 mAh g-1 and 702.8 mWh g-1). These findings offer valuable insights into the design of organic cathode materials with favorable redox chemistry in secondary batteries.

From π-conjugated macrocycles to heterocycloarenes based on benzo[2,1-b:3,4-b']dithiophene (BDTh): size- and geometry-dependent host-guest properties

π-Conjugated macrocycles have been highly attractive due to their challenging synthesis, fascinating aesthetic structure and unique physical and chemical properties. Although some progress has been made in synthesis, the study of π-macrocycles with different structural characteristics and supramolecular interactions still faces major challenges. In this paper, two new single-bond linked macrocycles (MS-4T/MS-6T) were reported, and the corresponding vinyl-bridged heterocycloarenes (MF-4T/MF-6T) were synthesized by the periphery fusion strategy. Further studies have indicated that the structure of these four macrocycles is determined by both size and curvature, showing unique variations from nearly planar to bowl and then to saddle. Interestingly, the nearly planar MS-4T with a small size and the rigid saddle-shaped MF-6T show no obvious response to fullerenes C60 or C70, while the bowl-shaped MS-6T and MF-4T demonstrate a strong binding affinity towards fullerenes C60 and C70. What's more, two kinds of co-crystals with capsule-like configurations, MS-6T@C60 and MS-6T@C70, have been successfully obtained, among which the former shows a loose columnar arrangement while the latter displays a unique three-dimensional honeycomb arrangement that is extremely rare in supramolecular complexes. This work systematically studies the π-conjugated macrocycles and provides a new idea for the development of novel host-guest systems and further multifunctional applications.

Fusion Position-Dependent Aromatic Transitions of Ligand Backbone Rings for Controlling the Redox Energetics of Photoredox Catalysts

To reveal, quantify, and rationalize the effect of backbone π-extension on ligand redox activity, we studied the ground- and excited-state reduction potentials of eight ruthenium photoredox catalysts with the formula Ru(ppy)2L (L is the redox-active ligand of the bipyridine family) using density functional theory. Our research underlines the profound importance of the fusion position of backbone aromatic C6 rings on the redox activity of ligands in transition metal photoredox catalysts. Namely, certain fusion positions lead to the dearomatization of C6 rings in ligand-centered electron transfer events, resulting in a thermodynamic penalty equivalent to a half-volt negative shift in the reduction potential. Contrarily, the extent of backbone delocalization shows a minimal impact on redox energetics, which can be explained by the charge concentration at the nitrogen contact atoms in ligand-centered reductions. Grounded in Caulton's conceptual framework, we reaffirm the predictive potency of Lewis structures in ligand-centered redox energetics with qualitative and quantitative data. Our hypothesis regarding the effect of backbone ring dearomatization on redox energetics is further corroborated using magnetic and structure-based aromaticity indicators. Highlighting fusion-dependent dearomatization as a determining factor of ligand-centered electron transfer energetics, our findings hold implications for molecular-level design in advanced electroactive materials and catalysts.

Partial restoration of aromaticity of pentacene-5,7,12,14-tetrone on Cu(111)

The π-conjugation of organic molecules can be strongly influenced when functional groups are added to a molecule, for example when pentacene is converted into pentacene-5,7,12,14-tetrone (P4O) by substitution of four H-atoms with four O-atoms, leading to four CO double bonds. In fact, although free P4O resembles the parent hydrocarbon pentacene structurally at a first glance, its electronic properties differ drastically and can be more accurately described by three benzene units connected via four carbonyl groups. If P4O is deposited onto Cu(111), the electronic interaction across the interface has previously been reported to fully restore the π-conjugation through a weakening of the CO double bonds and a redistribution of electrons, both of which have been explained with the model of surface-induced aromatic stabilization. Here, we observe for the case of P4O on Cu(111) that the molecule does not exhibit full π-conjugation upon interaction with the surface, likely because of the special electronic nature of the hybridized P4O on Cu(111). Our results are derived from CO-functionalized noncontact atomic force microscopy measurements in combination with dispersion-corrected density functional theory calculations yielding bond lengths and molecular geometries. To characterize the aromaticity, we apply the harmonic oscillator model of aromaticity.

HOMA Index Establishes Similarity to a Reference Molecule

The article shows that the definition of the HOMA index of geometrical aromaticity satisfies the axioms of a similarity function between the examined and benzene ring. Consequently, for purely mathematical reasons, the index works exceptionally well as an index of aromaticity: it expresses a geometric similarity to the archetypal aromatic benzene. Thus, if the molecule is geometrically similar to benzene, then it is also chemically similar, and therefore, it is aromatic. However, the similarity property legitimizes using the HOMA-like indices to express similarity to molecules other than benzene, whether cyclic or linear and existing or hypothetical. The paper demonstrates an example of HOMA-similarity to cyclohexane, which expresses a (relaxed)-saturicity property not accompanied by strong structural strains or steric hindrances. Further, it is also shown that the HOMA index can evaluate the properties of whole molecules, such as 25 unbranched catacondensed isomers of hexacene. The index exhibits a significant quadratic correlation with the total energy differences of planar isomers from which the nonplanar ones deviate. Moreover, the HOMA index of hexacene isomers significantly correlates with the Kekulé count connected to the resonance energy in the Hückel approximation. As a result, the study shows that the HOMA index can be used not only for aromaticity analyses but also as a general chemical descriptor applicable to rings, chains, composed molecular moieties, or even whole molecules.

Quantum Chemical Insight into 1,2-Shift Rearrangement in Bromination of Allylaryls

In this work, we have provided mechanistic insight into the addition of bromine to an allylic double bond of allylaryl derivatives using experimental and DFT-based electronic structure methods. The experimental yields indicate the influence of the functional group on the aryl ring on the ratio of 1,2-dibromo and 1,3-dibromo adducts formed in the reaction. The optimized geometry and the electron density maps of the allylaryls and their cationic intermediates from DFT simulations revealed that electron-rich aryl rings promoted formation of cationic spiro[2.5] intermediate II, whereas electron-poor aryl rings resulted in formation of bromonium intermediate I. It was observed that electron-rich allylaryls promoted the 1,2-shift of the aryl ring that resulted in bond formation between the carbon atom (C1) on the aryl ring and the central carbon atom (C3) in the allylic double bond and formed spiro[2.5] intermediate II, a trend which was confirmed by harmonic oscillator model of aromaticity index. Also, Wiberg bond order analysis is in good agreement with the experimental work. Thermochemical analysis indicates that smaller C1···C3 distance resulted in favorable values for the difference in free energy change (ΔΔG). The favorable ΔΔG values are a result of higher electron density on the aryl ring, making it more nucleophilic toward C3 carbon and promoting 1,2-shift that led to formation of the spiro[2.5] intermediate. Thus, the underlying mechanism indicates that the electron-rich allylaryls promote the formation of 1,3-dibromo compounds through formation and stabilization of the spiro[2.5] intermediate II.

Cyclo[n]carbons and catenanes from different perspectives: disentangling the molecular thread

All-carbon atomic rings, cyclo[n]carbons, have recently attracted vivid attention of experimentalists and theoreticians. Among them, cyclo[18]carbon is the most studied system. In this paper, we summarize and review various properties of cyclo[n]carbons, emphasising the aspects of their aromaticity/antiaromaticity. In the first part, the trends in bonding patterns and selected aromaticity indices with the increasing size of the rings are discussed. In the second part we explore the properties of catenane models based on interlocked cyclo[18]carbon rings from different perspectives and investigate their behaviour under the action of external force using computational experiments.

Gender, Obesity, Fat Distribution and 25-Hydroxyvitamin D

Background and Objectives: Obesity is a worldwide disease associated with systemic complications. In recent years, there has been growing interest in studying vitamin D but data related to obese subjects are still poor. AIM: The aim of this study was to evaluate the relationship between obesity degree and 25-hydroxyvitamin D [25(OH)D] levels. Materials and Methods: We recruited 147 Caucasian adult obese patients (BMI > 30 Kg/m²; 49 male; median age 53 years), and 20 overweight subjects as control group (median age 57 years), who had been referred to our Obesity Center of Chieti (Italy) between May 2020 and September 2021. Results: The median BMI was 38 (33-42) kg/m² for obese patients and 27 (26-28) kg/m² for overweight patients. 25(OH)D concentrations were lower in the obese population compared to the overweight population (19 ng/mL vs. 36 ng/mL; p < 0.001). Considering all obese subjects, a negative correlation was observed between 25(OH)D concentrations and obesity-related parameters (weight, BMI, waist circumference, fat mass, visceral fat, total cholesterol, LDL cholesterol) and glucose metabolism-related parameters. 25(OH)D was also negatively correlated with blood pressure. Conclusions: Our data confirmed the inverse relationship between obesity and blood concentration of 25(OH)D and highlighted how 25(OH)D levels decrease in the presence of glucose and lipid metabolism alterations.

The Topology of Molecules with Twelve Fused Phenyl Rings ([12]Circulenes): Rings, Infinitenes, and Möbius Infinitenes

Following the recent preparation of infinitene (J. Am. Chem. Soc. 2022, 144, 862-871), a computational (ωB97XD/6-311G(d)) exploration of 42 isomeric compounds with 12 fused phenyl rings identified structures with linking number of zero (ring, saddle, and ribbon shapes), two (infinitene-like shape), and one (Möbius infinitene shape) is reported. An infinitene isomer composed of two [5]helicene fragments connected to two stacked phenyl rings and a Möbius infinitene isomer are identified that are more stable than the known infinitene. The energies of the structures are examined by assessing their macrocyclization (strain) energies, π-stacking, and possible aromaticity. Examples of fused phenyl molecules with linking numbers of 3, 4, 5, and 6 are shown, indicating the potential topological range that these molecules can possess.

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.

Non-Alcoholic Fatty Liver Disease and Metabolic Syndrome in Women: Effects of Lifestyle Modifications

Non-alcoholic fatty liver disease (NAFLD) is the most widespread liver disease, characterized by fatty acids liver accumulation and subsequent fibrosis. NAFLD prevalence ranges from 80% to 90% in obese subjects and is estimated to be around 50% in patients with metabolic syndrome. In this clinical scenario, diet and lifestyle modifications can play an important role. There are several imaging techniques that can accurately diagnose fatty liver. Recently, ultrasound has acquired a leading role in the diagnosis and follow-up of fatty liver disease. Furthermore, elastosonography represents a valid alternative to liver biopsy. Shear wave elastosonography evaluates the elastic and mechanical properties of liver tissue. The aim is to evaluate the effects of lifestyle and nutritional interventions and a loss of body weight during hepatic steatosis through ultrasonographic and elastosonographic techniques. Thirty-two female subjects with metabolic syndrome were subjected to clinical, anthropometric, and laboratory assessments, as well as abdominal ultrasonographic/elastosonographic measurements taken from enrollment time (T0) and after 3 months (T1) of lifestyle modifications. After 3 months of lifestyle changes, significant weight loss was observed, with a marked improvement in all adiposity indices. The laboratory parameters at T1 showed significant decreases in total and LDL cholesterol, triglycerides, basal blood glucose, 120 min glycaemia, basal insulin and HOMA Index (p < 0.001). A similar improvement was observed at T1 for steatosis degree (p < 0.01) and elastosonographic measurements (Kpa p < 0.001). The linear regression analysis of the baseline conditions documented that the size of the liver positively correlated with body weight, BMI, neck and waist circumferences, waist to height ratio (WhtR), insulin and HOMA Index, fat mass and visceral fat, and steatosis grade. After 3 months, the liver size showed improvement with positive correlations to all previous variables. Hepatic stiffness (Kpa) positively correlated with neck circumference, visceral fat, and ALT, with basal insulin, gamma-GT, and AST, and with waist circumference, WhtR, and fat mass. The degree of steatosis was positively correlated with more variables and with greater statistical significance at T1 with respect to T0. Particularly, the positive correlations between the degree of steatosis and neck circumference (p < 0.001), HOMA Index, and triglycerides (p < 0.001) appeared to be very significant. NAFLD management in women with metabolic syndrome should be focused on lifestyle modifications. Moreover, liver involvement and improvement at follow-up could be evaluated in a non-invasive manner through ultrasonographic and elastosonographic techniques.

Self-Assembled Lanthanide Antenna Glutathione Sensor for the Study of Immune Cells

The small molecule 8-methoxy-2-oxo-1,2,4,5-tetrahydrocyclopenta[de]quinoline-3-carboxylic acid (2b) behaves as a reactive non-fluorescent Michael acceptor, which after reaction with thiols becomes fluorescent, and an efficient Eu³⁺ antenna, after self-assembling with this cation in water. This behavior makes 2b a highly selective GSH biosensor, which has demonstrated high potential for studies in murine and human cells of the immune system (CD4⁺ T, CD8⁺ T, and B cells) using flow cytometry. GSH can be monitored by the fluorescence of the product of addition to 2b (445 nm) or by the luminescence of Eu³⁺ (592 nm). 2b was able to capture baseline differences in GSH intracellular levels among murine and human CD4⁺ T, CD8⁺ T, and B cells. We also successfully used 2b to monitor intracellular changes in GSH associated with the metabolic variations governing the induction of CD4⁺ naïve T cells into regulatory T cells (T_REG).

Geometrical, electrical, and energetic parameters of hetero-disubstituted cumulenes and polyynes in the presence and absence of the external electric field

Cumulenes and polyynes have the potential to be applied as linear, sp-hybridized, one-dimensional all-carbon nanowires in molecular electronics and optoelectronics. The delocalization and conductivity descriptors of the two π-conjugated systems, heterodisubstituted with the NO2, CN, NH2, and OH groups, were studied using the B3LYP, B3LYP/D3, CAM-B3LYP, and ωB97XD DFT functionals, combined with the aug-cc-pVTZ basis set. Three independent types of molecular descriptors, based on geometry (the HOMA index), electrical properties (trace of the polarizability tensor), and energetic (the HOMO-LUMO energy gap) were shown to be mutually correlated and provided concordant indication that communication through the cumulene chain was considerably better than through the polyyne one. The communication can be tuned by using substituents of significantly different π-electron donor-acceptor properties as well as by the external electric field directed along the carbon chain.

Doubly-Reduced Pentacene in Different Coordination Environments: X-ray Crystallographic and Theoretical Insights into Structural and Electronic Changes

Chemical reduction of pentacene (C22H14, 1) with Group 1 metals ranging from Li to Cs revealed that 1 readily undergoes a two-fold reduction to afford a doubly-reduced 12- anion in THF. With the help of 18-crown-6 ether used as a secondary coordinating agent, five π-complexes of 12- with different alkali metal counterions have been isolated and fully characterized. This series of complexes enables the first evaluation of alkali-metal ion binding patterns and structural changes of the 12- dianion based on the crystallographically confirmed examples. The difference in coordination of the smallest Li+ ion vs. heavier Group 1 congeners has been demonstrated. In addition, the use of benzo-15-crown-5 in the reaction of 1 with Na metal allowed the isolation of the unique solvent-separated ion product with a "naked" dianion, 12-. The detailed structural analyses of the series revealed the C-C bond alteration and core deformation of pentacene upon two-fold reduction and complexation. The negative charge localization at the central six-membered ring of 12- identified by theoretical calculations corroborates with the X-ray crystallographic results. Subsequent in-depth theoretical analysis provided a detailed description of changes in the electronic structure and aromaticity of pentacene upon reduction.

Porphyrinoids, a unique platform for exploring excited-state aromaticity

Recently, Baird (anti)aromaticity has been referred to as a description of excited-state (anti)aromaticity. With the term of Baird's rule, recent studies have intensively verified that the Hückel aromatic [4n + 2]π (or antiaromatic [4n]π) molecules in the ground state are reversed to give Baird aromatic [4n]π (or Baird antiaromatic [4n + 2]π) molecules in the excited states. Since the Hückel (anti)aromaticity has great influence on the molecular properties and reaction mechanisms, the Baird (anti)aromaticity has been expected to act as a dominant factor in governing excited-state properties and processes, which has attracted intensive scientific investigations for the verification of the concept of reversed aromaticity in the excited states. In this scientific endeavor, porphyrinoids have recently played leading roles in the demonstration of the aromaticity reversal in the excited states and its conceptual development. The distinct structural and electronic nature of porphyhrinoids depending on their (anti)aromaticity allow the direct observation of excited-state aromaticity reversal, Baird's rule. The explicit experimental demonstration with porphyrinoids has contributed greatly to its conceptual development and application in novel functional organic materials. Based on the significant role of porphyrinoids in the field of excited-state aromaticity, this review provides an overview of the experimental verification of the reversal concept of excited-state aromaticity by porphyrinoids and the recent progress on its conceptual application in novel functional molecules.

Substituent Effect in the Cation Radicals of Monosubstituted Benzenes

In 30 monosubstituted benzene cation radicals, studied at the ωB97XD/aug-cc-pVTZ level, the phenyl rings usually adopt a compressed form, but a differently compressed form-equivalent to an elongated one-may coexist. The computational and literature ionization potentials are well correlated. The geometrical and magnetic aromaticity, estimated using HOMA and NICS indices, show the systems to be structurally aromatic but magnetically antiaromatic or only weakly aromatic. The partial charge is split between the substituent and ring and varies the most at C(ipso). In the ring, the spin is 70%, concentrated equally at the C(ipso) and C(p) atoms. The sEDA(D) and pEDA(D) descriptors of the substituent effect in cation radicals, respectively, were determined. In cation radicals, the substituent effect on the σ-electron system is like that in the ground state. The effect on the π-electron systems is long-range, and its propagation in the radical quinone-like ring is unlike that in the neutral molecules. The pEDA(D) descriptor correlates well with the partial spin at C(ipso) and C(p) and weakly with the HOMA(D) index. The correlation of the spin at the ring π-electron system and the pEDA(D) descriptor shows that the electron charge supplied to the ring π-electron system and the spin flow oppositely.

Aromaticity indices, electronic structural properties, and fuzzy atomic space investigations of naphthalene and its aza-derivatives

The aromaticity and CDFT properties of naphthalene and its aza-derivatives were theoretically investigated using density functional theory (DFT) electronic structure method. The reactivity and chemistry of Azanaphthalene (1-AN), 1, 2-diazanaphthalene (1, 2-DAN), 1, 3-diazanaphthalene (1, 3-DAN), 1, 4-diazanaphthalene (1,4-DAN), 1, 5-diazanaphthalene (1, 5-DAN), 1, 6-diazanaphthalene (1, 6-DAN), 1, 7-diazanaphthalene (1,7-DAN) and 1, 8-diazanaphthalene (1, 8-DAN) were thoroughly explored and predicted focusing more on the fuzzy atomic space analysis, quantum chemical descriptors (CDFT), natural bond orbital (NBO), and structural electronic properties. The CDFT is focused on predicting the condensed Fukui function and dual descriptors along with condensed local electrophilicity and nucleophilicity investigation. From the aromaticity computational study, 1,7-DAN gave PDI, FLU, FLU- π , PLR, HOMA, BIRD and LOLIPOP values of approximately one (1) was found to be the most aromatic in the group, and strongest π -stacking ability. The aromaticity follows the trend: 1, 7-DAN > 1, 8-DAN > 1, 5-DAN > 1, 6-DAN > 1, 4-DAN > 1, 2-DAN > 1-AN > naphthalene. The second order perturbation energy NBO analysis revealed that the 3 highest stabilization energies in the molecules are C₆-N_a to C₃-C₄ ( π ∗ - π ∗ 236.90 kcal/mol) of 1, 6-DAN, C₃-C₄ to C₁-C₂ ( π ∗ - π ∗ 236.37 kcal/mol) of 1-AN and C₇-N₁₀ to C₂-C₄ ( π ∗ - π ∗ 235 kcal/mol) of 1, 3-DAN.

On the aromaticity of uracil and its 5-halogeno derivatives as revealed by theoretically derived geometric and magnetic indexes

The problem of aromaticity in heterocyclic rings of uracil and its 5-halogenoderivatives (5XU) was analyzed theoretically by calculating modified harmonic oscillator model of aromaticity (HOMA) for Heterocycle Electron Delocalization (HOMHED), nucleus-independent chemical shift parameters (NICS) and the so-called scan experiments, using helium-3 atom as a magnetic probe. The impact of halogen electronegativity on C5 atom’s NBO charges was also investigated. Water, as a polar environment, has a negligible impact on 5XU aromaticity. The most stable diketo tautomer shows a very low aromaticity while the “rare” dihydroxy form (tautomer No 6) is aromatic and resembles benzene. This is in agreement with traditional drawing of chemical formula of uracil’s six-membered ring, directly showing three alternating single and double bonds in its tautomer No 6. No good correlation between magnetic and geometric indexes of aromaticity for the studied 5XU tautomers was found. Linear correlation between the magnitude of NICS minimum, as well as the distance of the minimum above uracil ring plane center from 3He NMR chemical shift scan plot with respect to halogen electronegativity were observed. A strong linear dependence of magnetic index of aromaticity and the electronegativity of 5X substituent was observed.

Machine Learning Predicts Degree of Aromaticity from Structural Fingerprints

Prediction of whether a compound is "aromatic" is at first glance a relatively simple task-does it obey Hückel's rule (planar cyclic π-system with 4n + 2 electrons) or not? However, aromaticity is far from a binary property, and there are distinct variations in the chemical and biological behavior of different systems which obey Hückel's rule and are thus classified as aromatic. To that end, the aromaticity of each molecule in a large public dataset was quantified by an extension of the work of Raczyńska et al. Building on this data, a method is proposed for machine learning the degree of aromaticity of each aromatic ring in a molecule. Categories are derived from the numeric results, allowing the differentiation of structural patterns between them and thus a better representation of the underlying chemical and biological behavior in expert and (Q)SAR systems.

Substituent Effect in the First Excited Triplet State of Monosubstituted Benzenes

The structure of 30 monosubstituted benzenes in the first excited triplet T₁ state was optimized with both unrestricted (U) and restricted open shell (RO) approximations combined with the ωB97XD/aug-cc-pVTZ basis method. The substituents exhibited diverse σ- and π-electron-donating and/or -withdrawing groups. Two different positions of the substituents are observed in the studied compounds in the T₁ state: one distorted from the plane and the other coplanar with a quinoidal ring. The majority of the substituents are π-electron donating in the first group while π-electron withdrawing in the second one. Basically, U- and RO-ωB97XD approximations yield concordant results except for the B-substituents and a few of the planar groups. In the T₁ state, the studied molecules are not aromatic, yet aromaticity estimated using the HOMA (harmonic oscillator model of aromaticity) index increases from ca. -0.2 to ca. 0.4 with substituent distortion, while in the S₁ state, they are only slightly less aromatic than in the ground state (HOMA ≈0.8 vs ≈1.0, respectively). Unexpectedly, the sEDA(T₁) and pEDA(T₁) substituent effect descriptors do not correlate with analogous parameters for the ground and first excited singlet states. This is because in the T₁ state, the geometry of the ring changes dramatically and the sEDA(T₁) and pEDA(T₁) descriptors do not characterize only the functional group but the entire molecule. Thus, they cannot provide useful scales for the substituents in the T₁ states. We found that the spin density in the T₁ states is accumulated at the C_ipso and C_p atoms, and with the substituent deformation angle, it nonlinearly increases at the former while decreases at the latter. It appeared that the gap between singly unoccupied molecular orbital and singly occupied molecular orbital (SUMO-SOMO) is determined by the change of the SOMO energy because the former is essentially constant. For the nonplanar structures, SOMO correlates with the torsion angle of the substituent and the ground-state pEDA(S₀) descriptor of the π-electron-donating substituents ranging from 0.02 to 0.2 e. Finally, shapes of the SOMO-1 instead of SOMO frontier orbitals in the T₁ state somehow resemble the highest occupied molecular orbital ones of the S₀ and S₁ states. For several planar systems, the shape of the U- and RO-density functional theory-calculated SOMO-1 orbitals differs substantially.