The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization

Proton transfer induced excited-state aromaticity gain for chromophores with maximal Stokes shifts

Excited state aromaticity (ESA) offers a fascinating route for driving photophysical and photochemical processes but is challenging to harness fully due to its inherent association with unstable antiaromatic ground states. Here, we propose to circumvent this problem via the introduction of a new class of photophysical processes, the generation of ESA via an excited-state intramolecular proton transfer. We select twelve candidate molecules based on the cyclobutadiene and pentalene scaffolds and investigate their ground and excited state properties using computation. The study highlights the feasibility of proton transfer induced ESA gain and shows that it gives rise to pronounced excited-state relaxation producing Stokes shifts in excess of 2 eV. The underlying electronic structure properties are analysed in terms of the orbitals involved as well as aromaticity descriptors illustrating the pronounced changes these molecules undergo upon both excitation and proton transfer. In summary, we believe that the present work will pave the way toward a new class of chromophores with maximal Stokes shifts and excited-state relaxation.

From (Sub)Porphyrins to (Sub)Phthalocyanines: Aromaticity Signatures in the UV-Vis Absorption Spectra

The development of novel synthetic methods has greatly expanded the toolbox available to chemists for engineering porphyrin and phthalocyanine derivatives with precise electronic and optical properties. In this study, we focus on the UV-vis absorption characteristics of substituted phthalocyanines and their contracted analogs, subphthalocyanines, which feature nonplanar, bowl-shaped geometries. These macrocycles, which are central to numerous applications in materials science and catalysis, possess extensive π-conjugated systems that drive their unique electronic properties. We explore how the change from a metalloid (B) to a metal (Zn) and the resulting coordination environments influence the aromaticity and, consequently, the spectroscopic features of these systems. A combined computational and experimental approach reveals a direct correlation between the aromaticity of the external conjugated pathways and the Q bands in the UV-vis spectra. Our findings highlight key structural modifications that can be leveraged to fine-tune the optical properties of porphyrinoid systems, offering new pathways for the design of advanced materials and catalysts with tailored functionalities.

Aromaticity in the Spectroscopic Spotlight of Hexaphyrins

Spectroscopic properties are commonly used in the experimental evaluation of ground- and excited-state aromaticity in expanded porphyrins. Herein, we investigate if the defining photophysical properties still hold for a diverse set of hexaphyrins with varying redox states, topologies, peripheral substitutions, and core-modifications. By combining TD-DFT calculations with several aromaticity descriptors and chemical compound space maps, the intricate interplay between structural planarity, aromaticity, and absorption spectra is elucidated. Our results emphasize that the general assumption that antiaromatic porphyrinoids exhibit significantly attenuated absorption bands as compared to aromatic counterparts does not hold even for the unsubstituted hexaphyrin macrocycles. To connect the spectroscopic properties to the hexaphyrins' aromaticity behaviour, we analyzed chemical compound space maps defined by the various aromaticity indices. The intensity of the Q-band is not well described by the macrocyclic aromaticity. Instead, the degeneracy of the frontier molecular orbitals, the HOMO-LUMO gap, and the |ΔHOMO-ΔLUMO|2 values appear to be better indicators to identify hexaphyrins with enhanced light-absorbing abilities in the near-infrared region. Regions with highly planar hexaphyrin structures, both aromatic and antiaromatic, are characterized by an intense B-band. Hence, we advise using a combination of global and local aromaticity descriptors rooted in different criteria to assess the aromaticity of expanded porphyrins instead of solely relying on the absorption spectra.

CuGBasis: High-performance CUDA/Python library for efficient computation of quantum chemistry density-based descriptors for larger systems

CuGBasis is a free and open-source CUDA®/Python library for efficient computation of scalar, vector, and matrix quantities crucial for the post-processing of electronic structure calculations. CuGBasis integrates high-performance Graphical Processing Unit (GPU) computing with the ease and flexibility of Python programming, making it compatible with a vast ecosystem of libraries. We showcase its utility as a Python library and demonstrate its seamless interoperability with existing Python software to gain chemical insight from quantum chemistry calculations. Leveraging GPU-accelerated code, cuGBasis exhibits remarkable performance, making it highly applicable to larger systems or large databases. Our benchmarks reveal a 100-fold performance gain compared to alternative software packages, including serial/multi-threaded Central Processing Unit and GPU implementations. This paper outlines various features and computational strategies that lead to cuGBasis's enhanced performance, guiding developers of GPU-accelerated code.

Core-electron contributions to the magnetic response of molecules with heavy elements and their significance in aromaticity assessments

This study delves into the magnetic response of core electrons and their influence on the global magnetic response of planar and three-dimensional systems containing heavy elements, employing the removing valence electron (RVE) approximation. We also explore electronic aromaticity indices to understand the potential role of core electrons on electron delocalization in the absence of an external perturbation. The study reveals that core electrons significantly contribute to the overall magnetic response, especially to the magnetic shielding, affecting the interpretation of aromaticity. In contrast, the calculation of the electronic aromaticity indices suggests a negligible participation of the core electrons on electron delocalization. Despite their widespread use, the study emphasizes caution in labeling systems as strongly aromatic based solely on shielding function computations. It is noteworthy to emphasize the limitations associated with each aromaticity criterion; particularly in the context of magnetic shielding function calculations, the core-electron effect contamination is undeniable. Hence, the integration of various criteria becomes imperative for attaining a comprehensive understanding of magnetic responses within complex systems.

Heptacyclic aromatic hydrocarbon isomers with two azulene units fused

Azulene, known for its unique electronic properties and structural asymmetry, serves as a promising building block for the design of novel non-benzenoid polycyclic aromatic hydrocarbons (PAHs). Herein, we present the synthesis, characterization, and physical properties of three diazulene-fused heptacyclic aromatic hydrocarbons, 8,17-dioctyldiazuleno[2,1-a:2',1'-h]anthracene (trans configuration), 16,18-dioctyldiazuleno[2,1-a:1',2'-j]anthracene (cis configuration) and 3,18-dioctyldiazuleno[2,1-a:1',2'-i]phenanthrene (zigzag configuration). Three compounds are configurational isomers with different fusing patterns of aromatic rings. All three isomers exhibit pronounced aromaticity, as revealed by nuclear magnetic resonance spectroscopy and theoretical calculations. They exhibit characteristics of both azulene and benzenoid PAHs and are much more stable than their all-benzene analogues. The optical and electrochemical properties of these three isomers were investigated through UV-vis absorption spectra and cyclic voltammetry, revealing distinct behaviors influenced by their molecular configurations. Furthermore, the isomer in trans configuration exhibits promising semiconducting properties with a hole mobility of up to 0.22 cm2 V-1 s-1, indicating its potential in organic electronics applications.

Can Aromaticity Be Evaluated Using Atomic Partitions Based on the Hilbert-Space?

Aromaticity is a fundamental concept in chemistry that explains the stability and reactivity of many compounds by identifying atoms within a molecule that form an aromatic ring. Reliable aromaticity indices focus on electron delocalization and depend on atomic partitions, which give rise to the concept of an atom-in-the-molecule (AIM). Real-space atomic partitions present two important drawbacks: a high computational cost and numerical errors, limiting some aromaticity measures to medium-sized molecules with rings up to 12 atoms. This restriction hinders the study of large conjugated systems like porphyrins and nanorings. On the other hand, traditional Hilbert-space schemes are free of the latter limitations but can be unreliable for the large basis sets required in modern computational chemistry. This paper explores AIMs based on three robust Hilbert-space partitions - meta-Löwdin, Natural Atomic Orbitals (NAO), and Intrinsic Atomic Orbitals (IAO) - which combine the advantages of real-space partitions without their disadvantages. These partitions can effectively replace real-space AIMs for evaluating the aromatic character. For the first time, we report multicenter index (MCI) and Iring values for large rings and introduce ESIpy, an open-source Python code for aromaticity analysis in large conjugated rings.

Electron Transport through Linear-, Broken-, and Cross-Conjugated Polycyclic Compounds

Quantum interference (QI) effects offer unique opportunities to modulate charge transport through single molecules. In recent years, several transmission selection rules have been developed to determine constructive and destructive QIs in an intuitive and simple manner, although some of these rules fail for cross-conjugated systems. In this work, we evaluate the performance of distinct transmission rules on a broad series of anthracene and fluorene derivatives with distinctive structural features including linear-, broken-, and cross-conjugation, heteroatoms, and five-membered rings as such species affords a predictive challenge for the qualitative selection rules for QI effects. The electron transport properties and local transmission plots are first evaluated by combining DFT and the nonequilibrium Green function method allowing for an equal-footing comparison of the conductance of the different polycyclic compounds. Our findings are in line with experimental observations on the influence of the type of conjugation and the connectivity to the metallic electrodes on the transport properties. Thus, cross-conjugated systems exhibit reduced conductance values as compared to the linear-conjugated ones, although the transmission is enhanced in the meta-connected junctions. Remarkably, our study reveals that aromatic cores exhibit generally larger zero-bias conductance for a given connectivity, in contrast to the negative aromaticity-conductance relationship found in literature.

Aromaticity of six-membered nitro energetic compounds through molecular electrostatic potential, magnetic, electronic delocalization and reactivity-based indices

The electron density depletion associated with π-hole at the ring center typical of energetic compounds was clearly revealed by the molecular electrostatic potential (ESP). In addition, the spatial arrangement of NO2 groups appears to affect the ESP value in the ring center, and therefore sensitivity to detonation. Indeed, for monocyclic nitrobenzene compounds with the same number of NO2 groups, the ESP value in the ring center decreases as the NO2 groups are more closely spaced. As expected, the central rings become less aromatic as NO2 groups are added. The MCI, PDI, PLR, NICSzz(1), FLU indices are all strongly correlated with the ESP values observed in the ring center of the set of nitrobenzenes. Aromaticity indices based on electron delocalization criteria appear to be very sensitive to small variations in aromaticity. Among magnetic-based indices, only NICSzz(1) is capable to predict small changes in aromaticity. The PLR index derived from conceptual DFT is quite relevant for predicting small variations in aromaticity. According to our results, the most suitable aromaticity index is not based on a single criterion, and that selecting it is more subtle. Therefore, it is important to combine information from several criteria to obtain a more complete description of the aromaticity of the studied compounds.

3,4-Dimethylenecyclobutene: A Building Block for Design of Macrocycles with Excited State Aromatic Low-Lying High-Spin States

3,4-Dimethylenecyclobutene (DMCB) is an unusual isomer of benzene. Motivated by recent synthetic progress to substituted derivatives of this scaffold, we carried out a theoretical and computational analysis with a particular focus on the extent of (anti)aromatic character in the lowest excited states of different multiplicities. We found that the parent DMCB is non-aromatic in its singlet ground state (S0), lowest triplet state (T1), and lowest singlet excited state (S1), while it is aromatic in its lowest quintet state (Q1) as this state is represented by a triplet multiplicity cyclobutadiene (CBD) ring and two uncoupled same-spin methylene radicals. Interestingly, the Q1 state, despite having four unpaired electrons, is placed merely 4.8 eV above S0, and there is a corresponding singlet tetraradical 0.16 eV above. The DMCB is potentially a highly useful structural motif for the design of larger molecular entities with interesting optoelectronic properties. Here, we designed macrocycles composed of fused DMCB units, and according to our computations, two of these have low-lying nonet states (i. e., octaradical states) at energies merely 2.40 and 0.37 eV above their S0 states as a result of local Hückel- and Baird-aromatic character of individual 6π- and 4π-electron monocycles.

Dynamic effects on the nonlinear optical properties of donor acceptor stenhouse adducts: insights from combined MD + QM simulations

The second-order nonlinear optical (NLO) responses of a donor-acceptor stenhouse adduct (DASA) are investigated by using a computational approach combining molecular dynamics simulations and density functional theory (DFT) calculations. Specific force fields for the open and closed photoswitching forms are first parameterized and validated according to the Joyce protocol, in order to finely reproduce the geometrical features and potential energy surfaces of both isomers in chloroform solution. Then, DFT calculations are performed on structural snapshots extracted at regular time steps of the MD trajectories to address the influence of the thermalized conformational dynamics on the NLO responses related to hyper-Rayleigh scattering (HRS) experiments. We show that accounting for the structural dynamics largely enhances the HRS hyperpolarizability (βHRS) compared to DFT calculations considering solely equilibrium geometries, and greatly improves the agreement with experimental measurements. Furthermore, we show that the NLO responses of the NLO-active open form are correlated with the bond order alternation along the triene bridge connecting the donor and acceptor moieties, which is rationalized using simple essential state models.

Unveiling the Reaction Mechanisms of the Synthesis and the Excited State Intramolecular Proton Transfer of 2-(2'-hydroxyphenyl)imidazo[1,2-a]pyridine

Given its wide variety of applications in the pharmaceutical industry, the synthesis of imidazo[1,2-a]pyridines has been extensively studied since the beginning of the last century. Here, we disclose the mechanism for the synthesis of imidazo[1,2-a]pyridines by means of the Ortoleva-King reaction. We also reveal the reaction pathway leading to the formation of a iodinated byproduct, demonstrating the challenge of preventing the formation of such a byproduct because of the low energy barrier to access it. Moreover, quantum chemistry tools were employed to investigate the mechanism of intramolecular proton transfer in the excited state, and connections with aromaticity were explored.

The σ+π dual aromaticity of typical bi-tetrazole ring molecule TKX-50

Two complexes of dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate (TKX-50) were employed to evaluate the aromaticity of their tetrazole rings via deep analysis such as the electronic structure, the ZZ component of the natural chemical shielding tensor (NICSZZ) and component orbitals, localized orbital locator purely contributed by σ-orbitals (LOL-σ) and localized orbital locator purely contributed by π-orbitals (LOL-π), the anisotropy of the induced current density (AICD) and the ZZ component of iso-chemical shielding surface (ICSSZZ) of these tetrazole rings thereof. The conclusion shows: that all tetrazole rings and bi-tetrazole rings in complexes have strong σ and a comparable strength π double aromaticity; all these magnetic shields almost symmetrically increase from the central axis to the tetrazole ring atoms; tetrazole rings in complex II show a little stronger dual aromaticity than that in complex I mainly due to the different orientation of the fragment 2 encompassing two hydroxylamine groups resulting in different effects on the contributions of σ orbitals and π orbitals to total aromaticity of tetrazole rings thereof; the difference in aromaticity is fundamentally caused by the atoms O with stronger electron-withdrawing than atom N in fragment 2 interact with bi-tetrazole ring through O in complex I but through N in complex II.

An Exploration of Substituent Effects on the Photophysical Properties of Monobenzopentalenes

Monobenzopentalenes have received moderate attention compared to dibenzopentalenes, yet their accessibility as stable, non-symmetric structures with diverse substituents could be interesting for materials applications, including molecular photonics. Recently, monobenzopentalene was considered computationally as a potential chromophore for singlet fission (SF) photovoltaics. To advance this compound class towards photonics applications, the excited state energetics must be characterized, computationally and experimentally. In this report we synthesized a series of stable substituted monobenzopentalenes and provided the first experimental exploration of their photophysical properties. Structural and opto-electronic characterization revealed that all derivatives showed 1H NMR shifts in the olefinic region, bond length alternation in the pentalene unit, low-intensity absorptions reflecting the ground-state antiaromatic character and in turn the symmetry forbidden HOMO-to-LUMO transitions of ~2 eV and redox amphotericity. This was also supported by computed aromaticity indices (NICS, ACID, HOMA). Accordingly, substituents did not affect the fulfilment of the energetic criterion of SF, as the computed excited-state energy levels satisfied the required E(S1)/E(T1)>2 relationship. Further spectroscopic measurements revealed a concentration dependent quenching of the excited state and population of the S2 state on the nanosecond timescale, providing initial evidence for unusual photophysics and an alternative entry point for singlet fission with monobenzopentalenes.

Understanding Aromaticity in [5]Helicene-Bridged Cyclophanes: A Comprehensive Study

This study explores the aromaticity of doubly [5]helicene-bridged (1,4)cyclophane and triply [5]helicene-bridged (1,3,5)cyclophane via calculations of the magnetic response and of electronic aromaticity indices. The primary objective is to assess the π-electron delocalization to determine whether they sustain global ring currents associated with π aromaticity. The molecules show local ring currents in the presence of an external magnetic field. The ring currents flow diatropically in the stacked six-membered rings and in the helicene arms. However, these π currents are not interconnected due to the discontinuity of the π delocalization at the C-C single bonds connecting the central six-membered rings to the helicene arms. Electronic indices suggest that the helicene-arm systems have significantly smaller electron delocalization than benzene. The reduction in the delocalization does not compromise their ability to exhibit ring currents in the presence of an external magnetic field. The analysis provides further evidence that the magnetic criteria yield a different degree of aromaticity for the helicene arms than obtained in the calculation of the electronic aromaticity indices. However, both approaches confirm that the studied molecules are not globally aromatic.

Phosphonium-substituted Diphosphaindenylide (PPI): Exploration of Biradical Character and Ligand Properties

Starting from C6 H4 (PCl2 )2 and the TMS-substituted ylide (TMS)2 C=PR3 (TMS=trimethylsilyl, R=p-tolyl), the phosphonium-substituted diphosphaindenylide PPI was prepared in two steps. CASSCF calculations as well as the reactivity toward diphenyl acetylene suggest a notable biradical character in PPI. Reaction with [Cr(CO)3 (MeCN)3 ] affords the complex [Cr(CO)3 (η5 -PPI)] (5). This complex was employed to explore the ligand properties of PPI, which demonstrates considerable potential through the combination of strong metal-ligand interactions and the possibility of a pronounced indenyl effect.

Unraveling the Push-Pull Effect in Acenes, Polyenes and Polyynes

Substituent effects (SEs) are fundamental for predicting molecular reactivity, while polyene, polyyne and acene derivatives are precursors to compounds with diverse applications. Computations were performed for Y-R-X systems, where reaction sites Y=NO2 and O- , substituents X=NO2 , CN, Cl, H, OH, NH2 , and spacers R=polyene, polyyne (n=1-5, 10 repeating units) and acene (up to tetracene). The cSAR (charge of the substituent active region) approach allowed to present, for the first time, quantitative relations describing the spacer's electron-donating and withdrawing properties as a function of n and the spacer type. The electronic properties of the X substituents depend on the type of spacer, its length and the Y group, which is an example of the reverse SE. To describe how the SE between Y and X weakens with n, two approaches were compared: cSAR and SESE (SE stabilization energy). The EDDB (electron density of delocalized bonds) characterize changes in electron delocalization in spacers due to the SE. A new approach - EDDB differential maps - allow to extract the effect of X substitution on the electron delocalization. The charges at spacer's C atoms correlate with cSAR; changes in the slopes confirm the charge transfer by resonance.

Boronyl-Based Polycyclic Superhalogens

Superhalogenity refers to the tendency of radicals to have higher electron affinity (EA) than halogens or anions to possess higher vertical detachment energy (VDE) than do halides (3.64 eV). In Srivastava, A. K. J. Phys. Chem. A 2023, 127, 4867-4872, we demonstrated a simple strategy in which some polycyclic hydrocarbons (PHs) can be turned into polycyclic superhalogens (PSs) by substituting CN groups in the place of hydrogens. We also notice that the superhalogenity of cyanide-based PSs is related to their aromaticity. Boronyl (BO) is an isoelectronic and inorganic analog of the cyano (CN) group. Therefore, we consider the substitution of BO in PHs and compare them with CN-based PSs using the density functional theory. In the case of C5H5-, we notice that the B3LYP and CCSD(T) calculated VDEs of resulting C5H5-n(BO)n- anions increase with the increase in the number of BO substituents (n) such that they become superhalogens for n ≥ 3 like C5H5-n(CN)n- anions. However, their aromaticity does not correspond to the superhalogenity, unlike C5H5-n(CN)n-. Similarly, all BO-substituted PHs possess structures similar to their CN analogs. Although their aromaticity is reduced compared to CN-based anions, the VDE of all these BO-based polycyclic anions and the EA of their radicals exceed 5 eV than those of the corresponding CN-based PSs. Therefore, this study proposes a new class of boronyl-based polycyclic superhalogens. These superhalogen anions might attract synthetic chemists and experimentalists for further explorations.

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.

The electrophilic aromatic bromination of benzenes: mechanistic and regioselective insights from density functional theory

The HBr-assisted electrophilic aromatic bromination of benzene, anisole and nitrobenzene was investigated using static DFT calculations in gas phase and implicit apolar (CCl4) and polar (acetonitrile) solvent models at the ωB97X-D/cc-pVTZ level of theory. The reaction profiles corresponding to either a direct substitution reaction or an addition-elimination process were constructed and insight into the preferred regioselectivity was provided using a combination of conceptual DFT reactivity indices, aromaticity indices, Wiberg bond indices and the non-covalent interaction index. Our results show that under the considered reaction conditions the bromination reaction preferentially occurs through an addition-elimination mechanism and without formation of a stable charged Wheland intermediate. The ortho/para directing effect of the electron-donating methoxy-group in anisole was ascribed to a synergy between strong electron delocalisation and attractive interactions. In contrast, the preferred meta-addition on nitrobenzene could not be traced back to any of these effects, nor to the intrinsic reactivity property of the reactant. In this case, an electrostatic clash between the ipso-carbon of the ring and the nitrogen atom resulting from the later nature of the rate-determining step, with respect to anisole, appeared to play a crucial role.

Substituent Effect versus Aromaticity─A Curious Case of Fulvene Derivatives

A computational study on amino- and nitro-substituted penta- and heptafulvenes reveals the interplay between the aromaticity and the substituent effect (SE). Ring substitution alone has little influence on the aromaticity, but in combination with an exo substituent of opposite properties, it substantially enhances the cyclic π-electron delocalization. Despite the SE being stronger for β substitution, only γ substitution leads to higher aromaticity. An explanation is provided by the electron density of delocalized bonds (EDDB) method, which proves to be a valuable tool in analyzing both cyclic delocalization and the SE.

Directionality and additivity effects of molecular acidity and aromaticity for substituted benzoic acids under external electric fields

Our recent study [M. Li et al.Phys. Chem. Chem. Phys., 2023, 25, 2595-2605] unveiled that the impact of an external electric field on molecular acidity and aromaticity for benzoic acid is directional, which can be understood using changes in frontier orbitals and partial charges. However, it is unclear if the effect will disappear when substituting groups are present and whether new patterns of changes will show up. In this work, as a continuation of our efforts to appreciate the impact of external electric fields on physiochemical properties, we find that the directionality effect is still in place for substituted benzoic acid derivatives and that there exists the additivity effect with respect to the number of substituent groups, regardless of the direction of the applied field and the type of substituting groups. We confirm the findings using electron-donating and electron-accepting groups with the electric field applied either parallelly or perpendicularly to the carboxyl group along the benzene ring. The directionality and additivity effects uncovered from this work should enrich the body of our knowledge about the impact of external electric fields on physiochemical properties and could be applicable to other systems and properties as well.

Exploring the influence of graphene on antiaromaticity of pentalene

Theoretical investigations on the influence of graphene fragments on the antiaromaticity of pentalene are conducted by employing multiple aromaticity descriptors based on magnetic, geometric and electronic criteria. NICS as a sole descriptor for analysing the antiaromaticity of pentalene on graphene fragments has to be carefully considered while looking through the other aromaticity indicators.

Excited-State (Anti)Aromaticity Explains Why Azulene Disobeys Kasha's Rule

Fluorescence exclusively occurs from the lowest excited state of a given multiplicity according to Kasha's rule. However, this rule is not obeyed by a handful of anti-Kasha fluorophores whose underlying mechanism is still understood merely on a phenomenological basis. This lack of understanding prevents the rational design and property-tuning of anti-Kasha fluorophores. Here, we propose a model explaining the photophysical properties of an archetypal anti-Kasha fluorophore, azulene, based on its ground- and excited-state (anti)aromaticity. We derived our model from a detailed analysis of the electronic structure of the ground singlet, first excited triplet, and quintet states and of the first and second excited singlet states using the perturbational molecular orbital theory and quantum-chemical aromaticity indices. Our model reveals that the anti-Kasha properties of azulene and its derivatives result from (i) the contrasting (anti)aromaticity of its first and second singlet excited states (S1 and S2, respectively) and (ii) an easily accessible antiaromaticity relief pathway of the S1 state. This explanation of the fundamental cause of anti-Kasha behavior may pave the way for new classes of anti-Kasha fluorophores and materials with long-lived, high-energy excited states.

Gad S, M. El-Mehasseb I, E. El-Kelany K. Isosterism in pyrrole via azaboroles substitution, a theoretical investigation for electronic structural, stability and aromaticity

This work uses ab-initio CBS-QB3 and density functional theory (B3LYP) to analyze the structure, stability, and aromaticity of all isosteric nitrogen-boron pyrroles. The mono-NB unit substituted group of the isosteric NB pyrrole has four isosteres, whereas the multi-NB unit substituted group has two isosteres. These two groups make up all isosteric NB pyrrole. For structural, energetic, magnetic, and electron delocalization criteria, the results highlight the predominance of the PN3B2 isostere and its greater stability over other conformers. In addition, the global reactivity indices, ESP, HOMO-LUMO, and NBO charges have all been estimated to forecast the active side's electron donation and acceptance. These isosteres are categorized as weak electrophiles and marginal nucleophiles. NB-isosteres have poorer stability, HOMO-LUMO gap, and aromaticity than the parent (pyrrole). In general, NB compounds with more ring sharing are less aromatic than NB molecules with less ring sharing. The current study is anticipated to help in understanding of the chemistry of NB substituted molecules and their experimental identification and characterization.

Beryllium compounds for the carbon-halogen bond activation of phenyl halides: the role of non-innocent ligands

Beryllium is a metallomimetic main-group element, i.e., it behaves similarly to transition metals (TMs) in some bond activation processes. To investigate the ability of Be compounds to activate C-X bonds (X = F-I), we have computationally investigated, using DFT methods, the reaction of (CAAC)2Be (CAAC = 1-(2,6-diisopropylphenyl)-3,3,5,5-tetramethylpyrrolidin-2-ylidene) and a series of five-membered heterocyclic beryllium bidentate ligands with phenyl halides. We have analysed all plausible reaction mechanisms and our results show that, after the initial C-X oxidative addition, migration of the phenyl group occurs towards the less electronegative heteroatom. Our theoretical study highlights the important role of bidentate non-innocent ligands in providing the required electrons for the initial Ph-X oxidative addition. In contrast, the monodentate ligand, CAAC, does not favour this oxidative addition.

Pioneering the Power of Twin Bonds in a Revolutionary Double Bond Formation. Unveiling the True Identity of o-Carboryne as o-Carborene

The homolytic elimination of two H atoms from two adjacent carbons in benzene results in the aromatic product o-benzyne. In a similar way, the homolytic elimination of two H atoms from the two adjacent carbons in 1,2-C2 B10 H12 results in the aromatic product o-carboryne. In this work, we provide experimental and computational evidences that despite the similarity of o-carboryne and o-benzyne, the nature of the C-C bond generated between two adjacent carbons that lose H atoms is different. While in o-benzyne the C-C bond behaves as a triple bond, in o-carboryne the C-C bond is a double bond. Therefore, we must stop naming 1,2-dehydro-o-carboryne as o-carboryne but instead call it o-carborene.

Controlling the Diradical Character of Thiele Like Compounds

Organic diradicals play an important role in many fields of chemistry, biochemistry, and materials science. In this work, by means of high-level theoretical calculations, we have investigated the effect of representative chemical substituents in p-quinodimethane (pQDM) and Thiele's hydrocarbons with respect to the singlet-triplet energy gap, a feature characterizing their diradical character. We show how the nature of the substituents has a very important effect in controlling the singlet-triplet energy gap so that several compounds show diradical features in their ground electronic state. Importantly, steric effects appear to play the most determinant role for pQDM analogues, with minor effects of the substituents in the central ring. For Thiele like compounds, we found that electron-withdrawing groups in the central ring favor the quinoidal form with a low or almost null diradical character, whereas electron-donating group substituents favor the aromatic-diradical form if the electron donation does not exceed 6-π electrons. In this case, if there is an excess of electron donation, the diradical character is reduced. The electronic spectrum of these compounds is also calculated, and we predict that the most intense bands occur in the visible region, although in some cases characteristic electronic transition in the near-IR region may appear.

Electric-field induced second harmonic generation responses of push-pull polyenic dyes: experimental and theoretical characterizations

The second-order nonlinear optical properties of four series of amphiphilic cationic chromophores involving different push-pull extremities and increasingly large polyenic bridges have been investigated both experimentally, by means of electric field induced second harmonic (EFISH) generation, and theoretically, using a computational approach combining classical molecular dynamics (MD) and quantum chemical (QM) calculations. This theoretical methodology allows to describe the effects of structural fluctuations on the EFISH properties of the complexes formed by the dye and its iodine counterion, and provides a rationale to EFISH measurements. The good agreement between experimental and theoretical results proves that this MD + QM scheme constitutes a useful tool for a rational, computer-aided, design of SHG dyes.

Calculation of the ELF in the excited state with single-determinant methods

Since its first definition, back in 1990, the electron localization function (ELF) has settled as one of the most commonly employed techniques to characterize the nature of the chemical bond in real space. Although most of the work using the ELF has focused on the study of ground-state chemical reactivity, a growing interest has blossomed to apply these techniques to the nearly unexplored realm of excited states and photochemistry. Since accurate excited electronic states usually require to account appropriately for electron correlation, the standard single-determinant ELF formulation cannot be blindly applied to them, and it is necessary to turn to correlated ELF descriptions based on the two-particle density matrix (2-PDM). The latter requires costly wavefunction approaches, unaffordable for most of the systems of current photochemical interest. Here, we compare the exact, 2-PDM-based ELF results with those of approximate 2-PDM reconstructions taken from reduced density matrix functional theory. Our approach is put to the test in a wide variety of representative scenarios, such as those provided by the lowest-lying excited electronic states of simple diatomic and polyatomic molecules. Altogether, our results suggest that even approximate 2-PDMs are able to accurately reproduce, on a general basis, the topological and statistical features of the ELF scalar field, paving the way toward the application of cost-effective methodologies, such as time-dependent-Hartree-Fock or time-dependent density functional theory, in the accurate description of the chemical bonding in excited states of photochemical relevance.

Understanding the electronic pi-system of 2D covalent organic frameworks with Wannier functions

We investigate a family of hexagonal 2D covalent organic frameworks (COFs) with phenyl and biphenyl spacer units and different chemical linker species. Chemical trends are elucidated and attributed to microscopic properties of the [Formula: see text]-electron-system spanned by atomic [Formula: see text]-orbitals. We systematically investigate the electronic structure, delocalization of electronic states, effects of disorder, bond torsion, and doping, and correlate these with variable [Formula: see text]-conjugation and nucleus-independent chemical shift (NICS) aromaticity. Molecular orbitals are obtained from maximally localized Wannier functions that have [Formula: see text]- and [Formula: see text]-character, forming distinct [Formula: see text]- and [Formula: see text]-bands for all valence states. The Wannier-orbital description goes beyond simple tight-binding models and enables a detailed understanding of the electronic topology, effective electronic coupling and delocalization. It is shown that a meaningful comparison between COFs with different chemical elements can only be made by examining the entire [Formula: see text]-electron system, while a comparison of individual bands (e.g., bands near the Fermi energy) can be a insufficient to derive general design rules for linker and spacer monomer selection. We further identify delocalized states that are spread across tens or hundreds of pores of the 2D COFs and analyze their robustness against structural and energetic disorders like out-of-plane rotations of molecular fragments, different strength of energetic disorder and energetic shifts due to chemical doping.

Quest for the Most Aromatic Pathway in Charged Expanded Porphyrins

Despite the central role of aromaticity in the chemistry of expanded porphyrins, the evaluation of aromaticity remains difficult for these extended macrocycles. The presence of multiple conjugation pathways and different planar and nonplanar π-conjugation topologies makes the quantification of global and local aromaticity even more challenging. In neutral expanded porphyrins, the predominance of the aromatic conjugation pathway passing through the imine-type nitrogens and circumventing the amino NH groups is established. However, for charged macrocycles, the question about the main conjugation circuit remains open. Accordingly, different conjugation pathways in a set of neutral, anionic, and cationic expanded porphyrins were investigated by means of several aromaticity indices rooted in the structural, magnetic, and electronic criteria. Overall, our results reveal the predominance of the conjugation pathway that passes through all nitrogen atoms to describe the aromaticity of deprotonated expanded porphyrins, while the outer pathway through the perimeter carbon atoms becomes the most aromatic in protonated macrocycles. In nonplanar and charged macrocycles, a discrepancy between electronic and magnetic descriptors is observed. Nevertheless, our work demonstrates AVmin remains the best tool to determine the main conjugation pathway of expanded porphyrins.

Impacts of external fields on aromaticity and acidity of benzoic acid: a density functional theory, conceptual density functional theory and information-theoretic approach study

The impact of external fields on the molecular structure and reactivity properties has been of considerable interest in the recent literature. Benzoic acid as one of the most widely used compounds in medicinal and materials sciences is known for its dual propensity in aromaticity and acidity. In this work, we systematically investigate the impact of a uniform external electric field on these properties. We apply density functional theory, conceptual density functional theory, and an information-theoretic approach to appreciate the change pattern of aromaticity and acidity properties in external fields with different strengths. Our results show that they possess different change patterns under external fields, which can be satisfactorily rationalized by variations in reactivity descriptors and partial charges. The surprising yet novel results from this study should enrich the body of our knowledge about the impact of external fields for different kinds of electronic properties and provide guidance and foundation for future studies of this phenomenon in other molecular systems.

A Benchmark Study of Aromaticity Indexes for Benzene, Pyridine, and the Diazines - II. Excited State Aromaticity

In this work, one geometrical aromaticity index and four electron sharing indexes are benchmarked for their application in excited state aromaticity calculations. Two computationally feasible and reliable procedures are identified, namely, CAM-B3LYP/cc-pVTZ and ωB97X-D/cc-pVTZ. Topological effects on the first excited singlet and triplet electronic manifold were investigated, and the latter was in general found to display more aromatic character compared to the S₁ surface. Besides, geometrical relaxation on each of the manifolds was observed to hamper the aromaticity, thereby resulting in more antiaromatic character. The relative order of excited state aromaticity within the studied molecules was noted to resemble the reversed version of the relative order of ground state aromaticity. Thereby, the following generalization was postulated: The more aromatic a molecule is in its ground state, the more antiaromatic it will be in its electronic first excited manifolds.

A Germapyramidane Switches Between 3D Cluster and 2D Cyclic Structures in Single-Electron Steps

Reaction of the imidazolium-substituted iphosphate-diide, (Ipr)₂ C₂ P₂ (IDP), with GeCl₂  ⋅ dioxane and KBArF₂₄ [(BarF₂₄ )^- =tetrakis[(3,5-trifluoromethyl)phenyl]borate)] afforded the dicationic spherical-aromatic nido-cluster [Ge(η⁴ -IDP)]²⁺ ([1]²⁺ ) (Ipr=1,3-bis(2,6-diisopropylphenyl)imidazolium-2-ylidene). This complex is a rare heavy analogue of the elusive pyramidane [C(η⁴ -C₄ H₄ )]. [1]²⁺ undergoes two reversible one-electron reductions, which yield the radical cation [2]⋅⁺ and the neutral Ge^II species 3. Both [2]⋅⁺ and 3 rearrange in solution forming the 2D aromatic and planar imidazolium-substituted digermolide [4]²⁺ and germole-diide 5, respectively. Both planar species can be oxidized back to [1]²⁺ using AgSbF₆ . These redox-isomerizations correspond to the fundamental transformation of a 3D aromatic cluster into a 2D aromatic ring compound upon reduction and vice versa. The mechanism of these reactions was elucidated using DFT calculations and cyclic voltammetry experiments.

A QCT View of the Interplay between Hydrogen Bonds and Aromaticity in Small CHON Derivatives

The somewhat elusive concept of aromaticity plays an undeniable role in the chemical narrative, often being considered the principal cause of the unusual properties and stability exhibited by certain π skeletons. More recently, the concept of aromaticity has also been utilised to explain the modulation of the strength of non-covalent interactions (NCIs), such as hydrogen bonding (HB), paving the way towards the in silico prediction and design of tailor-made interacting systems. In this work, we try to shed light on this area by exploiting real space techniques, such as the Quantum Theory of Atoms in Molecules (QTAIM), the Interacting Quantum Atoms (IQA) approaches along with the electron delocalisation indicators Aromatic Fluctuation (FLU) and Multicenter (MCI) indices. The QTAIM and IQA methods have been proven capable of providing an unbiased and rigorous picture of NCIs in a wide variety of scenarios, whereas the FLU and MCI descriptors have been successfully exploited in the study of diverse aromatic and antiaromatic systems. We used a collection of simple archetypal examples of aromatic, non-aromatic and antiaromatic moieties within organic molecules to examine the changes in π delocalisation and aromaticity induced by the Aromaticity and Antiaromaticity Modulated Hydrogen Bonds (AMHB). We observed fundamental differences in the behaviour of systems containing the HB acceptor within and outside the ring, e.g., a destabilisation of the rings in the former as opposed to a stabilisation of the latter upon the formation of the corresponding molecular clusters. The results of this work provide a physically sound basis to rationalise the strengthening and weakening of AMHBs with respect to suitable non-cyclic non-aromatic references. We also found significant differences in the chemical bonding scenarios of aromatic and antiaromatic systems in the formation of AMHB. Altogether, our investigation provide novel, valuable insights about the complex mutual influence between hydrogen bonds and π systems.

3D and 2D aromatic units behave like oil and water in the case of benzocarborane derivatives

A large number of 2D/2D and 3D/3D aromatic fusions that keep their aromaticity in the fused compounds have been synthesized. In addition, we have previously proven the electronic relationship between the 3D aromaticity of boron hydrides and the 2D aromaticity of PAHs. Here we report the possible existence of 3D/2D aromatic fusions that retain the whole aromaticity of the two units. Our conclusion is that such a 3D/2D aromatic combination is not possible due to the ineffective overlap between the π-MOs of the planar species and the n + 1 molecular orbitals in the aromatic cage that deter an effective electronic delocalization between the two fused units. We have also proven the necessary conditions for 3D/3D fusions to take place, and how aromaticity of each unit is decreased in 2D/2D and 3D/3D fusions.

2D/2D fusion of aromatic halves leading to a global aromatic is found in many polycyclic aromatic hydrocarbons, whereas 2D/3D aromaticity is difficult to achieve. Here the authors report a computational chemistry investigation showing that 3D/2D aromatic combination is not possible.

Evaluation of Slight Changes in Aromaticity through Electronic and Density Functional Reactivity Theory-Based Descriptors

Aromaticity is a useful tool to rationalize the structure, stability, and reactivity in several compounds. Although aromaticity is not directly an observable, it is well accepted that electronic delocalization around the molecular ring is a key stabilizing feature of aromatic compounds. This contribution presents a systematic evaluation of the capability of delocalization and reactivity criteria to describe aromaticity in a set of fluorinated benzenes. The aromaticity indices are compared with quantities obtained from the magnetic criteria of aromaticity, i.e., the strength of the ring current induced by an external magnetic field and the popular NICS _zz (1) index. In this evaluation, the indices based on delocalization criteria used are aromatic fluctuation index (FLU), para-delocalization index (PDI), PDI_π, and the multicenter delocalization index (MCI). In addition, indices based on the bifurcation values of scalar functions are derived from electron density such as electron localization function (the π contribution, ELF_π) and the π contribution of the localized orbital locator (LOL_π). Furthermore, reactivity indices based on chemical reactivity and the information-theoretic (reactivity) approach are para-linear response (PLR), Shannon entropy, Fisher information, and Ghosh-Berkowitz-Parr (GBP) entropy. The results obtained show that the delocalization-based indicators present a high sensitivity to slight changes in aromaticity and that the reactivity criterion can be considered as a complementary tool for the study of this phenomenon, even when these changes are minimal. These results encourage the use of multiple indicators for a complete understanding of aromaticity in various chemical compounds.

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.

Aromaticity and Extrusion of Benzenoids Linked to [o-COSAN]- : Clar Has the Answer

Benzene and pyrene can be synthetically linked to [o-COSAN]^- keeping their aromaticity. In contrast, naphthalene and anthracene are extruded in the same reaction. We have proven that extrusion is only favorable if the number of Clar's π-sextets remains constant. Thus, Clar has the answer to whether an attached polycyclic aromatic hydrocarbon to [o-COSAN]^- is extruded or not.

Retaining Hückel Aromaticity in the Triplet Excited State of Azobenzene

The implication of the potential concept of aromaticity in the relaxed lowest triplet state of azobenzene, an efficient molecular switch, using elementary aromaticity indices based on magnetic, electronic, and geometric criteria has been discussed. Azobenzene exhibits a major Hückel aromatic character retained in the diradical lowest relaxed triplet state (T₁ ) by virtue of a twisted geometry with partial delocalization of unpaired electrons in the perpendicular p-orbitals of two nitrogen atoms to the corresponding phenyl rings. The computational analysis has been expanded further to stilbene and N-diphenylmethanimine for an extensive understanding of the effect of closed-shell Hückel aromaticity in double-bond-linked phenyl rings. Our analysis concluded that stilbene has Hückel aromatic character in the relaxed T₁ state and N-diphenylmethanimine has a considerable Hückel aromaticity in the phenyl ring near the carbon atom while a paramount Baird aromaticity in the phenyl ring near the nitrogen atom of the C=N double bond. The results reveal the application of excited-state aromaticity as a general tool for the design of molecular switches.

Benzene and Borazine, so Different, yet so Similar: Insight from Experimental Charge Density Analysis

Although benzene and borazine are isoelectronic and isostructural, they have very different electronic structures, mainly due to the polar nature of the B-N bond. Herein, we present an experimental study of the charge density distribution obtained from the multipole model formalism and Hirshfeld atom refinement (HAR) based on high-resolution X-ray diffraction data of borazine B₃N₃H₆ (1) and B,B',B″-trichloroborazine (2) crystals. These data are compared to those obtained from HAR for benzene (4) and 1,3,5-trichlorobenzene (5) and further compared with values obtained from density functional theory calculations in the gas phase, where N,N',N″-trichloroborazine (3) was also included. The results confirm that, unlike benzene, borazines are only weakly aromatic with an island-like electronic delocalization within the B₃N₃ ring involving only the nitrogen atoms. Furthermore, delocalization indices and interacting quantum atom energy for bonded and non-bonded atoms were found to be highly suitable indicators capable of describing the origin of the discrepancies observed when the degree of aromaticity in 2 and 3 is evaluated using common aromaticity indices. Additionally, analysis of intermolecular interactions in the crystals brings further evidence of a weakly aromatic character of the borazines as it reveals surprising similarities between the crystal packing of borazine and benzene and also between B,B',B″-trichloroborazine and 1,3,5-trichlorobenzene.

Unsymmetrical Thienopentalenes: Synthesis, Optoelectronic Properties, and (Anti)aromaticity Analysis

The synthesis and properties of a series of unsymmetrical thienopentalenes are explored, including both monoareno and diareno derivatives. For the synthesis of monoareno pentalenes, a carbopalladation cascade reaction between alkynes and gem-dibromoolefins was applied. Diareno pentalene derivatives were accessed via gold-catalyzed cyclization of diynes. Thiophene was fused to pentalene in two different geometries via its 2,3 and 3,4 bonds. 2,3-Fusion resulted in increased antiaromaticity of the pentalene unit compared to the 3,4-fusion both in the monoareno and diareno framework. Monothienopentalenes that contained the destabilizing 2,3-fusion could not be isolated. For diareno derivatives, the aromatic character of the different aryl groups fused to the pentalene was not independent. Destabilizing fusion on one side resulted in alleviated aromaticity on the other side and vice versa. The synthesized molecules were characterized experimentally by ¹H NMR and UV-vis spectroscopies, cyclic voltammetry, and X-ray crystallography, and their aromatic character was assessed using magnetic (NICS and ACID) and electronic indices (MCI and FLU).

Porphyriynes: 18-π-Conjugated Macrocycles Incorporating a Triple Bond

Tetraphenylporphyriyne (Pyne1), a novel porphyrin analogue with a C≡C bond incorporated into an 18-π-conjugated system, has been created via cleavage of the N-confused pyrrolic ring in Ag(III) N-confused tetraphenylporphyrin. The structure of Pyne1 was confirmed by X-ray crystallography and ¹H NMR, IR, and UV-vis spectroscopy. The mechanism of cleavage of the N-confused pyrrolic ring was investigated by theoretical calculations. The successful synthesis of other Pynes indicated the generality of this protocol.

Simple and efficient visualization of aromaticity: bond currents calculated from NICS values

Aromaticity is a fundamental concept in chemistry, underpinning the properties and reactivity of many organic compounds and materials. The ability to easily and accurately discern aromatic behavior is key to leveraging it as a design element, yet most aromaticity metrics struggle to combine accurate quantitative evaluation, intuitive interpretability, and user-friendliness. We introduce a new method, NICS2BC, which uses simple and inexpensive NICS calculations to generate information-rich and easily-interpreted bond-current graphs. We test the quantitative and qualitative characterizations afforded by NICS2BC for a selection of molecules of varying structural and electronic complexity, to demonstrate its accuracy and ease of analysis. Moreover, we show that NICS2BC successfully identifies ring-current patterns in molecules known to be difficult cases to interpret with NICS and enables deeper understanding of local aromaticity trends, demonstrating that our method adds additional insight.