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.

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.

Probing the Limit of the Number of Saturated Atoms for Achieving Hyperconjugative Aromaticity

Aromaticity is a fundamental concept in organic chemistry. Hyperconjugative aromaticity, also known as hyperconjugation-induced aromaticity, has evolved from its origin from main group substituents to transition metal analogues, establishing itself as an important category of aromaticity. Additionally, aromatic compounds comprising two sp3-carbon atoms have recently been reported both experimentally and computationally. However, what is the maximum number of sp3-hybridized atoms needed to maintain hyperconjugative aromaticity? Here, we report that hyperconjugative aromaticity can be achieved in hexa-substituted indoliums and octa-substituted pyrroliums, possessing three-five sp3-hybridized carbon/nitrogen atoms by means of density functional theory (DFT) calculations. The aromaticity was confirmed by using various aromaticity indices, i.e., NICS, MCI, and EDDB. Notably, the strong electron-donating ability and aurophilicity of Au(I) substituents play a pivotal role in maintaining the aromaticity and structural integrity. In addition, increasing the number of hyperconjugative centers will decrease the aromaticity in these five-membered rings. Our findings highlight the significance of transition metal substituents in hyperconjugative aromaticity and offer a novel approach for designing aromatic organometallics.

InnTl4-nH+ (n = 0∼4): Tetracoordinate Hydrogen in a Planar Fashion?

The recent report of planar tetracoordinate hydrogen (ptH) in In4H+ is very intriguing in planar hypercoordinate chemistry. Our high-level CCSD(T) calculations revealed that the proposed D4h-symmetric ptH In4H+ is a first-order saddle point with an imaginary frequency in the out-of-plane mode of the hydrogen atom. In fact, at the CCSD(T)/aug-cc-pV5Z/aug-cc-pV5Z-PP level, the C4v isomer, with the H atom located 0.70 Å above the In4 plane, is 0.5 kcal/mol more stable than the D4h isomer. However, given the small perturbation from planarity and essentially barrierless C4v ↔ D4h ↔ C4v transition, the vibrationally averaged structure can still be considered as a planar. Extending our exploration to the InnTl4-nH+ (n = 0-3) systems, we found all these ptH structures, except for In2Tl2H+, to be the putative global minimum. The single σ-delocalized interaction between the central hydrogen atom and InnTl4-n ligand rings proves pivotal in establishing planarity and aromaticity and conferring substantial stability upon these rule-breaking ptH species.

Probing the Structural and Electronic Properties of the Anionic and Neutral Tellurium-Doped Boron Clusters TeBnq (n = 3-16, q = 0, -1)

In this study, we employ density functional theory along with the artificial bee colony algorithm for cluster global optimization to explore the low-lying structures of TeBnq (n = 3-16, q = 0, -1). The primary focus is on reporting the structural properties of these clusters. The results reveal a consistent doping pattern of the tellurium atom onto the in-plane edges of planar or quasi-planar boron clusters in the most energetically stable isomers. Additionally, we simulate the photoelectron spectra of the cluster anions. Through relative stability analysis, we identify three clusters with magic numbers -TeB7-, TeB10, and TeB12. The aromaticity of these clusters is elucidated using adaptive natural density partitioning (AdNDP) and magnetic properties analysis. Notably, TeB7- exhibits a perfect σ-π doubly aromatic structure, while TeB12 demonstrates strong island aromaticity. These findings significantly contribute to our understanding of the structural and electronic properties of these clusters.

Chemistry of Cyclo[18]Carbon (C18): A Review

Carbon-based allotropes are propelling a technological revolution in communication, sensing, and computing, concurrently challenging fundamental theories of the previous century. Nevertheless, the demand for advanced carbon-based materials remains substantial. The crux lies in the efficient and reliable engineering of novel carbon allotrope. Although C18 has undergone theoretical and experimental investigation for an extended period, its preparation and direct observation in the condensed phase occurred only recently through STM/AFM techniques. The distinctive cyclic ring structure and the dual 18-center π delocalization character introduce various uncommon properties to C18, rendering it a subject worthy of in-depth exploration. In this context, this review delves into past developments contributing to the state-of-the-art understanding of C18 and provides insights into how future endeavours can expedite practical applications. Encompassing a broad spectrum, this review comprehensively investigates almost all facets of C18, including geometric characteristics, electron delocalization, bonding nature, aromaticity, reactivity, electronic excitation, UV/Vis spectrum, intermolecular interaction, response to external fields, electron affinity, ionization, and other molecular properties. Moreover, the review also outlines representative strategies for the direct synthesis and characterization of C18 using atom manipulation techniques. Following this, C18-based complexes are summarized, and potential applications in catalysis, electrochemical devices, optoelectronics, and sensing are discussed.

On the aromaticity of actinide compounds

The chemistry of actinides has flourished since the late 2010s with the synthesis of new actinide complexes and clusters. On the theoretical side, a range of tools is available for the characterization of these heavy element-containing compounds, but discrepancies in the assessment of aromaticity using different tools have led to controversies. In this Perspective, we examine the origin of controversies relating to the aromaticity of metallic compounds, with a focus on actinides. The aromaticity of actinides is important, not because these molecules are numerous or have a special role in catalysis or reactivity, but because this topic pushes theories of aromaticity to their limits. Owing to its reference independence, the magnetic criterion of aromaticity has been the most popular choice for the characterization of the aromaticity of metallic compounds, including actinide compounds. Through examination of several case studies, we show why this criterion might be misleading for metallic species and explain how findings relating to actinide compounds could reshape theories of aromaticity, not just for actinides but perhaps also for well-known hydrocarbons.

Revisiting the Structure and Bonding in Li5H6- and the Exploration of Reactivity: Planar Pentacoordinate Hydrogen

Recently, Guha and co-workers (Sarmah, K.; Kalita, A.; Purkayastha, S.; Guha, A. K. Pushing The Extreme of Multicentre Bonding: Planar Pentacoordinate Hydride. Angew. Chem. Int. Ed. 2024, e202318741) reported a highly intriguing bonding motif: planar pentacoordinate hydrogen (ppH) in Li5H6-, featuring C2v symmetry in the singlet state with two distinct H-Li (center-ring) bond distances. We herein revisited the potential energy surface of Li5H6- by using a target-oriented genetic algorithm. Our investigation revealed that the lowest-energy structure of Li5H6- exhibits a ppH configuration with very high D5h symmetry and a 1A1' electronic state. We did not find any electronic effect like Jahn-Teller distortion that could be responsible for lowering its symmetry. Moreover, our calculations demonstrated significant differences in the relative energies of other low-lying isomers. An energetically very competitive planar tetracoordinate hydrogen (ptH) isomer is also located, but it corresponds to a very shallow minimum on the potential energy surface depending on the used level of theory. Chemical bonding analyses, including AdNDP and EDA-NOCV, uncover that the optimal Lewis structure for Li5H6- involves H- ions stabilized by the Li5H5 crown. Surprisingly, despite the dominance of electrostatic interactions, the contribution from covalent bonding is also significant between ppH and the Li5H5 moiety, derived from H-(1s) → Li5H5 σ donation. Magnetically induced current density analysis revealed that due to minimal orbital overlap and the highly polar nature of the H-Li covalent interaction, the ppH exhibits local diatropic ring currents around the H centers, which fails to result in a global aromatic ring current. The coordination of Li5H6- with Lewis acids, BH3 and BMe3, instantly converts the ppH configuration to (quasi) ptH. These Lewis acid-bound ptH complexes show high electronic stability and high thermochemical stability against dissociation and, therefore, will be ideal candidates for the experimental realization.

Aromaticity in Semi-Condensed Figure-Eight Molecules

Electron delocalization and aromaticity was comparatively evaluated in recently synthesized figure-eight molecules made of two condensed U-shaped polycyclic aromatic hydrocarbon moieties connected either by two single bonds or by two para-phenylene groups. The selected examples include molecules that incorporate eight-membered and sixteen-membered rings, as well as a doubly [5]helicene-bridged (1,4)cyclophane. We probe whether some electron delocalization could occur through the stereogenic single bonds in these molecules: Is aromaticity purely (semi-)local, or possibly also global in these molecules? It was concluded that the situation can go from a purely (semi-)local character when the dihedral angle at the connecting single bonds is large, such as in biphenyl, to a predominantly (semi-)local character with a minor global contribution when the dihedral angle is small, such as in the para-phenylene connectors of the [5] helicene-bridged cyclophane.

New Perspectives on Delocalization Pathways in Aromatic Molecular Chameleons

This study comprehensively analyzes the magnetically induced current density of polycyclic compounds labeled as "aromatic chameleons" since they can arrange their π-electrons to exhibit aromaticity in both the ground and the lowest triplet state. These compounds comprise benzenoid moieties fused to a central skeleton with 4n π-electrons and traditional magnetic descriptors are biased due to the superposition of local magnetic responses. In the S0 state, our analysis reveals that the molecular constituent fragments preserve their (anti)aromatic features in agreement with two types of resonant structures: one associated with aromatic benzenoids and the other with a central antiaromatic ring. Regarding the T1 state, a global and diatropic ring current is revealed. Our aromaticity study is complemented with advanced electronic and geometric descriptors to consider different aspects of aromaticity, particularly important in the evaluation of excited state aromaticity. Remarkably, these descriptors consistently align with the general features on the main delocalization pathways in polycyclic hydrocarbons consisting of fused 4n π-electron rings. Moreover, our study demonstrates an inverse correlation between the singlet-triplet energy difference and the antiaromatic character of the central ring in S0.

Insight into the Stability of Pentazolyl Derivatives based on Covalent Bond

Pentazole is regarded as a unique inorganic molecule that possess organic heterocyclic structure. Therefore, the research on pentazolyl derivatives represents a cutting-edge direction in both contemporary inorganic chemistry and heterocyclic chemistry. Moreover, their synthesis is regarded as the most significant research topic in the field of energetic materials due to the great potential of pentazolyl derivatives to breakthrough the energy bottleneck of CHNO-based energetic materials. However, synthesizing pentazolyl derivatives is challenging. To provide a theoretical support for the synthesis, we conducted theoretical studies on six single-ring pentazolyl derivatives with different functional groups. The results suggest that derivatization reduces the bond strength and weakens the aromaticity of the pentazolate ring. Further analysis showed that derivatization mainly affects the π aromaticity of the pentazolate ring, and ultimately causing poor stability of the pentazolyl derivatives. Among the six derivatives investigated in this study, fluoro pentazole (cyclo-N5-F) and hydroxyl pentazole (cyclo-N5-OH) possess good aromaticity, which is similar to the reported cyclo-N5-NCHN(CH3)2. Further calculations show that the kinetic stability of cyclo-N5-OH is higher than that of cyclo-N5-F. These results collectively indicate that cyclo-N5-OH is a promising candidate for synthesizing single-ring pentazolyl derivatives.

Comment on: "Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation"

A recent benchmark study of two-photon absorption (2PA) strengths using meta-generalized gradient approximation (MGGA) exchange-correlation functionals by Ahmadzadeh, Li, Rinkevicius, Norman, and Zaleśny (ALRNZ24) [ J. Phys. Chem. Lett. 2024, 15, 969] misrepresents the state of the field in this area. Not only was an assessment of 2PA strengths for the exact same benchmark published previously; ALRNZ24 also uses a gauge-variant form of MGGA response theory which produces erratic behavior for certain benchmark systems. Applications of MGGAs to optical and magnetic response properties should use a gauge-invariant extension of MGGA functionals such as paramagnetic current-dependent MGGAs.

Spectroscopic Manifestations of (Anti)Aromaticity in Oxidized and Reduced Porphyrin and Norcorrole

Aromaticity and antiaromaticity are foundational principes in organic chemistry, regularly invoked to explain stability, structure, and magnetic and electronic properties. There are ongoing challenges in assigning molecules as aromatic or antiaromatic using optical spectroscopy. Here we report spectroelectrochemical and computational analyses of porphyrin (18π neutral, aromatic) and norcorrole (16π neutral, antiaromatic), and their oxidized (16π porphyrin dication) and reduced (norcorrole 18π dianion) forms. Our results show that while the visible spectra are characteristic of (anti)aromaticity consistent with Hückel's rules, the IR spectra are much less informative, owing to the relative rigidity of norcorrole. The results have implications for the assignment of (anti)aromaticity in both ground-state and time-resolved spectra.

Stabilization of the Neutral [25]Hexaphyrin(1.0.1.0.1.0) Radical by Hetero-Bimetal-Coordination

Stabilization of hexaphyrin(1.0.1.0.1.0) (named "rosarin") in its 25π radical state is achieved using a hetero-bimetal-coordination strategy. The antiaromatic BF2 complex B-1 was first synthesized, and then rhodium ion was inserted into B-1 to produce the BF2/Rh(CO)2 mixed complex Rh-B-1 as a highly air-stable radical. The structures of B-1 and Rh-B-1 were determined by single-crystal X-ray diffractions, and the antiaromatic or radical character was identified by various spectroscopy evidence and theoretical calculations. Rh-B-1 exhibits excellent redox properties, enabling amphoteric aromatic-antiaromatic conversion to their 24/26π states. Compared to the 24/26π conjugation systems on the same skeleton, Rh-B-1 has the narrowest electrochemical and optical band gaps, with the longest absorption band at 1010 nm. The ring-current analysis reveals intense paratropic currents for B-1 and co-existing diatropic-paratropic currents for Rh-B-1. This hetero-bimetal-coordination system provides a novel platform for organic radical stabilization on porphyrinoids, showing the prospect of modulating ligand oxidation states through rational coordination design.

Effect of Benzo-Annelation on Triplet State Energies in Polycyclic Conjugated Hydrocarbons

In a series of earlier studies, the effect of benzo-annelation was found to be a useful tool for tuning the aromaticity in polycyclic conjugated compounds to desired level. In this work we studied the (anti)aromaticity of benzo-annelated derivatives of three conjugated hydrocarbons (anthracene, fluoranthene and biphenylene) in their lowest lying singlet (S0) and triplet (T1) states by means of the energy effect (ef), harmonic oscillator model of aromaticity (HOMA), multicentre delocalization indices (MCI), magnetically induced current densities (MICDs) and nucleus independent chemical shifts (NICS). We showed that benzo-annelation is a topology-based effect which can be used to modify the T1 state excitation energies (E(T1)). A quantitative model was established being able to accurately predict the E(T1) based only on the numbers of angularly, linearly and geminally annelated benzene rings. In addition, it was demonstrated that the E(T1) can be directly related to the (anti)aromatic character of the central ring in the studied molecules in their S0 state.

Comparison of Various Theoretical Measures of Aromaticity within Monosubstituted Benzene

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

N2 cleavage by silylene and formation of H2Si(μ-N)2SiH2

Fixation and functionalisation of N2 by main-group elements has remained scarce. Herein, we report a fixation and cleavage of the N ≡ N triple bond achieved in a dinitrogen (N2) matrix by the reaction of hydrogen and laser-ablated silicon atoms. The four-membered heterocycle H2Si(μ-N)2SiH2, the H2SiNN(H2) and HNSiNH complexes are characterized by infrared spectroscopy in conjunction with quantum-chemical calculations. The synergistic interaction of the two SiH2 moieties with N2 results in the formation of final product H2Si(μ-N)2SiH2, and theoretical calculations reveal the donation of electron density of Si to π* antibonding orbitals and the removal of electron density from the π bonding orbitals of N2, leading to cleave the non-polar and strong NN triple bond.

Close Stacking of Antiaromatic Ni(II) Norcorrole Originating from a Four-Electron Multicentered Bonding Interaction

A π-conjugated molecule with one electronic spin often forms a π-stacked dimer through molecular orbital interactions between two unpaired electrons. The bonding is recognized as a multicentered two-electron interaction between the two π-conjugated molecules. Here, we disclose a multicentered bonding interaction between two antiaromatic molecules involving four electrons. We have synthesized an antiaromatic porphyrin analogue, Ni(II) bis(pentafluorophenyl)norcorrole. Its dimer adopts a face-to-face stacked structure with an extremely short stacking distance of 2.97 Å. The close stacking originates from a multicenter four-electron bonding interaction between the two molecules. The bonding electrons were experimentally observed via synchrotron X-ray diffraction analysis and corroborated by theoretical calculations. The intermolecular interaction of the molecular orbitals imparts the stacked dimer with aromatic character that is distinctly different from that of its monomer.

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.

Metallaantiaromaticity of 10-Platinacorrole Complexes

The aromaticity of cyclic π-conjugated organometallic compounds is known as metallaaromaticity. π-Conjugated metallacycles, such as metallabenzenes and metallapentalenes, have been investigated in order to understand the involvement of the d electrons from the metal center in the π-conjugated systems of the organic ligands. Here, we report the synthesis of Pd(II) 10-platinacorrole complexes with cyclooctadiene (COD) and norbornadiene (NBD) ligands. While the Pd(II) 10-platinacorrole COD complex adopts a distorted structure without showing appreciable antiaromaticity, the corresponding NBD complex exhibits a distinct antiaromatic character due to its highly planar conformation. Detailed density functional theory (DFT) calculations revealed that two d orbitals are involved in macrocyclic π-conjugation. We furthermore demonstrated that Craig-Möbius antiaromaticity is not present in the studied system. The synthesis of 10-platinacorroles enables a systematic comparison of the antiaromaticity and aromaticity of closely related porphyrin analogues, providing a better understanding of π-conjugation that involves d orbitals.

Dibenzoindolo[1,8]naphthyridines: Synthesis and Characterization of X-Shaped Aza[4,6]helicenes

This report describes a one-pot multi-step procedure to obtain double azahelicenes via nucleophilic fluorine substitution of 2,2-di(2-bromophenyl)-1,1-difluoroalkenes and palladium-catalysed ring closing reaction. The developed synthesis approach allows easy diversification of substituents at all four fragments of the obtained X-shaped aza[4,6]helicene entity. Yields range from 20 % to 60 % among 12 product examples. X-ray single crystal analysis reveals formation of (P,P) and (M,M) enantiomer mixture of products. Optical and electrochemical properties of selected products were studied by performing UV/Vis absorption, photoluminescence and cyclic voltammetry measurements. Experimental results are supported by (TD)-DFT, NICS and NICS2BC calculations.

QSym2: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, and they are not able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym2 that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym2 is able to address all of these shortcomings. To illustrate these capabilities of QSym2, four sets of case studies are examined in detail in this article: (i) high-symmetry C84H64, C60, and B9- to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)63- to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H3+ to demonstrate the analysis of density symmetries.

On the aromaticity and stability of benzynes in the ground and lowest-lying triplet excited states

In this work, we have revisited the aromaticity of benzyne isomers at the unrestricted density functional theory level (UDFT) using the energetic, magnetic, and delocalization criteria. In addition, this last criterion has also been analyzed employing complete active space (CASSCF) calculations. The results show conservation of aromaticity in these monocycles. Additionally it is observed that this trend is maintained in polycyclic aromatic hydrocarbon derivatives such as biradical didehydrophenanthrenes. Do these results imply a violation of Baird's rule? The answer is No, because this conservation in aromaticity is due to the loss of hydrogen atoms affects only the electronic σ skeleton and exerts a minor influence on the π cloud. Additionally, we have analyzed the relative stability of benzyne isomers and their relationship with experimental ΔES-T values. According to the literature, the stability of the benzynes in the singlet state is due to an effective interaction between the electrons of the biradical centers; however, this effect is completely reversed in the triplet state, which explains why the para isomer has the lowest ΔES-T gap.

Aromaticity and Magnetic Behavior in Benzenoids: Unraveling Ring Current Combinations

Nowadays, an active research topic is the connection between Clar's rule, aromaticity, and magnetic properties of polycyclic benzenoid hydrocarbons. In the present work, we employ a meticulous magnetically induced current density analysis to define the net current flowing through any cyclic circuit, connecting it to aromaticity based on the ring current concept. Our investigation reveals that the analyzed polycyclic systems display a prominent global ring current, contrasting with subdued semi-local and local ring currents. These patterns align with Clar's aromatic π-sextets only in cases where migrating π-sextet structures are invoked. The results of this study will enrich our comprehension of aromaticity and magnetic behavior in such systems, offering significant insights into coexisting ring current circuits in these systems.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.

Exploring the Aromaticity Differences of Isoelectronic Species of Cyclo[18]carbon (C18), B6C6N6, and B9N9: The Role of Carbon Atoms as Connecting Bridges

The cyclo[18]carbon (C18) has piqued widespread interest in recent years for its geometrical aesthetic and unique electronic structure. Inspired by it, theoretical investigations of its isoelectronic B9N9 have been published occasionally; however, few studies considered their other companion B6C6N6. In this work, we study the geometric structure, charge distribution, bonding characteristic, aromaticity, and electron delocalization of B6C6N6 and B9N9 for the first time and compare the relevant results with those of C18. Based on the comprehensive analysis of aromaticity indicators such as AV1245, nucleus-independent chemical shifts, anisotropy of the induced current density, magnetically induced current density, iso-chemical shielding surface, and induced magnetic field (Bind), we found that B6C6N6 has definitely a double aromatic character similar to C18 and the aromaticities of the two are very close, while B9N9 is a nonaromatic species. In response to this novel finding, we delved into its nature from an electron delocalization perspective through a localized orbital locator, electron localization function, Fermi hole, and atomic remote delocalization index analyses. The C atom between B and N as an interconnecting bridge strengthens the electron delocalization of the conjugate path, which is the essence of the significant enhancement of the molecular aromaticity from B9N9 to B6C6N6. This work elucidates that within the framework of the isoelectronicity of C18, different methods of atomic doping can achieve molecules with completely different properties.

Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin-orbit coupling

We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin-orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Single─Not Double─3D-Aromaticity in an Oxidized Closo Icosahedral Dodecaiodo-Dodecaborate Cluster

3D-aromatic molecules with (distorted) tetrahedral, octahedral, or spherical structures are much less common than typical 2D-aromatic species or even 2D-aromatic-in-3D systems. Closo boranes, [BnHn]2- (5 ≤ n ≤ 14) and carboranes are examples of compounds that are singly 3D-aromatic, and we now explore if there are species that are doubly 3D-aromatic. The most widely known example of a species with double 2D-aromaticity is the hexaiodobenzene dication, [C6I6]2+. This species shows π-aromaticity in the benzene ring and σ-aromaticity in the outer ring formed by the iodine substituents. Inspired by the hexaiodobenzene dication example, in this work, we explore the potential for double 3D-aromaticity in [B12I12]0/2+. Our results based on magnetic and electronic descriptors of aromaticity together with 11B{1H} NMR experimental spectra of boron-iodinated o-carboranes suggest that these two oxidized forms of a closo icosahedral dodecaiodo-dodecaborate cluster, [B12I12] and [B12I12]2+, behave as doubly 3D-aromatic compounds. However, an evaluation of the energetic contribution of the potential double 3D-aromaticity through homodesmotic reactions shows that delocalization in the I12 shell, in contrast to the 10σ-electron I62+ ring in the hexaiodobenzene dication, does not contribute to any stabilization of the system. Therefore, the [B12I12]0/2+ species cannot be considered as doubly 3D-aromatic.

Semiempirical Methods for Molecular Systems in Strong Magnetic Fields

A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, |B | ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, |B | > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.

Theoretical investigation of anion perfluorocubane

CONTEXT

In this work, we did a theoretical exploration of C8F8 (Ib) and its anion radical analogue (IIb) in this work. By investigating the thermochemistry of electron capture, we find that the free energy associated with the conversion of C8H8 (Ia) into its anion radical analogue IIa is of the order of + 92.83 kcal.mol-1, while the conversion of Ib into IIb is - 6.42 kcal.mol-1. Therefore, species IIb is thermodynamically more stable than its neutral analogue. Natural bond orbitals (NBO) analyses revealed that compound Ib exhibits a relative electronic stability as a function of intramolecular delocalisations of the type [Formula: see text] of the order of 2.70 kcal.mol-1. Similar delocalizations for Ia are energetically lower (1.45 kcal.mol-1). Topological analyses of compounds Ib and IIb indicate that the addition of an electron to Ib enhances the covalency of the C-C bond, as can be seen by the reduction in the ellipticity of the C-C bond. The opposite is observed for Ia, whose addition of the electron (leading to IIa) reduces the covalency of the C-C bond. By comparing the free and packaged forms of the species, it is found that, in the crystalline form, the system will present greater relative stability due to the dispersive interactions involved, as evidenced by non-covalent interactions (NCI) analysis. Finally, it was possible to verify that the manifestation of the current density with a lower paratropic and less antiaromatic character in Ib and IIb point to C8F8 as a strong candidate for electron capture.

METHODS

Geometry optimization calculations were carried out, for all monomer structures using the hybrid functional B3LYP-D3 and the 6-31+G(d,p) basis set. To determine the formation thermochemistry of the ions, electronic energy corrections was performed using the DLPNO-CCSD(T)/aug-cc-pVTZ/C method. Starting from the optimised forms, shielding, nuclear magnetic resonance (NMR) spectra employing gauge-independent atomic orbital (GIAO), and NBO calculations were performed for these monomers, using the PBE0 functional and the pCSseg-2 atomic basis set. The magnetochemical analysis of ring currents was performed using the GIMIC formalism. For the topological analysis, it was applied the combination DLPNO-CCSD(T)/aug-cc-pVTZ/C, previously used for correcting the electronic energy.

Current-Density Calculations on Zn-Porphyrin40 Nanorings

Two porphyrinoid nanorings have been studied computationally. They were built by linking 40 Zn-porphyrin units with butadiyne bridges. The molecular structures belonging to the D40h point group were fully optimized with the Turbomole program at the density functional theory (DFT) level using the B3LYP functional and the def2-SVP basis sets. The aromatic character was studied at the DFT level by calculating the magnetically induced current-density (MICD) susceptibility using the GIMIC program. The neutral molecules are globally non-aromatic with aromatic Zn-porphyrin units. Charged nanorings could not be studied because almost degenerate frontier orbitals led to vanishing optical gaps for the cations. Since DFT calculations of the MICD are computationally expensive, we also calculated the MICD using three pseudo-π models. Appropriate pseudo-π models were constructed by removing the outer hydrogen atoms and replacing all carbon and nitrogen atoms with hydrogen atoms. The central Zn atom was either replaced with a beryllium atom or with two inner hydrogen atoms. Calculations with the computationally inexpensive pseudo-π models yielded qualitatively the same magnetic response as obtained in the all-electron calculations.

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.

Bismuth Infrared Star: Being at a Glance

Bismuth polycations have garnered significant attention from researchers due to their extraordinary and counter-intuitive structures and stoichiometries. Despite extensive experimental and theoretical investigations, understanding of the bonding in such clusters remains insufficient. An AdNDP bonding analysis was conducted to elucidate the bonding characteristics using both homoatomic and heteroatomic bismuth clusters with various stoichiometries. Analysis of the calculated nucleus-independent chemical shift data confirmed the aromatic nature of these species. Universal bonding patterns were identified that can be applied to a range of homoatomic and heteroatomic bismuth clusters. Additionally, calculations of absorbance and fluorescence spectra were performed to gain insights into the near-infrared emission and establish a potential correlation between absorbance and the identified bonding patterns.

Rational Design of Persistent Phosphorus-Centered Singlet Tetraradicals and Their Use in Small-Molecule Activation

Biradicals are important intermediates in the process of bond formation and breaking. While main-group-element-centered biradicals have been thoroughly studied, much less is known about tetraradicals, as their very low stability has hampered their isolation and use in small-molecule activation. Herein, we describe the search for persistent phosphorus-centered tetraradicals. Starting from an s-hydrindacenyl skeleton, we investigated the introduction of four phosphorus-based radical sites linked by an N-R unit and bridged by a benzene moiety. By varying the size of the substituent R, we finally succeeded in isolating a persistent P-centered singlet tetraradical, 2,6-diaza-1,3,5,7-tetraphospha-s-hydrindacene-1,3,5,7-tetrayl (1), in good yields. Furthermore, it was demonstrated that tetraradical 1 can be utilized for the activation of small molecules such as molecular hydrogen or alkynes. In addition to the synthesis of P-centered tetraradicals, the comparison with other known tetraradicals as well as biradicals is described on the basis of quantum mechanical calculations with respect to its multireference character, coupling of radical electrons, and aromaticity. The strong coupling of radical electrons enables selective discrimination between the first and the second activations of small molecules, which is shown by the example of H₂ addition. The mechanism of hydrogen addition is investigated with parahydrogen-induced hyperpolarization NMR studies and DFT calculations.

Benzo[1,2-d:4,5-d']bis([1,2,3]thiadiazole) and Its Bromo Derivatives: Molecular Structure and Reactivity

Benzo[1,2-d:4,5-d']bis([1,2,3]thiadiazole) (isoBBT) is a new electron-withdrawing building block that can be used to obtain potentially interesting compounds for the synthesis of OLEDs and organic solar cells components. The electronic structure and delocalization in benzo[1,2-d:4,5-d']bis([1,2,3]thiadiazole), 4-bromobenzo[1,2-d:4,5-d']bis([1,2,3]thiadiazole), and 4,8-dibromobenzo[1,2-d:4,5-d']bis([1,2,3]thiadiazole) were studied using X-ray diffraction analysis and ab initio calculations by EDDB and GIMIC methods and were compared to the corresponding properties of benzo[1,2-c:4,5-c']bis[1,2,5]thiadiazole (BBT). Calculations at a high level of theory showed that the electron affinity, which determines electron deficiency, of isoBBT was significantly smaller than that of BBT (1.09 vs. 1.90 eV). Incorporation of bromine atoms improves the electrical deficiency of bromobenzo-bis-thiadiazoles nearly without affecting aromaticity, which increases the reactivity of these compounds in aromatic nucleophilic substitution reactions and, on the other hand, does not reduce the ability to undergo cross-coupling reactions. 4-Bromobenzo[1,2-d:4,5-d']bis([1,2,3]thiadiazole) is an attractive object for the synthesis of monosubstituted isoBBT compounds. The goal to find conditions for the selective substitution of hydrogen or bromine atoms at position 4 in order to obtain compounds containing a (het)aryl group in this position and to use the remaining unsubstituted hydrogen or bromine atoms to obtain unsymmetrically substituted isoBBT derivatives, potentially interesting compounds for organic photovoltaic components, was not set before. Nucleophilic aromatic and cross-coupling reactions, along with palladium-catalyzed C-H direct arylation reactions for 4-bromobenzo[1,2-d:4,5-d']bis([1,2,3]thiadiazole), were studied and selective conditions for the synthesis of monoarylated derivatives were found. The observed features of the structure and reactivity of isoBBT derivatives may be useful for building organic semiconductor-based devices.

Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH₃ radical and the superoctazethrene molecule are also illustrated.

φ-Aromaticity in prismatic {Bi6}-based clusters

The occurrence of aromaticity in organic molecules is widely accepted, but its occurrence in purely metallic systems is less widespread. Molecules comprising only metal atoms (M) are known to be able to exhibit aromatic behaviour, sustaining ring currents inside an external magnetic field along M-M connection axes (σ-aromaticity) or above and below the plane (π-aromaticity) for cyclic or cage-type compounds. However, all-metal compounds provide an extension of the electrons' mobility also in other directions. Here, we show that regular {Bi₆} prisms exhibit a non-localizable molecular orbital of f-type symmetry and generate a strong ring current that leads to a behaviour referred to as φ-aromaticity. The experimentally observed heterometallic cluster [{CpRu}₃Bi₆]^-, based on a regular prismatic {Bi₆} unit, displays aromatic behaviour; according to quantum chemical calculations, the corresponding hypothetical Bi₆^2- prism shows a similar behaviour. By contrast, [{(cod)Ir}₃Bi₆] features a distorted Bi₆ moiety that inhibits φ-aromaticity.

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 AV_min remains the best tool to determine the main conjugation pathway of expanded porphyrins.

Synthesis and characterization of bi(metallacycloprop-1-ene) complexes

In all previously reported metallacycloprop-1-ene or η²-vinyl complexes, the metal center bears only one vinyl moiety. We have now successfully synthesized and structurally characterized the first complexes bearing two η²-vinyl moieties or spiro bi(metallacycloprop-1-ene) complexes from reactions of alkynes with rhenium phosphine complexes. Computational studies indicate that the metallacycloprop-1-ene rings are aromatic and the complexes represent a rare σ-type spirometalla-aromatic system.

Magnetically Induced Current Densities in π-Conjugated Porphyrin Nanoballs

Magnetically induced current densities (MICDs) of Zn-porphyrinoid nanostructures have been studied at the density functional theory level using the B3LYP functional and the def2-SVP basis set. Six of the studied Zn-porphyrinoid nanostructures consist of two crossing porphyrinoid belts, and one is a porphyrinoid nanoball belonging to the octahedral (O) point group. The Zn-porphyrin units are connected to each other via butadiyne linkers as in a recently synthesized porphyrinoid structure resembling two crossed belts. The MICDs are calculated using the gauge-including magnetically induced current method. Current-density pathways and their strengths were determined by numerically integrating the MICD passing through selected planes that cross chemical bonds or molecular rings. The current-density calculations show that the studied neutral molecules are globally nonaromatic but locally aromatic sustaining ring currents only in the individual porphyrin rings or around two neighboring porphyrins. The ring-current strengths of the individual porphyrin rings are 20% weaker than in Zn-porphyrin, whereas oxidation leads to globally aromatic cations sustaining ring currents that are somewhat stronger than for Zn-porphyrin.

B3Al4+: A Three-Dimensional Molecular Reuleaux Triangle

We systematically explore the potential energy surface of the B3Al4+ combination of atoms. The putative global minimum corresponds to a structure formed by an Al4 square facing a B3 triangle. Interestingly, the dynamical behavior can be described as a Reuleaux molecular triangle since it involves the rotation of the B3 triangle at the top of the Al4 square. The molecular dynamics simulations, corroborating with the very small rotational barriers of the B3 triangle, show its nearly free rotation on the Al4 ring, confirming the fluxional character of the cluster. Moreover, while the chemical bonding analysis suggests that the multicenter interaction between the two fragments determines its fluxionality, the magnetic response analysis reveals this cluster as a true and fully three-dimensional aromatic system.

On the JAP Method for the Indirect Determination of Delocalized Currents from Experimental Chemical Shifts

The JAP model (after Jirásek, Anderson, and Peeks) to retrieve global current strengths from experimental ¹ H chemical shifts has been tested with DFT computations. Both global and local tropicities are correctly predicted in most cases and the quantitative agreement is overall fair. An extension of the model is found to give improvement in an exemplary critical case, where the global delocalized current is negligible and the current density map is dominated by local currents.

Correspondence on "How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring"

A recent Research Article in this journal by Matito and co-workers claimed that none of the oxidation states of a butadiyne-linked six-porphyrin nanoring exhibit global aromaticity or antiaromaticity. Here we show that this conclusion is incorrect. Experimental data from NMR spectroscopy for a whole family of nanorings provide strong evidence for global ring currents. The NMR data reveal these ring currents directly, without needing analysis by density functional theory (DFT). Furthermore, DFT calculations reproduce the experimental results when a suitable functional is used.

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.

Communication: Impact of the current density on paramagnetic NMR properties

Meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals generally depend on the kinetic energy density τ. For magnetic properties, this necessitates generalizations to ensure gauge invariance. In most implementations, τ is generalized by incorporating the external magnetic field. However, this introduces artifacts in the response of the density matrix and does not satisfy the iso-orbital constraint. Here, we extend previous approaches based on the current density to paramagnetic NMR shieldings and EPR g-tensors. The impact is assessed for main-group compounds and transition-metal complexes considering 25 density functional approximations. It is shown that the current density leads to substantial improvements-especially for the popular Minnesota and SCAN functional families. Thus, we strongly recommend to use the current density generalized τ in paramagnetic NMR and EPR calculations with meta-GGAs.

Aromaticity of Singlet and Triplet Boron Disk-like Clusters: A Test for Electron Counting Aromaticity Rules

Boron clusters are polyhedral boron-containing structures that have unique features and properties. The disk-like boron clusters are among the most fascinating boron cluster forms. These clusters have a molecular orbital (MO) distribution similar to the one derived from the simple particle-on-a-disk model. In this model, the MOs come in pairs except for m = 0. Disk-like boron clusters in their singlet ground state are aromatic when they reach a closed-shell structure. One could expect that disk-like aromatic boron clusters in the singlet state, when acquiring or releasing two electrons, may also be aromatic in the lowest-lying triplet state. We use magnetically induced current densities and bond current strengths to analyze the aromatic character of a series of disk-like boron clusters. Our results show that, with the exception of triplet ³B₁₉^-, the disk-like boron clusters follow Hückel and Baird's rules if one considers the different MOs grouped by their symmetry. We also found that if the lowest-lying triplet state in disk-like boron clusters is aromatic, this triplet state is the ground state for this species.