Counter‐Rotating Spin‐Polarised Ring Currents in Odd‐Electron Carbocycles

We propose a molecular‐orbital model to explain how majority and minority spins in odd‐π‐electron carbocycles sustain counter‐rotating magnetic‐field‐induced ring currents. The model is based on the ipsocentric approach to magnetic response, in which ring currents are dominated by frontier‐orbital contributions obeying angular‐momentum selection rules. Coupled unrestricted Hartree–Fock ab initio calculations of the ring‐current responses for singly charged benzene and planarised cyclo‐octatetraene ions confirm the predictions of the qualitative model, and are consistent with correlated MP2 spin‐polarised current calculations.     

An Amphoteric Switch to Aromatic and Antiaromatic States of a Neutral Air‐Stable 25π Radical

Ever since the discovery of the trityl radical, isolation of a stable and neutral organic radical has been a synthetic challenge. A (4n+1)π open‐shell configuration is one such possible neutral radical but an unusual state between aromatic (4n+2)π and antiaromatic (4n)π electronic circuits. The synthesis and characterization of an air‐ and water‐stable neutral 25π pentathiophene macrocyclic radical is now described. It undergoes reversible one‐electron oxidation to a 24π antiaromatic cation and reduction to a 26π aromatic anion, thus confirming its amphoteric behavior. Structural determination by single‐crystal X‐ray diffraction studies revealed a planar configuration for the neutral radical, antiaromatic cation, and aromatic anion. In the solution state, the cation shows the highest upfield chemical shift ever observed for a 4nπ system, while the anion adhered to aromatic nature. Computational studies revealed the delocalized nature of the unpaired electron as confirmed by EPR spectroscopy.     

Ring-current aromaticity in open-shell systems

The ab initio ipsocentric approach to calculation and mapping of induced orbital current density is extended to open-shell π systems. ROHF/6-31G^** calculations document the (magnetic) aromaticity of planar 4nπ triplet states of 4π/8π annulenes and isobenzofulvene, and quintet excited-state azulene. An orbital model for currents rationalises the generalised form of Baird’s rules, by which 4n + 2 annulenes are aromatic (antiaromatic) in states of even (odd) total spin (vice versa for 4nπ annulenes). In contrast to geometric criteria, ring-currents predict antiaromaticity for the doublet naphthalene radical anion.     

Aromaticity of caffeine,xanthine and the dimethyl xanthines

Xanthine, caffeine and three isomeric dimethyl xanthines (theobromine, theophylline and paraxanthine) are often described as aromatic on various criteria. Here we complete the picture by assessing these molecules for aromaticity on the ring-current criterion. Magnetic response calculations are performed at the B3LYP and CHF/6-31G^∗∗ ipsocentric levels of theory on structures optimised at the B3LYP/6-31G^∗∗ level. All five systems display consistent π-electron ring-currents delocalised around the imidazole moiety in all cases; these are accompanied by localised features on the six-membered rings attributed to nitrogen and oxygen ‘lone-pair’ π-electron circulations. All are therefore aromatic on the magnetic criterion, with a ‘locally delocalised’ ring current in the imidazole moiety, similar to those in the isolated imidazole and methylimidazole molecules.     

Relativistic ring currents in metallabenzenes: an analysis in terms of contributions of localised orbitals

Ring currents calculated in the ipsocentric CTOCD-DZ formalism are presented for four representative metallabenzenes, compounds in which a benzene CH group is formally replaced by a transition metal atom with ligands. Aromaticity is probed using ring currents computed using non-relativistic and relativistic orbitals (derived with relativistic effective core potentials or ZORA). Maps computed at different levels of relativistic theory turn out to be similar, showing that orbital nodal character is the main determinant of ring current. Diatropic/paratropic global ring currents in these compounds, and also circulations localised on the metal centre, are interpreted in terms of contributions of localised π-type orbitals and metal d-orbitals, respectively. All four considered metallabenzenes should be regarded as 6π electron species, despite the fact that three support diatropic ('aromatic') ring currents and one a paratropic ('anti-aromatic') current. The current-density maps determine the correct way to count electrons in these species: differential occupation of d-orbitals of formal π-symmetry contributes to circulation on the metal centre, but not around the benzenoid ring. The overall trend from strongly diatropic to weakly paratropic ring currents along the series 1 to 4 is explained by the increasing strength of interaction between formally non-bonding orbitals on the metal centre and C(5)H(5) moiety, which together make up the six-membered ring.     

Visualising aromaticity of bowl-shaped molecules

Superposition of slices (planar maps of induced current density calculated within the ipsocentric pseudo-π model of electronic response to a magnetic field) gives a simple route to visual diagnosis of ring-current aromaticity in bowl-shaped molecules. Results are presented for currents in the recently synthesized indenocorannulene precursors of [60]fullerene.     

Aromaticity of organic heterocyclothiazenes and analogues

Members of a series of carbon-poor sulfur-nitrogen heterocycles and polycycles are shown by direct ab initio ipsocentric calculation to support diatropic ring currents and hence to be aromatic on the basis of magnetic criteria. They include 7-cycles S(3)N(2)(CH)(2), S(3)N(3)(CH), and S(3)N(4) and 8-cycles S(2)N(4)(CH)(2) and S(2)N(2)(CH)(4), all with 10 pi electrons. The unknown trithiatetrazepine S(3)N(4) is predicted to be at least as aromatic as its known diaza and triaza homologues. Angular-momentum arguments show that the pi-electron-rich nature of (4n + 2) SN heterocycles is the key to their diatropic current. The Woodward dithiatetrazocine parent framework S(2)N(4)(CH)(2) supports a diatropic ring current, as does its analogue in which N and CH groups are formally exchanged. Formal expansion of (4n + 2)-pi carbocyclic systems by insertion of NSN motifs in every CC bond is predicted to lead to structures that support diatropic ring currents: explicit ab initio calculation of magnetic response predicts the 24-center, 30-pi-electron heterocycle S(6)N(12)(CH)(6), formally derived from benzene, to be aromatic on the basis of this criterion.     

Rational Control of Conformational Distributions and Mixed‐Valence Characteristics in Diruthenium Complexes

The electronic characteristics of mixed‐valence complexes are often inferred from the shape of the inter‐valence charge transfer (IVCT) band, which usually falls in the near infrared (NIR) region, and relationships derived from Marcus‐Hush theory. These analyses typically assume one single, dominant molecular conformation. The NIR spectra of the prototypical delocalised (Class III Robin–Day mixed‐valence) complexes [{Ru(pp)Cp’}₂(μ‐C≡C?C≡C)]⁺ ([ 1 ]⁺: Cp’=Cp, pp=(PPh₃)₂; [ 2 ]⁺: Cp’=Cp, pp=dppe; [ 3 ]⁺: Cp’=Cp*, pp=dppe) feature a ‘two‐band’ pattern, which complicates band‐shape analysis using these traditional methods. In the past, the appearance of sub‐bands within or near the IVCT transition has been attributed to vibronic effects or localised d‐d transitions. Quantum‐chemical modelling of a series of rotational conformers of [ 1 ]⁺–[ 3 ]⁺ reveals the two components that contribute to the NIR absorption band envelope to be a π‐π* transition and an MLCT transition. The MLCT components only gain appreciable intensity when the orientation of the half‐sandwich ruthenium ligand spheres deviates from idealised cis (Ω P?Ru?Ru?P=0°) or trans (Ω P?Ru?Ru?P=180°) conformations. The increased steric demand of the supporting ligands, together with some underlying inter‐phosphine ligand T‐shaped CH???π stacking interactions across the series [ 1 ]⁺ to [ 2 ]⁺ to [ 3 ]⁺ results in local minima biased towards such non‐idealised conformations of the metal‐ligand fragments (Ω P?Ru?Ru?P=33–153°). Experimentally, this is indicated by appearance of multiple bands within the IR (C≡C) band envelopes and increasing intensity of the higher‐energy MLCT transition(s) relative to the π‐π* transition across the series, and the appearance of a pronounced ‘two‐band’ pattern in the experimental NIR absorption envelopes. These conformational effects and the methods of analysis presented here, which combine analysis of IR and NIR spectra with quantum‐chemical calculations on a range of energetically similar conformational minima, are expected to be quite general for mixed‐valence systems.     

Canonical orbital contributions to the magnetic fields induced by global and local diatropic and paratropic ring currents

The induced magnetic field (IMF) of naphthalene, biphenyl, biphenylene, benzocyclobutadiene, and pentalene is dissected to contributions from the total π system, canonical π‐molecular orbitals (CMO), and HOMO→π* excitations, to evaluate and interpret relative global and local diatropicity and paratropicity. Maps of the IMF of the total π system reveal its relative strength and topology that corresponds to global and local diatropic and paratropic ring currents. The total π magnetic response is determined by this of canonical HOMOs and particularly by paratropic contributions of rotational excitations from HOMOs to unoccupied π * orbitals. Low energy excitations and similar nodal structure of HOMO and π * induce strong paratropic fields that dominate on antiaromatic rings. High energy excitations and different nodal structures lead to weak paratropic contributions of canonical HOMOs, which are overwhelmed by diatropic response of lower energy canonical orbitals in aromatic rings. CMO‐IMF analysis is found in agreement with ring current analysis. © 2017 Wiley Periodicals, Inc.     

π‐Electron currents in larger fully aromatic benzenoids

Recently, we have reported on calculation of π‐electron ring currents in several smaller fully benzenoid hydrocarbons having up to eight fused benzene rings and five Clar π‐aromatic sextets. In contrast to early HMO ring current calculations and more recent ab initio calculations of π‐electron density, our current calculations are based on a graph theoretical model in which contributions to ring currents comes from currents associated with individual conjugated circuits. In this contribution, we consider several larger fully benzenoid hydrocarbons having from 9 to 13 fused rings and from six or seven π‐aromatic sextets. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

π Aromaticity and Three‐Dimensional Aromaticity: Two sides of the Same Coin?

A bridge between classical organic polycyclic aromatic hydrocarbons (PAH) and closo borohydride clusters is established by showing that they share a common origin regulated by the number of valence electrons in an electronic confined space. Application of the proposed electronic confined space analogy (ECSA) method to archetypal PAHs leads to the conclusion that the 4n+2 Wade–Mingos rule for three‐dimensional closo boranes is equivalent to the (4n+2)π Hückel rule for two‐dimensional PAHs. More importantly, use of ECSA allows design of new interesting fused closo boranes which can be a source of inspiration for synthetic chemists.     

π Aromaticity and Three‐Dimensional Aromaticity: Two sides of the Same Coin?

A bridge between classical organic polycyclic aromatic hydrocarbons (PAH) and closo borohydride clusters is established by showing that they share a common origin regulated by the number of valence electrons in an electronic confined space. Application of the proposed electronic confined space analogy (ECSA) method to archetypal PAHs leads to the conclusion that the 4n+2 Wade–Mingos rule for three‐dimensional closo boranes is equivalent to the (4n+2)π Hückel rule for two‐dimensional PAHs. More importantly, use of ECSA allows design of new interesting fused closo boranes which can be a source of inspiration for synthetic chemists.     

Domino Friedel-Crafts-type cyclizations of difluoroalkenes promoted by the α-cation-stabilizing effect of fluorine: an efficient method for synthesizing angular PAHs

In order to synthesize polycyclic aromatic hydrocarbons with nonlinear arrangements (angular PAHs), acid‐promoted domino cyclizations of 1,1‐difluoroalk‐1‐enes and 1,1‐difluoroalka‐1,3‐dienes were studied. 1,1‐Difluoroalkenes, each bearing two aryl substituents, were regioselectively protonated with FSO₃H?SbF₅ to generate fluorine‐stabilized carbocations, which readily underwent domino Friedel–Crafts‐type cyclizations to give carbocycles based on 6/n/m/6 ring systems (n,m=5–7) in good to high yields. Protonation of 1,1‐difluoroalka‐1,3‐dienes took place at their electron‐rich methylene (CH₂) carbon atoms in the presence of milder acids such as camphorsulfonic acid and trifluoromethanesulfonic acid. Domino cyclizations of the resulting fluorine‐stabilized allylic carbocations afford carbocycles based on 6/6/6/6 or 6/6/5/6 ring systems in high yields.     

The phenalenyl motif: a magnetic chameleon

The 12pi cation (3) and 14pi anion (4) derived from the phenalenyl radical (2) support diatropic ("aromatic") perimeter ring currents, but isoelectronic replacement of the central atom by either boron (5) or nitrogen (6) leads to paratropic ("antiaromatic") current; the ipsocentric approach to molecular magnetic response accounts for all four patterns in terms of competition between translationally and rotationally allowed virtual pi-pi* excitations.     

π‐electron currents in polycyclic conjugated hydrocarbons: Coronene and its isomers having five and seven member rings

We have outlined novel graph theoretical model for computing π‐electron currents in π‐electron polycyclic conjugated hydrocarbons. We start with Kekulé valence structures of a polycyclic conjugated hydrocarbon and their conjugated circuits. To each 4n+2 conjugated circuits we assign counter clockwise current i and to each 4n conjugated circuit we assign clockwise current i. By adding the contributions from all conjugated circuits in a single Kekulé valence structure one obtains π‐electron current pattern for the particular Kekulé valence structure. By adding the conjugated circuit currents in all Kekulé valence structure one obtains the pattern of π‐electron currents for considered molecule. We report here π‐electron current patters for coronene and 17 its isomers, which have been recently considered by Balaban et al., obtained by replacing one or more pairs of peripheral benzene rings with five and seven member rings. Our results are compared with their reported π‐electron current density patters computed by ab initio molecular orbital (MO) computations and satisfactory parallelism is found between two so disparate approaches. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Aromaticity and ring currents in ferrocene and two isomeric sandwich complexes

Ring currents induced in the ferrocene molecule and its two hypothetical isomers (η⁴-C₄H₄)Fe(η⁶-C₆H₆) and (η³-C₃H₃)Fe(η⁷-C₇H₇) by an external magnetic field directed along the principal axis are plotted within the ipsocentric approach (at the B3LYP/6-31G∗∗//B3LYP/6-31G∗∗ level). The carbocyclic ligands in all three species are found to be aromatic, i.e. to support individual diatropic ring currents, with formal charges that are consistent with the 4n + 2 rule and the +2 oxidation state of iron.     

D6h‐Au42 Isomer: A Golden Aromatic Toroid Involving Superatomic π‐Orbitals that Follow the Hückel (4n+2)π rule

Recently, it has been shown that the superatom concept is intimately connected to relevant tools of great chemical significance, such as the Lewis structure model and the VSEPR theory, which has been employed to understand hybridized and dimeric‐like molecules. This suggests a potential rational construction of superatomic clusters mimicking more complex structures. Here, we extend another well‐employed concept to the superatomic clusters, to construct a novel Au₄₂ isomer with resemblance to cyclic aromatic molecules. It is shown that the Hückel (4n+2)π rule is ready to be applied, predicting aromatic behavior latterly supported by the favorable evaluation of the induced shielding cone formation. The D₆h isomer of Au₄₂ described here exhibits inherent characteristics mimicking aromatic hydrocarbon rings, displaying π‐superatomic orbitals and related properties. This new cluster is the first member of the superatomic clusters family to exhibit an aromatic π‐electron system.     

The nature of structure and bonding between transition metal and mixed Si‐Ge tetramers: A 20‐electron superatom system

A novel superatom species with 20‐electron system, Si_xGe_yM⁺ (x + y = 4; M = Nb, Ta), was properly proposed. The trigonal bipyramid structures for the studied systems were identified as the putative global minimum by means of the density functional theory calculations. The high chemical stability can be explained by the strong p‐d hybridization between transition metal and mixed Si‐Ge tetramers, and closed‐shell valence electron configuration [1S²1P⁶2S²1D¹⁰]. Meanwhile, the chemical bondings between metal atom and the tetramers can be recognized by three localized two‐center two‐electron (2c‐2e) and delocalized 3c‐2e σ‐bonds. For all the doped structures studied here, it was found that the π‐ and σ‐electrons satisfy the 2(N + 1)² counting rule, and thus these clusters possess spherically double (π and σ) aromaticity, which is also confirmed by the negative nucleus‐independent chemical shifts values. Consequently, all the calculated results provide a further understanding for structural stabilities and electronic properties of transition metal‐doped semiconductor clusters. © 2016 Wiley Periodicals, Inc.     

Global Aromaticity in Macrocyclic Cyclopenta‐Fused Tetraphenanthrenylene Tetraradicaloid and Its Charged Species

A stable cyclopenta‐fused tetraphenanthrenylene macrocycle, CPTP‐M , was synthesized, and the structure was confirmed by X‐ray crystallographic analysis. It exhibits a large radical character (number of unpaired electron, N_U=3.52) and a small singlet–triplet energy gap (ΔE_S‐T=?2.8 kcal mol^?1 by SQUID). Its backbone contains 60 ([4n]) conjugated π electrons and is globally antiaromatic. NMR measurements and theoretical calculations revealed that its dication/dianion is globally aromatic owing to the existence of [4n?2]/[4n+2] π‐conjugated electrons. Remarkably, the ring‐current map of the tetraanion shows a unique ring‐in‐ring structure, with a diamagnetic outer ring and a paramagnetic inner ring. Accordingly, both the inner‐rim and outer‐rim protons are deshielded in its ¹H NMR spectrum. The tetraanion can be regarded as an isoelectronic structure of the known octulene, which shows similar electronic properties.     

Nature of Bonding in Bowl‐Like B36 Cluster Revisited: Concentric (6π+18π) Double Aromaticity and Reason for the Preference of a Hexagonal Hole in a Central Location

The bowl‐shaped C_6v B₃₆ cluster with a central hexagon hole is considered an ideal molecular model for low‐dimensional boron‐based nanosystems. Owing to the electron deficiency of boron, chemical bonding in the B₃₆ cluster is intriguing, complicated, and has remained elusive despite a couple of papers in the literature. Herein, a bonding analysis is given through canonical molecular orbitals (CMOs) and adaptive natural density partitioning (AdNDP), further aided by natural bond orbital (NBO) analysis and orbital composition calculations. The concerted computational data establish the idea of concentric double π aromaticity for the B₃₆ cluster, with inner 6π and outer 18π electron counting, which both conform to the (4n+2) Hückel rule. The updated bonding picture differs from existing knowledge of the system. A refined bonding model is also proposed for coronene, of which the B₃₆ cluster is an inorganic analogue. It is further shown that concentric double π aromaticity in the B₃₆ cluster is retained and spatially fixed, irrespective of the migration of the hexagonal hole; the latter process changes the system energetically. The hexagonal hole is a destabilizing factor for σ/π CMOs. The central hexagon hole affects substantially fewer CMOs, thus making the bowl‐shaped C_6v B₃₆ cluster the global minimum.