Aromaticity and magnetotropicity of dicyclopenta-fused polyacenes

Most dicyclopenta-fused polyacenes are predicted to be moderately aromatic and diatropic, although they have no (4n + 2)-site conjugated circuits. We applied our graph theory of aromaticity and magnetotropicity to these molecules and found that these anomalous properties arise from a set of non-conjugated circuits, which contribute collectively to aromaticity and diatropicity. This result indicates that the conjugated circuit model is not always applicable to such non-alternant hydrocarbons. Dianions of dicyclopenta-fused polyacenes are more aromatic than their respective neutral species, because they are iso-pi-electronic with aromatic polyacenes.     

Magnetically induced current densities in Al4 (2-) and Al4 (4-) species studied at the coupled-cluster level

Magnetically induced current densities in the four-membered rings of Al4(2-) and Al4(4-) species have been calculated at the coupled-cluster singles and doubles (CCSD) level by applying the recently developed gauge-including magnetically induced current (GIMIC) method. The strength of the ring-current susceptibilities were obtained by numerical integration of the current densities passing through a cross section perpendicular to the Al4 ring. The GIMIC calculations support the earlier notion that Al4 (2-) with formally two pi electrons sustains a net diatropic ring current. The diatropic contribution to the ring-current susceptibility is carried by the electrons in both the sigma (16.7 nAT) and the pi (11.3 nAT) orbitals. The induced ring current in the Al4 (4-) compounds, with four pi electrons, consists of about equally strong diatropic sigma and paratropic pi currents of about 14 and -17 nAT, respectively. The net current susceptibilities obtained for Al4Li-, Al4Li2, Al4Li3(-), and Al4Li4 at the CCSD level using a triple-zeta basis set augmented with polarization functions are 28.1, 28.1, -5.9, and -3.1 nAT, respectively. The corresponding diatropic (paratropic) contributions to the ring-current susceptibilities are 32.4 (0.0), 36.7 (0.0), 18.9 (-19.9), and 18.6 (-16.8) nAT, respectively. For the Al4(2-) and Al4(4-) species, the net currents circling each Li+ cation is estimated to 4.3 and 2.4 nAT, respectively.     

Induced currents and electron counting in aromatic boron wheels: B8(2-) and B9-)

The newly discovered atom-centered polygonal wheels B8(2-) and B9- are predicted to show ring currents characteristic of aromatic systems. Ipsocentric mapping of induced current density for both molecules attributes a pi diatropic current to the four electrons of the doubly degenerate pi HOMO and a sigma diatropic current to the four electrons of the doubly degenerate sigma HOMO, each orbital pair having an available transition to corresponding LUMO orbitals in which the angular node count increases by one. Thus, on the magnetic criterion, B8(2-) and B9- are each both pi- and sigma-aromatic as a consequence of the nodal properties of the frontier orbitals of the pi- and sigma-stacks.     

Perimeter Effects on Ring Currents in Polycyclic Aromatic Hydrocarbons: Circumcoronene and Two Hexabenzocoronenes

Current‐density maps are calculated at an ab initio level for the three symmetrical polycyclic aromatic hydrocarbons, circumcoronene [ 1 (D_6h)], hexabenzo[bc,ef,hi,kl,no,qr]coronene [ 2 a (D_6h) and 2 b (D_3d)], and hexabenzo[a,d,g,j,m,p]coronene [ 3 a (D_6h), 3 b (D₆) and 3 c (D_3d)], all of which can be formally derived by annelation of benzene rings to a coronene core. Whilst 1 is planar, 2 has a non‐planar minimum that is effectively isoenergetic with its planar form, and 3 has a well defined non‐planar structure. The shape of the molecular boundary rather than the planarity of the molecule plays the critical rôle in the character of the predicted currents. Formal deletion of outer hexagons from circumcoronene ( 1 ) in two different ways produces either hexabenzocoronene 2 with a prediction of disjoint local benzenoid diatropic currents linked by a global perimeter, or 3 with a giant diatropic perimeter current enclosing a weak paramagnetic circulation on the central hexagon. The current density map of 1 is effectively a superposition of those of 2 and 3 . Its strong diatropic perimeter current subsumes the six weaker diatropic benzenoid circulations evident in 2 , and bifurcates in the six outer benzenoid rings that form the corners of the giant hexagon; its benzene “hub” sustains a diatropic current, as would be expected from the partial cancellation of the strong diatropic hub current of 2 by the weaker paratropic hub current of 3 . The relationship between the three molecules is rationalised by considering orbital contributions to their current density maps.     

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.     

Aromatic pathways in mono- and bisphosphorous singly Möbius twisted [28] and [30]hexaphyrins

Magnetically induced current densities and strengths of currents passing through selected bonds have been calculated for monophosphorous [28]hexaphyrin ((PO)[28]hp) and for bisphosphorous [30]hexaphyrin ((PO)(2)[30]hp) at the density functional theory level using our gauge-including magnetically induced current (GIMIC) approach. The current-density calculations yield quantitative information about electron-delocalization pathways and aromatic properties of singly M?bius twisted hexaphyrins. The calculations confirm that (PO)[28]hp sustains a strong diatropic ring current (susceptibility) of 15 nA T(-1) and can be considered aromatic, whereas (PO)(2)[30]hp is antiaromatic as it sustains a paratropic ring current of -10 nA T(-1). Numerical integration of the current density passing through selected bonds shows that the current is generally split at the pyrroles into an outer and an inner pathway. For the pyrrole with the NH moiety pointing outwards, the diatropic ring current of (PO)[28]hp takes the outer route across the NH unit, whereas for (PO)(2)[30]hp, the paratropic ring current passes through the inner C(β)=C(β) double bond. The main diatropic ring current of (PO)[28]hp generally prefers the outer routes at the pyrroles, whereas the paratropic ring current of (PO)(2)[30]hp prefers the inner ones. In some cases, the ring current is rather equally split along the two pathways at the pyrroles. The calculated ring-current pathways do not agree with those deduced from measured (1)H NMR chemical shifts.     

Hydrogen–hydrogen bonding: The current density perspective

Current density plots of closed‐shell intermolecular H? H interactions characterized by a bond critical point (BCP) show two vortices separated by a saddle, a pattern which allows for a clear definition of a pair current strength. This H? H current strength turns out to be roughly related to the potential energy density at the BCP and then to the dissociation energy. The same pattern is also recognizable, at least for an azimuthal orientation of a field perpendicular to the H? H line, for the intramolecular interactions previously investigated to propose the H? H bonding. In the case of the H atoms of the bay region of polycyclic aromatic hydrocarbons, the current of the H? H delocalized diatropic vortex gives a quantitative indication of stabilization; however, on rotation of the field and the subsequent onset of a bay‐delocalized paratropic vortex (a typical signature of antiaromaticity), the diatropic vortex can be reshaped or it can even disappear, consistently with its smallness, and thus showing the effect of other more relevant interactions. © 2015 Wiley Periodicals, Inc.     

Four- and two-electron rules for diatropic and paratropic ring currents in monocyclic pi systems

The pi ring current in an even-eletron monocycle is dominated by the HOMO-LUMO transition, and hence corresponds to circulation of four electrons in a diatropic (4n + 2)-electron, but two in a paratropic (4n)-electron cycle.     

Magnetic euripi in corannulene

Ab initio current densities induced by an external magnetic field have been computed for corannulene dianion, dication, and tetraanion. The pi-ring currents are found to be large with respect to benzene and to undergo remarkable changes in response to variations in the oxidation state. According to the results obtained here, the three corannulene ions plus the neutral species constitute a very special set that spans all of the possible patterns of rim and hub circulations: diatropic/hub-paratropic/rim (the dianion), paratropic/hub-paratropic/rim (the dication, assuming conformationally averaged current density), diatropic/hub-diatropic/rim (the tetraanion), and paratropic/hub-diatropic/rim (the neutral, as already reported by other authors). Orbital contributions and their breakdown into explicit contributions from virtual excitations have been analyzed. It is shown that the dianion and dication are both (2p) systems characterized by a single highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) rotationally allowed transition. For the dianion, this transition is responsible not only for the outer paratropic circulation but also for the inner diatropic circulation, a behavior that requires an extension of the few electron model based on orbital contributions to be fully rationalized. For the dication, the HOMO-LUMO transition provides a paratropic circulation localized on one indene subunit. However, because of the fast exchange of conformers, it is sensible to calculate an averaged current density field, which is characterized by con-rotating paratropic inner and outer ring currents. For the tetraanion, the calculated current pattern is in agreement with a previous indication, while the orbital analysis reveals that the HOMO and the HOMO - 1 contribute to both inner and outer circulations. Despite the small 6-31G** basis set employed to calculate current densities and magnetic properties, a satisfactory agreement between computed and available experimental (1)H and (13)C chemical shifts is found, providing a firm basis for the above conclusions. Remarkably, the "diamagnetic" corannulene dianion observed in NMR at low temperature is predicted to be a paramagnetic closed-shell species.     

Ring-current models from the differential Biot-Savart law

The differential Biot-Savart law provides simple models for the pi ring currents induced in diatropic and paratropic planar conjugated molecules by a perpendicular magnetic field. The model predictions are confirmed by ab initio maps of nuclear magnetic shielding density. The effects on the protons and on the ring carbon atoms from the closest and furthest segments of the current loop are easily interpreted. [structure: see text]     

Control of the diatropic pi ring current in strained benzenes: effects of annelation with cyclopropa,cyclobuta, and cyclobutadieno clamping groups

Direct visualization of the pi current density maps of highly strained annelated benzenes containing cyclopropa, cyclobuta, and cyclobutadieno clamps, alone and in combination, using a reliable distributed-origin, coupled Hartree-Fock method, shows the robustness of the classical benzene diatropic pi ring current. When only saturated clamps are used, the benzene ring current is essentially unchanged. In contrast, annelation with one or more cyclobutadieno clamps disrupts the benzene ring current. Analysis of orbital contributions to the current density maps gives a unified account of these observations in terms of the nature of the HOMO-LUMO transition.     

Phosphonium ylides from nucleophilic addition of triphenylphosphine to [26]hexaphyrin(1.1.1.1.1.1)

[reaction: see text] Nucleophilic addition of triphenylphosphine to neutral meso-hexakis(pentafluorophenyl)-substituted [26]hexaphyrin(1.1.1.1.1.1) (1) provided a stable phosphonium ylide of [28]hexaphyrin (3), which was quantitatively oxidized to its 26pi-counterpart (4) that exhibited a planar and rectangular conformation and a diatropic ring current.     

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.     

Ring currents in tangentially p-p bonded sigma-aromatic systems

We report a theoretical study of ring systems that delocalize electrons in a cyclic array of p orbitals arranged tangentially in sigma-bonding fashion. Sigma-bonded arrays are compared to conventional pi-bonded analogues with respect to orbital symmetry and aromatic/antiaromatic behavior. In a one-to-one correspondence between pi and tangential molecular orbitals of a cycle, local rotation turns each pi to a tangential basis function, changing bonding interactions to antibonding and inverting the order of filling of molecular orbitals. The ipsocentric ring-current mapping approach is used to evaluate aromaticity on the magnetic criterion. As for conventional pi-ring currents, the sigma-ring current in tangential p-p bonded systems is dominated by the HOMO-LUMO transition, corresponding to circulation of four electrons in diatropic (4n + 2)-electron cycles but two in paratropic (4n)-electron cycles. The systems examined here utilize either C 2p or Si 3p orbitals for delocalization. Although interchangeable with C with respect to the fundamental orbital symmetry and ring-current rules, Si bonds at greater internuclear distances, a feature that allows easier design of potentially stable sigma-aromatic structures. Calculations show the wheel-like Si10C50H70 structure 6 as a stable, neutral aromatic molecule with a diatropic ring current following the sigma-bond path formed by Si 3p orbitals.     

22]Porphyrin-(3.1.1.3), a new vinylogous expanded porphyrin system

Acid-catalyzed condensation of a pyrrole bisacrylaldehyde with a tripyrrane, followed by oxidation with ferric chloride, gave a [22]porphyrin-(3.1.1.3). This stretched macrocycle shows a strong diamagnetic ring current by (1)H NMR spectroscopy and gives red-shifted porphyrin-like UV-vis spectra; coordination with palladium(II) induces an EZ isomerization to accommodate the metal cation while retaining highly diatropic characteristics. [structure: see text]     

Tetraaryldimethoxybenziporphyrins. At the edge of carbaporphyrinoid aromaticity

A series of eight dimethoxybenziporphyrins were prepared in three steps from 1,3-dimethoxybenzene or 2,6-dimethoxytoluene. Dibromination, followed by lithium-halogen exchange and reaction with benzaldehyde gave dicarbinol intermediates. These reacted with pyrrole and aryl aldehydes in the presence of BF3.Et2O in chloroform, followed by oxidation with DDQ, to give the benziporphyrins in 15-25% yield. These compounds readily gave nickel(II) and palladium(II) organometallic derivatives and could be selectively reduced with sodium borohydride to give unstable benziphlorins. Regioselective oxidation with silver acetate afforded the related 22-acetoxybenziporphyrins in 52-64% yield. The dimethoxybenziporphyrins showed chemical shifts by proton NMR spectroscopy that were consistent with weakly diatropic macrocycles. However, addition of TFA gave dications that showed far more significant shifts that are attributed to the presence of a more substantial diatropic ring current. The internal CH for 11H2(2+) was observed at 3.5 ppm, but this effect was diminished for the 3-methylbenziporphyrins 12H2(2+) where this resonance appears at 4.7 ppm. Even in the absence of the methoxy substituents, the dication derived from tetraphenylbenziporphyrin 8H2(2+) shows an upfield shift for this resonance to 5.5 ppm. The dications of the 22-acetoxybenziporphyrins also show similar effects despite the presence of an internal ester moiety. These results demonstrate that a spectrum of diatropic character can manifest even in highly crowded benziporphyrin derivatives.     

Interpreting Aromaticity and Antiaromaticity through Bifurcation Analysis of the Induced Magnetic Field

In all molecules, a current density is induced when the molecule is subjected to an external magnetic field. In turn, this current density creates a particular magnetic field. In this work, the bifurcation value of the induced magnetic field is analyzed in a representative set of aromatic, non-aromatic and antiaromatic monocycles, as well as a set of polycyclic hydrocarbons. The results show that the bifurcation value of the ring-shaped domain adequately classifies the studied molecules according to their aromatic character. For aromatic and nonaromatic molecules, it is possible to analyze two ring-shaped domains, one diatropic (inside the molecular ring) and one paratropic (outside the molecular ring). Meanwhile, for antiaromatic rings, only a diatropic ring-shaped domain (outside the molecular ring) is possible to analyze, since the paratropic domain (inside the molecular ring) is irreducible with the maximum value (attractor) at the center of the molecular ring. In some of the studied cases, i. e., in heteroatomic species, bifurcation values do not follow aromaticity trends and present some inconsistencies in comparison to ring currents strengths, showing that this approximation provides only a qualitative estimation about (anti)aromaticity.     

The electronic structure of inorganic benzenes: valence bond and ring-current descriptions

Valence bond (VB) theory and ring-current maps have been used to study the electronic structure of inorganic benzene analogues X(6)H(6) (X = C (1), Si (2)), X(6) (X = N (3), P (4)), X(3)Y(3)H(6) (X,Y = B,N (5), B,P (6), Al,N (7), Al,P (8)), and B(3)Y(3)H(3) (Y = O (9), S (10)). It is shown that the homonuclear compounds possess benzene-like character, with resonance between two Kekulé-like structures and induced diatropic ring currents. Heteronuclear compounds typically show localization of the lone pairs on the electronegative atoms; Kekulé-like structures do not contribute. Of the heteronuclear compounds, only B(3)P(3)H(6) (6) has some benzene-like features with a significant contribution of two Kekulé-like structures to its VB wave function, an appreciable resonance energy, and a discernible diatropic ring current in planar geometry. However, relaxation of 6 to the optimal nonplanar chair conformation is accompanied by the onset of localization of the ring current.     

The Curious Case of a Parasitic Twin of the Corroles

An expanded porphyrinoid has been obtained by a simple ring expansion from a contracted porphyrinoid, namely corrole. Spectroscopic, structural, and computational investigations reveal peculiar π‐conjugation and geometry. The effect of extended π‐conjugation is evident from perturbed redox behavior and photophysical properties. Owing to the strong diatropic ring current of the corrole and cross‐conjugation, the molecule exhibits a non‐aromatic nature for the expanded π‐circuit, as evident from NMR studies.     

Spatial ring current model for the prismane molecule

Spatial models of magnetic-field induced electronic ring currents have been constructed for the prismane molecule via stagnation graphs and current density maps. These tools provide an insight into the complicated phenomenology resulting from competition of diatropic and paratropic regimes that determine the magnitude of various components of magnetic susceptibility and magnetic shielding of hydrogen and carbon nuclei. Shielding density maps show that the differential Biot-Savart law, along with an atlas of the current density field, explains magnetic shielding at hydrogen and carbon nuclei and virtual shielding at ring and cage centers.