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.     

Implications of molecular orbital symmetries and energies for the electron delocalization of inorganic clusters.

Isostructural clusters exhibit contrasting magnetic properties when the number of electrons differs. Surprisingly, the same is true even for isoelectronic cages (e.g. O(h) B6H6(2-) is diatropic, whereas O(h) Si6(2-) is paratropic) or for those with different substitutents (e.g. T(d) B4H4 is paratropic, whereas T(d) B4F4 is diatropic). Indeed, the total nucleus-independent chemical shift (NICS) values, based on shieldings computed at cluster centers, may range considerably in magnitude and even change from diatropic (up-field shifted) to paratropic (down-field shifted). Similarly, individual dissected canonical molecular orbital contributions to the total NICS values computed at the "gauge-including atomic orbitals" (GIAO) level vary greatly. This contrasting behavior arises from molecular orbital energy differences, from the extent of orbital overlap, as well as from symmetry-based selection rules derived from group theory. Differences in magnetic properties may originate from the symmetry of the orbitals; specifically from the forbidden nature of the highest occupied molecular orbital --> lowest unoccupied molecular orbital (HOMO --> LUMO) electronic excitation weighted by the occupied-unoccupied orbital energy difference. Thus, HOMO-NICS values are generally highly paratropic if the HOMO --> LUMO rotational transition is allowed by symmetry selection rules.     

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.     

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.     

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.     

Reduction of bowl-shaped hydrocarbons: dianions and tetraanions of annelated corannulenes

[structure: see text] The reduction of several annelated corannulene derivatives was undertaken using lithium and potassium metals. It was found that annelation affects the annulenic character of corannulene by changing its charge distribution; the dianions of derivatives that are annelated with six-membered rings have less annulenic character and are less paratropic than corannulene dianion. This effect is even more pronounced in corannulenes that are peri-annelated with five-membered rings. The alkali metal used in the reduction process has a great influence on the outcome, especially on the degree of reduction. Most derivatives get reduced to tetraanions only with potassium, and not with lithium, the exception being systems that can stabilize the tetraanion with lithium by special means, such as aggregation or dimerization. One such system is cyclopenta[bc]corannulene (acecorannulylene), which gives a coordinative dimer that consists of two cyclopentacorannulene tetraanions, bound together in a convex-convex fashion by lithium cations. The points of contact in this dimer are two rehybridized carbons from each cyclopentacorannulene unit, which are bridged together by two lithium cations.     

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.     

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.     

Diamagnetic and paramagnetic ring currents in expanded porphyrins

Ipsocentric current density maps are computed at the coupled Hartree-Fock level in the 6-31G** basis set for the planar C(2v) B3LYP geometries of the expanded porphyrins, sapphyrin and orangarin. Both give clearly dominant global macrocyclic ring currents, but with opposite senses of circulation: in 22[small pi] sapphyrin, a diatropic current runs, with some bifurcation, around the conventional 22-centre delocalisation pathway; in 20[small pi] orangarin, a paratropic current runs around the inner 17-atom pathway. In agreement with the annulene analogy for these macrocycles, analysis of orbital contributions shows that in each case topology, energy and symmetry of the frontier orbitals together determine the macrocyclic ring current. In sapphryrin, 4-electron diamagnetism (aromaticity) arises from translationally allowed HOMO-LUMO excitations as in benzene itself; in orangarin, 2-electron paramagnetism (antiaromaticity) arises from rotationally allowed HOMO-LUMO excitations as in planarised cyclooctatetraene. The active orbitals invoked in the explanation of ring currents are those involved in the longstanding four-orbital model of porphyrin electronic spectra.     

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.     

The aromaticity/antiaromaticity continuum. 1. Comparison of the aromaticity of the dianion and the antiaromaticity of the dication of tetrabenzo[5.5]fulvalene via magnetic measures

The aromaticity of the dianion (2) and the antiaromaticity of the dication (3) of tetrabenzo[5.5]fulvalene have been evaluated through magnetic criteria, (1)H NMR shifts, nucleus-independent chemical shifts, NICS, and magnetic susceptibility exaltation, Lambda. The sum of the NICS values, using the GIAO (gauge-independent atomic orbital) method, for 2 is -35.2; that of 3 is +38.2, indicating the aromaticity of 2 and the antiaromaticity of 3. Calculation of magnetic susceptibility exaltation using the CSGT (continuous set of gauge transformations) method gives a similar result, with Lambda of -81.8 ppm cgs for 2 and 95.8 ppm cgs for 3. The general validity of these values is supported by excellent agreement between the NMR shifts calculated by the GIAO and CSGT methods with experimental shifts. Comparison of 1H NMR shifts with those of model compounds allows evaluation of the magnitude of the diatropic shift in 2 and paratropic shift in 3 and supports their assignment as aromatic/antiaromatic, respectively. The agreement between calculated and experimental 1H NMR shifts is excellent for 3 in the absence of counterions but much better for 2 when counterions are included. Inclusion of counterions in the evaluation of diatropic shift for 2 gave a smaller shift than in the absence of counterions, suggesting a decreased aromaticity. When counterions were included in the calculation of Lambda, the value was also decreased, suggesting a decreased aromaticity. This observation has important consequences in the use of experimental data for the evaluation of aromaticity, and presumably antiaromaticity, of anions since, in most cases, there will be close interaction with counterions.     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.     

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.     

Doubly charged ions of bridged [4n] annulenes. An evaluation of diatropic ring current effects.

[4n]Annulenes are transformed into doubly charged ions (dianion, dication) and characterized NMR spectroscopically. The diatropic character of the ionic (4n+2)π-systems is studied as a function of the number of π-electrons.     

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.     

Curve-structured phenalenyl chemistry: synthesis, electronic structure, and bowl-inversion barrier of a phenalenyl-fused corannulene anion

We have demonstrated the features of curve-structured phenalenyl chemistry, for the first time. A phenalenyl-fused corannulene anion has been designed by the annelation of a six-memberd ring across peri-positions of corannulene and generated as a stable species in a degassed solution. The 1H and 13C NMR spectra have shown the highly symmetrical structure and high-field shifts of protons and carbons at the asterisked positions in the chemical structure, indicating the occurrence of large negative charge densities at these positions. These results well agree with the HOMO picture and the electrostatic potential surface, demonstrating the phenalenyl anion-type electronic structure is retained in the curved-surface pi-system. The calculated bowl-inversion barrier of the anion (11.3 kcal/mol) is larger than that of corannulene (9.2 kcal/mol) because of peri-annelation of the corannulene skeleton. The calculations of the barriers of the neutral radical (12.6 kcal/mol), radical dianion (8.1 kcal/mol), and trianion (5.4 kcal/mol) of the phenalenyl-fused corannulene have exhibited a stepwise flattening of the curvature with increase in negative charge. Therefore, we have revealed that the bowl-inversion barrier of the anion is governed by the setoff of the peri-annelation and negative charge effects.     

Do all-metal antiaromatic clusters exist?

As shown by detailed nucleus-independent chemical shift (NICS) analyses of the contributions of each molecular orbital, the very recently reported gas-phase all-metal Al4Li3- anion and its relatives (Kuznetsov, A.E.; Birch, K.A.; Boldyrev, A.I.; Li, X.; Zhai, A.I.; Wang, L.S. Science 2003, 300, 622) are aromatic rather than antiaromatic. The paratropic (antiaromatic) four-pi-electron contribution is overcome by the predominating diatropic effects of sigma aromaticity. However, true antiaromatic all-metal clusters, such as Sn62- (Schiemenz, B.; Huttner, G. Angew. Chem., Int. Ed. Engl. 1993, 32, 297), do exist.     

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.