Probing the aromaticity of bis(diazolo)pyrazine radical anions

The aromaticity of a series of heterocyclic radical anions of bis(diazolo)pyrazine type, X(CN)₂N₂(CN)₂Y (X, Y = O, S, Se, Te) was explored by the methods of electron density of delocalized bonds (EDDB) and gauge-included magnetically induced currents (GIMIC). The existence of T-aromaticity that encloses the entire molecule, which was due to delocalization of seven β-electrons, was shown. The degree of aromaticity depends on the nature of the X(Y) heteroatom and varies in the series S > O > Se > Te.     

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.     

Electronic Structure,Aromaticity and Optical Properties of Dehydro[10]annulene

Dehydro[10]annulene had been prepared experimentally recently, which is considered to be a highly rigid structure with planar configuration. In this paper, the electronic structure and bonding character of dehydro[10]annulene had been studied by means of molecular orbital (MO), density of states (DOS), bond order (BO) and interaction region indicator (IRI) analyses. The delocalization characters of out-of-plane and in-plane π-electrons (π^out- and πⁱⁿ-electrons) of the bond regions were studied by using localized orbital locator (LOL). The anisotropy of the induced current density (AICD), iso-chemical shielding surface (ICSS) and anisotropy of the gauge-including magnetically induced current (GIMIC) were used to investigate the molecular response to external magnetic field, including the induced ring current and the magnetic shielding characteristic. The results showed that the electron delocalization of dehydro[10]annulene is mainly contributed by π^out system. The apparent clockwise current in the π^out system proved that dehydro[10]annulene is π^out aromatic. Finally, the photophysical properties and (hyper)polarizability of dehydro[10]annulene were studied by TD-DFT calculation. The results showed that dehydro[10]annulene has strong local excitation characters. Its (hyper)polarizability decreases with the increase of frequency and has the characteristics of nonlinear anisotropy.     

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.     

Interplay of Hückel and Möbius Aromaticity in Metal-Metal Quintuple Bonded Complexes of Cr,Mo, and W with Amidinate Ligand: Ab initio DFT and Multireference Analysis**

The aromaticity of metal-metal quintuple bonded complexes of the type M₂L₂ (M=Cr, Mo, and W; L=amidinate) are studied employing gauge including magnetically induced ring current (GIMIC) analysis and electron density of delocalized bonds (EDDB). It is found that the complexes possess two types of aromaticity: i) Hückel aromaticity through delocalization of ligand π electrons with metal-metal δ-bond-forming 6 conjugated electrons (4π and 2δ) ring; ii) Craig-Möbius aromaticity through delocalization of π electrons of both the ligands with metal d-orbitals in Craig type orientation forming 10π electrons ring with a double twist. Extended transition state natural orbital chemical valence (ETS-NOCV) and canonical molecular orbital natural chemical shielding (CMO-NCS) analysis confirm the Craig-Möbius type arrangement of the orbitals. Furthermore, the unprecedented Hückel and Möbius type aromaticity is confirmed from the plot of the current pathways using 3D line integral convolution (3D-LIC) plots. The metal-metal bond order also increases down the group as justified from the complete active space self-consistent field (CASSCF) analysis. Due to an increase in the π and δ electron conjugation, both the Hückel and Möbius aromaticity increase down the group.     

Evaluating Shielding‐Based Ring‐Current Models by Using the Gauge‐Including Magnetically Induced Current Method

Magnetically induced current densities and integrated ring‐current strength susceptibilities have been calculated at the density functional theory (DFT) level for a test set consisting of 17 ring‐shaped molecules using the gauge‐including magnetically induced current (GIMIC) method. Reliable values for the ring‐current strengths have been obtained by performing numerical integration of the current‐density susceptibility passing a cut plane perpendicularly to the molecular ring. The current densities and ring current strengths were calculated at the DFT level using the B3LYP functional and def2‐TZVP basis sets. Current densities and ring‐current strengths have also been calculated at the Hartree‐Fock self‐consistent field (HF‐SCF) level using Dunning’s aug‐cc‐pVTZ basis sets, which allow a direct comparison with ring‐current strengths that have previously been estimated using ring‐current models based on magnetic shielding calculations. Current density calculations at both levels of theory show that the magnetic shielding based ring‐current models are not a very accurate means to estimate the magnetically induced ring current strengths, whereas they provide qualitatively the correct aromaticity trends for the studied molecules.     

The gauge including magnetically induced current method

An overview of applications of the recently developed gauge including magnetically induced current method (GIMIC) is presented. The GIMIC method is used to obtain magnetically induced current densities in molecules. It provides detailed information about electron delocalization, aromatic character, and current pathways in molecules. The method has been employed in aromaticity studies on hydrocarbons, complex multi-ring organic nanorings, M?bius twisted molecules, inorganic and all-metal molecular rings and open-shell species. Recent studies on hydrogen-bonded molecules indicate that GIMIC can also be used to estimate hydrogen-bond strengths without fragmentation of the system. Preliminary results are presented on the applicability of GIMIC for investigating current transport in molecules attached to clusters simulating molecular conductivity measurements. Advantages and limitations of the GIMIC method are reviewed and discussed.     

Synthesis,Aromaticity and Photophysical Behaviour of Ferrocene‐ and Ruthenocene‐Appended Semisynthetic Chlorin Derivatives

Two novel synthetic strategies to covalently link a metallocene electron‐donor unit to a chlorin ring are presented. In one approach, pyropheophorbide a is readily converted into its 13¹‐ferrocenyl dehydro derivative by nucleophilic addition of the ferrocenyl anion to the 13¹‐carbonyl group. In another approach, the corresponding 13¹‐pentamethylruthenocenyl derivative is synthesised from 13¹‐fulvenylchlorin by a facile ligand exchange/deprotonation reaction with the [RuCp*(cod)Cl] (Cp*=pentamethylcyclopentadienyl; cod=1,5‐cyclooctadiene) complex. The resulting metallocene–chlorins exhibit reduced aromaticity, which was unequivocally supported by ring‐current calculations based on the gauge‐including magnetically induced current (GIMIC) method and by calculated nucleus‐independent chemical shift (NICS) values. The negative ring current in the isocyclic E ring suggests the antiaromatic character of this moiety and also clarifies the spontaneous reactivity of the complexes with oxygen. The oxidation products were isolated and their electrochemical and photophysical properties were studied. The ruthenocene derivatives turned out to be stable under light irradiation and showed photoinduced charge transfer with charge‐separation lifetimes of 152–1029 ps.     

Three dimensional aromaticity in pyramidanes C4R4E and Ge4R4Ge

Three dimensional aromaticity in pyramidanes C₄(SiMe₃)₄E (E = Ge, Sn, Pb, P⁺, BCl, Mg) and Ge₄(SiMe₃)₄Ge was investigated using gauge-included magnetically induced currents and electron density of delocalized bonds as two criteria. For the C₄(SiMe₃)₄E compounds, different series of the aromaticity degree have been obtained by the two methods, respectively: P > Ge ≥ Sn ∼ Pb > B and Pb ≥ Sn ≥ Ge > B > P. Two isomers of Ge₄(SiMe₃)₄Ge possess nearly equal aromaticity.     

Disclosure of Ground-State Zimmerman-Möbius Aromaticity in the Radical Anion of [6]Helicene and Evidence for 4π Periodic Aromatic Ring Currents in a Molecular “Metallic” Möbius Strip

In 1966, Zimmerman proposed a type of Möbius aromaticity that involves through-space electron delocalization; it has since been widely applied to explain reactivity in pericyclic reactions, but is considered to be limited to transition-state structures. Although the easily accessible hexahelicene radical anion has been known for more than half a century, it was overlooked that it exhibits a ground-state minimum and robust Zimmerman-Möbius aromaticity in its central noose-like opening, becoming, hence, the oldest existing Möbius aromatic system and with smallest Möbius cycle known. Despite its overall aromatic stabilization energy of 13.6 kcal mol⁻¹ (at B3LYP/6-311+G**), the radical also features a strong, globally induced paramagnetic ring current along its outer edge. Exclusive global paramagnetic currents can also be found in other fully delocalized radical anions of 4N+2 π-electron aromatic polycyclic benzenoid hydrocarbons (PAH), thus questioning the established magnetic criterion of antiaromaticity. As an example of a PAH with nontrivial topology, we studied a novel Möbius[16]cyclacene that has a non-orientable surface manifold and a stable closed-shell singlet ground state at several density functional theory levels. Its metallic monoanion radical (0.0095 eV band gap at HSE06/6-31G* level) is also wave-function stable and displays an unusual 4π-periodic, magnetically induced ring current (reminiscent of the transformation behaviour of spinors under spatial rotation), thus indicating the existence of a new, Hückel-rule-evading type of aromaticity.     

The NICS‐XY‐Scan: Identification of Local and Global Ring Currents in Multi‐Ring Systems

Nucleus‐independent chemical shift (NICS)‐based methods are very popular for the determination of the induced magnetic field under an external magnetic field. These methods are used mostly (but not only) for the determination of the aromaticity and antiaromaticity of molecules and ions, both qualitatively and quantitatively. The ghost atom that serves as the NICS probe senses the induced magnetic field and reports it in the form of an NMR chemical shift. However, the source of the field cannot be determined by NICS. Thus, in a multi‐ring system that may contain more than one induced current circuit (and therefore more than one source of the induced magnetic field) the NICS value may represent the sum of many induced magnetic fields. This may lead to wrong assignments of the aromaticity (and antiaromaticity) of the systems under study. In this paper, we present a NICS‐based method for the determination of local and global ring currents in conjugated multi‐ring systems. The method involves placing the NICS probes along the X axis, and if needed, along the Y axis, at a constant height above the system under study. Following the change in the induced field along these axes allows the identification of global and local induced currents. The best NICS type to use for these scans is NICS_πZZ, but it is shown that at a height of 1.7 Å above the molecular plane, NICS_ZZ provides the same qualitative picture. This method, namely the NICS‐XY‐scan, gives information equivalent to that obtained through current density analysis methods, and in some cases, provides even more details.     

4-Component relativistic magnetically induced current density using London atomic orbitals

We present the implementation and application of 4-component relativistic magnetically induced current density using London atomic orbitals for self-consistent field models. We obtain a magnetically balanced basis by a simple scheme where orbitals obtained by imposing restricted kinetic balance are extended by their unrestricted kinetic balance complement. The presented methodology makes it possible to analyze the concept of aromaticity based on the ring current criterion for closed-shell molecules across the periodic table and is independent of the choice of gauge origin. As a first illustration of the methodology we study plots of the magnetically induced current density and its divergence in the series C(5)H(5)E (E = CH, N, P, As, Sb, Bi) at the Kohn-Sham level, as well as integrated ring current susceptibilities, which we compare to previous results (R. Bast et al., Chem. Phys., 2009, 356, 187) obtained using a common gauge origin approach. We find that the current strength decreases monotonically along the series, but that all molecules qualify as aromatic according to the ring current criterion.     

Probing the aromaticity in 2,3-pyrido-annulated N-heterocyclic carbene and its heavier analogues

The aromaticity in 2,3-pyrido-annulated 1,3,2λ²-diazatetroles C₅H₃N(NR)₂E^II (E^II = C, Si, Ge, Sn, Pb) was studied using a set of experimental and calculated criteria: UV-VIS, Raman, ISE, NICS, GIMIC and EDDB. The data obtained indicate either a slight decrease in aromaticity (NICS, GIMIC, ISE methods) or equal aromaticity (UV-VIS, ISE methods) compared to benzo-annulated analogues C₆H₄(NR)₂E. The π-aromaticity increases down the group from Si to Pb.     

Theoretical investigation of photoelectron spectra and magnetically induced current densities in ring-shaped transition-metal oxides

The molecular structures of cyclic group 6 transition-metal (M = Cr, Mo, W, Sg) oxides (M ₃O ₉ ^0/1?/2? ) species have been optimized at density functional theory (DFT) levels. The photoelectron spectra (PES) of M ₃O ₉ ^? (M = Cr, Mo, W) were calculated at the time-dependent DFT and approximate coupled-cluster singles doubles (CC2) levels and compared with experimental results. The CC2 calculations did not yield any reliable PES, whereas the molecular structures can be identified by comparing PES obtained at the DFT level with experiment. Magnetically induced current densities were calculated at the DFT level using the gauge-including magnetically induced current (gimic) approach. The current strengths and current pathways of the neutral M₃O₉ and the dianionic M₃O ₉ ^2? (M = Cr, Mo) oxides were investigated and analyzed with respect to a previous prediction of d-orbital aromaticity for Mo₃O₉ anions. Current-density calculations provide ring-current strengths that are used to assess the degree of aromaticity. Comparison of current-density calculations and calculations of nucleus-independent chemical shifts (NICS) shows that NICS calculations are not a reliable tool for determining the degree of aromaticity of the metal oxides.     

Aromatic pathways of porphins, chlorins, and bacteriochlorins

Magnetically induced current densities have been calculated for free-base porphynoids using the gauge including magnetically induce current (GIMIC) method. Numerical integration of the current density passing selected chemical bonds yields current pathways and the degree of aromaticity according to the magnetic criterion. The ring-current strengths of the porphins, chlorins, and bacteriochlorins are 1.5-2.5 times stronger than for benzene. The calculations show that the 18π [16]annulene inner cross is not the correct picture of the aromatic pathway for porphyrins. All conjugated chemical bonds participate in the current transport independently of the formal number of π electrons. The ring current branches at the pyrrolic rings taking both the outer and the inner route. The NH unit of the pyrrolic rings has a larger resistance and a weaker current strength than the pyrroles without inner hydrogens. The traditional 18π [18]annulene with inactive NH bridges is not how the ring-current flows around the macroring. The porphins have the strongest ring current of ca. 27 nA/T among the investigated porphynoids. The current strengths of the chlorins and bacteriochlorins are 19-24 nA/T depending on whether the ring current is forced to pass an NH unit or not. The current strengths of the 3-fold and 4-fold β-saturated porphynoids are 13-17 nA/T, showing that the inner-cross 18π [16]annulene pathway is not a preferred current route.     

An investigation of aromaticity in hydroxybenzenes based on the study of magnetically induced current density

Hydroxybenzenes are derivatives of benzene in which one or more H atoms are replaced by OH groups. This work considers the effect of such replacement on the aromaticity of the ring, by assessing the aromaticity through the values and patterns of the magnetically induced current density. The results show that aromaticity is quenched and the quenching depends on the number and positions of the substituting OH groups. The isosurfaces of the magnitude of the current density also highlight connections between the donor and acceptor atoms forming an intramolecular hydrogen bond.     

π-Electron ring currents and magnetic properties of porphyrin molecules in the MO LCAO SCF method

The coupled variant of double-parameter perturbation theory in the MO LCAO SCF method in the London approximation has been used for the calculation of π-electron current distributions in the molecules of porphin and its derivatives. The chemical shifts of¹H-NMR have been computed on the basis of calculations of ring currents and charge distributions. It is shown that π-electron ring currents are responsible for the dominant contribution to the shielding of protons. The theoretical and experimental values of proton chemical shifts are in a good agreement. Chemical shifts of the¹³C and¹⁵N nuclei have also been estimated. Two aromaticity scales are proposed for the compounds under study based on the calculations of the π-electron contribution to the diamagnetic susceptibility and of π-electron currents, respectively.     

Calculation of current densities using gauge-including atomic orbitals

A method for calculating the various components of the magnetically induced current-density tensor using gauge-including atomic orbitals is described. The method is formulated in the framework of analytical derivative theory, thus enabling implementation at the Hartree-Fock self-consistent-field (HF-SCF) as well as at electron-correlated levels. First-order induced current densities have been computed up to the coupled-cluster singles and doubles level (CCSD) augmented by a perturbative treatment of triple excitations [CCSD(T)] for carbon dioxide and benzene and up to the full coupled-cluster singles, doubles, and triples (CCSDT) level in the case of ozone. The applicability of the gauge including magnetically induced current method to larger molecules is demonstrated by computing first-order current densities for porphin and hexabenzocoronene at the HF-SCF and density-functional theory level. Furthermore, a scheme for obtaining quantitative values for the induced currents in a molecule via numerical integration over the current flow is presented. For benzene, a perpendicular magnetic field induces a (field dependent) ring current of 12.8 nA T(-1) at the HF-SCF level using a triple-zeta basis set augmented with polarization functions (TZP). At the CCSD(T)/TZP level the induced current was found to be 11.4 nA T(-1). Gauge invariance and its relation to charge-current conservation is discussed.