Aromaticity of N-heterocyclic carbene and its analogues: Magnetically induced ring current perspective

The N-heterocyclic carbene, imidazole-2-ylidene, and its main group (13-15) analogues contain cyclically conjugated 6π electrons. Experimental ¹H nuclear magnetic resonance (NMR) spectra suggest an increase in aromaticity along a period from left to right. Whereas the order along a group is as follows: period 2 > period 5 > period 4 > period 3 due to change in structure. To understand the order of aromaticity, the magnetically induced ring currents of the molecules are calculated using aromatic ring current shielding, gauge-including magnetically induced currents (GIMIC) method and Stanger's σ-model applying the gauge-including atomic orbitals NMR technique. It is found that GIMIC best describes the order of aromaticity especially along a group where current-profile changes on the bivalent atom down a group due to change in electron density. Moreover, the GIMIC provides the visualization of current by sign modulus and the anisotropy of the induced current density plots.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Experimental and computational studies of alkali-metal coinage-metal clusters

Coinage and alkali metal mixed clusters, M4Na- (M = Cu, Au) have been investigated experimentally using photoelectron spectroscopy and computationally at correlated ab initio levels. The related Cu4Li-, Ag4Li-, Ag4Na-, and Au4Li- clusters as well as the neutral Cu4Li2 and Cu4Na2 clusters have also been studied computationally. The calculations show that the two lowest isomers of the negatively charged clusters include a pyramidal C4v structure and a planar C2v species. For Cu4Li- and Cu4Na-, the C4v structure is calculated at correlated ab initio level to be 30.9 and 16.9 kJ/mol below the planar C2v isomer, whereas the planar isomers of Au4Li- and Au4Na- are found to be 29.7 and 49.4 kJ/mol below the pyramidal ones. For Ag4Li- and Ag4Na-, the pyramidal isomers are the lowest ones. Comparison of the calculated and measured photoelectron spectra of Cu4Na- and Au4Na- shows that the pyramidal Cu4Na- cluster of C4v symmetry and the planar Au4Na- of C2v symmetry are detected experimentally. Calculations of the magnetically induced current density in Cu4Li- and Cu4Li2 using the Gauge-Including Magnetically Induced Current (GIMIC) method show that strong ring currents are sustained mainly by the highest-occupied molecular orbital primarily derived from the Cu 4s. The GIMIC calculations thus show that the Cu4(2-) ring is -aromatic and that the d orbitals do not play any significant role for the electron delocalization effects. The present study does not support the notion that the square-planar Cu4(2-) is the first example of d-orbital aromatic molecules.     

Ring currents in boron and carbon buckyballs, B80 and C60

The ipsocentric method at the coupled Hartree-Fock level is used for the calculation of magnetically induced ring currents in the boron buckyball B(80), for both I(h) and distorted T(h) geometries. A close similarity between the current patterns in boron and carbon buckyballs is noted, but with a higher current density in B(80). Paratropic currents on the pentagons are predominant in the boron buckyball, and the central NICS value is positive. These observations support the conclusion that B(80) should be considered (weakly) anti-aromatic. The largest orbital contributions to the ring currents in both molecules are identified and related to specific excitations in the frontier orbital region.     

Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability: theory and applications

A current emphasis in empirical force fields is on the development of potential functions that explicitly treat electronic polarizability. In the present article, the commonly used methodologies for modeling electronic polarization are presented along with an overview of selected application studies. Models presented include induced point-dipoles, classical Drude oscillators, and fluctuating charge methods. The theoretical background of each method is followed by an introduction to extended Lagrangian integrators required for computationally tractable molecular dynamics simulations using polarizable force fields. The remainder of the review focuses on application studies using these methods. Emphasis is placed on water models, for which numerous examples exist, with a more thorough discussion presented on the recently published models associated with the Drude-based CHARMM and the AMOEBA force fields. The utility of polarizable models for the study of ion solvation is then presented followed by an overview of studies of small molecules (e.g., CCl₄, alkanes, etc.) and macromolecule (proteins, nucleic acids and lipid bilayers) application studies. The review is written with the goal of providing a general overview of the current status of the field and to facilitate future application and developments.     

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.     

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.     

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.     

The induced current strengths and aromatic pathways of heteroporphyrins and their antiaromatic derivatives

The magnetically induced current strengths as well as nucleus independent chemical shifts of aromatic heteroporphyrins and antiaromatic 22,24‐dideazaheteroporphyrins have been studied using the density functional theory method. The induced current strengths and pathways are obtained by numerical integration of the induced current densities following the specific chemical bonds. The total induced current strengths of antiaromatic 22,24‐dideazaheteroporphyrins is about 6 nA/T weaker than the one for the heteroporphyrins in absolute value. The substitution of pyrrole NH groups by O and S atoms does not change the total induced current strengths. The induced currents around the molecular macroring split at the heterocycles (pyrrole, furan, and thiophene) into the inner and outer routes. The heteroatoms (N, O, and S) have high resistance and consequently lead to a weaker induced current strength than the one passing the outer route in aromatic heteroporphyrins. For antiaromatic 22,24‐dideazaheteroporphyrins, the heteroatoms enhance the current strength and change the main current pathway into the inner route. The induced current strength following the NH moiety is stronger than the one passing the oxygen moiety of furan ring and the sulfur moiety of the thiophene ring in both heteroporphyrins and 22,24‐dideazaheteroporphyrins. © 2015 Wiley Periodicals, Inc.     

Tuning the Structure and Properties of N-doped Positively Charged Polycyclic Aromatic Hydrocarbons

A detailed study of the geometry, aromatic character, electronic and magnetic properties for a series of positively charged N-doped polycyclic aromatic hydrocarbons (PAHs) was performed. Magnetic properties of the examined molecules were analyzed by means of the magnetically induced current density calculated using the diamagnetic-zero version of the continuous transformation of origin of current density (CTOCD-DZ) method. The comparative study of the local aromaticity of the studied molecules was performed using several different indices: energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six centre delocalization index (SCI) and nucleus independent chemical shifts (NICS). The presence of N-atoms in the inner rings was found to cause a planarity distortion in the studied N-doped systems. The geometric changes and charged nature of the studied N-doped systems do not significantly influence the current density and the local aromaticity distribution in comparison with the corresponding parent benzenoid hydrocarbons. The present study demonstrates how quantum chemical calculations can be used for rational design of novel PAHs and for fine tuning of their properties.     

Optical properties of current carrying molecular wires

We consider several fundamental optical phenomena involving single molecules in biased metal-molecule-metal junctions. The molecule is represented by its highest occupied and lowest unoccupied molecular orbitals, and the analysis involves the simultaneous consideration of three coupled fluxes: the electronic current through the molecule, energy flow between the molecule and electron-hole excitations in the leads, and the incident and/or emitted photon flux. Using a unified theoretical approach based on the nonequilibrium Green's function method we derive expressions for the absorption line shape (not an observable but a useful reference for considering yields of other optical processes) and for the current induced molecular emission in such junctions. We also consider conditions under which resonance radiation can induce electronic current in an unbiased junction. We find that current driven molecular emission and resonant light induced electronic currents in single molecule junctions can be of observable magnitude under appropriate realizable conditions. In particular, light induced current should be observed in junctions involving molecular bridges that are characterized by strong charge-transfer optical transitions. For observing current induced molecular emission we find that in addition to the familiar need to control the damping of molecular excitations into the metal substrate the phenomenon is also sensitive to the way in which the potential bias is distributed on the junction.