The vorticity of the current density tensor and 3D-aromaticity

The induced current density ( J ( r )) vector field has been extensively used as a criterion of aromaticity and electron delocalization. However, the selection of the direction of the perturbing magnetic field ( B ) is arbitrary and in the case of three-dimensional electron delocalization/aromaticity the selection could be ambiguous. The J ( r ) has also recently received some criticism as an aromaticity index. We propose the Trace of the Vorticity of the Current Density tensor (TVCD) scalar field as a more suitable quantity for the evaluation of electron delocalization of three-dimensional systems. It does not depend on the orientation of B and contrary to other related scalar fields like the anisotropy of the induced current density, it does not lose the information of the direction of the currents. We show that not only the currents parallel to the molecular plane are important in the evaluation of the aromaticity, as is largely believed, but also the perpendicular ones, which information is included in the TVCD. The TVCD is very useful to study planar and 3D delocalized molecules (eg, fullerenes). Moreover, the integration of the TVCD over an internal surface of the 3D-cages serves as index for 3D-aromaticity.     

Self‐heating and conduction of an acetylene carbon black filled high‐density polyethylene composite at the electric–thermal equilibrium state

The electric self‐heating and conduction behaviors of a high‐density polyethylene/carbon black composite at the electric–thermal equilibrium state are studied. An equation describing the current density/electric‐field strength (J–E) characteristic is derived on the basis of an equation proposed for the self‐heating temperature as a function of the field strength. The conduction is related to the electronic tunneling and the resistor breakdown due to self‐heating that dominate the nonlinear J–E characteristic below and above a critical field strength corresponding to the J maximum, respectively. The influences of the initial structure of the percolation network and the physical state of the matrix on the conduction are also discussed on the basis of scaling arguments of the self‐heating and the nonlinear J–E characteristic with respect to the initial resistivity at various ambient temperatures from 19 to 120 °C. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2484–2492, 2005     

Molecular orientational motion in discotic liquid crystals

Abstract

The spectral densities of motion for the aromatic and chain deuterons of the discotic mesogen hexahexyoxytriphenylene (THE6) have been reported in the literature for a frequency of 46 MHz. Most spectral densities J_p (pω₀, 90°) have been obtained from samples consisting of a planar distribution of domains in which the directors were perpendicular to the magnetic field Limited data J_p (pω₀) have also been available from single-domain samples with the director aligned parallel to the magnetic field. We have applied the small-step rotational diffusion model of Nordio et al. to the data from the aromatic deuterons of THE6-ard in its uniaxial columnar D_ho phase, to describe the spinning (D _∥, rotational diffusion constant about the planar normal to the disc) and the tumbling (D?, rotational diffusion constant of the planar normal) motions of the molecular core. Although this model has been successfully used for rod-like nematic liquid crystals, its use has not been attempted for discotic liquid crystals. The model seems to indicate that molecular reorientation has slowed down in the D_ho phase, giving frequency dependence to the spectral densities. This can be explained by the high orientational order of the molecules. We are able to account for the four spectral densities J ₁ (ω₀), J ₁ (ω₀, 90°), J ₂ (2ω₀) and J ₂(2ω₀, 90°) with a calculated ratio D∥/D? of about 1. This is quite different from that of rodlike liquid crystals.     

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.     

Germanium,carbon‐germanium,and silicon‐germanium triangulenes

A series of germanium‐containing triangular molecules have been studied by density functional theory (DFT) calculations. The triangulene topology of the compounds provides for their high‐spin ground states and strong sign alternation of spin density and atomic charge distributions. High values of the exchange coupling constants witness ferromagnetic ordering of electronic structures of all studied triangulenes. The compounds bearing more electronegative atoms in a‐positions of the triangular networks possess higher aromatic character and stronger ferromagnetic ordering. © 2015 Wiley Periodicals, Inc.     

Trap mechanism based on frontier molecular orbitals of additives in polyethylene insulators: A theoretical study and molecular design strategy

In this work, the energy gaps (E_g) of highest occupied orbitals and lowest unoccupied orbitals, trap energies (E_t(e) and E_t(h)) and excited energies of polyethylene model compound, typical defect compound, acetophonene, and 33 designed additives are obtained using density functional method at B3LYP/6–311+G(d, p) level. The correlation between trapping‐electrons (holes) abilities of additives and molecular frontier orbitals is established, and a new understanding for trap mechanism based on chemical molecular orbital levels is given for the first time which could be used to filter qualitative additives as voltage stabilizers of polyethylene. The role of trap energies and the energy gaps on discussing space charge accumulation and electric breakdown is analyzed in detail. A molecular design strategy for potential additives of cross‐linked polyethylene insulated high‐voltage cable is shown based on conjugation effect, substituents character, and polycyclic aromatic compounds. © 2015 Wiley Periodicals, Inc.     

On CHF calculations of second-order magnetic properties using the method of continuous transformation of origin of the current density

Summary A fully analytical formulation is outlined for computing molecular magnetic susceptibilities and nuclear magnetic shieldings via a continuous change of origin of the electronic current density induced by an external magnetic field. The change of origin is described in terms of a (continuous) arbitrary shift functiond(r). Coupled Hartree-Fock second-order magnetic properties of CH₄ and CO₂ molecules have been computed, using the special choiced(r)=r as generating function. A detailed analysis of results obtained with a variety of basis sets reveals that such a method is not as good as previously suggested. Large basis sets must be used to obtain accurate magnetic properties. On the other hand, all the components of theoretical nuclear magnetic shielding evaluated via this approach are independent of the origin of the vector potential. In general, theoretical magnetic susceptibilities depend linearly on the distance between different coordinate frames, but are origin independent for centre-symmetric molecules.     

Reversible nonlinear conduction behavior for high‐density polyethylene/graphite powder composites near the percolation threshold

The reversible nonlinear conduction (RNC) behavior of high‐density polyethylene/graphite powder composites with various graphite powder volume concentrations slightly above the threshold has been studied. The relationships between the current density (J) and electric field (E) of the composites, as shown in J(E) curves, can be well described by the scaling functions of J/J_c ～ (E/E_c) when E < E_c and J/J_c ～ (E/E_c) when E > E_c, where J_c is the crossover current density and E_c is the crossover electric field. The results indicate that J_c scales with the linear conductivity σ₀ as J_c ～ σ. It is believed that the macroscopic RNC is a combined result of the microscopic conduction processes, involving electronic transporting along carbon chains and tunneling or hopping across thin polymer bridges. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2833–2842, 2001     

Cobalt(II)‐Terephthalate Frameworks Containing Bis(benz­imidazole) Derivative Co‐ligands: Syntheses,Crystal Structures,Catalytic and Fluorescence Properties

Two metal‐organic coordination polymers of Co^II with the molecular formulae [Co(L₁)(tp)(H₂O)₂]_n ( 1 ) and [Co(L₂)(tp) · H₂O]_n ( 2 ) [L₁ = 1, 4‐bis(benzimidazole‐1‐ylmethyl)‐ benzene; L₂ = 1, 1‐(1, 4‐butanediyl)bis(5, 6‐dimethylbenzimidazole); tp = terephthalate] were synthesized and characterized by single‐crystal X‐ray diffraction studies, infrared spectroscopy (IR), thermogravimetric analysis (TGA), X‐ray powder diffraction (XRPD), and elemental analysis. The structure determination of complex 1 reveals a 2D layer with (4, 4) topology, with Co^II ions at the nodes connected through tp and L₁ co‐ligands. Complex 2 is the first example of a four‐connected SrAl₂ structure type ( sra , 4²6³8 topology) with threefold interpenetration in Co^II coordination frameworks, forming by bridging L₂ and tp co‐ligands. In addition, the fluorescence and catalytic performances of the complexes for the degradation of methyl orange were investigated.     

Nature of the aromaticity of azulene and the dimers responsible for its chromaticity

A new interpretation of aromatic properties of azulene is suggested that differs from the one underlying current quantum-chemical models and considers azulene single molecules as its ground state. This new interpretation reflects the recent finding that the ground state of azulene is represented by supramolecular dimers existing in two equilibrium tautomeric forms, rather than by single molecules. It is established that aromatic properties of azulene are associated with the formation of supramolecular dimers, and this is explained in terms of Clar??s ideas on the imperative role of the benzenoid sextet in aromatic polycyclic hydrocarbons. It is concluded that aromaticity of azulene is due to the three-dimensional (3D) ?? system of its dimers rather than to the flat ?? system of its molecule.     

Molecular Dissociation on the SiC(0001) 3×3 Surface

In the framework of density functional theory, the adsorption of the halogenated polycyclic aromatic hydrocarbon 2,11‐diiodohexabenzocoronene (HBC‐I₂) on the SiC(0001) 3×3 surface has been investigated. Nondissociative and dissociative molecular adsorption is considered, and simulated scanning tunneling microscopy (STM) images are compared with the corresponding experimental observations. Calculations show that dissociative adsorption is favorable and reveal the crucial importance of the extended flat carbon core on molecule–surface interactions in dissociative adsorption; the iodine atom–surface interaction is of minor importance. Indeed, removing iodine atoms does not significantly affect the STM images of the central part of the molecule. This study shows that the dissociation of large halogenated polycyclic aromatic hydrocarbon molecules can occur on the SiC surface. This opens up interesting perspectives in the chemical reactivity and functionalization of wide band gap semiconductors.     

DFT studies and AIM analysis of AlN-polycycles

The structure and properties of AlN-polycycles were studied by DFT (density functional theory) method. The results of calculations were obtained at B3LYP/6-311G(d, p) level on model species. Topological parameters such as electron density, its Laplacian, kinetic electron energy density, potential electron energy density, and total electron energy density at the ring critical points (RCP) from Bader’s ‘Atoms in molecules’ (AIM) theory were analyzed in detail. These results indicate a good correlation between ρ(3, +1), G(r), H(r), and V(r) averaged values and hardness of AlN-polycycles. The aromaticity of all molecules has been studied by nucleus-independent chemical shift. There is a linear correlation between ΣNICS(0.0)_molecule values and polarizability.     

Magnetic exchange interactions in cyano‐bridged MoIII binuclear complexes: Broken‐symmetry and density functional theory calculations

Molecular magnetism in cyano‐bridged Mo^III binuclear complexes [Mo₂(CN)₁₁]^5? and [(Me₃tacn)₂Mo₂(CN)₅]⁺ (Me₃tacn?N, N′, N″‐trimethyl‐1,4,7‐triazacyclononane) has been calculated using Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Parr (B3LYP), a hybrid density functional theory (DFT), combined with a modified broken symmetry (BS) approach and the post–Hartree‐Fock (post‐HF) method difference‐dedicated configuration interaction (DDCI). We find B3LYP combined with broken‐symmetry approach (DFT‐BS) give the similar J values to those calculated by DDCI. So we use B3LYP combined with BS approach to investigate the magnetism above two molecules. Through calculations, we find that the absolute J values decrease with the increase of r (the Mo(2)‐C_brid and Mo(1)‐N_brid distances) and are linearly related to the differences of the squared spin populations [(ρ ? ρ)] on Mo^III atoms between the highest‐spin (HS) state and the broken symmetry (BS) state. Moreover, the absolute J values are linearly related to the sum of the square of the difference in energy of the unpaired electrons (ξ) with a limited variation of the r distance. We conclude that ξ can be used to scale the degree of the antiferromagnetic coupling interactions. At the end of the paper, the spin density distributions and the mechanisms of magnetic coupling interactions are analyzed by us. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Coordination bonding in dicopper and dichromium tetrakis(μ-acetato)-diaqua complexes: Nature,strength, length,and topology

Geometry optimization, energetics, electronic structure, and topology of electron density of dicopper ( I ) and dichromium ( II ) tetrakis(μ-acetato)-diaqua complexes are studied focusing on the metal–metal interactions. The performance of broken symmetry (BS) single-determinant ab initio (Hartree–Fock, Møller–Plesset perturbation theory to the second and third orders, coupled clusters singles and doubles) and density functional theory (BLYP, B3LYP, B3LYP-D3, B2PLYP, MPW2PLYP) methods is compared to multideterminant ab initio (CASSCF, NEVPT2) methods as well as to the multipole model of charge density from a single-crystal X-ray diffraction experiment (Herich et al., Acta Cryst. 2018, B74, 681–692). In vacuo DFT geometry optimizations (improper axial water ligand orientation) are compared against the periodic ones. The singlet state is found to be energetically preferred. J coupling of ( I ) becomes underestimated for all ab initio methods used, when compared to experiment. It is concluded that the strength of the direct M─M interactions correlates closely with the J coupling magnitude at a given level of theory. The double potential well character of (II) and of the dehydrated form of (II) are considered with respect to the Cr─Cr distance. The physical effective bond order of the metal–metal interaction is small (below 0.1 e) in ( I ) and moderate (0.4 e) in ( II ). The CASSCF results overestimate the electron density of the metal–metal bond critical point by 20% and 50% in ( I ) and ( II ), respectively, when compared to the multipole model. © 2019 Wiley Periodicals, Inc.     

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.     

A vector‐based representation of the chemical bond for the normal modes of benzene

We introduce a vector‐based interpretation of the chemical bond within the quantum theory of atoms in molecules (QTAIM), the bond‐path framework set B = {p, q, r}, to follow variations in the 3D morphology of all bonds for the four infrared active normal modes of benzene. The bond‐path framework set B comprises three unique paths p, q, and r where r is the familiar QTAIM bond concept of bond‐path (r) while the two new paths p and q are formulated from the least and most preferred directions of electron density accumulation, respectively. We find 3D distortions including bond stretching/compression, torsion, and curving. We introduce two fractional measures to quantify these variations away from linearity of the bond.     

Effect of Annulation Mode of Twistarene on the Physical Property and Self-Assembly Behavior of Functionalized Curved Aromatic Molecules

Four novel curved polycyclic aromatic hydrocarbons 3 a , 5 , 8 , 15 a have been synthesized and characterized, where molecules 3 a and 15 a bear [5]carbohelicene units. X-ray single crystal analyses indicate that compound 3 a shows offset packing arrangements of (P₅)- and (M₅)-isomers, and 15 a has a symmetrical plane and looks like a butterfly. In comparison, 8 exhibits a slightly curved structure, in which the significant convex-to-convex π-overlap with the shortest distance of 3.42 Å occurs. In addition, the effect of annulation mode of twistarenes on the physical properties, self-assembly behaviors, and switchable photoconductivity of the as-prepared curved aromatic compounds were further examined in a comparative manner.     

Theoretical study of bifurcated hydrogen bonding effects on the 1J(N,H), 1hJ(N,H), 2hJ(N,N) couplings and 1H, 15N shieldings in model pyrroles

According to the density functional theory calculations, the X···H···N (X?N, O) intramolecular bifurcated (three‐centered) hydrogen bond with one hydrogen donor and two hydrogen acceptors causes a significant decrease of the ^1hJ(N,H) and ^2hJ(N,N) coupling constants across the N? H···N hydrogen bond and an increase of the ¹J(N,H) coupling constant across the N? H covalent bond in the 2,5‐disubsituted pyrroles. This occurs due to a weakening of the N? H···N hydrogen bridge resulting in a lengthening of the N···H distance and a decrease of the hydrogen bond angle at the bifurcated hydrogen bond formation. The gauge‐independent atomic orbital calculations of the shielding constants suggest that a weakening of the N? H···N hydrogen bridge in case of the three‐centered hydrogen bond yields a shielding of the bridge proton and deshielding of the acceptor nitrogen atom. The atoms‐in‐molecules analysis shows that an attenuation of the ^1hJ(N,H) and ^2hJ(N,N) couplings in the compounds with bifurcated hydrogen bond is connected with a decrease of the electron density ρ_H···N at the hydrogen bond critical point and Laplacian of this electron density ?²ρ_H···N. The natural bond orbital analysis suggests that the additional N? H···X interaction partly inhibits the charge transfer from the nitrogen lone pair to the σ*_{N? H} antibonding orbital across hydrogen bond weakening of the ^1hJ(N,H) and ^2hJ(N,N) trans‐hydrogen bond couplings through Fermi‐contact mechanism. An increase of the nitrogen s‐character percentage of the N? H bond in consequence of the bifurcated hydrogen bonding leads to an increase of the ¹J(N,H) coupling constant across the N? H covalent bond and deshielding of the hydrogen donor nitrogen atom. Copyright © 2010 John Wiley & Sons, Ltd.     

One-bond 1J(15N,H) coupling constants at sp2-hybridized nitrogen of Schiff bases,enaminones and similar compounds: A theoretical study

¹J(¹⁵N,H) coupling constants for enaminones and NH-forms of intramolecularly hydrogen-bonded Schiff bases as model compounds for sp²-hybridized nitrogen atoms are evaluated using density functional theory (DFT) to find the optimal functionals and basis sets. Ammonia is used as a test molecule and its one-bond coupling constant is compared with experiment. A methylamine Schiff base of a truncated molecule of gossypol is used for checking the performance of selected B3LYP, O3LYP, PBE, BHandH, and APFD density functionals and standard, modified, and dedicated basis sets for coupling constants. Both in vacuum and in chloroform, modeled by the simple continuum model of solvent, the modified basis sets predict significantly better the ¹J(¹⁵N,H) value in ammonia and in the methylamine Schiff base of a truncated molecule of gossypol than the standard basis sets. This procure is then used on a broad set of intramolecularly hydrogen-bonded molecules, and a good correlation between calculated and experimental one-bond NH coupling constants is obtained. The ¹J(¹⁵N,H) couplings are slightly overestimated. The calculated data show for hydrogen-bonded NH interatomic distances that the calculated values depend on the NH bond lengths. The shorter the bond lengths, the larger the ¹J(¹⁵N,H). A useful correlation between ¹J(¹⁵N,H) and NH bond length is derived that enables realistic predictions of one-bond NH coupling constants. The calculations reproduce experimentally observed trends for the studied molecules.