Conjugated circuits currents in hexabenzocoronene and its derivatives formed by joining proximal carbons

We report on calculated CC bond currents for a dozen derivatives of hexabenzocoroenene in which one or more proximal carbon atoms at the molecular periphery have been bridged. The approach that we use is graph‐theoretical in nature, following our outline of this method in 2003, which is based on finding all conjugated circuits in all Kekulé valence structures of these molecules. To the π‐electrons having 4n + 2 π‐electrons are assigned anticlockwise π‐electron currents and to conjugated circuits having 4n π‐electrons are assigned π‐electron currents. One may summarize the results reported in this work by stating that CC bond currents in the compounds considered decrease on going from peripheral rings to the central ring of the molecule, and also that CC bond currents decrease by insertion of bridges to proximal peripheral benzenoid rings. © 2012 Wiley Periodicals, Inc.     

π‐Electron currents in larger fully aromatic benzenoids

Recently, we have reported on calculation of π‐electron ring currents in several smaller fully benzenoid hydrocarbons having up to eight fused benzene rings and five Clar π‐aromatic sextets. In contrast to early HMO ring current calculations and more recent ab initio calculations of π‐electron density, our current calculations are based on a graph theoretical model in which contributions to ring currents comes from currents associated with individual conjugated circuits. In this contribution, we consider several larger fully benzenoid hydrocarbons having from 9 to 13 fused rings and from six or seven π‐aromatic sextets. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Resonance energies of large conjugated hydrocarbons by a statistical method

We developed a theoretical method for studying the aromatic stability of large molecules, molecules having a dozen and more fused benzene rings. Such molecules have so far often been outside the domain of theoretical studies. Combining the statistical approach and a particular graph theoretical analysis, it is possible to derive the expressions for molecular resonance energy for molecules of any size. The basis of the method is enumeration of conjugated circuits in random Kekulé valence structures. The method has been applied to evaluation of the resonance energies of conjugated hydrocarbons having about a dozen fused benzene rings. The approach consists of (1) construction of random Kekulé valence structures, (2) enumeration of conjugated circuits within the generated random valence structures, and (3) application of standard statistical analysis to a sufficiently large sample of structures. The construction of random valence forms is nontrivial, and some problems in generating random structures are discussed. The random Kekulé valence structures allow one not only to obtain the expression for molecular resonance energies (RE ) and numerical estimates for RE , but also they provide the basis for discussion of local molecular features, such as ring characterization and Pauling bond orders.     

π-Electron currents in fixed π-sextet aromatic benzenoids

In view of different patterns of π-electron density currents in benzenoid aromatic compounds it is of interest to investigate the pattern of ring currents in various classes of compounds. Recently such a study using a graph theoretical approach to calculating CC bond currents was reported for fully benzenoid hydrocarbons, that is, benzenoid hydrocarbons which have either π-sextets rings or “empty” rings in the terminology of Clar. In this contribution we consider π-electron currents in benzenoid hydrocarbons which have π-electron sextets and C=C bonds fully fixed. Our approach assumes that currents arise from contributions of individual conjugated circuits within the set of Kekulé valence structures of these molecules.     

Benzenoid rings resonance energies and local aromaticity of benzenoid hydrocarbons

In this article, we consider partitioning of the analytical expression for resonance energy (RE) in smaller benzenoid hydrocarbons, to individual benzenoid rings of polycyclic molecules. The analytical expression for molecular RE, available since 1976, is given by the count of all linearly independent conjugated circuit in all Kekulé structures in a molecule. Analytical expression for local ring RE (RRE) is given by counting all linearly independent conjugated circuits involving single benzenoid ring in all Kekulé structures, which when added, gives the molecular RE. If for benzene ring the RRE is taken to be 1.000, rings in polycyclic benzenoid hydrocarbons have their ring RRE, which give the degree of their local aromaticity, smaller than 1.000. The difference to 1.000 is a measure of the similarity of a ring to benzene in this one-dimensional (1-D) representation of local aromaticities of benzenoid hydrocarbons. The plot of RRE against the distance of the same ring from benzene in the Local Aromaticity Map, in which benzenoid rings are characterized ring bond orders and average variations of adjacent CC bonds, shows linear correlation (with r = 0.91), reducing the local aromaticity in benzenoid hydrocarbons to 1-D molecular property. © 2018 Wiley Periodicals, Inc.     

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.     

Stability of Conjugated Carbon Nanocones

We use interlacing techniques to prove that carbon nanocones who have a Fries Kekulé structure have closed Hückel shells, and that this result can be extended to all conjugated cones where each edge belongs to a hexagonal face and the configuration of the non-hexagonal faces are consistent with a Fries Kekulé structure. Cones with Fries Kekulé structure or substructure are topical—not only from a valence bond theoretical point of view—since a previous ab initioanalysis favored cones where the pentagons at the tip are configured as in a Fries Kekulé structure. The question of interdependence will therefore be addressed.     

A Dicyanomethylene‐Substituted Triangulene: Effects of Molecular‐Symmetry Reduction and Electron‐Accepting Substituents on a Fused Polycyclic Neutral π‐Radical System

A triangulene‐based C₂‐symmetric 33 π‐conjugated stable neutral π‐radical, 2^. , which possesses two dicyanomethylene groups and one oxo group, has been designed, synthesized, and isolated as an analogue of tris(dicyanomethylene) derivative 1^. and trioxo derivative TOT^. with C₃ symmetry. Effects of molecular‐symmetry reduction and electron‐accepting substituents on this fused polycyclic neutral π‐radical system were studied in terms of their molecular structure, electronic‐spin structure, and electrochemical and optical properties with the help of theoretical calculations. Interestingly, this system ( 2^. ) has a four‐stage redox ability, like TOT^. , as well as low frontier energy levels and a small SOMO–LUMO gap, similar to 1^. , in spite of the loss of the degenerate LUMOs in symmetry‐lowered 2^. , which is associated with the attachment of the weaker electron‐accepting oxo group instead of the dicyanomethylene group in 1^. . These prominent results are attributable to the structural and electronic properties in the triangulene‐based highly delocalized fused polycyclic neutral π‐radical system.     

Ordering of Kekulé structures using nonadjacent numbers

Kekulé indices and conjugated circuits are computed for 36 Kekulé structures, together with two VB quantities associated with the corresponding factor graphs (previously called submolecules). These latter quantitites are nonadjacent numbers of Hosoya and the reciprocal of the connectivity indices of Randi?. It was found that the index of Hosoya successfully orders a set of Kekulé structures belonging to the same hydrocarbon in a parallel order as their Kekulé indices and branching indices. This substantiates the relation between VB and MO theories. A code is derived by summing contributions of nonadjacent numbers in all Kekulé stuctures of a hydrocarbon. The order of the resulting codes is found to be identical to the order of the molecular properties (resonance energies, π-energies, and eigenvalues) of the hydrocarbons.     

Synthesis of π‐conjugated polymer containing both thiophene and phosphole sulfide in the main chain by simultaneous post‐element transformation of organotitanium polymer

The synthesis and unique optoelectronic features of a π‐conjugated polymer containing both thiophene and 1‐phenylphosphole sulfide units (multiple heteroles) in the main chain by the post‐element transformation of a regioregular organometallic polymer possessing titanacyclopentadiene‐2,5‐diyl unit are described. The π‐conjugated polymer containing multiple heteroles was obtained in 73% yield by the simultaneous reaction of the organotitanium polymer with sulfur monochloride and dichlorophenylphosphine (0.6 equiv each), whose number‐average molecular weight (M_n) and the molecular‐weight distribution (M_w/M_n) were estimated to be 11,000 and 3.4, respectively, by the size exclusion chromatography (SEC). The π‐conjugated polymer thus obtained was found to have the high HOMO and the low LUMO energy levels due to the electron‐rich thiophene and electron‐deficient phosphole sulfide units, respectively, as supported by its cyclic voltammetry (CV) analysis. Compared to a mixture of a polymer containing sole thiophene‐unit and that containing sole phosphole sulfide units, the π‐conjugated polymer‐containing multiple heteroles proved to exhibit interesting optical properties. For example, a specific emission peak was observed at 608 nm in the photoluminescence spectrum, which was not observed in the case of the thiophene‐containing polymer, the phosphole‐containing polymer, and their mixture. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2519–2525     

Synthesis and photovoltaic investigation of dithieno[2,3‐d:2′,3′‐d′]‐benzo[1,2‐b:3,4‐b′:5,6‐d″]trithiophene‐based conjugated polymer with an enlarged π‐conjugated system

Compared with benzo[1,2‐b:3,4‐b′:5,6‐d″]trithiophene (BTT), an extended π‐conjugation fused ring derivative, dithieno[2,3‐d:2′,3′‐d′]benzo[1,2‐b:3,4‐b′:5,6‐d″]trithiophene (DTBTT) has been designed and synthesized successfully. For investigating the effect of extending conjugation, two wide‐bandgap (WBG) benzo[1,2‐b:4,5‐b′]dithiophene (BDT)‐based conjugated polymers (CPs), PBDT‐DTBTT, and PBDT‐BTT, which were coupled between alkylthienyl‐substituted benzo[1,2‐b:4,5‐b′]dithiophene bistin (BDT‐TSn) and the weaker electron‐deficient dibromides DTBTTBr₂ and BTTBr₂ bearing alkylacyl group, were prepared. The comparison result revealed that the extending of conjugated length and enlarging of conjugated planarity in DTBTT unit endowed the polymer with a wider and stronger absorption, more ordered molecular structure, more planar and larger molecular configuration, and thus higher hole mobility in spite of raised highest occupied molecular orbital (HOMO) energy level. The best photovoltaic devices exhibited that PBDT‐DTBTT/PC₇₁BM showed the power conversion efficiency (PCE) of 2.73% with an open‐circuit voltage (V_OC) of 0.82 V, short‐circuit current density (J_SC) of 6.29 mA cm^?2, and fill factor (FF) of 52.45%, whereas control PBDT‐BTT/PC₇₁BM exhibited a PCE of 1.98% under the same experimental conditions. The 38% enhanced PCE was mainly benefited from improved absorption, and enhanced hole mobility after the conjugated system was extended from BTT to DTBTT. Therefore, our results demonstrated that extending the π‐conjugated system of donor polymer backbone was an effective strategy of tuning optical electronic property and promoting the photovoltaic property in design of WBG donor materials.     

Analytical expressions for the count of LM-conjugated circuits of benzenoid hydrocarbons

A recursive method for enumeration of linearly independent and minimal conjugated circuits of benzenoid hydrocarbons had previously been given which is valid for several classes of benzenoid hydrocarbons. In the present article, the properties and constructions of unique minimal conjugated circuits and pairs of minimal conjugated circuits of a ring s in a benzenoid hydrocarbon B are investigated. An analytical expression for the count of LM-conjugated circuits of B is given which is based on the counts of Kekulé structures of selected subgraphs of B. By using the method, the LMC expression of any benzenoid hydrocarbon can be obtained. © 1996 John Wiley & Sons, Inc.     

Electronegativity Scaled as a Average Attracting Energy of Valence‐Shell Electrons in a Ground‐State Free Atom

The total capability of an atom attracting valence electrons can be measured by the sum of ionization energies of valence electron in a ground‐state free atom plus its electron affinity called Total Attracting Energy, TAE = Σn_iE_i + EA, where, E_i is the ionization energy of the ith valence‐shell electron in a ground‐state free atom, n_i is the number of valence‐shell electron bearing energy E_i, and EA is the electron affinity. And the electronegativity χ_CL is proportional to the average of TAE, AAE = TAE_av, divided by Σn_i, the number of atomic valence‐shell electrons. χ_CL = 0.1813 TAE_av = 0.1813 AAE = 0.1813 TAE/Σn_i, = 0.1813 (Σn_iE_I + EA)/Σn_i. Further, the atomic valence orbital electronegativity can be also obtained from the TAE value of an atom. Some discussions were made on several special aspects such as scale of rare gases, comparisons with Pauling's and Allen's scales, etc.     

Tuning the Electronic Properties and Acid‐Response Behavior of N‐Heteroacene‐Based π‐Conjugated Liquids by Changing the Number of π‐Conjugated Substituents

We have designed and synthesized two room‐temperature‐fluorescent π‐conjugated liquids based on the N‐heteroacene framework ( 1 and 2 ). These two π‐conjugated liquids, which contained one and two thiophene rings, respectively, exhibited different electronic properties and rheology behaviors. Single‐crystal X‐ray analysis of dithiophene‐appended compound 4 revealed that two thiophene rings hindered the interactions of the imino N atoms with acids through the formation of interactions between the S atoms of the thiophene rings and the imino N atoms of the pyrazine group. On the other hand, monothiophene‐appended molecules 1 and 3 each contained an unhindered imino N atom on the opposite site to the thiophene ring. Upon dissolving various acids with different pK_a values in compounds 1 and 2 , these slight structural differences gave rise to marked differences in their acid‐response behaviors, thereby resulting in the emission of variously colored fluorescence in the liquid state. Furthermore, when acids with lower pK_a values was dissolved in compounds 1 and 2 , phase transition occurred from an isotropic liquid state to a self‐organized liquid‐crystalline phase.     

Conjugated circuits and resonance energies of benzenoid hydrocarbons

A concept of conjugated circuits contained in Kekulé forms of benzenoid hydrocarbons is considered. Circuits of size (4n + 2) in which CC single and double bonds formally alternate are enumerated and serve as the basis for the characterization of a given system. Resonance energies of benzenoid systems are given by contributions of conjugated circuits of different size. The scheme permits the expression of resonance energies of different molecules in terms of selected reference compounds, such as linear acenes. The approach is illustrated on a dozen benzenoid hydrocarbons and the calculated resonance energies are on average within 0.05 eV of the values obtained by SCF MO calculations.     

Computing the Kekulé structure count for alternant hydrocarbons

A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekulé structure count. A simple method is presented for determining the Kekulé structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekulé structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 × N/2 matrix need be evaluated. The Kekulé structure count correlates with topological indices. The inclusion of the number of cycles improves the fit. When comparing with previous results, the variance decreases 74%. The calculated standard heat of formation correlates with the logarithm of the Kekulé structure count. This heat increments 349 kJ/mol each time the Kekulé structure count increases by one order of magnitude. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002