On total π-electron energy of benzenoid hydrocarbons

Hall's observation that the total π-electron energy E of benzonoid hydrocarbons is a linear functions of the number of Kukule structures is supported by theoretical arguments and extensive numerical work. A rather accurate topological formula for E is obtained.     

Hamiltonian circuits,Hamiltonian paths and branching graphs of benzenoid systems

A benzenoid systemH is a finite connected subgraph of the infinite hexagonal lattice with out cut bonds and non-hexagonal interior faces. The branching graphG ofH consists of all vertices ofH of degree 3 and bonds among them. In this paper, the following results are obtained:

1. A necessary condition for a benzenoid system to have a Hamiltonian circuit.
2. A necessary and sufficient condition for a benzenoid system to have a Hamiltonian path.
3. A characterization of connected subgraphs of the infinite hexagonal lattice which are branching graphs of benzenoid systems.
4. A proof that if a disconnected subgraph G of the infinite hexagonal lattice given along with the positions of its vertices is the branching graph of a benzenoid system H, then H is unique.

     

Comparability graphs and electronic spectra of condensed benzenoid hydrocarbons

A systematic topological approach to the search for regularities in molecular properties has been proposed on the basis of the so-called comparability graphs of isomeric classes of molecules. It is shown that the ordering of the isomeric benzenoid hydrocarbons in the comparability graphs coincides with that of the longest wavelenght in the p band of their electronic spectra.     

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.     

The conjugated-circuit model: The optimum parameters for benzenoid hydrocarbons

A search for the optimum set of parameters for the conjugated-circuit computations on benzenoid hydrocarbons in reported. The SCFπ-MO resonance energies (REs) of Dewar and de Llano were used as standards for the determination ofR _n (n= l,2,3) parameters, which correspond to 4n + 2 conjugated circuits. The following set of parameters:R ₁ = 0.827 eV.R ₂ = 0.317 andR ₃ = 0.111 eV produced the best agreement between the REs calculated by the conjugated-circuit model and the REs calculated using the SCF π-MO model.     

Total resonant sextet benzenoid hydrocarbon isomers and their molecular orbital and thermodynamic characteristics

The more stable strain-free total resonant sextet isomers of benzenoid hydrocarbons are predicted to be probable combustion pollutants. These benzenoid hydrocarbons have been enumerated, and their topological characteristics examined. Total resonant sextet benzenoid isomers make up less than 1% of all the benzenoid hydrocarbons having formulas with N_c divisible by 6. There is a thermodynamic preference for the larger and more highly condensed polycyclic aromatic hydrocarbon molecule. The Hückel molecular orbital (HMO) and thermodynamic parameters of these total resonant sextet benzenoid hydrocarbons have been computed and tabulated.     

Enumeration and classification of benzenoid hydrocarbons

The enumeration of benzenoids is studied with the aid of different modifications of a computer program. Known values for the number of cata-condensed and of all benzenoids with h (number of hexagons) up to eight are reproduced. These benzenoids are classified into (a) unbranched of different symmetries and branched cata-condensed, and (b) normal, essentially disconnected and non-Kekuléan peri-condensed. Within the normal benzenoids a more detailed classification is performed: basic benzenoids, fused, or annelated. For h = 9 an almost complete classification along the same lines was achieved.     

PI indices of pericondensed benzenoid graphs

The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n _eu (e|G) and n _ev (e|G) over all the edges e = uv of a connected graph G, i.e., , where n _eu (e|G) is the number of edges of G lying closer to u than to v and n _ev (e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of a class of pericondensed benzenoid graphs consisting of three rows of hexagonal of various lengths.     

Strain in strain-free benzenoid hydrocarbons: the case of fibonacenes

In a recent paper (Radenkovic et al. Chem Phys Lett 625:69–72, 2015), a new method for quantifying the strain energy in benzenoid molecules, resulting from the repulsion between the bay H-atoms was elaborated. In this work, we present a modified procedure, capable of estimating the strain energy in a single-step calculation. Strain energies were obtained at the B3LYP/def2-TZVP level of density functional theory. It was found that in benzenoid molecules with a single bay region, the strain energy is essentially constant, equal to around 7.3 kJ/mol. On the other hand, in the case of the first four members of the fibonacene series, the strain energy is found to be linearly proportional to the number of bay regions.     

On isospectral benzenoid graphs

The recently Proposed procedure [5] for the construction of isospectral benzenoid graphs has been examined in detail. Necessary and sufficient conditions for the construction of isospectral benzenoid graphs with isomorphicH-graphs are formulated. The inapplicability of the Procedure for the construction of isospectral benzenoid graphs with an even number of vertices has been proven.     

Recognizing Kekuléan benzenoid systems byC-P-V path elimination

In this paper, we define the concept of a canonicalP-V pathP(p _i– _i ) on the boundary of a benzenoid systemH, and prove thatH has a Kekulé structure if and only ifH-P(p _i–v _i) has a Kekulé structure, whereH-P(p _i–v _i) is the graph obtained fromH by deleting the vertices onP(p _i–v _i) . It is also proved that there are at least two canonicalP-V paths in a benzenoid system. By the above results, we give an efficient and simple algorithm, called the canonicalP-V (C-P-V) path elimination, for determining whether or not a given benzenoid systemH has Kekulé structures. IfH is Kekuléan, the algorithm can find a Kekulé structure ofH.Supported by NSFC.     

A concept to explain the variation of the triplet zero-field splitting parameters with the structure of aromatic hydrocarbons in terms of local benzenoid characteristics

The zero-field splitting (ZFS) parameters D and E of the lowest electronically excited triplet state T₁ of a series of systematically selected pyrene derivatives have been determined by ODMR techniques. With this class of compounds as an example we intended to gain some insight into the variation of the ZFS-parameters with the structure and topology of aromatic hydrocarbons. The variation of the experimental ZFS-parameters could be explained in terms of the dipole—dipole model together with criteria describing the local benzene likeness of single C₆-rings in the molecule. For these the character orders according to Polansky were calculated on an MO-basis and the local benzenoid indices according to Randi? on a graph-theoretical basis. As these quantities for the local aromaticity were in accordance with Clar's qualitative sextet concept a qualitative principle could be formulated explaining the variation of the D-parameter with molecular structure. This principle correctly describes all known D-parameters of aromatic molecules measured so far. So for the first time, a clear and consistent explanation for the variation of D with molecular structure can be given. Also for the E-parameter a connection with molecular structure could be established; it could be demonstrated in which way the criteria of local aromaticity mentioned can be applied to decide on the sign of E. For the acene-analogue pyrene derivatives linear correlations could be established between the averaged local quantities and the ZFS-parameters D and E. These correlations allow a quantitative determination of the ZFS-parameters of further analogue pyrene compounds. Also for other series of aromatic hydrocarbons such correlations could be found as shown for the polyacene series as an example. For the latter also a strong similarity to the series of the acene-analogue pyrene derivatives was found. D- and E-values are given for the six molecules pentacene to decacene. These were calculated from both the correlation with the character orders and that with the Randi?-indices, and the result of both methods are compared.     

A unified theory of the stability of benzenoid hydrocarbons

The spectral density operator technique is proved to be a convenient tool for derivation of approximate topological formulae for total pi-electron energy (E_pi) of benzenoid hydrocarbons (BH s). Developed mathematical formalism points out a common origin of three different measures for the stability of BH s, namely: resonance energy (RE), number of Kekule structures (K) and HOMO -LUMO separation (X_HL). In turn, a novel topological invariant corresponding to “normalized” RE is derived. Numerical calculations for a representative set of BH s demonstrate effectiveness of the present approach. Various approaches to an estimation of BH stabilities are discussed.     

Topological hamiltonian spectra of polycyclic benzenoid hydrocarbons

A general theory which points out the relations between Hückel-electron energy, the number of Kekulé structures and the HOMO-LUMO separation is presented. Some normalized topological invariants are derived from the concept of the spectral density function. A reasonably simple (three parameters) model spectral density function leads to universal relations between topological invariants that, although valid for any alternant molecule, were tested numerically for polycyclic benzenoid hydrocarbons. Some general conclusions concerning a distribution of the adjacency matrix eigenvalues are drawn.     

Analytical approach to very large benzenoid polymers

We consider rigorous evaluation of conjugated-circuit resonance energies for families of structurally related benzenoid hydrocarbons of increasing size. Local and global aromatic properties of such molecules are investigated with particular interest in modeling high polymers. Using the algebra of large numbers, exact formulas for contributions from individual benzene rings of polymers with up to 25,000 repeating units (close to half a million carbon atoms) were derived. All arithmetic procedures were carried out in terms of whole numbers retaining all digits, of which there were sometimes more than 10⁵. © 1995 by John Wiley & Sons, Inc.     

Additivity of resonance energy in benzenoid hydrocarbons

A simple method is described for the calculation of resonance energies (RE ) of linear acenes based on their number of Kekulé structures. The values obtained for the first five linear acenes are used to graph–theoretically calculate RES of a wide variety of benzenoid hydrocarbons. Excellent linear relationships are found between RES and each of A-II, graph-theoretical (GT ), Hess–Schaad (HS ), and Dewar resonance energies (SCF ). These relations apply to 42 hydrocarbons and lead to the following equations: A-II = 0.084RE + 0.080 (0.9999); GT = 0.072RE + 0. 135 (0.9832); HS = 0. 106RE + 0. 169 (0.9889); and SCF = 0.316RE + 0. 166 (0.9899). Correlation coefficients are shown in parentheses. A linear relation also exists between RES and the square roots of the wavelengths of the UV spectra of hydrocarbons of the linear acenes and phene series. Least-squares analysis of the data leads to the following equation: RE = 0.412(λ)^½ ?15.479, with a correlation coefficient equal to 0.9903, in which λ is the wavelength of the β band of the UV spectra of these hydrocarbons. The method predicts no resonance energies for both open chain polyenes and the radialenes.     

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.     

Bond length interrelations in benzenoid hydrocarbons and their heteroatom analogues

The geometries of some benzenoid hydrocarbons and their analogues with XY (XY = BB, BC, BN, CN, and NN) bonds have been determined at the B3LYP/6-311++G^∗∗ level of theory. It is shown that the lengths of peripheral XY bonds are strictly correlated with the lengths of their CC counterparts in native hydrocarbons. No correlation of this type is observed for the XY bonds located inside the rings.     

Resonance in catacondensed benzenoid hydrocarbons

We consider resonance in cata-condensed benzenoids having six and seven fused benzene rings. The resonance relationship between the Kekule valence structures of the molecules is represented by the resonance graphs in which the vertices represent the Kekule valence structures, and the edges, the presence of the quantum chemical resonance integral involving permutation of three CC double bonds (within a single six-membered ring). The construction of the resonance graphs for large benzenoids is outlined and the properties of the derived resonance graphs are discussed. It is shown that the leading eigenvalue of the resonance graphs correlates with the resonance energy of benzenoids. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 585–600, 1997     

Isoskeletomerism as an intermediate concept for mediating between stereoisomerism and isomerism. A remedy for conceptual defects of organic chemistry

After isoskeletomerism is introduced as an intermediate concept for mediating between stereoisomerism and isomerism, so-called ‘constitutional isomerism’ is critically discussed as one of the roots of confusion in organic chemistry. The convention that isomerism is subdivided into stereoisomerism and ‘constitutional isomerism’ is concluded to be misleading, because these concepts are conceptually distinct from a viewpoint of the concepts of equivalence relationships and equivalence classes. The indifference toward these concepts is one of the conceptual defects of organic chemistry. A new flowchart for judging enantiomerism, RS-stereoisomerism, stereoisomerism, isoskeletomerism, and isomerism is discussed to generate an isomer-classification diagram, where RS-stereoisomerism and isoskeletomerism are contained as new matters for remedying the conceptual defects. Skeletons are derived from basic skeletons by three operations (the bond operation, the replacement operation, and the substitutive operation), and they are used to examine the action of isoskeletomeric relationships. Equivalent molecular entities under an isoskeletomeric relationship are collected to give a set of isoskeletomers, which is concluded to be an equivalence class. The confusion caused by so-called ‘constitutional isomerism’ and its subcategories (‘skeletal isomerism’, ‘positional isomerism’, and so on) is critically discussed from the viewpoint of isoskeletomerism as a missing link. The double-entendre of the term constitution is examined when applied to both a 3D entity (a set of stereoisomers) and a 2D entity (a graph). Taxonomy of organic compounds and rational formulas, nomenclature of organic compounds, and combinatorial enumeration of chemical compounds are discussed from the viewpoint of isoskeletomerism.