Combinatorial Clar sextet theory

Clar structures recently used as basis-set to compute resonance energies [9] are identified as maximal independent sets of benzenoid hydrocarbons colored in a special way. Binomial properties of such objects are induced for several catafusenes and perifusenes (Eqs. 2–31). Novel polynomials, called Clar polynomials, are given for perifusens in terms of units of catafusenes which allow display and enumeration of the populations of their Clar structures. The work is particularly pertinent to that of [8] and [9].This paper is dedicated to Professor Eric Clar; the Doyen of aromatic chemistry.     

Zhang–Zhang Polynomials of Multiple Zigzag Chains Revisited: A Connection with the John–Sachs Theorem

Multiple zigzag chains Zm,n of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains Zm,n. The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the Zm,n multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size m2×m2 consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains Zkm,n, i.e., derivatives of Zm,n with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains Zm,n and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains Zm,n.     

Partitioning of <Emphasis Type="Italic">π</Emphasis> -electrons in rings of polycyclic conjugated hydrocarbons: Part 6. Comparison with other methods for estimating the local aromaticity of rings in polycyclic benzenoids

By adopting the convention that shared double bonds in polycyclic conjugated hydrocarbons contribute with one -electron and unshared ones with two -electrons, a partition of -electrons in each ring (-electron content, EC) can be obtained by averaging over all Kekulé structures, which are assumed to have equal weights. This affords a simple measure of local aromaticity that is comparable with other such local aromaticity indices in polycyclic benzenoids.     

Clar Goblet and Aromaticity Driven Multiradical Nanographenes

The Clar Goblet, the first radical bowtie nanographene proposed by Erich Clar nearly 50 years ago, was recently synthesized. Bowtie nanographenes present quasi-degenerate magnetic ground states, which make them so elusive as unique. A thorough analysis is presented of the spin-state energetics of Clar Goblet and bowtie nanographenes by a battery of existing and novel ab initio procedures ranging from density functional theory to complete active space Hamiltonians. With this, it was proven that π radicals of bowtie nanographenes sit on BP (Benzo[cd]Pyrene) moieties driven by their local aromaticity, a purely chemical concept, which confers global stability to the whole structure. Besides, a novel Pauli energy densities analysis provided a visual intuitive explanation for this preference. These findings allow envisioning that analogous bowtie nanographenes with arbitrary polyradical character are not only feasible at the molecular scale but will share Clar Goblet's peculiar properties.     

关于一类六角系统的共振多项式

本文揭示了单洞 Cata 型六角系统的共振多项式与广义冠的匹配多项式的关系、将1977年 Gutman 提出的方法推广应用到有洞的六角系统,并得到一些共振多项式的比较定理.     

Isomer enumeration of practical benzenoids

Recent development of the leapfrog operation in enumeration and understanding the chemical properties of benzenoid isomer sets having at least one synthesized representative is stressed. Some new enumeration results and correlations of the periodic table for the more stable total resonant sextet (TRS) benzenoid hydrocarbon subset [Table PAH6(sextet)] are presented.     

Zhang–Zhang polynomials of cyclo-polyphenacenes

The Zhang–Zhang polynomial (i.e., Clar covering polynomial) of hexagonal systems is introduced by H. Zhang and F. Zhang, which can be used to calculate many important invariants such as the Clar number, the number of Kekulé structures and the first Herndon number, etc. In this paper, we give out an explicit recurrence expression for the Zhang–Zhang polynomials of the cyclo-polyphenacenes, and determine their Clar numbers, numbers of Kekulé structures and their first Herndon numbers.     

Theoretical study with rovibrational and dipole moment calculation of sextet states of the CrCl molecule

The potential energy curves have been investigated for the 13 lowest sextet electronic states in the representation below 53,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 16. Nine electronic states have been studied theoretically here for the first time. The comparison of these values with the theoretical and experimental results available in the literature shows a good agreement. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

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