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Closed-form, general formulas for the Zhang-Zhang (ZZ) polynomials for two important classes of benzenoid structures, chevrons ݄ܥሺ݇ǡ ݉ǡ ݊ሻ and generalized chevrons ݄ܥሺ݇ǡ ݉ǡ ݊ ଵ ǡ ݊ ଶ ሻ, are formally derived. The derivations rely on a new and important theorem, which states that the ZZ polynomial of two fused parallelograms can be represented as the… (More)
The Zhang–Zhang(ZZ) polynomials (aka Clar covering polynomial) for several subclasses of catacondensed and pericondensed benzenoid systems have been computed using an automatic computer code developed in our group and described in [C.-P. Chou and H.A. expressions for several series of catacondensed benzenoids and for the prolate rectangular pericondensed… (More)
We employ a graphical proof-oriented tool, ZZDecomposer, to discover formal derivations of Zhang-Zhang (ZZ) polynomials for various families and subfamilies of benzenoid structures including tripods, zigzag-edge coronoids fused with a starphene, oblate rectangles ܱݎሺ݉ǡ ʹሻ, decompositions of the analyzed structures. The decompositions provide appropriate… (More)
We present a detailed analysis of the factors influencing the formation of epoxide and ether groups in graphene nanoflakes using conventional density functional theory (DFT), the density-functional tight-binding (DFTB) method, π-Hückel theory, and graph theoretical invariants. The relative thermodynamic stability associated with the chemisorption of oxygen… (More)
Variational Transition State Theory with Multidimensional Tunneling (VTST/MT) has been successfully used for calculating rate constants of reactions in gas and condensed phases. The current software implementation of VTST/MT is, however, based on the assumption of a fast, serial evaluation of the energetic information of a given molecular structure. We… (More)
In our recent paper [MATCH Commun. Math. Comput. Chem. 71 (2013) 741-764] some formulas and figures were misprinted. In this paper, we correct these problems giving formal derivations of Zhang-Zhang (ZZ) polynomials for two classes of benzenoid systems, zigzag-edge coronoids and fenestrenes.