Global Forcing Number of Benzenoid Graphs

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons.     

Ground-state properties of benzenoid hydrocarbons by simple bond orbital resonance theory approach

π-electron energies and bond orders of benzenoid hydrocarbons with up to five fused hexagons have been considered by the simple Bond Orbital Resonance Theory (BORT) approach. The corresponding ground states were determined according to four BORT models. In the first three models a diagonalisation of the Hückel-type Hamiltonian was performed in the bases of Kekulé, of Kekulé and mono-Claus and of Kekulé and Claus resonance structures, respectively. In the fourth model a simple BORT ansatz was used. According to this ansatz, the ground state is a linear combination of the positive Kekulé structures, all with equal coefficients. It was shown that π-electron energies and bond orders obtained by these models correlate much better with the PPP energies and bond orders than with the Hückel energies and bond orders. This indicates that a simple BORT approach is quite reliable in predicting the more sophisticated PPP results. Concerning the relative performance of the four BORT models, the best results were obtained with the BORT ansatz. The performance deteriorates with the expansion of the basis set. This is attributed to the fact that in these models the improvement of the basis set is not accompanied with the corresponding improvement of the Hamiltonian. Comparing the BORT-ansatz bond orders with the Pauling bond orders, it was shown that BORT-ansatz bond orders correlate much better with the PPP bond orders. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heats of atomization of some conjugated molecules containing nitrogen or oxygen by a novel semiempirical method

Heats of atomization for a range of conjugated molecules containing nitrogen or oxygen are calculated by a semiempirical method that combines some features of both the MO and VB theories. The π ground state of each conjugated molecule is represented as a linear combination of Kekulé structures. Unlike in the VB theory, each Kekulé structure is a determinant containing bond orbitals. Here experimental heats of atomization are reproduced approximately as well as by the more sophisticated SCF –MO approach. The use of this method is, however, much simpler since it amounts to a single diagonalization of a matrix of the order equal to the number of Kekulé structures only.     

On lower bounds of number of perfect matchings in fullerene graphs

Couting perfect matchings in graphs is a very difficult problem. Some recently developed decomposition techniques allowed us to estimate the lower bound of the number of perfect matchings in certain classes of graphs. By applying these techniques, it will be shown that every fullerene graph with p vertices contains at least p/2+1 perfect matchings. It is a significant improvement over a previously published estimate, which claimed at least three perfect matchings in every fullerene graph. As an interesting chemical consequence, it is noted that every bisubstituted derivative of a fullerene still permits a Kekulé structure.     

A simple method for the calculation of π-bond orders in alternant hydrocarbons

A new method for the calculation of bond orders in alternant hydrocarbons is presented. The method requires a summation over the contributions of various superposition diagrams. Quantitatively, the method is almost as reliable as PPP, and due to its simplicity it can be used for fast and relatively accurate calculation of bond orders. In addition some simple rules are derived, which in many cases can be used to predict the signs of bond orders between nonbonded atoms.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayResearch supported by the Robert A. Welch Foundation of Houston, Texas     

Highly efficient nickel-catalyzed cross-coupling of succinic and glutaric anhydrides with organozinc reagents

A nickel-catalyzed alkylation of succinic and glutaric anhydrides with alkyl- and arylzinc reagents has been developed. A dramatic olefin effect has been investigated resulting in the identification of several styrene-based promoters which show pronounced enhancements in reaction rate. The substrate scope with respect to electrophilic and nucleophilic coupling partners has been examined and found to be remarkably broad, allowing for rapid introduction of molecular complexity through the use of functionalized coupling partners. Regioselective alkylation of an unsymmetrical succinic anhydride and a profound effect of pendent coordinating olefins on reaction rate suggest a mechanism involving discrete oxidative addition of the nickel complex into the cyclic anhydride followed by a transmetalation event.