Planar polycyclic graphs and their Tutte polynomials

We consider several classes of planar polycyclic graphs and derive recurrences satisfied by their Tutte polynomials. The recurrences are then solved by computing the corresponding generating functions. As a consequence, we obtain values of several chemically and combinatorially interesting enumerative invariants of considered graphs. Some of them can be expressed in terms of values of Chebyshev polynomials of the second kind.     

Development of Gradient Retention Model in Ion Chromatography. Part I: Conventional QSRR Approach

New retention methodology that integrates the conventional quantitative structure-retention relationship (QSRR) approach and gradient retention modeling based on isocratic retention data is developed and presented in this paper. Such an integrated approach removes the general QSRR limitation of highly predefined application conditions (i.e., QSRR are generally applicable only under the conditions used during model development) and allows the prediction of retentions over a wide range of different elution conditions (practically for any isocratic or gradient elution profile). At the same time, it retains the ability to predict retention of components unknown to the model, i.e., the components that have not been used in modeling. Ion-exchange chromatography (IC) analysis of carbohydrates was selected as modeling environment. Three regression techniques were applied and compared during QSRR modeling, namely: stepwise multiple linear regression, partial least squares (PLS), and uninformative variable elimination–PLS regression. The obtained prediction results of the best QSRR model (root-mean-square error of prediction = 22.69 %) were similar to those found in the literature. The upgrade from QSRR to the integrated model did not diminish the predictive ability of the model, indicating an excellent potential of the developed methodology not only in IC but also in chromatography in general.     

Development of CN Coupling Using Mechanochemistry: Catalytic Coupling of Arylsulfonamides and Carbodiimides

Reported herein is the mechanochemical synthesis of sulfonyl guanidines, a family of molecules which are relevant as pharmaceuticals and herbicides, by direct coupling of sulfonamides and aromatic or aliphatic carbodiimides. Attempts to conduct the coupling in solution have either failed or given very low conversions, thus demonstrating mechanochemistry as the necessary component for the discovery of this synthetic strategy.     

Vertex-weightings for distance moments and thorny graphs

Valence-weightings are considered for shortest-path distance moments, as well as related weightings for the so-called “Wiener” polynomial. In the case of trees the valence-weighted quantities are found to be expressible as a combination of unweighted quantities. Further the weighted quantities for a so-called “thorny” graph are considered and shown to be related to the weighted and unweighted quantities for the underlying parent graph.     

Computing the bipartite edge frustration of fullerene graphs

Bipartite edge frustration of a graph is defined as the smallest number of edges that have to be deleted from the graph to obtain a bipartite spanning subgraph. We show that for fullerene graphs this quantity can be computed in polynomial time and obtain explicit formulas for the icosahedral fullerenes. We also report some computational results and discuss a potential application of this invariant in the context of fullerene stability.     

Appell Polynomials and Asymptotic Expansions

Some properties of the Appell polynomials are studied and analyzed. Various formulas and expressions for the Appell quotient are derived and connection with asymptotic expansions is presented.     

A stepwise mechanism for the mechanochemical synthesis of halogen-bonded cocrystal architectures

A molecular-level mechanism is proposed for two cases of mechanochemical cocrystallization via halogen bonds. The proposed stepwise mechanism is based on the observation and structural characterization of intermediates that appear in early stages of the reaction. The mechanism arises from the competition of strong and weak intermolecular halogen bonds of the N...I and S...I type and involves the initial formation of finite molecular assemblies, held together via N...I bonds that subsequently polymerize into infinite chains by cross-linking through S...I bonds. This mechanism has been observed in the synthesis of linear as well as zigzag halogen-bonded chain architectures.