Hosoya Matrix - A Source of New Molecular Descriptors

We introduce a novel matrix associated with molecular graphs, the construction of which is related to the construction of the Hosoya Z topological index. The new matrix provides a source of novel invariants that may be of interest in structure-property and structure-activity studies. Construction of the novel matrices is outlined and a few novel invariants extracted. A comparison with closely related topological indices is illustrated on regressions with the boiling points in octanes

Graph Theoretical Derivation of Pauling Bond Orders

A method of evaluating Pauling bond orders of conjugated hydrocarbons is outlined. It is based on the reduction of a molecular graph by excising the bond in question and other bonds for which a unique assignment of bond character is possible. The method is general and applicable to alternant and non-alternant systems as well as to cata- and pericondensed hydrocarbons

Comparative Regression Analysis. Regressions Based on a Single Descriptor

In this article we report the results on over 750 linear regressions based on a single descriptor, using some twenty molecular properties of alkanes and some forty distinct molecular descriptors. It is shown that, among the numerous descriptors, less than a dozen descriptors outperform all the others. Hence, while the search for graph invariants has been fruitful, few of the constructed descriptors show sufficiently novel characteristics and have displayed sufficiently different behavior in correlations with physico-chemical properties. At the same time, we find that some properties are more susceptible to a successful single-descriptor regression analysis, while few properties remain difficult to characterize by a single descriptor. At the end of this report, we have listed a few challenges to be considered by those involved in structure-property-activity studies. We have drawn attention to some properties of alkanes (octanes in particular) for which better regression results are warranted. We also recommend that the performance of novel indices be compared with the known results, like those reported here. If a novel index shows a better behavior with respect to any of the properties already reported in the literature, they certainly deserve publicity. If an index shows a performance comparable to some existing descriptors, they ought to have other advantages in order to replace the existing descriptors. The burden of »proof« ought to be on the »inventor« of a novel topological index. Vague statements that an index may show promise in structure-property studies ought to be replaced by a comparative study, such as shown here for octanes. While the present paper answers the questions which are the best single simple descriptors for correlations of octane physico-chemical properties, our restriction to the use of a single descriptor in structure-property correlations neither signifies that we expect all properties to be well represented by simple regressions, nor that the best single descriptors will necessarily remain the dominant descriptor in multiple regression analysis

Compact Codes. 2. Bicyclic Saturated Hydrocarbons

Compact codes, recently introduced (ref. 1), have been applied to all known bicyclic saturated hydrocarbons as the first step in a systematic deriving compact codes for more complex ring systems. The codes are compared with IUPAC nomenclature for bicyclic compounds, as well as with WLN (Wiswesser Line Notation). Advantages of the compact codes are outlined, including qualified algebraic manipulations on the codes to derive codes for structurally related compound

Positronium – Hydrogen Like and Unlike

On the occasion of the 2008 Brijuni Conference on Hydrogen – the most abundant atomic species in the Universe, it seems fitting to draw attention of the participants of this conference, as well as chemists at large, to Positronium – one of the least abundant atom-like species in the Universe, if for no other reasons then because it was theoretically predicted by a Croatian scientist, Stjepan Mohorovičić some 75 years ago, about 100 miles away, in the city of Zagreb, the capitol of the Republic of Croatia. Abstract. A brief review on positronium, Ps, hydrogen-like system built from positron and electron, is outlined from its beginning in 1935, the first theoretical study on this relatively stable matter-antimatter system by Stjepan Mohorovičić, to the most recent works on positronim hydride PsH, and positronium molecule Ps2, analogue of hydrogen molecule. Mohorovičić calculated spectra of Ps and was even looking for it in the sky searching for its spectrum, but experimental observations of positronium Lyman-α radiation Lyα λ2430 line waited for another 40 years before being successful identified in a laboratory in 1975 by Canter and collaborators. It took another ten years for astronomical observation of the presence of positronium in outer space in 1984 by McClintock, who observed Lyα λ2430 line in spectra of Crab Nebula, 50 years after the attempts of S. Mohorovičić to detect positronium lines. The work of Mohorovičić was mostly ignored in his native Croatia, until the most recent time, an illustration of “historical blunder” of local physics community – phenomenon not so unheard of in science in general, as has been recently worldwide illustrated with hesitation of acceptance of the notion of nonlinear dose response (hormesis); the density functional theory; and chemical graph theory.</p

Graph Theoretical Derivation of Pauling Bond Orders

A method of evaluating Pauling bond orders of conjugated hydrocarbons is outlined. It is based on the reduction of a molecular graph by excising the bond in question and other bonds for which a unique assignment of bond character is possible. The method is general and applicable to alternant and non-alternant systems as well as to cata- and pericondensed hydrocarbons

Search for Optimal Molecular Descriptors

We illustrate, on a set of heptane isomers and van der Waals molecular areas as a property, a search for optimal descriptors to be used in multivariate analyses. We employed molecular connectivities as the basis descriptors and examined their various combinations as alternative descriptors that could lead to a better regression. The critical step in the search appears to be the selection of the first descriptor to which, subsequently, other descriptors are made orthogonal. A well constructed descriptor can yield a regression equation superior to regressions using several standard descriptors. The approach is illustrated by considering, among others, the molecular ID numbers, the Wiener numbers and Balaban’s J index, as well as novel graphical bond orders based on the above indices. A by-product of the systematic search for better structure-property relationship is a novel property-property correlation (between octane number and molecular cavity areas)

On Complexity of Transitive Graphs Representing Degenerate Rearrangements

Graphs representing degenerate rearrangements are vertex and edge transitive. First such graph of interest in Chemistry was considered by Balaban. It describes the rearrangements of trigonal bipyramid complex XY5 by a mechanism in which axial bonds become equatorial and three equatorial bonds become axial. We will discuss complexity of such graphs based on considering the shells of neighbors at increasing distance from a single vertex

Nenad Trinajstić – Pioneer of Chemical Graph Theory

We present a brief overview of many contributions of Nenad Trinajstić to Chemical Graph Theory, an important and fast developing branch of Theoretical Chemistry. In addition, we outline briefly the various activities of Trinajstić within the chemical community of Croatia. As can be seen, his scientific work has been very productive and has not abated despite the hostilities towards the Chemical Graph Theory in certain chemical circles over the past 30 years. On the contrary, Trinajstić continued, widened the areas of his research interest, which started with investigating the close relationship between Graph Theory and HMO, and demonstrated the importance of Chemical Graph theory for chemistry. In more than one way he has proven the opponents of Chemical Graph Theory wrong, though some continue to fail to recognize the importance of Graph Theory in Chemistry