Douglas J. Klein

Graphitic polymer strips with edge states

Abstract The Huckel band structure is analytically investigated for a family of arbitrary-width π-network polymers which may be viewed as being cut from the graphite lattice. For wider strips a portion of two nearly nonbonding bands on either side of the Fermi energy are found to be localized to opposite edges of the strip. Novel consequences of these edge-localized band orbitals are considered and correlated to a simple resonating valence bond picture.

C60 carbon cages

Abstract Arrangements of carbon atoms in cage-like structures with no dangling bonds are considered as possible novel allotropic forms of carbon. Five different C60 cages, having certain favorable structural characteristics, are identified. Quantitative resonance-theoretic calculations are made and compared to simpe Huckel results. The favored structure is found to be the so-called Buckminsterfullerene structure.

High‐spin hydrocarbons

The existence of a class of (very) high‐spin hydrocarbons is predicted on the basis of (a) new theorems for valence‐bond models, (b) classical structure theory, (c) standard theorems for molecular orbital theory, (d) several small‐system calculations with Hubbard and PPP Hamiltonians, and (e) a large‐system cluster expansion calculation applied to the polyallyl high‐spin candidates. Some properties, especially the magnetic ones, for these conjugated alternants are briefly discussed.

Extensions of the Wiener number

Particularly for structure−property correlations there are many chemical graph-theoretic indices, one of which is Wieners “path number”. Because Wieners original work focused on acyclic structure...

Favorable structures for higher fullerenes

A study is made of elemental carbon cages corresponding to polyhedra with hexagonal and pentagonal faces such that no two pentagons abut. All such preferable cages of up to ν=94 vertices are generated, and simple Huckel MO and resonance-theoretic computations are made. The graphical structures more favored by these computations are reported for the experimentally relevant vertex (or atomic) counts of ν=60, 70, 76, 78, 84, and 90. The NMR line patterns for these favorable structures are also given.

Graphical properties of polyhexes: Perfect matching vector and forcing

From the viewpoint of graph theory and its applications, subgraphs of the tiling of the plane with unit squares have long been studied in statistical mechanics, In organic chemistry, a much more relevant case concerns subgraphs of the tiling with unit hexagons. Our purpose here is to take a mathematical view of such polyhex graphsG and study two novel concepts concerning perfect matchingsM. First, the forcing number ofM is the smallest number of edges ofM which are not contained in any other perfect matching ofG. Second, the perfect matching vector ofM is written (n3,n2,n1,n0), wherenk is the number of hexagons with exactlyk edges inM. We establish some initial results involving these two concepts and pose some questions.

Modeling the bioconcentration factors and bioaccumulation factors of polychlorinated biphenyls with posetic quantitative super-structure/activity relationships (QSSAR).

SummaryDuring bioconcentration, chemical pollutants from water are absorbed by aquatic animals via the skin or a respiratory surface, while the entry routes of chemicals during bioaccumulation are both directly from the environment (skin or a respiratory surface) and indirectly from food. The bioconcentration factor (BCF) and the bioaccumulation factor (BAF) for a particular chemical compound are defined as the ratio of the concentration of a chemical inside an organism to the concentration in the surrounding environment. Because the experimental determination of BAF and BCF is time-consuming and expensive, it is efficacious to develop models to provide reliable activity predictions for a large number of chemical compounds. Polychlorinated biphenyls (PCBs) released from industrial activities are persistent pollutants of the environment that produce widespread contamination of water and soil. PCBs can bioaccumulate in the food chain, constituting a potential source of exposure for the general population. To predict the bioconcentration and bioaccumulation factors for PCBs we make use of the biphenyl substitution-reaction network for the sequential substitution of H-atoms by Cl-atoms. Each PCB structure then occurs as a node of this reaction network, which is some sort of super-structure, turning out mathematically to be a partially ordered set (poset). Rather than dealing with the molecular structure via ordinary QSAR we use only this poset, making different quantitative super-structure/activity relationships (QSSAR). Thence we developed cluster expansion and splinoid QSSARs for PCB bioconcentration and bioaccumulation factors. The predictive ability of the BAF and BCF models generated for 20 data sets (representing different conditions and fish species) was evaluated with the leave-one-out cross-validation, which shows that the splinoid QSSAR (r between 0.903 and 0.935) are better than models computed with the cluster expansion (r between 0.745 and 0.887). The splinoid QSSAR models for BAF and BCF yield predictions for the missing PCBs in the investigated data sets.

Diamond-graphite hybrids

Abstract The possibility of a general multifold class of novel allotropic forms of carbon is suggested. They consist of cubic or hexagonal diamond blocks or layers interconnected by blocks or layers of “graphitic” strips. Some simple consequences are noted with special attention to the possibility of electrical conduction along with the “graphitic” strips.

Wiener Index Extension by Counting Even/Odd Graph Distances

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, and similarity and diversity assessment. A new set of topological indices is introduced representing a partitioning of the Wiener index based on counts of even and odd molecular graph distances. These new indices are further generalized by weighting exponents which can be optimized during the quantitative structure-activity/-property relationship (QSAR/QSPR) modeling process. These novel topological indices are tested in QSPR models for the boiling temperature, molar heat capacity, standard Gibbs energy of formation, vaporization enthalpy, refractive index, and density of alkanes. In many cases, the even/odd distance indices proposed here give notably improved correlations.

Partial Orderings in Chemistry

The cosmopolitan relevance of partially ordered mathematical structures in chemistry is argued. Many examples are briefly noted, including those involving chemical periodicities, reactivities, aromaticities, electronegativities, molecular branching, molecular shapes, symmetries, complexities, curve fittings, and more. A few fundamental theorems concerning metrics (or distance functions) on partially ordered sets are noted, first for the intuitively appealing “scaled” posets, then for the more general “transformed” posets. Interspersed along the way are a few examples which are developed to a greater extent, including Randic−Wilkins periodicity for alkanes; the general concept of aromaticity; molecular branching; least-squares fittings; and (most extensively) molecular shapes, chiralities, and symmetries. In each of these types of examples clarifications, alternative views, and extensions of previous works result.