Milan Randic

Development of 3-dimensional molecular descriptors

Abstract Structural invariants used currently as molecular descriptors in structure-property (SPR) and structure-activity relationship (SAR) studies are based on molecular graphs rather than on a structure as a 3-dimensional (3-D) object. Here we outline an approach which extends graph-theoretical methodology to structures embedded in 3-D space. Derived descriptors are sensitive to the 3-D characteristics of a molecular structure and change with variations in molecular conformations. We illustrate the approach by examining conformations of smaller alkanes, including selected conformations of cyclohexane, methyl-cyclohexanes and cyclooctane. In particular, we report the atomic path numbers and atomic ID numbers (i.e. local descriptors), and molecular path numbers and molecular ID numbers (i.e. global descriptors). The path numbers were weighted so that a path of length 1 corresponds to the molecular connectivity index χ. This paper should correct the widely held misconception that graph-theoretical analysis is not applicable to 3-D molecular structures, and at the same time should alert those interested in SPR and SAR to the availability of 3-D structural invariants of potential use in QSPR and QSAR models. The examples given and the computational background suffice to inform a potential user to write her/his own software, or to modify the existing ALL PATH program in order to obtain the novel 3-D molecular invariants. The computations were performed on an Apple IIe personal computer (with a program written in BASIC).

Use of atom codes for the classification of chemical shifts of benzenoid hydrocarbons

Abstract Atomic codes which enumerate the first, second, third, etc., nearest neighbors are considered as the basis of a systematic search for regularities in available molecular data. Specifically, benzenoid conjugated hydrocarbons are considered and proton chemical shifts are reviewed in an effort to detect trends among the observed values and features characterizing the atomic environment.

A statistical approach to resonance energies of large molecules

Abstract For large conjugated molecules, resonance energies of SCF MO quality are not available. Here we outline a method of determining molecular resonance energies by combining a graph theoretical approach to aromaticity with a statistical analysis of random Kekule valence structures. The approach involves construction of random Kekule valence forms and subsequent enumeration of conjugated circuits within each such structure.

Chemical shift sums

Abstract Graph theoretical schemes have been found useful in systematic searches for regularities in available molecular data. In particular, enumeration of paths of different lengths provides a basis for characterization of atomic environments in a molecule as well as the molecule as a whole. Various thermodynamic properties have been reported in the literature as showing regularities in trends when one orders structures on a coordinate grid using paths of length 2 and paths of length 3 alone. Here it is shown that simple sums of carbon-13 chemical shifts in alkanes show the same topological regularity, and can be viewed as legitimate molecular quantities which reflect some salient structural features. Such additional information, easily derived from available NMR spectra, may assist one in locating missing chemical shifts, in checking assignment, or in making structural deductions—provided that the preliminary finding for alkanes proves more general.

Small variations in chemical shifts for atoms in similar environments

Abstract It is shown that, at least for the particular case of selected proton chemical shifts in benzenoid conjugated hydrocarbons, minor variations in chemical shifts for atoms in similar environments have definite structural origin. The analysis is based on the construction of a partial order (in the algebraic sense) for structures induced by an ordered list of a particular atomic property. Specifically, selected CH environments for catacondensed benzenoid hydrocarbons are discussed. The minor variations, i.e., the gradual decrease of chemical shifts, show a parallelism with the similar decrease in the degree of local aromaticity for the rings at which the corresponding protons are attached. The differences in chemical shifts to which significance is now attached fall in the range of 0.1 to less than 0.01 ppm.

Aromaticity in polycyclic conjugated hydrocarbon dianions

Abstract Dianions of polycyclic conjugated hydrocarbons are classified into aromatic, partially aromatic and anti-aromatic types. The classification has been based on a single structural concept: the conjugated circuits model. The negative charge in dianions is formally treated as a “double” bond contracted to a single carbon atom. Most dianions have been found to belong to the type “partially aromatic”, the degree of aromaticity being rather small, even zero or corresponding to weakly antiaromatic systems. The degree of aromaticity has been determined by the relative roles of RE (4n + 2) and RE (4n) which represent the positive and the negative contributions to molecular resonance energy, respectively. Our approach is contrasted to the still occasionally used peripheral model, the limitations of which are more serious than generally recognized. Its premise is that large (peripheral) conjugation is dominant, whilst in fact small conjugated cycles (circuits) play the dominant role in aromaticity and conjugation.

Structural Approach to Aromaticity and Local Aromaticity in Conjugated Polycyclic Systems

After an introductory brief discussion of the important and much debated concept of aromaticity, we elaborate on a recently proposed scheme for the partition of π-electrons of Kekulean polycyclic conjugated hydrocarbons to individual rings, so that by summing π-electrons within individual rings of polycyclic conjugated hydrocarbons one obtains the total number of π-electrons in a molecule. We discuss separately for various types of hydrocarbons the π-Electron Content of individual rings, to be denoted as EC. In particular we summarize the EC results that we published in a series of papers which included: benzenoid catafusenes, benzenoid coronafusenes, benzenoid perifusenes, alternant and nonalternant conjugated hydrocarbons. Finally we return to Clar structures of benzenoid hydrocarbons as well as Clar structures of a selection of non-benzenoid alternant hydrocarbons like biphenylene, and point to a significant difference in distribution of π-electrons when instead of using all Kekule valence structures one focuses on the subset of Kekule valence structures indicated by Clar’s model.

Computer generation of generalized Wheland polynomials

Abstract Generalized Wheland polynomials enumerate the valence structures of different degrees of excitation. As such they are structural invariants which may be of interest in discussions of similarities and differences among unsaturated compounds. Brute force enumeration of valence structures is already impractical for graphs having n = 10 vertices (e.g. naphthalene C 10 H 8 ). Here we outline a computer program which enumerates valence structures of any degree of excitation. The results are illustrated on linear chains, cycles, and smaller benzenoid systems. Some properties of the derived polynomials are discussed. The recursive relation for the generalized Wheland polynomials is given. Because of the nonpolynomial character of the problem the computer application is practical only for graphs having n = 16 and less vertices.

Average carbon-13 chemical shifts in benzenoid dications

Abstract The resonance energies and the average carbon-13 chemical shifts for a number of dications of benzenoid hydrocarbons are examined. The resonance energies have been derived by applying a graph theoretical approach based on enumeration of conjugated circuits present in the collection of Kekule valence structural formulas for the dications, while carbon-13 chemical shifts have been taken from the literature. Average carbon-13 chemical shifts decrease sharply with increase in the molecular resonance energy. The derived correlation allows one to discuss the relative changes in the average carbon-13 chemical shifts and relative differences in resonance energies at a quantitative level.