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).

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