Use of moment of inertia in comparative molecular field analysis to model chromatographic retention of nonpolar solutes

A quantitative structure-retention relationship (QSRR) was developed from chromatographic data on 31 unsubstituted 3-6-ring polycyclic aromatic hydrocarbons (PAHs) using the 3D-QSAR method known as comparative molecular held analysis (CoMFA). The resulting CoMFA model gave an excellent correlation to high-performance liquid chromatography retention data for these PAHs yielding r(2) values of 0.947 (conventional) and 0.865 (cross-validated). The steric and electrostatic contributions to the CoMFA model were 100% and 0%, respectively. A unique feature of this study was the use of moment of inertia, I, as a basis for CoMFA alignment of the PAH molecules. The moment of inertia also provided an alternative method for calculating the solute length-to-breadth ratio (L/B), which has been applied in previous QSRR studies as a molecular descriptor for PAH retention. By virtue of its mathematical simplicity and lack of ambiguity, the present derivation of L/B from I offers several advantages over other geometry-based schemes. Finally, I-x was evaluated for use as a molecular descriptor in QSRR regression analysis to predict the log of the retention index (log I) for these PAHs. The correlation with PAH retention was weak when the moment of inertia was considered alone but improved dramatically (r(2) = 0.928) when the moment of inertia and connectivity index chi were used in combination as descriptors.