For the isomers of hexane, heptane, and octane as typical candidates for gasoline of motor vehicles and propeller airplanes correlation between the research octane number (RON) and the molecular structure of alkane was studied. Three topological indices, Z (Hosoya index), p (3-step number of Wiener), and B (Balaban's centric index) were selected for this QSAR (QSPR) study not only to attain good correlation but also to clarify the mechanism of gasoline combustion in the engine. As generally accepted RON increases with the degree of branching, correlated well with B and -Z. Another known feature of this problem that RON decreases with the number of carbon atoms can be taken into account by -Z. On the other hand, p, which shows the highest correlation with the density of liquid, has almost nothing to do with RON by itself. Although B has the highest correlation with RON among various single indices, it cannot explain the difference among the mode of branching, such as 2,2-dimethyl and 2,3-dimethy substitution. This weak point of B can be overcome by the combination with p and Z as B+4p-2Z, leading to the conclusion that the more spherical the alkane molecule becomes the lower the boiling point and the more dense the unburned liquid gasoline can be pressed for effective burning without knocking. Finally, it should be pointed out that the strange behavior of 2,2,3,3-tetramethylbutane, with extraordinary high melting point but predicted to have high RON, cannot be explained by this simple QSAR study.
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