Physical Significance of Molecular Connectivity Indexes

Consider a simplified illustration of the foregoing QSAR examples. Consider a list of normal alkanes together with their water solubility and boiling points. A plot shows that solubility (in logarithmic form) is linear with number of carbon atoms and that boiling point is nonlinear. Such a relation is a QSAR based on the simple structure feature, number of carbon atoms. A linear equation captures all the structure information available in this data set. (The structure information could, of course, be represented in other ways, such as number of methylene groups, number of hydrogen atoms, number of carbon-carbon bonds, etc.) It is important to note here that no assumption has been made about the relation between water solubility and number of carbon atoms. This is an example of what Adamson has called a mechanism-free model. 

In similar fashion, a QSAR can be developed for the boiling point, although the mathematical relation is more complicated, perhaps a logarithmic form. In both cases, however, one may proceed to use the mathematical equations to interpolate and extrapolate or to attempt to invert the process and determine the molecular structure that corresponds to a given property value. It is clearly seen here that the physical significance of the regression correlate, number of carbon atoms, is molecular structure. That is, what is encoded in the number of carbon atoms adequately expresses what we know about the normal alkanes in terms of molecular structure for this particular data set. 

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