The Structural Interpretation of the Randi Index

Motivation. The Randiü index is one of the most successful molecular descriptors in structure–property and structure–activity relationships studies. In spite of some attempts to interpret the physical meaning of this index it is still not clear what exactly this index measures in a molecular structure. The finding of the structural interpretation of this topological index will open the doors to novel applications as well as to a better understanding of the models developed with its use. Results. The inverse squared–root of the vertex degree is identified here as a measure of the relative accessible perimeter of an atom from the outside. These perimeters, which have length units, are proposed to be measured in a new unit called the Randiü (R). One Randiü correspond to the perimeter of a carbon atom with degree one. On this basis, the bond contributions to the Randiü index are relative areas of bond accessibility from the environment. Consequently, the Randiü index is interpreted as the relative molecular area of external accessibility, that is the sum of relative accessibility bond areas in a molecule. Conclusions. The results obtained here provide the Randiü index with a clear structural interpretation, which is very close to the physical thinking commonly used in chemistry.