In the vastness of molecular space, there are many series X, XY, …, XYn…XYN, where N lies between 3 and say 10, whose data for a given property and phase are approximately linear with respect to n. A vectorial representation of the tabulated data in a series and a vector index to describe the series have been developed. The authors started with X as a metallic atom and with the property as heat of atomization, and showed that the vector index manifested periodicity. Then they moved to cases where X itself is a molecule and where the properties are enthalpies of formation, entropy, retention index, hydrophobicity, and boiling point. The vector index is a two-dimensional vector whose upper element describes the value of the property for the atom or molecule X and whose lower element describes the abscissa difference of any two members of the series after the data have been fitted, in least-squares fashion, to a standard, linear with n, series A, AL, … ALn, … ALN. Matrices can transform the data vectors of any series of species whatsoever to any other series of the same dimensionality. Matrices can also transform the vector index for property data of any approximately linear series, in any phase, to the vector index for any other approximately linear series.
Hefferlin, Ray and Luk, Ken, "A Periodicity-Sensitive Vector Index for Small Molecules" (2006). Faculty Works. 5.