Harary index - Twelve years later

A modification of the Harary index, denoted by H and introduced twelve years ago, is proposed. Unlike the original index, this index, called the modified Harary index and denoted by H-m, consists of two parts: the first relates to greater contributions of outer bonds and the second to smaller contributions of inner bonds of an alkane, which is in accordance with the chemists' intuition. The Wiener index W Harary index and modified Harary index are compared in the structure-property modeling of eight representative properties of lower alkanes. The models considered were linear, Wiener-like and linear and nonlinear multivariate. Multivariate models were obtained using our variable selection procedure CROMRsel (B. Lucid and N. Trinajstic, J. Chem. Inf. Comput. Sci. 39 (1999) 121-132). Multivariate models represent considerable improvements over the other two kinds of models. For example, the standard error of estimate improves on going from the best linear structure-boiling point model involving H-m (S = 7.6 degreesC) to the best Wiener-like model based on the reduced Wiener number W/N-2 and the number of paths of the length of three p(3) (S = 6.2 degreesC) to the best four-parameter multivariate model containing In values of W H and H-m, and p(3) (S = 1.5 degreesC). All good models obtained in this work involve H-m, suggesting that this index has a great potential to be used in QSPR. Its advantage over W and H is due to the fact that the main contribution to H-m comes from the outer, more exposed, bonds, which is not the case of the other two indices.