Topological Index and Thermodynamic Properties. IV. Size Dependency of the Structure-Activity Correlation of Alkanes

Abstract

Correlation coefficients between twelve thermodynamic properties (ΔS, ΔHf, ΔGf, bp, d, nD, Rm, Vm, pc, Tc, Vc, dc) of 624 isomers of nonane through dodecane and five different topological indices (Z, p3, w, p2, A3) were calculated, where the new index A3 is proposed to be defined as the half sum of the off-diagonal elements of the cube of the adjacency matrix A. These properties can be classified into several types, according to the behavior of the two correlation coefficients, ρ(Z) and ρ(p3), against the change of the size of molecules. ΔS and bp depend largely on Z, while d and nD on p3, irrespective of the size change of molecules. On the other hand, ΔHf of smaller alkanes is largely dependent on Z, but for larger alkanes it turns out to be a p3-dependent property. Various interesting behaviors of the structure-activity relationships including the “pentane effect” were observed and discussed.

Topological Index and Thermodynamic Properties. 5. How Can We Explain the Topological Dependency of Thermodynamic Properties of Alkanes with the Topology of Graphs?

“…[6][7][8] In this respect only integer topological indices (ITI's) with a simple and straightforward definition are concerned for clarifying the chemicomathematical secret of the topological dependency of typical thermodynamic properties of the most common alkanes. 1,[9][10][11][12] Those indices are derived from either the distance matrix, D, or nonadjacent number, p(G,k). 2 From the former category Wiener's w and p (path number) 1 are selected.…”

Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index

“…In a series of subsequent papers, Hosoya and his coworkers [16,39,43,48,49,[76][77][78] and others [20] showed that the "topological index" Z is related with a variety of physicochemical properties of alkanes. Another series of researches revealed the applicability of Z in the theory of conjugated π -electron systems [25,30,31,37,46,47].…”

Distance Polynomial and the Related Counting Polynomials

“…[13][14][15] Thus, a number of interesting features seem to be hidden in the distance polynomial, S G (x), of a graph.…”