Abstract
Some of the elements of the Universal matrix and their combinations are useful topological indices of physicochemical properties of octanes. Whereas single elements of the Universal matrix give rise to 0.70 < R < 0.99, mutually optimized combinations of only four to six out of 56 of them in the Universal matrix of octanes give rise to R > 0.99 and in the worst cases to R > 0.98. Also a new measure of goodnes of correlation, the Amount of information in the topological index, Ainfo (%), is introduced. Structural interpretation of some of the physicochemical properties of octanes is demonstrated as well as of the contribution by the most useful elements of the Universal matrix.
Highlights
Mathematical methods occupy an eminent place in the field of prediction of properties and activities of chemical compounds, and even materials
As the first step to assess the usefulness of particular elements of the Universal matrix, uij(a, b, c), as topological indices is the goodness of their correlation with the physicochemical properties of octanes
The best correlations between tested physicochemical properties (PCP) and uij(a, b, c) elements using grid values of exponents are presented in the form |Rmax grid| (PCP, uij) as follows: 0.99 > (MON, u75) > (RON, u75) > (Pc, u53) > (BON, u75) > 0.95 > (BP/Tc, u63) > (R2, u75) > (Tc2/Pc, u75) > (B, u63) > > (ω, u63) > (Tc/Pc, u65) > 0.90 > (Tc, u63) > (ST, u63) > (Vm, u63) > (d, u63) > (C, u65) > (A, u75) > (S, u32) > (BP, u72) > (CED, u52) > (ΔHf°g, u72) > (ΔHv, u76) > (Sol.par., u52) > (MR, u31) > (Vc, u63) > 0.85 > > > 0.80 > > (Zc, u84) > 0.70
Summary
Mathematical methods occupy an eminent place in the field of prediction of properties and activities of chemical compounds, and even materials. These methods, known under the acronym QSPR/QSAR (quantitative-structure-property or structure-activity relationship) use graph-theoretical descriptors, where molecules are seen as chemical graphs, i.e. as a set of vertices attached to each other by a set of non-metrical connections.[1] These descriptors are proposed as topological indices They are the simplest means of describing the structure of a molecule, characterizing it by a single number.[2]. There is known a plethora of topological indices.[3,4,5,6,7,8,9] After their compilations, a huge number of new ones has been described and new and new ones are being developed, cf e.g.10,11
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