Cetane numbers of hydrocarbons: calculations using optimal topological indices

Abstract

The QSPR problem for cetane numbers of hydrocarbons, a key property of oil fuels, was considered for the first time. Based on the approach developed, calculations have been carried out and relations derived for prediction of the cetane numbers of alkanes and cycloalkanes. Results of cetane number calculations for 180 unknown and non studied hydrocarbons are presented.Relationships between certain physicochemical prop erties of organic compounds and the structures of their molecules can successfully be modeled using various to pological indices (TIs). 1-3 At the same time for some other properties, e.g., melting points (T m ) and surface tension, models giving a reasonable accuracy 2 were constructed only for particular classes of hydrocarbons. 4,5 Properties for which no attempts to solve the QSPR problem have been reported as yet include, in particular, the ce tane number, a practically important property of oil fuels. In the present work we present a model for calculations and prediction of cetane numbers of saturated hydrocarbons in cluding those whose molecules contain five and six membered rings. We will also give a theoretical explanati on for difficulties in constructing structure-property re lationships for cetane numbers using the known methods.The first group of properties (especially, such addi tive properties, as molecular refraction and molecular volume) suitable for constructing simple models can qualitatively be treated as "simple" properties. The sec ond group including all other properties that can be treat ed as "complex" ones. For instance, a study 2 was devoted to simulation of eight physicochemical properties of al kanes. These properties differ in complexity of descrip tion using various topological descriptors, as is shown by corresponding correlation coefficients. The simplest for modeling is the molecular refraction, the melting point being the most complex. In the former case rather high correlation coefficients (from 0.99 to 0.9999) were obtained using the simplest computational schemes, whereas in the latter case the correlation coefficient was at most 0.41.Earlier, 6 a successful attempt was made to strictly order the properties in question based on mathematical relations for quantitative estimation of the "complexity" Х and "simplicity" Y of the physicochemical characteristics of organic compounds. Suppose we have experimental values of a property P exp for a number of alkanes (set Q). For instance, these can be all known isomers of the al kanes С 5 -С 10 . This choice is due to the fact that (i) butane С 4 has only two isomers, (ii) experimental data for certain properties (e.g., molecular refraction or mo lecular volume) are unavailable, and (iii) only a few out of seventy five possible isomers of decane С 10 have been studied. The quantity(1) will be called "complexity" of the property P on Q. Here s 0 2 and ∆ 0 2 are respectively the chemical and conven tional (mathematical) dispersions of P on Q. They are given by (2) and ,(where l i are the numbers of isomers, y i are experimen...

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