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## Journal of the Chilean Chemical Society

##
*versión On-line* ISSN 0717-9707

### J. Chil. Chem. Soc. v.49 n.4 Concepción dic. 2004

#### http://dx.doi.org/10.4067/S0717-97072004000400015

Chil. Chem. Soc., 49, N 4 (2004): págs: 351-354
Departament of Inorganic and Analytical Chemistry. Faculty of Chemical and Pharmaceutical Sciences, University of Chile. Santiago, Chile. e-mail: ecornwe@abello.dic.uchile.cl
Multiplicative numerical factors (F The F It was shown for a group of fifty saturated hydrocarbons that smaller differences were obtained between experimental boiling points (B.
The idea of chemical structure is of great importance to chemical science. Two mathematical tools are frequently used to describe chemical structure, the topological and graph theories Various attempt have been reported to express by means a numerical index the connectivity of atoms in a molecule. Among these, the first Zagreb group index M1 is defined as a sum of the squared vertex degrees, where, the second Zagreb group index M2 is defined as the sum of all edges product of the vertex degrees of neighboring vertices
Milan Randic
L. B. Kier and L. H. Hall advanced the used of the valence connectivity index
Where Z Within QSPR discipline (Quantitative Structure-Property Relationship), the L. B. Kier and L. H. Hall firstorder valence connectivity index ( Very often in QSPR discipline is used a single independent variable in correlation mathematical model and when the objective is to evaluate a new index (A) with a set {a The thesis proposed in this study is based in two classical set within the QSPR discipline: {L} set represented by experimental boiling points (B
An optimal linear regression model was adopted corresponding to the mathematical structure
The correlation consistency was evaluated by classical statistical parameters commonly used in QSPR field, these parameters are: correlation index (r), deviation standard of correlation (s.d.) and Fisher ration (F) The relation described in equation 6 is compared with the modification proposed by the author on (d To calculated boiling point of a particular molecular structure is necessary to sum (d
The factor F The calculated boiling points obtained by means of 6 and 7 equations are compared by statistical parameters. Also were compared the differences obtained between experimental boiling point vs. calculated one for both systems.
The evaluation of the numerical factors (F The total number of different two-carbons fragments found in the 50 saturated hydrocarbons is nine. This number is the maximum possible value for the whole saturated hydrocarbons homologous series. For the nine different type of two-carbon fragments, a specific numerical value corresponding to (d
Where exponent 1 implies the inverse matrix of the original (d _{c} factors, the boiling point were calculated for 50 saturated hydrocarbons by adding the different fractions (d_{i*}d_{j} )^{-0.5} *F_{c }in function of the bound type of each saturated hydrocarbon.
The following example using 2,2-dimethyl pentane shows how one linear equation is set out, equation 9:
The process of configuring the rest (eight equations) of the linear equations is done in a similar way. The structure of 2,2-dimethyl pentane, boiling point 79.2 C, is shown below.
Designating f: Experimental boiling point ® If T represent the two theories, it was found that: This relation will be related on equation 12 and 13 The linear regression, f: Experimental boiling point ®
The linear regression between experimental boiling points an the boiling points calculated by means of equation 11 is expressed by equation 12
The boiling points calculated by the thesis II are presented in Table 3 and its were calculated adding all (d _{i*}d_{j} )^{-0.5} *F_{c }over all two-carbon fragments of the molecular graph.
Linear regression between the experimental boiling points and calculated boiling points by means of thesis II is represented by equation 13.
All the regression procedures were conducted using Statgraphic Plus Nevertheless, the values of r, s.d. and F of equation 13 are better than equation 12, this implies the better quality of thesis II over thesis I, confirmed by the F
1. F. Haray, Graph Theory; Addison-Wesley. Reading, MA, 1969. [ Links ] 2. A. T. Balaban, Chemical Applications of Graph Theory. Ed. Aca demic Press: London 1976. [ Links ] 3. N. Trinajstic. Chemical Graph Theory 2nd. Ed. CRC Press: Boca Raton, FL, 1992. [ Links ] 4. I. Gutman, J. Chem. Phys. 62, 3399-3405 5. M. Randic. J. Am. Chem. Soc. 97, 6609-6615 (1975). [ Links ] 6. L. B. Kier, L. H. Hall. W. J. Murria, M. Randic. J. Pharm. Sci. 64, 1971-1974 7. L. B Kier, L. H. Hall. Molecular Connectivity in Chemistry and Drug Research: Academic Press: New York, 1976. [ Links ] 8. L. B. Kier, L. H. Hall, Molecular Connectivity in Structure-Activ ity Analysis; Research Studies Press. Chichester, UK., 1986. [ Links ] 9. L. B. Kier, W. J. Murria. M. Randic. L. H. Hall, J. Pharm. Sci, 65, 1226-1230 10. L. B. Kier, L. H. Hall. J. Pharm. Sci, 65, 1806-1809 (1976). [ Links ] 11. L. B. Kier. J. Med. Chem. 20, 1631-1636 (1977). [ Links ] 12. L. H. Hall, L. B. Kier, 13. L. B. Hall, L. B. Kier,. J. Phar. Sci. 67, 1743-1747 14. L. B. Kier, L. H. Hall. J. Pharm. Sci. 72, 1170-1173 15. L. B Kier, L. H. Hall 16. A. Sabljic, D. Horvatic. J. Chem. Inf. Comput. Sci 17. P. G. Seybolt, M. May, V Bagal. J. Chem. Educ., 64, 575-581 (1987). [ Links ] 18. A. T. Balaban. J. Chem. Inf. Comput. Sci. 35, 339-350 19. V. Padmakar, Khadikar, S. Karmarkar. V. K. Agrawal, J. Chem. Inf. Comput. Sci. 41, 934-949 20 21. O. Exner, I. Kramasil, I. Bajad. J. Chem. Inf. Comput. Sci 22. Statgraphic Plus for Windows 4.0 Profesional Version Copyright 1994-1999 Statical Graphics Corp. Serial Number 4650004167. [ Links ]
(Received: March 1, 2004 - Accepted: October 21, 2004) |