Determination of Critical Properties of Alkanes Derivatives Using Multiple Linear Regression

Document Type : Research Paper


Islamic Azad University of Arak Branch


This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. Multiple linear regression was used to estimate the correlation between these critical properties and molecular descriptors using proper coefficients. To achieve this aim, the most appropriate molecular descriptors were chosen from among 11 structural and geometric descriptors in order to determine the critical properties of the intended molecules. The results showed that among all the proposed models to predict critical temperature, pressure and volume, a model including the combination of such descriptors as HyperWiener, Platt, MinZL is the most appropriate one.


Main Subjects

  1. R. T. Morison and R. Neilson Boyd, Organic Chemistry, Allyn & Bacon, 2003.
  2. H. Wiener, Correlation of heats of isomerization and differences in heats of vaporization of isomers, among the paraffin hydrocarbons, J. Am. Chem. Soc. 69 (1947) 2636–2638.
  3. A. A. Gakh, E. G. Gakh, B. G. Sumpter and D. W. Noid, Neural network–graph theory approach to the prediction of the physical properties of organic compounds, J. Chem. Inf. Comput. Sci. 34 (1994) 832–839.
  4. O. Ivanciuć, The neural network MolNet prediction of alkane enthalpies, Anal. Chem. Acta. 384 (1999) 271–284.
  5. D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, John Wiley & Sons, Inc, 2006.
  6. R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Methods and Principles in Medicinal Chemistry, Wiley–VCH Verlag GmbH, 2008.
  7. I. Gutman and B. Furtula (eds), Novel Molecular Structure Descriptors–Theory and Applications I and II, University of Kragujevac and Faculty of Science Kragujevac, 2010.
  8. I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y. 27 (1994) 9−15.
  9. R. B. King, Chemical Applications of Topology and Graph Theory, Elsevier, Amsterdam, 1983.
  10. I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry,Springer–Verlag, Berlin, 1986.
  1. M. Randić, Chemical Graph Theory–Facts and Fiction, NISCAIR–CSIR, India, 2003.
  2. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.
  1. M. Randić, Quantitative Structure–property relationship: boiling points of planar 1009-benzenoids, New. J. Chem. 20 (1996) 1001–1009.
  2. M. Shamsipur, B. Hemmateenejad and M. Akhond, Highly Correlating Distance/Connectivity–Based Topological Indices. 1: QSPR Studies of Alkanes, Bull. Korean Chem. Soc. 25 (2004) 253–259.
  3. H. Hosseini and F. Shafiei, Quantitative Structure Property Relationship Models for the Prediction of Gas Heat Capacity of Benzene Derivatives Using Topological Indices, MATCH Commun. Math. Comput. Chem. 75 (2016) 583–592.
  4. M. Goodarzi and E. Mohammadinasab, Theoretical investigation of relationship between quantum chemical descriptors, topological indices, energy and electric moments of zig–zag polyhex carbon nanotubes TUHC6[2p,q] with various circumference [2p] and fixed lengths, Fullerenes, Nanotubes Carbon Nanostructures. 21 (2013) 102–112.
  5. A. Alaghebandi and F. Shafiei, QSPR modeling of heat capacity, thermal energy and entropy of aliphatic aldehydes by using topological indices and MLR method, Iranian J. Math. Chem.7 (2016) 235–251.
  6. M. Pashm Forush, F. Shafie and F. Dialamehpour, QSPR study on benzene derivatives to some physico chemical properties by using topological indices, Iranian J. Math. Chem.7(1) (2016) 93–110.
  1. G. Cash, S. Klavžar and M Petkovsek, Three Methods for Calculation of the Hyper-Wiener Index of Molecular Graphs, J. Chem. Inf. Comput. Sci. 42 (2002) 571–576.
  2. X. Li and Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem. 59 (2008) 127–156.
  3. M. Randić, Characterization of atoms, molecules and classes of molecules based on paths. enumerations, MATCH Commun. Math. Comput. Chem. 7 (1979) 5–64.
  4. B. Liu and I. Gutman, On general Randić indices, MATCH Commun. Math. Comput. Chem. 58 (2007) 147–154.
  5.  M. Randić, Charactrization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609–6615.
  6.  A. T. Balaban and T. S. Balaban, New Vertex Invariant and topological indices of chemical graphs based on information on distance, J. Math. Chem. 8 (1991) 383–397.
  7.  A. T. Balaban, Topological index based on topological distances in molecular graph,Pure Appl. Chem. 55 (1983) 199–206.
  8.  K. C. Das, B. Zhou and N. Trinajstić, Bounds on Harary index, J. Math. Chem. (2009) 1377–1393.
  10. M. Randić and S. C. Basak, Multiple regression analysis with optimal molecular descriptors,SAR QSAR Environ. Res. 11 (2000) 1–23.
  11. G. A. F. Seber and C. J. Wild, Nonlinear Regression, Hoboken, NJ: Wiley–Interscience, 2003.
  12. K. Roy and I. Mitra, On various metrics used fo r validation of predictive QSAR models with applications in virtual screening and focused library design, Comb. Chem. High Throughput Screen. 14 (2011) 450–474.