2159 ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2015, Vol. 89, No. 12, pp. 2159–2173. © Pleiades Publishing, Ltd., 2015. Original Russian Text © Yu.A. Kruglyak, I.V. Peredunova, 2015, published in Zhurnal Fizicheskoi Khimii, 2015, Vol. 89, No. 12, pp. 1825–1840. New Invariants of Weighted Graphs for Calculating the Critical Properties of Freons Yu. A. Kruglyak and I. V. Peredunova Odessa State Environmental University, Odessa, 65000 Ukraine e-mail: quantumnet@yandex.ua Received October 8, 2014 Abstract—A new approach to structure–property problems using new invariants of fully weighted graphs to provide a quantitative description of the critical properties of freons is proposed. A general principle for con- structing topological invariants of fully weighted graphs for structure–property correlations is formulated. Two new invariants are proposed and used to calculate critical properties of freons of the methane, ethane, and propane series. It is shown that unlike all other known incremental methods, the proposed approach does not require the use of experimental data or calibrations to calculate critical properties. It ensures a statistically reliable linear dependence of all critical properties of freons on the value of the matching index for our corre- sponding molecular graph. Over 2.5 thousand previously unknown values of the critical properties of lower freons are calculated. Keywords: freon, critical properties, critical temperature, critical pressure, critical volume, molecular graphs, graph invariants, weighted graphs, matching index. DOI: 10.1134/S0036024415120171 INTRODUCTION The problem of establishing relationships between the structure of molecules and properties of molecular substances is complex and varied. This is due not only the number of properties of substances and the diffi- culty of studying both the structure and properties of their constituent molecules experimentally. The main methods for studying structure–property relationship are those of regression and correlation analysis and pattern recognition. These methods depend on the numerical characteristics of the structure of mole- cules. Such natural numerical characteristics of molecular structure as bond lengths, valence and dihedral angles, and a number of the quantum chemi- cal computational properties of molecules are often successfully used in methods of pattern recognition, but are not suitable for regression and correlation analysis. Integral numerical characteristics of molecu- lar structure are preferred for these methods. Topolog- ical invariants that allow us to describe the structure of a molecule using a single number are therefore of great interest [1–7]. The invariant of a molecular graph is a value that takes the same numerical value at any arbitrary num- bering of vertices in the graph. In the literature, invari- ants of molecular graphs are referred to as topological indices (TIs). A molecular graph is one whose vertices are in one-to-one correspondence with the atoms of a molecule, and whose edges correspond to chemical bonds. Using TIs as numerical integral characteristics of the structure of molecules to establish structure– property relationships has a number of advantages. First, topological descriptions of molecules are based on the well-developed theory of graphs. Second, TIs are calculated only on the basis of the structural for- mulas of molecules. Third, these calculations do not require large computational resources. CRITICAL PROPERTIES OF FREONS AS OBJECTS OF STUDY We chose to study the critical properties of freons for three reasons: (1) There are no sufficiently reliable methods to calculate them, so measuring the critical properties of freons experimentally is quite difficult. (2) Freons are convenient model compounds for developing methods of parameterization for our approach, since freon molecules have simple struc- tures and a wide variety of atoms. (3) Changes in the critical properties of a series of halogenated alkanes are characterized by a number of features that do not allow us to describe the depen- dence of these properties on the alkanes’ molecular structures using additive methods. Let us consider the advantages and disadvantages of the best known methods of calculating the critical properties of substances. CHEMICAL THERMODYNAMICS AND THERMOCHEMISTRY