Recurrent relations for the approximation of the physicochemical constants of homologues

In addition to the earlier revealed physicochemical constants of homologues whose changes in arbitrary series obey the simplest linear recurrent relations A (n + k) = aA(n) + b, such equations are shown to be applicable to the approximation of the solubility of organic compounds in water (k = 1), temperature dependences of the solubility of organic and inorganic compounds in water (k = ΔT), and nematic-isotropic phase transition temperatures for liquid crystals (k = 2). The a and b coefficients of linear recurrent relations are only determined by the nature of the homologous difference, and, if the homologous difference is the same, they are close for different series. This enables various properties of virtually arbitrary organic compounds to be described by unified recurrent equations, which is equivalent to the existence of a general method for their calculation. For continuous properties (for the example of the temperature dependence of solubility), a method for solving recurrent equations with nonintegral or nonequidistant argument values is suggested.