Energetic consideration of the vibrational potential function in the effective nuclear charge model. VII

Abstract

The homogeneity characteristics of the molecular energy with respect to the atomic number are discussed in detail on the basis of the local and nonlocal homogeneity hypothesis which has been proposed in a previous report [J. Chem. Phys. 85, 5882 (1986)]. It is first shown that the homogeneity hypothesis is convenient for describing the local and nonlocal properties of molecules. Inhomogeneous linear second-, third-, fourth-, and nth-order differential equations are constructed from the constrianed linear first-order differential equation and solved for understanding general potential forms of molecules. The results obtained give the theoretical basis to various models so far presented. The approximate potential function obtained by solving the constrained linear third-order differential equation is successfully applied to the calculations of higher-order potential constants as well as molecular energy components. Lastly, all the expressions of molecular energy components with the homogeneity constraint are given by making use of the general solution derived from the constrained linear nth-order differential equation.