On the set of locally equilibrium configurations of the potential energy of a multiatomic cluster

The paper studies the question of the set (uniqueness) of locally equilibrium configurations of the potential energy of a multiatomic cluster. A molecular system consisting of many, generally speaking, different atoms is called a multiatomic cluster. A formalism is proposed for constructing the entire line of multiparticle potentials to describe an arbitrary molecular system. The concepts of “shape matrix” or “morph” for each of the multiparticle potentials are intro-duced and discussed. The algorithm for constructing the potential energy function of a multia-tomic cluster is determined so that one could talk about building a well-defined configuration of cluster atoms as the only possible one. This algorithm is considered as a way to solve the problem of choosing the configuration of cluster atoms as locally equilibrium. The sets of locally equilibrium configurations of binary and multiparticle potentials are studied in detail. A set of locally equilibrium configurations of a linear combination of binary and multiparticle potentials is also considered. It is shown that in the latter case, the set of locally equilibrium configurations is determined mainly by the binary potential. The general constructions and conclusions are illustrated by examples of reproduction as locally equilibrium standard configurations of water, methane, ethylene and benzene molecules. Suitable potentials are constructed having the specified configurations as global minima. Using examples of the description of clusters of water, benzene and carbon, the question of the causes of the appearance of a variety of locally equilibrium con-figurations is investigated. An algorithm for constructing a complex, composite shape matrix for clusters consisting of many identical molecules is discussed. The use of the concept of “shape matrix” allows us to naturally take into account all possible integral subunits in the molecular system, as well as describe the limits within which these wholes are reproduced unchanged.