Abstract:
The paper defines the concept of a shape matrix to describe the potential energy of an arbitrary molecular system. The question of the set (uniqueness) of locally equilibrium configurations of the potential energy of a multiatomic cluster is studied. A molecular system consisting of many, generally speaking, different atoms is called a multiatomic cluster. A formalism for constructing the entire line of many-particle potentials to describe an arbitrary molecular cluster is proposed. The algorithm for constructing the potential energy function of a multiatomic 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 an equilibrium one. The general constructions and conclusions are illustrated by examples of reproduction of water, methane, ethylene and benzene molecules as equilibrium standard configurations. Suitable potentials are constructed having the specified configurations as global minima. 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 integralities are reproduced unchanged.
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