About One Numerical Method for Finding the Positions of Hydrogen and Oxygen Nuclei in a Water Cluster

The results of modeling the spatial positions of hydrogen and oxygen nuclei in a water cluster are presented as a direct computational experiment. The method for the numerical solution of the Schrödinger equation, which was previously developed by the author and is based on the Monte Carlo method, is used. This method has proven to be very efficient in terms of computer time. The input data of this method are the average positions of the particles included in the quantum system, for the calculation of which another method is developed. In the method of constructing the average positions of quantum particles, several energy isomers of water clusters are constructed. It is this multiplicity that is of primary theoretical interest. For the purpose of testing the technique, a model of an individual water molecule with the generally accepted geometry of particle arrangement, as well as the so-called geometry of an unfolded water molecule, is built. The energy isomers of the dimer, trimer, and hexamer of water presented in this study are considered as possible geometric structures of water clusters and serve as an illustration of the use of the proposed method for calculating quantum systems. The water dimer model is constructed in the form of three geometric structures of the arrangement of hydrogen and oxygen nuclei, conventionally called quasi-two-dimensional, octahedral, and quasi-one-dimensional. The water trimer model is reduced to a discussion of two geometries: three-dimensional and quasi-two-dimensional. Finally, the geometry of the water hexamer in the form of an octahedron, at the vertices of which there are oxygen nuclei, and all twelve protons are located in the center, is considered. Water cluster models are understood as the construction of scattering clouds of all quantum particles included in the cluster.