Abstract:
The article presents the results of modeling the spatial positions of hydrogen and oxygen
nuclei in a water cluster from the point of view of a direct computational experiment. The
method of numerical solution of the Schrodinger equation, previously developed by the
author, which is based on the Monte Carlo method, is involved. This solution has proven
itself to be very efficient in terms of the cost of computer time. The input data of the
method under consideration are the average positions of the particles included in the
quantum system, for the calculation of which another method was developed. Within the
framework of the method of constructing the average positions of quantum particles,
several energy isomers of water clusters have been constructed. It is this multiplicity that
causes the main theoretical interest. For the purpose of testing the technique, a model of
an individual water molecule was built with the generally accepted geometry of the arrangement of particles, as well as the so-called geometry of an unfolded water molecule.
The energy isomers of the dimer, trimer and hexamer of water given in the paper are considered as possible geometric designs 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, octahedron-shaped and
quasi-one-dimensional. The water trimmer model was reduced to a discussion of two geometries: three-dimensional and quasi-two-dimensional. Finally, the geometry of the
hexamer of water in the form of an octahedron is considered, in the vertices of which
there are oxygen nuclei, and all twelve protons are placed in the center. Water cluster
models are understood as the construction of scattering clouds of all quantum particles
included in the cluster.
Keywords:Schrodinger equation, numerical methods, ordinary differential equations,
Monte Carlo method, average positions of quantum system particles, water cluster.
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