About one numerical method of finding positions of hydrogen and oxygen nuclei in water cluster

K. E. Plokhotnikov

Matematičeskoe modelirovanie, Tome 34 (2022) no. 4, pp. 43-58.

Résumé

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.

Détail

Keywords: Schrodinger equation, numerical methods, ordinary differential equations, Monte Carlo method, average positions of quantum system particles, water cluster.

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