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  1. Plokhotnikov K.E.
    The problem of choosing solutions in the classical format of the description of a molecular system
    Computer Research and Modeling, 2023, v. 15, no. 6, pp. 1573-1600

    The numerical methods developed by the author recently for calculating the molecular system based on the direct solution of the Schrodinger equation by the Monte Carlo method have shown a huge uncertainty in the choice of solutions. On the one hand, it turned out to be possible to build many new solutions; on the other hand, the problem of their connection with reality has become sharply aggravated. In ab initio quantum mechanical calculations, the problem of choosing solutions is not so acute after the transition to the classical format of describing a molecular system in terms of potential energy, the method of molecular dynamics, etc. In this paper, we investigate the problem of choosing solutions in the classical format of describing a molecular system without taking into account quantum mechanical prerequisites. As it turned out, the problem of choosing solutions in the classical format of describing a molecular system is reduced to a specific marking of the configuration space in the form of a set of stationary points and reconstruction of the corresponding potential energy function. In this formulation, the solution of the choice problem is reduced to two possible physical and mathematical problems: to find all its stationary points for a given potential energy function (the direct problem of the choice problem), to reconstruct the potential energy function for a given set of stationary points (the inverse problem of the choice problem). In this paper, using a computational experiment, the direct problem of the choice problem is discussed using the example of a description of a monoatomic cluster. The number and shape of the locally equilibrium (saddle) configurations of the binary potential are numerically estimated. An appropriate measure is introduced to distinguish configurations in space. The format of constructing the entire chain of multiparticle contributions to the potential energy function is proposed: binary, threeparticle, etc., multiparticle potential of maximum partiality. An infinite number of locally equilibrium (saddle) configurations for the maximum multiparticle potential is discussed and illustrated. A method of variation of the number of stationary points by combining multiparticle contributions to the potential energy function is proposed. The results of the work listed above are aimed at reducing the huge arbitrariness of the choice of the form of potential that is currently taking place. Reducing the arbitrariness of choice is expressed in the fact that the available knowledge about the set of a very specific set of stationary points is consistent with the corresponding form of the potential energy function.

    Keywords: problem of choice of solutions, space marking, monatomic cluster, computational experiment, gradient descent, potential energy function, binary and multiparticle potentials.

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