The Development of a Parallel Algorithm and Program for Solving the Stationary Many-Body Schrodinger Equation by the Monte Carlo Method on the Example of S States of Atomic Systems

Abstract

This paper is devoted to the development of a specialized oriented to the use of supercomputers algorithm for solving the stationary multiparticle Schrodinger equation - the eigenvalues problem and the corresponding eigenfunctions of many-electron systems (atoms, molecules, ions) - and their software implementation. The algorithm under development is based on several methods for numerical solving of eigenvalue problems by the Monte Carlo method (MCM) which are used in the calculation of neutron transport problems in nuclear reactors. MCM for the integral form of the stationary Schrodinger equation looks very attractive, since it is intrinsically parallel and very convenient for calculations on multiprocessor systems. The paper presents an algorithm for calculating many-electron atomic systems with zero orbital angular momentum on multiprocessor systems. As a result of the research, an approach that contains a theoretical prediction of the boundaries of fundamental regions - those in which the wave function is of a constant sign - was proposed. The problem of electronic fluctuations introduced by the use of normalization algorithms was also solved to prevent unlimited growth (fall) in the number of particles in the packet. The new approach refuses normalization and assumes the existence of a corridor for the number of particles in the packet.