646 Russian Physics Journal, Vol. 48, No. 6, 2005 EFFECTIVE MANY-BODY INTERATOMIC POTENTIALS IN MOLECULAR DYNAMIC SIMULATIONS S. V. Eremeev 1,2 and A. I. Potekaev 2,3 UDC 53.072:681.3+539.2 INTRODUCTION Molecular dynamic (MD) simulation that offers a means to determine the equilibrium atomic structure, to compute dynamic and thermodynamic material properties, to simulate phase transformations, etc., has been successfully used in computational materials science. The key issue in MD-simulations is an effective description of interatomic forces. A limitation of the modern mixed quantum-classical molecular dynamics (which relies on either self-consistent solution of dynamic equations for the atom and electron sub-systems [1] or the Hellmann–Feynman theorem [2] and determination of the ground state of the electron subsystem in every atomic iteration) is the size of the system. On the other hand, while a classical MD approach can be used in modeling exercises with a million atoms and over, the limitations here appear due to a limited accuracy of empirical forces. As far as this is concerned, an alternative approach could be to derive interartomic forces from well-developed quantum-mechanical concepts. A basic idea of a large number of techniques for constructing effective many-body potentials is the density functional theory. 1. EFFECTIVE MEDIUM THEORY The fundamental concept in describing interatomic interactions is the theory of the electron density potential. The approaches by Stott and Zaremba [3] (theory of a quasiatom) and Nørskov and Lang [4] (effective medium theory) have been proposed for calculating the bonding energy of an impurity atom. The underlying idea is that of replacing the low- symmetry matrix by an effective high-symmetry one, which consists of homogeneous electron gas with a density that is “seen” by the impurity atom. In this way, a “jellium” consisting of homogeneous electron gas replaces the crystalline material in the effective medium theory (EMT). The metal ions are replaced by a constant positive background density. When an atom is embedded into this effective medium in position r, a change in the energy to a first approximation is expressed by the following: atom+jellium () Er E ∆ = − hom atom jellium 0 ( ) ( ( )) E E E n r + ≡∆ , (1) where hom () E n ∆ is the energy of embedding into homogeneous electron gas with density n, and n 0 (r) is the electron density in point r. The total energy of this N-atom system is tot [] N N R E E n = , (2) where n is the electron density of the ground state of the system. The difference between the energies of the N-atom system and that with a removed atom i is written as 1 Institute of Strength Physics and Materials Science of the Siberian Branch of the Russian Academy of Sciences, 2 V. D. Kuznetsov Siberian Physical-Technical Institute at Tomsk State University, 3 Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 82–90, June, 2005. Original article submitted March 28, 2005. 1064-8887/05/4806-0646 ©2005 Springer Science+Business Media, Inc.