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INTERATOMIC POTENTIALS FROM FIRST-PRINCIPLES CALCULATIONS FUtIO ERCOLESSI'* and JAMES B. ADAMS Materials Research Laboratory, University of Illinois at Urbana-Champaign, Ave., Urbana, IL 61801

104 S. Goodwin

ABSTRACT We propose a new scheme to extract "optinal" interatomic potentials starting from a large number of atomic configurations (and their forces) obtained from first-principles calculations. The method appears to be able to overcome the difficulties encountered by traditional fitting approaches when using rich and complex analytical forms, and constitute a step forward towards large-scale simulations of condensed matter systems with a degree of accuracy comparable to that obtained by ab initio methods. A first exploratory application to aluminum is presented.

INTRODUCTION In the last years, molecular dynamics (MD) computer simulation methods in condensed matter were developed mainly along two quite separate lines: 1. first-principle methods, where the ions are moved under the action of forces obtained by solving, with various degrees of approximation, the electronic structure problem for each configuration of the ions [1-3]. Such methods are often very accurate, but they require significant computational resources. At present, they are limited to number of particles N of the order of 100-1000 (depending on the accuracy of the method), and to simulation times of the order of picoseconds. 2. methods based on classical potentials [4], which allow simulations for a number of particles of the order of 10'4-10, and simulation times up to nanoseconds. O(N) algorithms can be easily adopted, due to the (usually) local nature of the interactions. Such methods are sometimes surprisingly accurate, in spite of their obvious approximate nature. While the first approach is usually more reliable, there is a clear need for fast but realistic schemes, in order to be able to attack a large variety of problems involving defects, surfaces, clusters, demanding large scale atomistic simulations and/or long simulation times. It has been recognized for a long time that pair potentials are inadequate to describe real materials-except perhaps rare gases-particularly when defects and surfaces are taken into account. Therefore, potential development in the last years focused on new powerful analytical forms for metals and semiconductors, including many-atom terms to model accurately the properties of materials. Such are, for example, the "embedded-atom" (EAM), "glue" and "effective medium" (EMT) models for metals [5-9] including a density-dependent term, and models for semiconductors including angular forces [10-13]. As analytical forms become richer, the fitting process becomes increasingly more difficult and cumbersome, often resulting in potentials with a limited amount of transferability from the bulk to surfaces or clusters. Usually, empirical models are composed of simple functions with few parameters, since they are only fit to a few data points, generally relevant to perfect crystals at T = 0. As a consequence, large discrep