Using genetic algorithms to map first-principles results to model Hamiltonians: Application to the generalized Ising model for alloys

Volker Blum, Gus L. W. Hart, Michael J. Walorski, and Alex Zunger
Phys. Rev. B 72, 165113 – Published 26 October 2005

Abstract

The cluster expansion method provides a standard framework to map first-principles generated energies for a few selected configurations of a binary alloy onto a finite set of pair and many-body interactions between the alloyed elements. These interactions describe the energetics of all possible configurations of the same alloy, which can hence be readily used to identify ground state structures and, through statistical mechanics solutions, find finite-temperature properties. In practice, the biggest challenge is to identify the types of interactions which are most important for a given alloy out of the many possibilities. We describe a genetic algorithm which automates this task. To avoid a possible trapping in a locally optimal interaction set, we periodically “lock out” persistent near-optimal cluster expansions. In this way, we identify not only the best possible combination of interaction types but also any near-optimal cluster expansions. Our strategy is not restricted to the cluster expansion method alone, and can be applied to select the qualitative parameter types of any other class of complex model Hamiltonians.

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  • Received 15 August 2005

DOI:https://doi.org/10.1103/PhysRevB.72.165113

©2005 American Physical Society

Authors & Affiliations

Volker Blum1,*, Gus L. W. Hart2, Michael J. Walorski3, and Alex Zunger1

  • 1National Renewable Energy Laboratory, Golden, Colorado 80401, USA
  • 2Department of Physics and Astronomy, Northern Arizona University, Flagstaff, Arizona 86011-6010, USA
  • 3Computer Science Department, Northern Arizona University, Flagstaff, Arizona 86011-5600, USA

  • *Present address: Abteilung Theorie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem, Germany.

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Issue

Vol. 72, Iss. 16 — 15 October 2005

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