Why do calculations of metals converge so slowly?

ORAL

Abstract

Calculating the energy of a metal from ``first principles'' requires a three-dimensional integration of a multivalued function over an irregular domain (the ``Fermi surface''). The numerical convergence of this integral is not only extremely slow but is also very irregular. We will give simple examples demonstrating the source of the difficulty and explain what strategies might be effective to combat the problem. We will show data on real materials and discuss why this problem is so central to computational materials science.

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Authors

  • Gus Hart

    Brigham Young University

  • Colin Roberts

    High Precision Devices, Boulder, CO, Raytheon, Tucson, AZ, Seagate Technology, Minneapolis, MN, Ball Aerospace (retired), Bloomfield, CO, New Mexico State University, Brigham Young University, Colorado State University, Heinrich-Heine-Universitat Dusseldorf, National Security Technologies, Universidad de Buenos Aires, Colorado State Univ, Colorado College, Utah State University, Advisor, Material Physics Group, Utah State University, Box Elder Innovations, LLC, JILA and Department of Physics, CU Boulder, JILA and Department of Mathematics, CU Boulder, Colorado State University, Fort Collins, Colorado 80523, USA, JILA, NIST and the University of Colorado, Boulder, NIST, University of Colorado / NIST, University of Colorado/JILA, Colorado Sch of Mines, Colorado School of Mines, Southwestern Indian Polytechnic Institute, UC-Berkeley, Colorado State University, Fort Collins, CO, Wroclaw University of Science and Technology, Wroclaw, Poland, JILA, University of Colorado and NIST, Harvard University and Harvard-MIT Center for Ultracold Atoms, Univ of Colorado - Boulder, USAFA, Univ of Denver, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Utah Valley University, University of Colorado Boulder, Brigham Young Univ - Provo, Oak Ridge National Laboratory, University of Sherbrooke, NIST Boulder, Universidad Complutense de Madrid, Electrical and Computer Engineering Department, Colorado State University, Fort Collins, Co 80525, Lawrence Livermore National Lab. (United States), Physics Department, Colorado State University, Fort Collins, Co 80525, JILA, Department of Physics, University of Colorado Boulder, Los Alamos National Laboratory, University of Alabama, University of Wyoming, University of Guelph, University of Guelph, Canadian Light source

  • Colin Roberts

    High Precision Devices, Boulder, CO, Raytheon, Tucson, AZ, Seagate Technology, Minneapolis, MN, Ball Aerospace (retired), Bloomfield, CO, New Mexico State University, Brigham Young University, Colorado State University, Heinrich-Heine-Universitat Dusseldorf, National Security Technologies, Universidad de Buenos Aires, Colorado State Univ, Colorado College, Utah State University, Advisor, Material Physics Group, Utah State University, Box Elder Innovations, LLC, JILA and Department of Physics, CU Boulder, JILA and Department of Mathematics, CU Boulder, Colorado State University, Fort Collins, Colorado 80523, USA, JILA, NIST and the University of Colorado, Boulder, NIST, University of Colorado / NIST, University of Colorado/JILA, Colorado Sch of Mines, Colorado School of Mines, Southwestern Indian Polytechnic Institute, UC-Berkeley, Colorado State University, Fort Collins, CO, Wroclaw University of Science and Technology, Wroclaw, Poland, JILA, University of Colorado and NIST, Harvard University and Harvard-MIT Center for Ultracold Atoms, Univ of Colorado - Boulder, USAFA, Univ of Denver, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Utah Valley University, University of Colorado Boulder, Brigham Young Univ - Provo, Oak Ridge National Laboratory, University of Sherbrooke, NIST Boulder, Universidad Complutense de Madrid, Electrical and Computer Engineering Department, Colorado State University, Fort Collins, Co 80525, Lawrence Livermore National Lab. (United States), Physics Department, Colorado State University, Fort Collins, Co 80525, JILA, Department of Physics, University of Colorado Boulder, Los Alamos National Laboratory, University of Alabama, University of Wyoming, University of Guelph, University of Guelph, Canadian Light source

  • Colin Roberts

    High Precision Devices, Boulder, CO, Raytheon, Tucson, AZ, Seagate Technology, Minneapolis, MN, Ball Aerospace (retired), Bloomfield, CO, New Mexico State University, Brigham Young University, Colorado State University, Heinrich-Heine-Universitat Dusseldorf, National Security Technologies, Universidad de Buenos Aires, Colorado State Univ, Colorado College, Utah State University, Advisor, Material Physics Group, Utah State University, Box Elder Innovations, LLC, JILA and Department of Physics, CU Boulder, JILA and Department of Mathematics, CU Boulder, Colorado State University, Fort Collins, Colorado 80523, USA, JILA, NIST and the University of Colorado, Boulder, NIST, University of Colorado / NIST, University of Colorado/JILA, Colorado Sch of Mines, Colorado School of Mines, Southwestern Indian Polytechnic Institute, UC-Berkeley, Colorado State University, Fort Collins, CO, Wroclaw University of Science and Technology, Wroclaw, Poland, JILA, University of Colorado and NIST, Harvard University and Harvard-MIT Center for Ultracold Atoms, Univ of Colorado - Boulder, USAFA, Univ of Denver, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Utah Valley University, University of Colorado Boulder, Brigham Young Univ - Provo, Oak Ridge National Laboratory, University of Sherbrooke, NIST Boulder, Universidad Complutense de Madrid, Electrical and Computer Engineering Department, Colorado State University, Fort Collins, Co 80525, Lawrence Livermore National Lab. (United States), Physics Department, Colorado State University, Fort Collins, Co 80525, JILA, Department of Physics, University of Colorado Boulder, Los Alamos National Laboratory, University of Alabama, University of Wyoming, University of Guelph, University of Guelph, Canadian Light source

  • Colin Roberts

    High Precision Devices, Boulder, CO, Raytheon, Tucson, AZ, Seagate Technology, Minneapolis, MN, Ball Aerospace (retired), Bloomfield, CO, New Mexico State University, Brigham Young University, Colorado State University, Heinrich-Heine-Universitat Dusseldorf, National Security Technologies, Universidad de Buenos Aires, Colorado State Univ, Colorado College, Utah State University, Advisor, Material Physics Group, Utah State University, Box Elder Innovations, LLC, JILA and Department of Physics, CU Boulder, JILA and Department of Mathematics, CU Boulder, Colorado State University, Fort Collins, Colorado 80523, USA, JILA, NIST and the University of Colorado, Boulder, NIST, University of Colorado / NIST, University of Colorado/JILA, Colorado Sch of Mines, Colorado School of Mines, Southwestern Indian Polytechnic Institute, UC-Berkeley, Colorado State University, Fort Collins, CO, Wroclaw University of Science and Technology, Wroclaw, Poland, JILA, University of Colorado and NIST, Harvard University and Harvard-MIT Center for Ultracold Atoms, Univ of Colorado - Boulder, USAFA, Univ of Denver, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Utah Valley University, University of Colorado Boulder, Brigham Young Univ - Provo, Oak Ridge National Laboratory, University of Sherbrooke, NIST Boulder, Universidad Complutense de Madrid, Electrical and Computer Engineering Department, Colorado State University, Fort Collins, Co 80525, Lawrence Livermore National Lab. (United States), Physics Department, Colorado State University, Fort Collins, Co 80525, JILA, Department of Physics, University of Colorado Boulder, Los Alamos National Laboratory, University of Alabama, University of Wyoming, University of Guelph, University of Guelph, Canadian Light source