Improving Band Interpolation and Band Integration in DFT

ORAL

Abstract

A multitude of energy band interpolation and integration methods have been developed as a means to improve the accuracy and reduce computer run times of material's properties calculations. Each method adjusts one or more of the following parameters: the location of the sampling points, the interpolation basis functions, the conditions imposed on the interpolation and the integration technique employed. Common problems encountered when interpolating energy bands include handling band crossings, band kissings, and cusps. Our approach fits the energy bands with splines, finds the Fermi level with ``adaptive cubes", integrates the bands using Gaussian quadrature, employing various smoothings at the Fermi level, and extrapolates the smoothed integrals of the spline representation to the band integral. We attempted to fix band crossings and kissings with band character decomposition; however, the resolution it provided was insufficient to distinguish one band from another in all cases. We discuss the potential of the tight-binding pseudo-atomic orbitals (PAO) basis to resolve band crossing and kissing issues.

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Authors

  • Jeremy Jorgensen

    Brigham Young Univ - Provo, Brigham Young University

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra