The Augmented Spherical Wave Method
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1 Introduction Institut für Physik, Universität Augsburg Electronic Structure in a Nutshell
2 Outline 1 Fundamentals Generations 2
3 Outline 1 Fundamentals Generations 2
4 Outline Fundamentals Generations 1 Fundamentals Generations 2
5 ASW? Fundamentals Generations Meaning: Three Levels of Consciousness Augmented Spherical Wave (for beginners)
6 ASW? Fundamentals Generations Meaning: Three Levels of Consciousness Augmented Spherical Wave (for beginners) Aussersinnliche Wahrnehmung ( extrasensory perception, for the experienced)
7 ASW? Fundamentals Generations Meaning: Three Levels of Consciousness Augmented Spherical Wave (for beginners) Aussersinnliche Wahrnehmung ( extrasensory perception, for the experienced) Always Slightly Wrong (for experts)
8 Outline Fundamentals Generations 1 Fundamentals Generations 2
9 Generations Fundamentals Generations 0th Generation, IBM Yorktown Heights, 1970s A. R. Williams, J. Kübler, C. D. Gelatt jr. original version built on the renormalized atom concept related to O. K. Andersen s LMTO 0th Generation, Darmstadt, 1980s J. Kübler, J. Sticht, V. E., L. Sandratskii optimization, vectorization non-collinear magnetism relativistics, spin-orbit coupling full potential code
10 Generations Fundamentals Generations 0th Generation, IBM Yorktown Heights, 1970s A. R. Williams, J. Kübler, C. D. Gelatt jr. original version built on the renormalized atom concept related to O. K. Andersen s LMTO 0th Generation, Darmstadt, 1980s J. Kübler, J. Sticht, V. E., L. Sandratskii optimization, vectorization non-collinear magnetism relativistics, spin-orbit coupling full potential code
11 Generations Fundamentals Generations 0th Generation, Nijmegen, 1980s R. A. degroot, H. van Leuken tight-binding -like ASW 0th Generation, San Diego, 1990s Biosym MSI Accelrys Electronic Structure Of Crystalline Solids) commercial version of the Darmstadt code
12 Generations Fundamentals Generations 0th Generation, Nijmegen, 1980s R. A. degroot, H. van Leuken tight-binding -like ASW 0th Generation, San Diego, 1990s Biosym MSI Accelrys Electronic Structure Of Crystalline Solids) commercial version of the Darmstadt code
13 Generations Fundamentals Generations 1st Generation, Europe, 1990s new implementation from scratch clean programming new algorithms accuracy, numerical stability improved file handling extended flexible basis set sphere packing, improved symmetry check convergence acceleration schemes all LDA-parametrizations, many GGA-schemes new interpretative tools
14 Generations Fundamentals Generations 1st Generation, Angel Fire/Le Mans, 1990s Materials Design Electronic Structure and Analysis commercial version of the 1st generation code 2nd Generation, Europe, 2000s linear tetrahedron method optical properties fast full potential code elastic properties, phonon spectra, EFGs
15 Generations Fundamentals Generations 1st Generation, Angel Fire/Le Mans, 1990s Materials Design Electronic Structure and Analysis commercial version of the 1st generation code 2nd Generation, Europe, 2000s linear tetrahedron method optical properties fast full potential code elastic properties, phonon spectra, EFGs
16 Outline 1 Fundamentals Generations 2
17 Features I: The ASW method... Foundation is based on Born-Oppenheimer approximation density functional theory (DFT) uses local density approximation (LDA) (all known parametrizations implemented) generalized gradient approximation (GGA) (Perdew-Wang 1986, Perdew-Wang 1991, Engel-Vosko 1993, Perdew-Burke-Ernzerhof 1996, Zhang-Yang 1998, Wu-Cohen 2005) exact exchange (future)
18 Features I: The ASW method... Foundation is based on Born-Oppenheimer approximation density functional theory (DFT) uses local density approximation (LDA) (all known parametrizations implemented) generalized gradient approximation (GGA) (Perdew-Wang 1986, Perdew-Wang 1991, Engel-Vosko 1993, Perdew-Burke-Ernzerhof 1996, Zhang-Yang 1998, Wu-Cohen 2005) exact exchange (future)
19 Features II: The ASW method... Characteristics is an all-electron method core electrons fully relaxed full coverage of periodic table applicable to metal, semiconductors, and insulators uses a minimal basis set atomic-like (s, p, d, f ) basis functions high computational efficiency intuitive interpretation of results allows for non-relativistic and scalar-relativistic calculations spin-restricted and spin-polarized calculations
20 Features II: The ASW method... Characteristics is an all-electron method core electrons fully relaxed full coverage of periodic table applicable to metal, semiconductors, and insulators uses a minimal basis set atomic-like (s, p, d, f ) basis functions high computational efficiency intuitive interpretation of results allows for non-relativistic and scalar-relativistic calculations spin-restricted and spin-polarized calculations
21 Features II: The ASW method... Characteristics is an all-electron method core electrons fully relaxed full coverage of periodic table applicable to metal, semiconductors, and insulators uses a minimal basis set atomic-like (s, p, d, f ) basis functions high computational efficiency intuitive interpretation of results allows for non-relativistic and scalar-relativistic calculations spin-restricted and spin-polarized calculations
22 Features III: The ASW method... Characteristics is a linearized method high computational speed is fully self-consistent speedup due to efficient convergence acceleration performs BZ integrations on Monkhorst-Pack mesh using simple sampling method high-precision sampling method (Methfessel/Paxton) linear tetrahedron method (including Blöchl s correction) is suited for closed-packed and open crystal structures automated placement of interstitial basis functions automated determination of augmentation radii
23 Features III: The ASW method... Characteristics is a linearized method high computational speed is fully self-consistent speedup due to efficient convergence acceleration performs BZ integrations on Monkhorst-Pack mesh using simple sampling method high-precision sampling method (Methfessel/Paxton) linear tetrahedron method (including Blöchl s correction) is suited for closed-packed and open crystal structures automated placement of interstitial basis functions automated determination of augmentation radii
24 Features III: The ASW method... Characteristics is a linearized method high computational speed is fully self-consistent speedup due to efficient convergence acceleration performs BZ integrations on Monkhorst-Pack mesh using simple sampling method high-precision sampling method (Methfessel/Paxton) linear tetrahedron method (including Blöchl s correction) is suited for closed-packed and open crystal structures automated placement of interstitial basis functions automated determination of augmentation radii
25 Features III: The ASW method... Characteristics is a linearized method high computational speed is fully self-consistent speedup due to efficient convergence acceleration performs BZ integrations on Monkhorst-Pack mesh using simple sampling method high-precision sampling method (Methfessel/Paxton) linear tetrahedron method (including Blöchl s correction) is suited for closed-packed and open crystal structures automated placement of interstitial basis functions automated determination of augmentation radii
26 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
27 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
28 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
29 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
30 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
31 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
32 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
33 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
34 Properties I Electronic electronic dispersions E(k) ( band structure ) electronic wave functions projected band structures total/partial (site/state projected) densities of states (DOS) Fermi surfaces optical spectra electron densities electric field gradients electron densities at nuclei isomer shifts core level spectra
35 Properties II Cohesive and Elastic cohesive energies bulk moduli elastic constants phonon spectra Chemical Laplacians of the electron density bonding indicators total/partial crystal orbital overlap populations (COOP) total/partial crystal orbital Hamiltonian populations (COHP) total/partial covalence energies (E cov )
36 Properties II Cohesive and Elastic cohesive energies bulk moduli elastic constants phonon spectra Chemical Laplacians of the electron density bonding indicators total/partial crystal orbital overlap populations (COOP) total/partial crystal orbital Hamiltonian populations (COHP) total/partial covalence energies (E cov )
37 Properties II Cohesive and Elastic cohesive energies bulk moduli elastic constants phonon spectra Chemical Laplacians of the electron density bonding indicators total/partial crystal orbital overlap populations (COOP) total/partial crystal orbital Hamiltonian populations (COHP) total/partial covalence energies (E cov )
38 Properties II Cohesive and Elastic cohesive energies bulk moduli elastic constants phonon spectra Chemical Laplacians of the electron density bonding indicators total/partial crystal orbital overlap populations (COOP) total/partial crystal orbital Hamiltonian populations (COHP) total/partial covalence energies (E cov )
39 Properties II Cohesive and Elastic cohesive energies bulk moduli elastic constants phonon spectra Chemical Laplacians of the electron density bonding indicators total/partial crystal orbital overlap populations (COOP) total/partial crystal orbital Hamiltonian populations (COHP) total/partial covalence energies (E cov )
40 Properties II Cohesive and Elastic cohesive energies bulk moduli elastic constants phonon spectra Chemical Laplacians of the electron density bonding indicators total/partial crystal orbital overlap populations (COOP) total/partial crystal orbital Hamiltonian populations (COHP) total/partial covalence energies (E cov )
41 Properties III Magnetic total and site/state projected magnetic moments magnetic ordering (ferro-, ferri-, antiferromagnetic) magnetic energies spin densities spin densities at nuclei hyperfine fields
42 Properties III Magnetic total and site/state projected magnetic moments magnetic ordering (ferro-, ferri-, antiferromagnetic) magnetic energies spin densities spin densities at nuclei hyperfine fields
43 Properties III Magnetic total and site/state projected magnetic moments magnetic ordering (ferro-, ferri-, antiferromagnetic) magnetic energies spin densities spin densities at nuclei hyperfine fields
44 Properties III Magnetic total and site/state projected magnetic moments magnetic ordering (ferro-, ferri-, antiferromagnetic) magnetic energies spin densities spin densities at nuclei hyperfine fields
45 Properties III Magnetic total and site/state projected magnetic moments magnetic ordering (ferro-, ferri-, antiferromagnetic) magnetic energies spin densities spin densities at nuclei hyperfine fields
46 Outline 1 Fundamentals Generations 2
47 The Code Programming written in Fortran 95 checked with ftnchek and forcheck 6 main programs for background calculations 6 main programs for plotting 300 ASW subroutines 46 BLAS routines (level 1, 2, 3) 77 LAPACK routines lines of source code 25%: BLAS/LAPACK 25%: comments 25%: user guidance 25%: physics
48 The Code Programming written in Fortran 95 checked with ftnchek and forcheck 6 main programs for background calculations 6 main programs for plotting 300 ASW subroutines 46 BLAS routines (level 1, 2, 3) 77 LAPACK routines lines of source code 25%: BLAS/LAPACK 25%: comments 25%: user guidance 25%: physics
49 The Code Programming written in Fortran 95 checked with ftnchek and forcheck 6 main programs for background calculations 6 main programs for plotting 300 ASW subroutines 46 BLAS routines (level 1, 2, 3) 77 LAPACK routines lines of source code 25%: BLAS/LAPACK 25%: comments 25%: user guidance 25%: physics
50 The Code Programming written in Fortran 95 checked with ftnchek and forcheck 6 main programs for background calculations 6 main programs for plotting 300 ASW subroutines 46 BLAS routines (level 1, 2, 3) 77 LAPACK routines lines of source code 25%: BLAS/LAPACK 25%: comments 25%: user guidance 25%: physics
51 The Code Programming written in Fortran 95 checked with ftnchek and forcheck 6 main programs for background calculations 6 main programs for plotting 300 ASW subroutines 46 BLAS routines (level 1, 2, 3) 77 LAPACK routines lines of source code 25%: BLAS/LAPACK 25%: comments 25%: user guidance 25%: physics
52 External Linear Algebra Routine Tasks... using public-domain standard math. libraries: LAPACK - Linear Algebra PACKage BLAS - Basic Linear Algebra Subroutines ATLAS - Automatically Tuned Linear Algebra GotoBLAS - K. Goto s fast implementation of the BLAS
53 External Linear Algebra Routine Tasks... using public-domain standard math. libraries: LAPACK - Linear Algebra PACKage BLAS - Basic Linear Algebra Subroutines ATLAS - Automatically Tuned Linear Algebra GotoBLAS - K. Goto s fast implementation of the BLAS
54 External Linear Algebra Routine Tasks... using public-domain standard math. libraries: LAPACK - Linear Algebra PACKage BLAS - Basic Linear Algebra Subroutines ATLAS - Automatically Tuned Linear Algebra GotoBLAS - K. Goto s fast implementation of the BLAS
55 External Visualization... using public-domain software: RasMol crystal structure XCrysDen crystal structure (electron density, Laplacian, ELF, potential) Fermi surface Gnuplot (weighted) bands (partial) DOS (partial) COOP, COHP, E cov optical spectra electron density, Laplacian, (ELF), potential
56 External Visualization... using public-domain software: RasMol crystal structure XCrysDen crystal structure (electron density, Laplacian, ELF, potential) Fermi surface Gnuplot (weighted) bands (partial) DOS (partial) COOP, COHP, E cov optical spectra electron density, Laplacian, (ELF), potential
57 External Visualization... using public-domain software: RasMol crystal structure XCrysDen crystal structure (electron density, Laplacian, ELF, potential) Fermi surface Gnuplot (weighted) bands (partial) DOS (partial) COOP, COHP, E cov optical spectra electron density, Laplacian, (ELF), potential
58 Portability Platforms and Compilers IBM HP/Compaq CRAY/SGI PC s running Linux Lahey/Fujitsu f95 PGI f90 Absoft f95 NAG f95 Intel f95 SNI Sun Apple PC s running Windows Lahey/Fujitsu f95 Intel f95 All platforms: g95, GNU Fortran 95
59 Portability Platforms and Compilers IBM HP/Compaq CRAY/SGI PC s running Linux Lahey/Fujitsu f95 PGI f90 Absoft f95 NAG f95 Intel f95 SNI Sun Apple PC s running Windows Lahey/Fujitsu f95 Intel f95 All platforms: g95, GNU Fortran 95
60 Portability Platforms and Compilers IBM HP/Compaq CRAY/SGI PC s running Linux Lahey/Fujitsu f95 PGI f90 Absoft f95 NAG f95 Intel f95 SNI Sun Apple PC s running Windows Lahey/Fujitsu f95 Intel f95 All platforms: g95, GNU Fortran 95
61 Portability Job Queuing Systems... accessible by the shell scripts IBM s LoadLeveler Network Queuing System - NQS Portable Batch System - PBS Distributed Queuing System - DQS Sun Grid Engine - SGE
62 Augmented Spherical Wave Method is a highly efficient electronic structure scheme allows for the calculation of many materials properties allows for an intuitive, atomic-like interpretation of results is easy to use in practice
63 Augmented Spherical Wave Method is a highly efficient electronic structure scheme allows for the calculation of many materials properties allows for an intuitive, atomic-like interpretation of results is easy to use in practice
64 Augmented Spherical Wave Method is a highly efficient electronic structure scheme allows for the calculation of many materials properties allows for an intuitive, atomic-like interpretation of results is easy to use in practice
65 Augmented Spherical Wave Method is a highly efficient electronic structure scheme allows for the calculation of many materials properties allows for an intuitive, atomic-like interpretation of results is easy to use in practice
66 Further Reading I A. R. Williams, J. Kübler and C. D. Gelatt, jr. Cohesive properties of metallic Compounds: Augmented-spherical-wave calculations Phys. Rev. B 19, 6094 (1979) V. Eyert Basic notions and applications of the augmented spherical wave method Int. J. Quantum Chem. 77, 1007 (2000)
67 Further Reading II J. Kübler and V. Eyert Electronic structure calculations, in: Electronic and Magnetic Properties of Metals and Ceramics ed by K. H. J. Buschow (VCH, Weinheim, 1992), pp Volume 3A of Materials Science and Technology V. Eyert A Comprehensive Treatment Lecture Notes in Physics, Vol. 719 (Springer, Heidelberg, 2007)
68 Further Reading III V. Eyert A comparative study on methods for convergence acceleration of iterative vector sequences J. Comput. Phys. 124, 271 (1996) V. Eyert and K.-H. Höck The electronic structure of V 2 O 5 : Role of octahedral deformations Phys. Rev. B 57, (1998)
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