T HE AUGMENTED S PHERICAL WAVE (ASW) M ETHOD
Foundation
Iron Pyrite: FeS2
• Born-Oppenheimer approximation
• density functional theory (DFT)
• Pa3̄ (Th6)
• local density approximation (LDA) and generalized gradient ap-
• a = 5.4160 Å
proximation (GGA) (most parametrizations implemented)
• “NaCl structure”
sublattices occupied by
– iron atoms, sulfur pairs
• sulfur pairs k h111i axes
Overview
• xS = 0.38484
• all-electron method
– core electrons fully included
– full coverage of the periodic table
Electronic Bands and Densities of States
– applicable to metals, semiconductors and insulators
40
• based on spherical waves (atomic-like; s, p, d, f )
30
(E - EV) (eV)
– natural interpretation of results
DOS (1/eV)
0
– spherical Hankel functions outside augmentation spheres
– numerical solutions inside augmentation spheres
Fe 3d
S 3s
S 3p
35
5
-5
20
15
10
-10
• atomic-sphere approximation (ASA)
25
5
-15
0
-15
– muffin-tin approximation (MTA), space-filling spheres
Γ
R
X
M
R
X
-10
M
-5
(E - EV) (eV)
0
5
– minimal basis set → very high computational efficiency
• non-relativistic and scalar-relativistic calculations
• spin-restricted and spin-polarized calculations
Partial Densities of States
8
• Brillouin-zone integrations based on Monkhorst-Pack mesh
• closed-packed and open crystal structures
– automated placement of additional interstitial basis functions
S 3px, 3py
S 3pz
6
1.5
5
DOS (1/eV)
DOS (1/eV)
– linear tetrahedron method (including Bl”ochl’s correction)
Fe 3d t2g
Fe 3d eg
7
– simple sampling method
– high-precision sampling method (Methfessel/Paxton)
2
4
3
2
1
0.5
1
0
0
-8
-6
– automated determination of augmentation radii
-4
-2
0
(E - EV) (eV)
2
4
6
-8
-6
-4
-2
0
(E - EV) (eV)
2
4
6
• efficient convergence acceleration scheme
References
Properties
• electronic properties
– 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
– charge densities at nuclei → isomer shifts
[1] V. Eyert, The Augmented Spherical Wave Method – A Comprehensive Treatment, Lecture Notes in Physics, Vol. 719 (Springer,
Heidelberg, 2007).
[2] V. Eyert, Basic notions and applications of the augmented spherical wave method, Int. J. Quantum Chem. 77, 1007-1031 (2000).
[3] V. Eyert and K.-H. Höck, Phys. Rev. B 57, 12727-12737 (1998).
[4] V. Eyert, J. Comput. Phys. 124, 271-285 (1996).
• cohesive properties
– cohesive energies
– bulk moduli
Contact
• chemical bonding
– total/partial crystal orbital overlap populations (COOP)
• magnetic properties
– total and site/state projected magnetic moments
– magnetic ordering (ferro-, ferri-, antiferromagnetic)
– magnetic energies
– spin densities at nuclei → hyperfine fields
Priv.-Doz. Dr. Volker Eyert
Potsdam Center for Materials Research
Baumschulenweg 6A, 14469 Potsdam, Germany
phone: +49 331 505 40 400
email: [email protected]
http: //www.physik.uni-augsburg.de/∼eyert/