Introduction to Solid State theory, DFT and the APW-method - WIEN 2k

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Linearization of energy dependenceLAPW suggested byO.K.Andersen,Phys.Rev. B 12, 3060(1975)antibondingcenterbondingk n m[ A ( k ) u ( E , r ) B ( k ) u( E , r )] Y ( rˆ) mn mn mexpand u l at fixed energy E l andaddu l u l/ A lmk , B lm k : join PWs invalue and slope General eigenvalue problem(diagonalization) additional constraint requiresmore PWs than APWAtomic sphereLAPWAPWPW
shape approximations to “real” potentials• Atomic sphere approximation (ASA)• overlapping spheres “fill” all volume• potential spherically symmetric• “muffin-tin” approximation (MTA)• non-overlapping spheres with sphericallysymmetric potential +• interstitial region with V=const.• “full”-potential• no shape approximations to V
Page 1 and 2: Density functional theory (DFT)and
Page 3 and 4: The WIEN2k code: comments• Walter
Page 5 and 6: Unit cellAssuming an ideal infinite
Page 7 and 8: 3D lattice types:7 Crystal systems
Page 9 and 10: Bloch-Theorem:1 2 r2 V( r ) ( r
Page 11 and 12: Bloch functions:• Wave functions
Page 13 and 14: DFT vs. MBT (many body theory)
Page 15 and 16: ESSENCE OF DENSITY-FUNTIONAL THEORY
Page 17 and 18: DFT Density Functional TheoryHohenb
Page 19 and 20: Kohn-Sham equationsEToLDA, GGA 1
Page 21 and 22: DFT thanks to Claudia Ambrosch (Gra
Page 23 and 24: CoO why is GGA better than LSDA•
Page 25 and 26: Accuracy of DFT for transition meta
Page 27 and 28: Can LDA be improved ?• better GGA
Page 29 and 30: FeO: LDA vs. LDA+U vs. Hybrids vs.
Page 31 and 32: and gaps by mBJ-LDA• LDA strongly
Page 33 and 34: Hybrid functional: only for (correl
Page 35 and 36: Solving Schrödingers equation:2V(
Page 37 and 38: pseudopotential plane wave methods
Page 39 and 40: • APW (J.C.Slater 1937)• Non-li
Page 41: Slater‘s APW (1937)H HamiltonianS
Page 45 and 46: Core, semi-core and valence statesF
Page 47 and 48: An alternative combination of schem
Page 49 and 50: Summary: Linearization LAPW vs. APW
Page 51 and 52: The WIEN2k authorsAn Augmented Plan
Page 53 and 54: The first publication of the WIEN c
Page 55 and 56: In Japan• Book published byShinya
Page 57 and 58: A series of WIEN workshops were hel
Page 59 and 60: Structure: a,b,c,,,, R , ...Struct
Page 61 and 62: Self-consistent field (SCF) calcula
Page 63 and 64: • init_lapwProgram structure of W
Page 65 and 66: Workflow of a WIEN2k calculation•
Page 67 and 68: w2web GUI (graphical user interface
Page 69 and 70: Quantum mechanics at workthanks to
Page 71 and 72: TiC, three valence states at ∆Ene
Page 73 and 74: TiC, bonding and antibonding states
Page 75 and 76: TiC, TiN, TiOTiC TiN TiORigid band
Page 77: Vienna, city of musicand the Wien2k

Introduction to Solid State theory, DFT and the APW-method - WIEN 2k

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