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

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non relativisticsemi-relativisticfully-relativisticConcepts when solving Schrödingers-equation in solidsRelativistic treatmentof the electrons1 2Form ofpotential(non-)selfconsistent“Muffin-tin” MTatomic sphere approximation (ASA)Full potential : FPpseudopotential (PP)exchange and correlation potential k k k V( r)i ii 2 Hartree-Fock (+correlations)Density functional theory (DFT)Local density approximation (LDA)Generalized gradient approximation (GGA)Beyond LDA: e.g. LDA+USchrödinger – equation(Kohn-Sham equation)non periodic(cluster)periodic(unit cell)Representationof solidTreatment ofspinNon-spinpolarizedSpin polarized(with certain magnetic order)Basis functionsplane waves : PWaugmented plane waves : APWatomic oribtals. e.g. Slater (STO), Gaussians (GTO),LMTO, numerical basis
DFT vs. MBT (many body theory)
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: Bloch functions:• Wave functions
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 and 42: Slater‘s APW (1937)H HamiltonianS
Page 43 and 44: shape approximations to “real”
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
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Introduction to Solid State theory, DFT and the APW-method - WIEN 2k

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