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

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Exchange and correlation• We divide the density of the N-1 electron systeminto the total density n(r) and an exchangecorrelationhole:Properties of the exchange-correlation hole:• Locality• Pauli principle• the hole contains ONE electron• The hole must ne negative• The exchange hole affects electrons with thesame spin and accounts for the Pauli principle• In contrast, the correlation-hole accounts for theCoulomb repulsion of electrons with the oppositespin. It is short range and leads to a smallredistribution of charge. The correlation holecontains NO charge:
Kohn-Sham equationsEToLDA, GGA 1 ( r ) ( r ) [ ] Vext ( r ) d r dr dr Exc[ ]2 | r r |vary EELDAxcGGAxc{ 121-electron equations (Kohn Sham)(r)(r)2 Vext( r ) VC( (r))Vxc( (r))}-Z/r ( r) E ) drxc(| r r | hom.xc[ (r)]drF[(r),(r)]dri( r) i( r ) i( r )iE F| LDA treats both,exchange and correlation effects,GGA but approximatelyNew (better ?) functionals are still an active field of researchi2|
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: DFT Density Functional TheoryHohenb
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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