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

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Local orbitals (LO)Ti atomic sphereLO• LOs[2E 1 E1EA u B u C u ] Y ( rm mm mˆ)• are confined to an atomic sphere• have zero value and slope at R• Can treat two principal QN nfor each azimuthal QN ( e.g. 3p and 4p)• Corresponding states are strictlyorthogonal• (e.g.semi-core and valence)• Tail of semi-core states can berepresented by plane waves• Only slightly increases the basis set(matrix size)D.J.Singh,Phys.Rev. B 43 6388 (1991)
An alternative combination of schemesE.Sjöstedt, L.Nordström, D.J.Singh,An alternative way of linearizing the augmented plane wave method,Solid State Commun. 114, 15 (2000)•Use APW, but at fixed E l (superior PW convergence)•Linearizewith additional local orbitals (lo)(add a few extra basis functions)k n mAm( k ) u ( E , r)Y ( rˆ)nmlo1 E B u] Y ( rˆ)E1[ A ummmoptimal solution: mixed basis• use APW+lo for states, which are difficult to converge:(f or d- states, atoms with small spheres)• use LAPW+LO for all other atoms and angular momenta
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 and 42: Slater‘s APW (1937)H HamiltonianS
Page 43 and 44: shape approximations to “real”
Page 45: Core, semi-core and valence statesF
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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