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

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Structure: a,b,c,,,, R , ...Structure optimizationunit cell atomic positionsk-mesh in reciprocal spaceiteration iSCFDFT Kohn-ShamV() = V C +V xc Poisson, DFTnoE i+1 -E i < yesE tot , forceMinimize E, force0propertieskk IBZ (irred.Brillouin zone)2[ V( )] kC knknk nKohn ShamkE k Variational method 0C Ek nGeneralized eigenvalue problem Ek EFHC ESC* k kk
Solving Schrödingers equation:2V( r)ki kiki• cannot be found analytically• complete “numerical” solution is possible but inefficient• Ansatz: • linear combination of some “basis functions”• different methods use different basis sets !1 2 kc kK• finding the “best” wave function using the variational principle:Ek*k*kH• this leads to the famous “Secular equations”, i.e. a set of linearequations which in matrix representation is called “generalizedeigenvalue problem”H C = E S CkH, S : hamilton and overlap matrix; C: eigenvectors, E: eigenvalueskEckk n0nnkn
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: Hybrid functional: only for (correl
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

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

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