2 - WIEN 2k

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Relativistic effects in the solid: Illustration♦ Scalar-relativistic (SREL):- LDA overbinding (2%)- Bulk modulus: 447 GPa+ spin-orbit coupling (SREL+SO):- LDA overbinding (1%)- Bulk modulus: 436 GPa⇒ Exp. Bulk modulus: 462 GPa
(1) Relativistic orbital contractionr 2 ρ (e/bohr)50Non relativistic (l=0)Radius of the 1s orbit (Bohr model):40e -+Ze30201000.00Au 1s0.01 0.02 0.03 0.04 0.05 0.06r (bohr)2n ah( 1s)= AND a0 = =1bohrZm cαr01r( 1s)= = 0.013 bohr79eAtomic units:ħ = m e = e = 1c = 1/ α ≈ 137 au
Page 1 and 2: 18 th WIEN2k WorkshopPennState Univ
Page 3 and 4: Few words about Special Theory of R
Page 5 and 6: Few words about Special Theory of R
Page 7 and 8: Relativistic effects+Ze1) The mass-
Page 9 and 10: Relativistic effects+Ze1) The mass-
Page 11 and 12: One electron radial Schrödinger eq
Page 13 and 14: One electron radial Schrödinger eq
Page 15 and 16: Dirac Hamiltonian: a brief descript
Page 17 and 18: Dirac equation: H D and Ψ are 4-di
Page 19 and 20: Dirac equation in a spherical poten
Page 25 and 26: Implementation in WIEN2kAtomic sphe
Page 27 and 28: Implementation in WIEN2k: core elec
Page 29 and 30: Implementation in WIEN2k: valence e
Page 31 and 32: Implementation in WIEN2k: valence e
Page 33 and 34: Controlling spin-orbit coupling in
Page 35: Relativistic effects in the solid:
Page 39 and 40: (1) Relativistic orbital contractio
Page 41 and 42: (2) Spin-Orbit splitting of p state
Page 47 and 48: (3) Orbital expansion: Au(d) states
Page 49 and 50: (3) Orbital expansion: Au(d) states
Page 51 and 52: Relativistic effects on the Au ener
Page 53 and 54: Ag - Au: the differences (DOS & opt
Page 55 and 56: SOC in magnetic systemsSOC couples
Page 57 and 58: 18 th WIEN2k WorkshopPennState Univ
Page 59 and 60: Pauli Hamiltonian for magnetic syst
Page 61 and 62: Pauli Hamiltonian for magnetic syst
Page 63 and 64: Non-collinear magnetismDirection of
Page 65 and 66: Non-magnetic calculationNo magnetiz
Page 67 and 68: Magnetism and WIEN2kSpin-polarized
Page 69 and 70: Non-collinear magnetismFor non-coll
Page 71 and 72: WienNCM: Usage1. Generate the atomi

2 - WIEN 2k

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