2 - WIEN 2k

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Dirac Hamiltonian: a brief descriptionDirac relativistic Hamiltonian provides a quantum mechanical descriptionof electrons, consistent with the theory of special relativity.E 2 = p 2 c 2 + m 2 c 4H Ψ D= ε ΨwithHD= cr2α ⋅ pr + βmec+ V
Dirac Hamiltonian: a brief descriptionDirac relativistic Hamiltonian provides a quantum mechanical descriptionof electrons, consistent with the theory of special relativity.E 2 = p 2 c 2 + m 2 c 4H Ψ D= ε ΨwithMomentumoperatorRest massHD= cr2α ⋅ pr + βmec+ VElectrostaticpotentialαk=⎛ 0⎜⎝σkσk0⎞⎟⎠β k=⎛1⎜⎝00 ⎞⎟−1⎠(2×2) unit matricesσ1=⎛0⎜⎝11⎞⎟0⎠σ2⎛0= ⎜⎝ i− i⎞⎟0 ⎠σ 3=⎛1⎜⎝00 ⎞⎟−1⎠(2×2) Pauli spin matrices
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: One electron radial Schrödinger eq
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 and 36: Relativistic effects in the solid:
Page 37 and 38: (1) Relativistic orbital contractio
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
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