Relativistic effects, spin-orbit coupling and non-collinear ... - WIEN 2k

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(1) Relativistic orbital contractionr 2 (e/bohr)0.50.40.30.20.1Au 6sNon relativistic (l=0)Relativistic (=-1)Orbitalcontraction0.00 2 4 6r (bohr) Z 79v e( 6s) 13.17 0. 096cn 611v ec2110.09621.0046Direct relativistic effect (mass enhancement) contraction of 0.46% onlyHowever, the relativistic contraction of the 6s orbital is large (>20%)ns orbitals (with n > 1) contract due to orthogonality to 1s
(1) Orbital Contraction: Effect on the energyr 2 (e/bohr)r 2 (e/bohr)Relativisticcorrection (%)ERELA EENRELANRELA50403020Non relativistic (l=0)Relativistic (=-1)Orbitalcontraction0.50.40.30.2Non relativistic (l=0)Relativistic (=-1)Orbitalcontraction201001s 2s1000.00Au 1s0.00.01 0.02 0.03 0.04 0.05 0.06 0 2 4 6r (bohr)r( (bohr)3s 4s5s 6s0.1Au 6s-10-20-30-40
Page 1 and 2: 20 th WIEN2k WorkshopPennStateUnive
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 are 4-dime
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: Relativistic effects in the solid:
Page 39: (1) Relativistic orbital contractio
Page 43 and 44: (2) Spin-Orbit splitting of p state
Page 45 and 46: (2) Spin-Orbit splitting of p state
Page 47 and 48: (3) Orbital expansion: Au(d) states
Page 53 and 54: Atomic spectra of goldSO splittingS
Page 55 and 56: Relativistic semicore states: p 1/2
Page 57 and 58: Relativity in WIEN2k: SummaryWIEN2k
Page 59 and 60: CuO interludeATOMIC STRUCTURE OF Cu
Page 61 and 62: CuO interludeATOMIC STRUCTURE OF Cu
Page 63 and 64: CuO interludeMAGNETIC STRUCTURE OF
Page 65 and 66: CuO interludeEstimation of the Magn
Page 67 and 68: Pauli Hamiltonian for magnetic syst
Page 69 and 70: Pauli Hamiltonian for magnetic syst
Page 71 and 72: Exchange and correlationFrom DFT ex
Page 73 and 74: Collinear magnetismMagnetization in
Page 75 and 76: Magnetism and WIEN2kWien2k can only
Page 77 and 78: Non-collinear magnetismIn case of n
Page 79 and 80: WienNCM: Spin spiralsTransverse spi

Relativistic effects, spin-orbit coupling and non-collinear ... - WIEN 2k

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