AB-INITIO SIMULATIONS IN MATERIALS SCIENCE - VASP

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$ ( r' ¨ r' r' , r' ¨ ¨ r' ( Hartree-Fock methods II Hartree-Fock equations # ¯h 2 2m ∆ e 2 ∑ j j )+*i r Ze2 φ i φ j ∆ szi s z j& ¨ r ©e2 ∑ j Problems with Hartree-Fock calculations r φi ¨ ¨ §i & % d 3 r φ j ¨ r φ j r 2 d 3 r ¦εiφi φ i r r (10) Computational effort scales badly with the number of electrons Neglect of correlations - Too wide band gaps, too small band widths - Exchange-operator for metallic systems singular at the Fermi level J. HAFNER, AB-INITIO MATERIALS SIMULATIONS Page 10
Post Hartree-Fock methods Express wavefunction as linear combination of Slater determinants to include correlation ”Configuration interactions” - HF-CI Even higher computational effort, scaling worse Convergence problematic Metals ???? J. HAFNER, AB-INITIO MATERIALS SIMULATIONS Page 11
Page 1 and 2: AB-INITIO SIMULATIONS IN MATERIALS
Page 3 and 4: Overview II DFT methods - an overvi
Page 5 and 6: ¦ ¦ ¡ ¨ ¡ © ¥ ¡ ¨ ¥ ¡
Page 7 and 8: ¦ ¨ Born-Oppenheimer
Page 9: ¦ ! ! ! ! ! ! ! ! ! q1 q1 1 """φ
Page 13 and 14: ¦T Total-energy fu
Page 15 and 16: 2 ©Exc ( 43 r(
Page 17 and 18: Basis sets I Localized orbitals Wel
Page 19 and 20: Pseudopotentials I Slow convergence
Page 21 and 22: Pseudopotentials III Modern pseudop
Page 23 and 24: Pseudopotentials vs. all-electron m
Page 25 and 26: ¦ Solving the Kohn-Sham equations
Page 27 and 28: Ionic structure and dynamics I Stat

AB-INITIO SIMULATIONS IN MATERIALS SCIENCE - VASP

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