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Day 01 – Review:�basics of DFT and QE

Abdul Muhaymin

Graduate student, MSN, Bilkent University

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A brief review of DFT

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What

    • Can be ab-initio (first-principle) i.e. no experimental or empirical input (only theory)
    • Mapping between electron density and ground state (HK theorem) - i.e. give chemical composition & geometry
    • Can be solved in the one-particle approximation limit (KS ansatz) using SCF procedure 
    • Better the approximation for XC functional, better the accuracy (circularly speaking, whatever left is XC)

Why

    • Laboratories ❌, Computers ✅
    • High-throughput investigations, screening of materials, time-cost-resource saving

How

    • Quantum ESPRESSO, VASP, CASTEP – these are plane wave pseudopotential code
    • PySCF, SIESTA, ORCA, Gaussian – localized basis set pseudopotential code
    • FLEUR, WIEN2K – all electron code, advanced basis set 
    • Machine learning methods – not actually DFT but the purpose is same (find the HK mapping)

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Approximation for XC functional

  • For HEG, X energy can be expressed analytically:
  • But even for HEG, no analytic form possible for C energy.
  • Solution: do QMC (we don't need!)
  • LDA:
  • GGA:
  • Higher-level of theory (but do you really need?) 

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Typical DFT run (SCF)

  • Each loop is a SCF cycle
  • Converged SCF gives us the ground state
  • Non-SCF calculation improves the ground state with fine parameters

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Electronic properties of solids

  • Band structure and Density of States (DOS) of Si
  • Interpreting the result – notice the gap, Fermi level
  • Smearing for metallic system 

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