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Forces and Phonons within WIEN2k

Forces and Phonons within WIEN2k. Claudia Ambrosch-Draxl Institute for Theoretical Physics University Graz claudia.ambrosch@uni-graz.at. Atomic Forces. Phonons. Molecular Dynamics. Geometry optimization The frozen phonon approach The Hellmann-Feynman theorem

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Forces and Phonons within WIEN2k

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  1. Forces and Phononswithin WIEN2k Claudia Ambrosch-DraxlInstitute for Theoretical PhysicsUniversity Grazclaudia.ambrosch@uni-graz.at

  2. Atomic Forces • Phonons • Molecular Dynamics Geometry optimization The frozen phonon approach The Hellmann-Feynman theorem Forces within density functional theory Pulay corrections Computational effort Examples Inputs Limitations Outline Forces in WIEN2k

  3. The Frozen Phonon Approach fit: harmonic case:

  4. Frozen Phonon Approach general case: N atoms: i=1,....,N 3N degrees of freedom force constants: dynamical martrix: atomic forces:

  5. Many particle Schrödinger equation The Hellmann-Feynman Force Many particle system electronic coordinates ionic coordinates groundstate wavefunction with respect to fixed ions Hellmann-Feynman theorem

  6. component of the electric field caused by the nuclear charge The Hellmann-Feynman Force Many particle system Hellmann-Feynman force: total classical Coulomb force acting on the nucleus a stemming from all other charges of the system = electrostatic force stemming from all other nuclei + electrostatic force stemming from the electronic charges

  7. Total energy: Forces in DFT Atomic force: Pulay corrections

  8. Forces in the LAPW Method

  9. G point mode in Si Example

  10. Computational Effort

  11. Example: YBa2Cu3O7 yttrium barium copper oxygen Lattice Vibrations

  12. Raman Active Phonons YBa2Cu3O7

  13. Example: YBa2Cu3O7 Ba / Cu modes Lattice Vibrations oxygen modes

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