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Forces and Phononswithin WIEN2k
Claudia Ambrosch-DraxlInstitute for Theoretical
PhysicsUniversity Grazclaudia.ambrosch_at_uni-graz.
at
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Outline
Forces in WIEN2k
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The Frozen Phonon Approach
fit
harmonic case
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Frozen Phonon Approach
general case
N atoms i1,....,N
3N degrees of freedom
force constants
dynamical martrix
atomic forces
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The Hellmann-Feynman Force
Many particle Schrödinger equation
Many particle system
electronic coordinates
ionic coordinates
groundstate wavefunction with respect to fixed
ions
Hellmann-Feynman theorem
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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
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Forces in DFT
Total energy

Atomic force
Pulay corrections
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Forces in the LAPW Method

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G point mode in Si
Example

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Computational Effort

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Example YBa2Cu3O7
yttrium barium copper oxygen
Lattice Vibrations
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Raman Active Phonons
YBa2Cu3O7
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Example YBa2Cu3O7
Ba / Cu modes
Lattice Vibrations
oxygen modes