Title: Hier%20Titel%20eingeben
1(No Transcript)
2Forces and Phononswithin WIEN2k
Claudia Ambrosch-DraxlInstitute for Theoretical
PhysicsUniversity Grazclaudia.ambrosch_at_uni-graz.
at
3Outline
Forces in WIEN2k
4The Frozen Phonon Approach
fit
harmonic case
5Frozen Phonon Approach
general case
N atoms i1,....,N
3N degrees of freedom
force constants
dynamical martrix
atomic forces
6The Hellmann-Feynman Force
Many particle Schrödinger equation
Many particle system
electronic coordinates
ionic coordinates
groundstate wavefunction with respect to fixed
ions
Hellmann-Feynman theorem
7The 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
8Forces in DFT
Total energy
Atomic force
Pulay corrections
9Forces in the LAPW Method
10G point mode in Si
Example
11Computational Effort
12Example YBa2Cu3O7
yttrium barium copper oxygen
Lattice Vibrations
13Raman Active Phonons
YBa2Cu3O7
14Example YBa2Cu3O7
Ba / Cu modes
Lattice Vibrations
oxygen modes