Phonon dispersions with Density-Functional Perturbation Theory

Getting ready

make ph pp tools("make all" is also ok).

tar -zxvf examples_disp.tgz cd examples_dispIn the following, $espresso_dir stands for the root directory of the Quantum ESPRESSO distribution.

Interatomic Force Constants in Real Space

Whenever the entire phonon dispersion is needed, it is convenient to calculate- the usual scf step for the unperturbed system
- the calculation of phonons and dynamical matrices on a grid
of
**q**-vectors (this can be done in a single step) - the transformation of the dynamical matrices from
**G**- to**R**-space

- scf step as usual:
$espresso_dir/bin/pw.x < si.scf.in > si.scf.out

- Calculation of dynamical matrices on a grid of
**q**-vectors (will require several minutes).Sample input file: si.ph.in. One has to specify the grid of

**q**-vectors as in a Monkhorst-Pack grid, with variables "nq1", "nq2", "nq3". The grid must contain Gamma and it must be a subdivision of the reciprocal lattice (i.e. it must correspond to a supercell in**R**-space). It is automatically generated. One has also to specify "ldisp=.true." to instruct the code to loop over all**q**-vectors.$espresso_dir/bin/ph.x < si.ph.in > si.ph.out

Note that for each**q**-vector the dynamical matrices are saved with a different name ("fildyn" + 1-8), while "fildyn" + 0 contains the information on the**q**-vector grid (type of grid and number of points) - Calculation of IFC's in real space.
This task is performed by auxiliary program "q2r.x". All dynamical matrices are read and Fourier-transformed. The input file for q2r.x contains very little data: file name "fildyn" of dynamical matrices (the same given in input to the phonon code), whether to apply ASR (better to do it: asr='simple' or 'crystal' are ok for simple crystals), the name ("flfrc") of the output file containing the force constants.

$espresso_dir/bin/q2r.x &input fildyn='si.dyn', zasr='simple', flfrc='si444.fc' /

Phonon Dispersions from Interatomic Force Constants

Once the IFC's in real space are available, one can calculate phonons at any value of- A plot of the phonon dispersions along selected high-symmetry lines.
Sample file: si.matdyn.in. You

*must*specify the name of the file ("flfrc") containing the IFC's, and a list of**q**-points for which the frequencies are to be calculated. You may specify various forms of ASR ('simple' or 'crystal' are ok in this case), where to write the frequencies ("flfrq").$espresso_dir/bin/matdyn.x < si.matdyn.in

The file selected in flfrc, "si.freq", contains a list of frequencies in a format that can be further processed by another auxiliary code, "plotband.x", the same used for band structure plotting:$espresso_dir/bin/plotband.x si.freq

Answer something sensible for Emin and Emax (0 530 for instance; units are cm-1) and for the file in "xmgr" format, for instance, "siph.xmgr"; you may also produce a file directly in printable (postscript) format. The file "siph.xmgr" can be easily plotted using xmgrace or gnuplot plotting programs. Does it look like you expected it? - A plot of the phonon DOS
If you choose option "dos=.true." you must specify the grid of

**q**-vectors used to calculate the DOS (variables "nk1", "nk2", "nk3", using the Monkhorst-Pack logic). You should also specify where you want the DOS written ("fldos") Sample file: si.phdos.in.$espresso_dir/bin/matdyn.x < si.phdos.in > si.phdos.out

The file selected in fldos, "si.phdos", contains the DOS in a format that can be plotted using xmgr, xmgrace, or gnuplot. Can you make the connection between the phonon dispersions with the phonon DOS?

Polar Materials

The calculation of IFC's in polar materials is basically the same as for nonpolar materials. You just have to remember to specify the appropriate option ("epsil=.true.") in the input of trhe phonon code. Can you produce a phonon dispersion plot for AlAs?Phonons with Ultrasoft pseudopotentials

Phonon calculations with Ultrasoft pseudopotentials are basically the same as for norm-conserving ones. You just have to be aware of the following tricks:- The cutoff for the density, "ecutrho", in the self-consistent calculation, often needs to be quite high (i.e. higher than what is good for total-energy or structural-optimization calculations). In the example provided for Diamond: c.scf.in, a cutoff of 450 Ry is used, while the cutoff for the wavefunction is just 27 Ry.
- The threshold for convergence in phonon calculations ("tr2_ph") should be set to quite low values, somewhat lower than what is good for norm-conserving pseudopotentials. In the example provided for the Gamma-point calculation in Diamond: c.ph.in, tr2_ph is set to 1.0E-16.

Phonons in magnetic systems

The example for Ni shows how to calculate phonon dispersions in a magnetic system (incidentally one that is also metallic and with ultrasoft pseudopotentials). The procedure is the same: self-consistency (pw.x) first (sample data: ni.scf.in), followed by the phonon calculation (ph.x) (sample data: ni.ph.in) and by inverse Fourier transform (q2r.x) to get the IFC's in real space (sample data: ni.q2r.in). Once you have the IFC's, you can plot the phonon dispersions using "matdyn.x" (sample data: ni.matdyn.in) and "plotband.x".