Infrared and Raman cross sections, electron-phonon coefficients

- Infrared and Raman cross sections
- Normal modes in isolated systems
- Electron-phonon interaction coefficients

Getting ready

- A short reminder of the relevant theory can be found here
- Download the exercise file
examples_advph.tgz
in a directory of your choice. Uncompress and unpack
the file and enter in the resulting directory:
tar -zxvf examples_advph.tgz cd examples_advph

- The following "make" targets (or equivalents) must have been
executed:
make ph gamma tools

Infrared and Raman cross section

The calculation of the effective charges and of (non-resonant!) Raman coefficients is performed by code ph.x. The subsequent calculation of Infrared and Raman cross sections is performed by auxiliary code dynmat.x . In this example the silane molecule SiH- make a structural optimization for SiH
_{4}in a suitable supercell. Sample input file:$espresso_dir/bin/pw.x < sih4.scf.in > sih4.scf.out

The optimization proceeds quite quickly. Note that the supercell used is quite small, that the chosen cutoff may be insufficient for H, that LDA is not the best functional for this kind of calculations, ... - calculate phonons, effective charges, and Raman coefficients
at wavevector
**q**=(0,0,0). To this end we have to set "epsil=.true." and "lraman=.true." (the latter option does not work for ultrasoft pseudopotentials). Sample input file: "sih4.nm.in"$espresso_dir/bin/ph.x < sih4.nm.in > sih4.nm.out

The calculations contains 3 steps:- linear response to an external electric field (dielectric response)
- second-order response to an external electric field
- linear response to lattice perturbations

- effective charges and dielectric tensor
- Raman tensors
- dynamical matrix

- calculate the cross sections. The auxiliary program "dynmat.x" reads
the file produced by ph.x, applies various forms of Acoustic Sum Rule
(ASR), applies the TO-LO splitting (if required: in this case it is not),
calculates Infrared and Raman cross sections (for a typical experimental
configuration)

Sample input file: "sih4.ir.in"$espresso_dir/bin/dynmat.x < sih4.ir.in > sih4.ir.out

The 'zero-dim' kind of ASR forces both translational and rotational modes to zero frequency.

Normal modes

In systems where the sum over the Brillouin Zone is well represented by- make a structural optimization for SiH
_{4}in a suitable supercell. In order to use the various Gamma-specific tricks to speed up the calculation, the keywordK_POINTS (gamma)

must be used to specify that the Gamma point,**k**=(0,0,0) is used. Note that any other equivalent specification, such as for instanceK_POINTS (crystal) 1 0.0 0.0 0.0 1.0

will use the same**k**=(0,0,0) as above but not the same algorithm: Gamma-specific tricks are not used. So one has to copy the sample input file for the previous calculation: "sih4.scf.in", for instance into "sih4.scf.gamma.in", modify it accordingly, and to re-run the structural optimization:$espresso_dir/bin/pw.x < sih4.scf.gamma.in > sih4.scf.gamma.out

- calculate phonons at wavevector
**q**=(0,0,0) (i.e. normal modes). Notice that we set "epsil=.true.", meaning that dielectric properties, including effective charges, have to be calculated. Both the Acoustic Sum Rule and symmetry are used to reduce the number of calculations to the strict minimum (notice that the symmetry of a molecule in a supercell is necessarily a subgroup of the lattice symmetry and may be for this reason lower than the true molecular symmetry).

Sample input file: "sih4.nm.in"$espresso_dir/bin/phcg.x < sih4.nm.in > sih4.nm.out

- calculate the Infrared cross section. The same "dynmat.x" program can
be used as in the previous example. Since Raman tensors cannot
be calculated by phcg.x, they are not present in the data file.
The results for Infrared cross sections are of course very similar
to those previously obtained.
$espresso_dir/bin/dynmat.x < sih4.cs.in > sih4.cs.out

Electron-phonon interaction coefficients

The specific case chosen is the electron-phonon interaction coefficient at X=(1,0,0) for fcc Al.The calculation requires four steps:

- a self-consistent calculation with a dense k-point grid.
The dense grid must contain all
**k**and**k+q**grid points used in the subsequent electron-phonon calculation and should be dense enough to produce accurate electron-phonon coefficients (in particular the double-delta integral at E_{f}is very critical). This example uses a (32 32 32) Monkhorst-Pack grid. Note that even such a large grid may not be dense enough for a serious calculation!

Sample input file: "al.scf.fit.in"$espresso_dir/bin/pw.x < al.scf.fit.in > al.scf.fit.out

The option "la2F=.true." instructs the code to save data into a
file that is subsequently read during the electron-phonon calculation
- a self-consistent calculation using a grid of
**k**points and a value of the gaussian broadening that is suitable for good self-consistency and for the phonon calculation. This example uses a (16 16 16) Monkhorst-Pack grid

Sample input file: "al.scf.in"$espresso_dir/bin/pw.x < al.scf.in > al.scf.out

- a non-self-consistent calculation that prepares the needed
**k**and**k+q**wavefunctions for a phonon run. You have to supply the**q**vector (X in this case) in variable "xq" and use the keyword "calculation='phonon'".

Sample input file: "al.nscfX.in"$espresso_dir/bin/pw.x < al.nscfX.in > al.nscfX.out

- make the phonon and electron-phonon calculation for the specified
**q**vector. Specify "elph=.true." and the name of a file where the derivative of the potential is stored, "fildvscf".

Sample input file: "al.elphX.in"$espresso_dir/bin/ph.x < al.elphX.in > al.elphX.out

The output contains the results for the electron-phonon coefficients
lambda(X), gamma(X), and the double-delta integral at several values
of the gaussian broadening (this is set in file PH/elphon.f90). These
are useful for convergence testing.

Once a suitable set of parameters has been determined, steps 2) and 3) can be collapsed into a single step: a phonon calculation for the entire grid of