4.5 Calculation of electron-phonon interaction coefficients with the tetrahedron method

When you perform a calculation of electron-phonon interaction coefficients with the tetrahedron method, you have to use an offset q -point grid in order to avoid a singularity at q = $\Gamma$ ; you can perform this calculation as follows:

1. Run pw.x with occupation = "tetraehdra_opt" and K_POINT automatic.
2. Run ph.x with lshift_q = .true. and electron_phonon = "" (or unset it) to generate the dynamical matrix and the deformation potential (in _ph*/{prefix}_q*/) of each q .
3. Run ph.x with electron_phonon = "lambda_tetra". You should use a denser k grid by setting nk1, nk2, and nk3. Then lambda*.dat are generated; they contain $\lambda_{{q \nu}}^{}$ .
4. Run alpha2f.x with an input file as follows:

   &input
         ne = (a), 
     ltetra = (b), 
     fildyn = (b), 
     mustar = (d), 
     prefix = (e),
   /
   

   1. The number of frequencies for $\alpha^{2}_{}$F($\omega$)
   2. = 1 for the linear tetrahedron method, = 2 for the optimized tetrahedron method.
   3. It must be the same as that in ph.x input.
   4. Coulomb pseudo potential $\mu^{*}_{}$
   5. It must be the same as that in ph.x input.
   Then $\alpha^{2}_{}$F($\omega$) , $\lambda$ , and $\omega_{{\ln}}^{}$ are calculated.

There is an example in PHonon/example/tetra_example/.