Dear Giorgio,

The following text describes the method to be used in your case. In addition, the following link depicts abstracts for publications deal with similar calculations that you intend to run:

EPW ( Electron- Phonon coupling using Wannier functions) is a program written in Fortran90 for calculating the electron-phonon coupling in periodic systems using density-functional perturbation theory and maximally localized Wannier functions. EPW can calculate electron-phonon interaction self-energies, electron-phonon spectral functions, and total as well as mode-resolved electron-phonon coupling strengths. The calculation of the electron-phonon coupling requires a very accurate sampling of electron-phonon scattering processes throughout the Brillouin zone, hence reliable calculations can be prohibitively time-consuming. EPW combines the Kohn-Sham electronic eigenstates and the vibrational eigenmodes provided by the Quantum ESPRESSO package (see Giannozzi et al., 2009 [1]) with the maximally localized Wannier functions provided by the wannier90 package (see Mostofi et al., 2008 [2]) in order to generate electron-phonon matrix elements on arbitrarily dense Brillouin zone grids using a generalized Fourier interpolation. This feature of EPW leads to fast and accurate calculations of the electron-phonon coupling, and enables the study of the electron-phonon coupling in large and complex systems. Program summaryProgram title: EPW Catalogue identifier: AEHA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Public License No. of lines in distributed program, including test data, etc.: 304 443 No. of bytes in distributed program, including test data, etc.: 1 487 466 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any architecture with a Fortran 90 compiler Operating system: Any environment with a Fortran 90 compiler Has the code been vectorized or parallelized?: Yes, optimized for 1 to 64 processors RAM: Heavily system dependent, as small as a few MB Supplementary material: A copy of the "EPW/examples" directory containing the phonon binary files can be downloaded Classification: 7 External routines: MPI, Quantum-ESPRESSO package [1], BLAS, LAPACK, FFTW. (The necessary Blas, Lapack and FFTW routines are included in the Quantum-ESPRESSO package [1].) Nature of problem: The calculation of the electron-phonon coupling from first-principles requires a very accurate sampling of electron-phonon scattering processes throughout the Brillouin zone; hence reliable calculations can be prohibitively timeconsuming. Solution method: EPW makes use of a real-space formulation and combines the Kohn-Sham electronic eigenstates and the vibrational eigenmodes provided by the Quantum-ESPRESSO package with the maximally localized Wannier functions provided by the wannier90 package in order to generate electron-phonon matrix elements on arbitrarily dense Brillouin zone grids using a generalized Fourier interpolation. Running time: Single processor examples typically take 5-10 minutes.

http://www.science.gov/topicpages/e/electron-phonon+coupling+calculations.html

If it is hard to get the software mentioned in the above text you may choose to use QUANTUM ESPRESSO:

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

http://iopscience.iop.org/article/10.1088/0953-8984/21/39/395502

Hoping this will be helpful,

Rafik

Thank you very much!

What if electron does not exist?