Successes and problems of verication and validation: electron-phonon and pseudopotentials comparisons

First-principles electronic-structure codes are in constant development. New codes are created, and computational capabilities increase with time. The verification and validation of those codes as well as theoretical methods are of utmost importance if one wants to provide reliable results. In this work we present first a comparative study of calculations based on electron-phonon matrix elements in Abinit and PWSCF+Yambo, with the aim to resolve a discrepancy, observed at the time of writing,between the zero-point motion (ZPM) renormalization of the band gap of diamond as implemented in Abinit with the one found with PWSCF+EPW [1] and PWSCF+Yambo [2]. We first present internal checks in Abinit using finite difference methods versus perturbative approaches (i.e. density functional perturbation theory) as implemented in Abinit. This gives good agreement for the zero point motion for an underconverged (in k and q points) calculation. We then make internal checks for the electron-phonon matrix elements by comparing DFPT with finite difference, which also gives satisfactory results. Afterwards, we compare ground states properties as well as electron-phonon matrix elements from Abinit and from PWSCF. Excellent agreement is observed. We then move forward and analyse the different quantities that make the zero-point motion correction as formulated by Allen, Heine and Cardona [3] both in Abinit and PWSCF+Yambo. The Fan, diagonal Debye-Waller and non-diagonal Debye-Waller are analysed separately. At the time of writing, discrepancies for those terms are still present. [1] F. Giustino, S.G. Louie and M.L. Cohen, Phys. Rev. Lett. 105, 265501 (2010). [2] E. Cannuccia and A. Marini, Phys. Rev. Lett. 107, 255501 (2011). [3] P. B. Allen and M. Cardona, Phys. Rev. B 24, 7479 (1981).