Verification of first-principles codes: Comparison of total energies, phonon frequencies, electron–phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo

S Poncé (1) , G Antonius (2) , P. Boulanger (3) , E Cannuccia (4) , A Marini (5) , M Côté (2) , X Gonze (1)

1 IMCN - Institut de la matière condensée et des nanosciences / Institute of Condensed Matter and Nanosciences
2 Département de Physique [Montréal]
3 NEEL - TMC - Théorie de la Matière Condensée
4 ILL - Institut Laue-Langevin
5 CNR - National Research Council of Italy | Consiglio Nazionale delle Ricerche

With the ever-increasing sophistication of codes, the verification of the implementation of advanced theoretical formalisms becomes critical. In particular, cross comparison between different codes provides a strong hint in favor of the correctness of the implementations, and a measure of the (hopefully small) possible numerical differences. We lead a rigorous and careful study of the quantities that enter in the calculation of the zero-point motion renormaliza-tion of the direct band gap of diamond due to electron-phonon coupling, starting from the total energy, and going through the computation of phonon frequencies and electron-phonon matrix elements. We rely on two independent implementations : Quantum Espresso + Yambo and ABINIT. We provide the order of magnitude of the numerical discrepancies between the codes, that are present for the different quantities: less than 10 −5 Hartree per atom on the total energy (-5.722 Ha/at), less than 0.07 cm −1 on the Γ, L, X phonon frequencies (555 to 1330 cm −1), less than 0.5% on the square of the electron-phonon matrix elements and less than 4 meV on the zero-point motion renormalization of each eigenenergies (44 to 264 meV). Within our approximations, the DFT converged direct band gap renormalization in diamond due to the electron-phonon coupling is-0.409 eV (reduction of the band gap).

Mots clés: Electron-phonon coupling; Density functional perturbation theory; Temperature dependence; Allen-Heine-Cardona theory; Zero-point motion renormalization; Verification; Diamond

Domaines: Physique [physics]

S Poncé, G Antonius, P. Boulanger, E Cannuccia, A Marini, et al.. Verification of first-principles codes: Comparison of total energies, phonon frequencies, electron–phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo. Computational Materials Science, 2014, 83, pp.341-348. ⟨10.1016/j.commatsci.2013.11.031⟩. ⟨hal-01330356⟩