TY - JOUR

T1 - Verification of first-principles codes

T2 - Comparison of total energies, phonon frequencies, electron-phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo

AU - Poncé, S.

AU - Antonius, G.

AU - Boulanger, P.

AU - Cannuccia, E.

AU - Marini, A.

AU - Côté, M.

AU - Gonze, X.

PY - 2014/2/15

Y1 - 2014/2/15

N2 - 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 renormalization 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 Ha per atom on the total energy (-5.722 Ha/at), less than 0.07 cm-1 on the Γ,L,X phonon frequencies (555-1330 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 (44-264 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).

AB - 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 renormalization 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 Ha per atom on the total energy (-5.722 Ha/at), less than 0.07 cm-1 on the Γ,L,X phonon frequencies (555-1330 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 (44-264 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).

KW - Allen-Heine-Cardona theory

KW - Density functional perturbation theory

KW - Diamond

KW - Electron-phonon coupling

KW - Temperature dependence

KW - Verification

KW - Zero-point motion renormalization

UR - http://www.scopus.com/inward/record.url?scp=84890535111&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2013.11.031

DO - 10.1016/j.commatsci.2013.11.031

M3 - Article

AN - SCOPUS:84890535111

VL - 83

SP - 341

EP - 348

JO - Computational Materials Science

JF - Computational Materials Science

SN - 0927-0256

ER -