Comment on First-principles calculation of the superconducting transition in MgB2 within the anisotropic Eliashberg formalism

Choi et al. [Phys. Rev. B 66, 020513 (2002)] recently presented first principles calculations of the electron-phonon coupling and superconductivity in MgB2, emphasizing the importance of anisotropy and anharmonicity. We point out that (1) variation of the superconducting gap inside the sigma- or the pi-bands can hardly be observed in real samples, and (2) taking the anisotropy of the Coulomb repulsion into account influences the size of the small gap, Delta_pi.