Effects of the Born-Oppenheimer approximation in the electronic band structure of MgB2 and ZrB2

Electronic band structure calculations are routinely applied to many problems in chemistry and physics. The methods rely on a number of approximations, where the treatment of exchange and correlation is a very prominent issue, probably the most prominent in the development of new density functionals in the framework of density functional theory (DFT). The present work highlights effects that arise from the more fundamental Born-Oppenheimer approximation. Based on this approximation, the original problem - the quantum-mechanical description of matter consisting of nuclei and electrons - is decomposed into a nuclear and an electronic problem, the latter of which is treated by electronic band structure methods. Utilizing the most common density functionals, the local density approximation (LDA) and the generalized gradient approximation (GGA), we observe deviations between experimental and theoretical de Haas van Alphen (dHvA) frequencies for MgB2 and ZrB2 that can be consistently understood by electron-phonon coupling effects, which the theory is lacking. The explanation is based on a highly accurate computation of dHvA frequencies indicating an electron-phonon coupling-induced shift of the electronic bands.