  The total two-photon decay rate of hydrogen-like ions is studied using
relativistic quantum electrodynamics. In particular, we analyse how finite
nuclear size and QED vacuum polarization corrections affect the decay rate. To
calculate these corrections, a finite basis set method based on $B$-splines is
used for the generation of quasi-complete atomic spectra and, hence, of the
relativistic Green's function. By making use of this $B$-spline approach, high
precision calculations have been performed for the $2s_{1/2} \to 1s_{1/2} +
2\gamma$ and $2p_{1/2} \to 1s_{1/2} + 2\gamma$ decay of hydrogen-like ions
along the entire isoelectronic sequence. The results of these calculations show
that both, QED and finite nuclear size effects, are comparatively weak for the
$2s_{1/2} \to 1s_{1/2} + 2\gamma$ transition. In contrast, they are much more
pronounced for the $2p_{1/2}\to 1s_{1/2} + 2\gamma$ decay, where, for
hydrogen-like Uranium, the decay rate is reduced by 0.484% due to the finite
nuclear size and enhanced by 0.239% if the vacuum polarization is taken into
account.
