  We present a first-principles study of native defects in NaAlH$_4$. Our
analysis indicates that the structure and energetics of these defects can be
interpreted in terms of elementary building blocks, which include
$V_{\rm{AlH_4}}^+$, $V_{\rm{Na}}^-$, $V_{\rm{H}}^+$, H$_i^-$, and (H$_2$)$_i$.
We also calculate migration barriers for several key defects, in order to
compare enthalpies of diffusion to experimentally measured activation energies
of desorption. From this, we estimate activation energies for diffusion of
defects and defect pairs. We suggest that $V_{\rm{AlH_4}}^+$ and H$_i^-$, or
$V_{\rm{Na}}^-$ and $V_{\rm{H}}^+$, may be responsible for diffusion necessary
for desorption. We discuss the possible role of $V_{\rm{H}}^+$-H$_i^-$ complex
formation. The values we find are in the range of activation energies reported
for catalyzed desorption.
