  The structure and electronic density of states in layered
LnFeAsO$_{1-x}$F$_x$ (Ln=La,Sm; $x$=0.0, 0.125, 0.25) are investigated using
density functional theory. For the $x$=0.0 system we predict a complex
potential energy surface, formed by close-lying single-well and double-well
potentials, which gives rise to the tetragonal-to-orthorhombic structural
transition, appearance of the magnetic order, and an anomaly in the specific
heat capacity observed experimentally at temperatures below $\sim$140--160 K.
We propose a mechanism for these transitions and suggest that these phenomena
are generic to all compounds containing FeAs layers. For $x>$0.0 we demonstrate
that transition temperatures to the superconducting state and their dependence
on $x$ correlate well with the calculated magnitude of the electronic density
of states at the Fermi energy.
