  Electronic and magnetic properties of the heavily H-doped
LaFeAsO$_{1-x}$H$_x$ $(x\sim0.5 )$ were studied in the framework of the density
functional theory combined with the dynamical mean field theory (DFT+DMFT). We
found a stripe-like-ordered structure of hydrogen and oxygen atoms, as a ground
state, with the same configuration as the antiferromagnetic (AF) order. The new
configuration could explain the existing experimental results related to the
heavily H-doped LaFeAsO$_{1-x}$H$_x$, such as an in-plane electronic anisotropy
and a non-uniform magnetic behavior. A significant anisotropy was observed
between Fe- 3d$_{xz}$ (xz) and Fe-3d$_{yz}$ (yz) orbitals in the ground state
in the absence of the pseudogap resulting from the spin density wave phase,
which was found to originate from the crystalline anisotropy. Magnetic moments
were not spatially uniform and were sensitive to the crystal configuration. We
found that a non-uniform magnetic behavior is associated with the As-Fe-As bond
angle in the structure. Our findings would clarify the importance of crystal
details and orbital degrees of freedom in iron-based superconductors.
