  Atomic metallic hydrogen has been produced in the laboratory at high pressure
and low temperature, prompting further investigations of its different
properties. However, purely experimental approaches are infeasible because of
the extreme requirements in producing and preserving the metastable phase. Here
we perform a systematic investigation of the electronic, optical, mechanical
and thermal properties of $I4_1/amd$ hydrogen at 495 GPa using first-principles
calculations. We calculate the electronic structure and dielectric function to
verify the metallic behaviour of $I4_1/amd$ hydrogen. The calculated total
plasma frequency from both intraband and interband transitions, 33.40 eV,
agrees well with the experimental result. The mechanical properties including
elastic stability and sound velocity are also investigated. The mechanical
stability of $I4_1/amd$ hydrogen is limited by shear modulus other than bulk
modulus, and the high Young's modulus indicates that $I4_1/amd$ hydrogen is a
stiff material. After investigating the lattice vibrational properties, we
study the thermodynamical properties and lattice anharmonicity to understand
thermal behaviours in metallic hydrogen. Finally, the lattice thermal
conductivity of $I4_1/amd$ hydrogen is calculated to be 194.72 W/mK and 172.96
W/mK along the $x$ and $z$ directions, respectively. Using metallic hydrogen as
an example, we demonstrate that first-principles calculations can be a
game-changing solution to understand a variety of material properties in
extreme conditions.
