  Understanding and designing inertial confinement fusion (ICF) implosions
through radiation-hydrodynamics simulations rely on the accurate knowledge of
the equation of state (EOS) of the deuterium and tritium fuels. To minimize the
drive energy for ignition, the imploding shell of DT fuel must be kept as cold
as possible. Such low-adiabat ICF implosions can access to coupled and
degenerate plasma conditions, in which the analytical or chemical EOS models
become inaccurate. Using the path-integral Monte Carlo (PIMC) simulations we
have derived a first-principles EOS (FPEOS) table of deuterium that covers
typical ICF fuel conditions at densities ranging from 0.002 to 1596 g/cm3 and
temperatures of 1.35 eV to 5.5 keV. We report the internal energy and the
pressure, and discuss the structure of the plasma in terms of pair-correlation
functions. When compared with the widely used SESAME table and the revised
Kerley03 table, discrepancies in the internal energy and in the pressure are
identified for moderately coupled and degenerate plasma conditions. In contrast
to the SESAME table, the revised Kerley03 table is in better agreement with our
FPEOS results over a wide range of densities and temperatures. Although subtle
differences still exist for lower temperatures (T < 10 eV) and moderate
densities (1 to 10 g/cc), hydrodynamics simulations of cryogenic ICF implosions
using the FPEOS table and the Kerley03 table have resulted in similar results
for the peak density, areal density ({\rho}R), and neutron yield, which are
significantly different from the SESAME simulations.
