  We model the nuclear evolution of an accreted matter as it sinks toward the
stellar center, in order to find its composition and equation of state. To this
aim, we developed a simplified reaction network that allows for redistribution
of free neutrons in the inner crust to satisfy the recently suggested neutron
hydrostatic and diffusion equilibrium condition. We analyse the main reaction
pathways for the three representative thermonuclear ash compositions:
Superburst, Kepler, and Extreme rp. In contrast to the previous results, which
neglect redistribution of free (unbound) neutrons in the inner crust, the most
significant reactions in our calculations are neutron captures and electron
emissions. The pycnonuclear fusion plays some role only for Kepler ashes. For
the direct application of our results in astrophysical codes we present
profiles of the average charge, $\langle Z\rangle$, impurity parameter,
$Q_\mathrm{imp}$ and equation of state for a set of models, parametrized by the
pressure at the outer-inner crust interface. Typically, for Superburst ashes
$Q_\mathrm{imp}\approx 1-4$, while for Kepler ashes $Q_\mathrm{imp}$ decreases
from $\approx23$ at the outer-inner crust interface to $\approx5$ at the end of
our simulation (the corresponding density equals
$\rho_\mathrm{dc}\approx2\times 10^{12}$ g cm$^{-3}$). At the same time, for
Extreme rp ashes $Q_\mathrm{imp}$ remains large $\approx 30-35$ in the
considered inner crust region. Our results are important for modeling the
thermal relaxation of transiently accreting neutron stars after the end of the
outburst.
