  (Abridged) The aim of this study is to investigate the chemical evolution
from the prestellar phase to the formation of the disk, and to determine the
impact that the chemical composition of the cold and dense core has on the
final composition of the disk. We performed 3D nonideal magneto-hydrodynamic
(MHD) simulations of a dense core collapse using the adaptive-mesh-refinement
RAMSES code. For each particle ending in the young rotationally supported disk,
we ran chemical simulations with the three-phase gas-grain chemistry code
Nautilus. Two different sets of initial abundances, which are characteristic of
cold cores, were considered. The final distributions of the abundances of
common species were compared to each other, as well as with the initial
abundances of the cold core. We find that the spatial distributions of
molecules reflect their sensitivity to the temperature distribution. The main
carriers of the chemical elements in the disk are usually the same as the ones
in the cold core, except for the S-bearing species, where HS is replaced by
H$_2$S$_3$, and the P-bearing species, where atomic P leads to the formation of
PO, PN, HCP, and CP. However, the abundances of less abundant species change
over time. This is especially the case for "large" complex organic molecules
(COMs) such as CH$_3$CHO, CH$_3$NH$_2$, CH$_3$OCH$_3$, and HCOOCH$_3$ which see
their abundances significantly increase during the collapse. These COMs often
present similar abundances in the disk despite significantly different
abundances in the cold core. In contrast, the abundances of many radicals
decrease with time. A significant number of species still show the same
abundances in the cold core and the disk, which indicates efficient formation
of these molecules in the cold core. This includes H$_2$O, H$_2$CO, HNCO, and
"small" COMs such as CH$_3$OH, CH$_3$CN, and NH$_2$CHO.
