  Advanced telescopes, such as ALMA and JWST, are likely to show that the
chemical universe may be even more complex than currently observed, requiring
astrochemical modelers to improve their models to account for the impact of new
data. However, essential input information for gas-grain models, such as
binding energies of molecules to the surface, have been derived experimentally
only for a handful of species, leaving hundreds of species with highly
uncertain estimates. We present in this paper a systematic study of the effect
of uncertainties in the binding energies on an astrochemical two-phase model of
a dark molecular cloud, using the rate equations approach. A list of
recommended binding energy values based on a literature search of published
data is presented. Thousands of simulations of dark cloud models were run, and
in each simulation a value for the binding energy of hundreds of species was
randomly chosen from a normal distribution. Our results show that the binding
energy of H$_{2}$ is critical for the surface chemistry. For high binding
energy, H$_{2}$ freezes out on the grain forming an H$_{2}$ ice. This is not
physically realistic and we suggest a change in the rate equations. The
abundance ranges found are in reasonable agreement with astronomical ice
observations. Pearson correlation coefficients revealed that the binding energy
of HCO, HNO, CH$_{2}$, and C correlate most strongly with the abundance of
dominant ice species. Finally, the formation route of complex organic molecules
was found to be sensitive to the branching ratios of H$_{2}$CO hydrogenation.
