The binding energies
(BE) of molecules on the interstellar grains
are crucial in the chemical evolution of the interstellar medium (ISM).
Both temperature-programmed desorption (TPD) laboratory experiments
and quantum chemistry computations have often provided, so far, only
single values of the BE for each molecule. This is a severe limitation,
as the ices enveloping the grain mantles are structurally amorphous,
giving rise to a manifold of possible adsorption sites, each with
different BEs. However, the amorphous ice nature prevents the knowledge
of structural details, hindering the development of a common accepted
atomistic icy model. In this work, we propose a computational framework
that closely mimics the formation of the interstellar grain mantle
through a water by water accretion. On that grain, an unbiased random
(but well reproducible) positioning of the studied molecule is then
carried out. Here we present the test case of NH
3
, a ubiquitous
species in the molecular ISM. We provide the BE distribution computed
by a hierarchy approach, using the semiempirical xTB-GFN2 as a low-level
method to describe the whole icy cluster in combination with the B97D3
DFT functional as a high-level method on the local zone of the NH
3
interaction. The final ZPE-corrected BE is computed at the
ONIOM(DLPNO-CCSD(T)//B97D3:xTB-GFN2) level, ensuring the best cost/accuracy
ratio. The main peak of the predicted NH
3
BE distribution
is in agreement with experimental TPD and computed data in the literature.
A second broad peak at very low BE values is also present, which has
never been detected before. It may provide the solution to a longstanding
puzzle about the presence of gaseous NH
3
also observed
in cold ISM objects.