  Energy redistribution after a chemical reaction is one of the few mechanisms
to explain the diffusion and desorption of molecules which require more energy
than the thermal energy available in quiescent molecular clouds (10 K). This
energy distribution can be important in phosphorous hydrides, elusive yet
fundamental molecules for interstellar prebiotic chemistry. We studied the
reaction dynamics of the \ce{P + H -> PH} reaction on amorphous solid water, a
reaction of astrophysical interest, using \emph{ab-initio} molecular dynamics
with atomic forces evaluated by a neural network interatomic potential. We
found that the exact nature of the initial phosphorous binding sites is less
relevant for the energy dissipation process because the nascent PH molecule
rapidly migrates to sites with higher binding energy after the reaction.
Non-thermal diffusion and desorption-after-reaction were observed and occurred
early in the dynamics, essentially decoupled from the dissipation of the
chemical reaction energy. From an extensive sampling of reactions on sites, we
constrained the average dissipated reaction energy within the simulation time
(50 ps) to be between 50 and 70 %. Most importantly, the fraction of
translational energy acquired by the formed molecule was found to be mostly
between 1 and 5 %. Including these values, specifically for the test cases of
2% and 5% of translational energy conversion, in astrochemical models, reveals
very low gas-phase abundances of PH$_{x}$ molecules and reflects that
considering binding energy distributions is paramount for correctly merging
microscopic and macroscopic modelling of non-thermal surface astrochemical
processes. Finally, we found that PD molecules dissipate more of the reaction
energy. This effect can be relevant for the deuterium fractionation and
preferential distillation of molecules in the interstellar medium.
