Formamide formation on forsterite and Mg(OH)$_2\cdot$H$_2$O
Context. Formamide formation in the Universe has been the subject of debate due to its importance as a precursor to amino acids and RNA. Current studies focus on the gas-phase and icy grain formation routes. However, formamide formation on bare silicate surfaces or hydrated Mg-bearing molecular models remains largely unexplored in environments relevant to protoplanetary disks. Aims. This study presents a quantum-chemical investigation of formamide formation on an Mg center and a silicate surface. $Mg(OH)_2\cdot H_2O$ and the bare (010) forsterite ($Mg_2SiO_4$) surface, used as an analog of a bare dust-grain surface, may promote formamide formation via $NH_2$ addition to $H_2CO$. Methods. I employed density functional theory (DFT) to study the addition of $NH_2$ to $H_2CO$ with an isolated $Mg(OH)_2\cdot H_2O$ molecular model and on the forsterite (010) surface. First, I benchmarked various theoretical methodologies. I then examined the ability of $Mg(OH)_2\cdot H_2O$ and the forsterite (010) surface to promote formamide formation. Finally, for the case with an entrance barrier, I computed unimolecular rate constants and half-lives to assess its kinetic behavior. Results. $Mg(OH)_2\cdot H_2O$ promotes proton transfer within the $NH_2$-$CH_2O$ intermediate via the O-H group coordinated with Mg following $NH_2$ addition to $H_2CO$, whereas on the forsterite, a barrier-less addition pathway is found when $NH_2$ is initially physisorbed close to the formaldehyde center, followed by proton transfer leading to formamide formation. Conclusions. The Mg-bearing model systems considered here can promote rapid proton transfer following $NH_2$ addition to $H_2CO$. For the $Mg(OH)_2\cdot H_2O$ model, the reaction step from the pre-reactive complex is predicted to occur on nanosecond timescales at temperatures approaching 300 K. The present work provides kinetic data for astrochemical models.