We report an ab-initio study of grain-boundary wetting (GBW) in three systems (Fe/Zn, Fe/Pb & Fe/Bi) on a Σ5 (013)[100] tilt grain boundary. An energy-based approach is pursued and adapted to the study of liquid-metal/ solid-metal interfaces. We provide a sound calculation of the wettability parameter S (i.e., defined as the minimum energy difference between the unbroken initial state and final state with liquid-metal/solid-metal interfaces). Solid/liquid interfaces are modelled by ab-initio molecular dynamics, also allowing a study of structural effects in the liquid phase near the solid interface. We show how surface energies for solid-metal/ liquid-metal interfaces need a special treatment for the liquid-metal chemical potential due to the change in crystallinity near the interface. The computation of the wettability criterion for the three systems correctly predicts the GBW trend known experimentally for these systems. The computations are compared with smallscale TEM experiments on GBW of two systems (Fe/Pb and Fe/Bi) and it is shown to provide reasonable results. This approach offers new perspectives in predicting GBW trends across various systems.