Gas-grain and gas-phase reactions dominate the formation of molecules in the interstellar medium ( ISM ) . Gas-grain reactions require a substrate ( e.g . a dust or ice grain ) on which the reaction is able to occur . The formation of molecular hydrogen ( H _ { 2 } ) in the ISM is the prototypical example of a gas-grain reaction . In these reactions , an atom of hydrogen will strike a surface , stick to it , and diffuse across it . When it encounters another adsorbed hydrogen atom , the two can react to form molecular hydrogen and then be ejected from the surface by the energy released in the reaction . We perform in-depth classical molecular dynamics ( MD ) simulations of hydrogen atoms interacting with an amorphous water-ice surface . This study focuses on the first step in the formation process ; the sticking of the hydrogen atom to the substrate . We find that careful attention must be paid in dealing with the ambiguities in defining a sticking event . The technical definition of a sticking event will affect the computed sticking probabilities and coefficients . Here , using our new definition of a sticking event , we report sticking probabilities and sticking coefficients for nine different incident kinetic energies of hydrogen atoms [ 5 K - 400 K ] across seven different temperatures of dust grains [ 10 K - 70 K ] . We find that probabilities and coefficients vary both as a function of grain temperature and incident kinetic energy over the range of 0.99 - 0.22 .