The study of adsorption of glycine and glycylglycine (or diglycine) on a copper surface is an important step for the comprehension of mechanisms that determine the stability of biological functionalizers on metal substrates. These two molecules can be considered as prototypes and essential models to investigate, theoretically and experimentally, the adaptability of flexible short peptide chains to a definite interface. In this work, we have improved and updated earlier molecular dynamics simulations by including reactivity of the various species and the comparison of ab initio calculated C, N, and O core photoelectron chemical shifts with the ones found in previous studies. New diglycine-copper bonding is predicted, and the results of the chemical shift analysis are, in all cases, fully compatible with structural information obtained through experimental measurements. Moreover, we have found that the process of proton transfer, which is fundamental in the dynamics of amino acids and peptides, occurs mainly by intermolecular interaction between the first and second layer of the adsorbate.