Sigma complexes containing η²-H₂ ligands, with both hydrogen atoms interacting with the metal center and with each other, are well known nowadays. The possibility of η¹-H₂ coordination, with only one hydrogen atom interacting with the metal center, remains an intriguing, but unreported, possibility. In this study, we used the hidden descriptors (HD) strategy previously developed in our group to investigate the capacity of well-established metal fragments to achieve stable L_nM(η¹-H₂) metal complexes. Computational techniques, including low-cost density functional theory (DFT) calculations and the BDE Matrix App are used. The results confirm that the search for stable L_nM(η¹-H₂) complexes is challenging, as no obvious candidate can be identified. Hints are obtained about what the properties of this hypothetic metal fragment should be, such as a strong tendency to covalent association with ligands. The outcomes of this research provide a comprehensive framework for comparing and investigating atypical candidates for this type of bonding and serve as a valuable resource for future explorations in this field.