The successful large-scale implementation of hydrogen as an energy vector requires high performance electrodes and catalysts made of abundant materials. Rational materials design strategies are the most efficient means of reaching this goal. Here we present a study on the adsorption of H-atoms onto fcc transition metal surfaces and propose descriptors for the rational design of electrodes and catalysts by means of correlations between fundamental properties of the materials and among other properties, their experimentally measured performance as hydrogen evolution electrodes (HEE). A large set of quantum mechanical modelling data at the DFT level was produced, covering the adsorption of H-atoms onto the most stable surfaces (100), (110) and (111) of: Ag, Au, Co, Cu, Ir, Ni, Pd, Pt and Rh. For each material and surface, a coverage dependent set of minimum energy structures was produced and chemical potentials for adsorption of H-atoms were obtained. Averaging procedures are here proposed to approach modelling to the experiments. Several correlations between the computed data and experimentally measured quantities are done to validate our methodology: surface plane dependent adsorption energies, chemical potentials and experimentally determined surface energies and work functions. We search for descriptors of catalytic activity by testing correlations between the DFT data obtained from our averaging procedures and experimental data on HEE performance. Our methodology allows us to obtain linear correlations between the adsorption energy of H-atoms and the exchange current density (i0) in a HEE, avoiding the volcano-like plots. We show that the chemical potential has limitations as a descriptor of i0 because it reaches an early plateau in terms of i0. Simple quantities obtained from database data such as the first stage electronegativity (χ) as devised by Mulliken has a strong linear correlation i0. With a quantity we denominate modified second-stage electronegativity (χ2m) we can reproduce the typical volcano plot in a correlation with i0. A theoretical and conceptual framework is presented. It shows that both χ and χ2m, that depend on the first ionization potential, second ionization potential and electron affinity of the elements can be used as descriptors in rational design of electrodes or of catalysts for hydrogen systems.