We have measured vibrational population of H(2) and D(2) molecules produced by atom (H or D) recombination on tungsten and copper material. The vibrational spectroscopy, based on the properties of dissociative electron attachment to hydrogen molecule, was used. The vibrationally excited molecules were produced by atom recombination in a cell where the studied sample is exposed to hydrogen atoms, from hot tungsten filament. Vibrational populations were obtained for the studied materials, which can be well described by the Boltzmann distribution, with specific vibrational temperatures for each material. The experimentally obtained vibrational populations for copper approximately agree with the theoretical predictions, whereas the experimentally obtained vibrational temperature for tungsten is higher and thus showing a considerable overpopulation of highly excited vibrational states than predicted. We propose that the origin of this higher excitation is related to the existence of high hydrogen surface coverage on tungsten, where hydrogen is occupying binding sites with different desorption energies. In order to obtain an insight into the recombination mechanism with more than one binding site per unit cell, a Monte Carlo simulation was performed, where it was assumed that the main production of molecules proceeds through the hot-atom recombination with an adsorbed atom. The results show that the recombination proceeds mainly through the weak binding sites, once they are occupied.