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Abstract: Titanium borates show promising hydrogen storage characteristics. Structural relaxation around individual hydrogen atoms and the binding energies are studied by means of the density functional theory methods for a number of hydrogenated TiB2 , TiB and Ti2B structures. Starting with the possible symmetric hydrogen sites a random structure searching has been performed, in addition to locate all energetically stable adsorption sites. It is shown that for the three bulk compounds considered, the lowest binding energies are obtained for TiB2 (in the 0.3–1.8 eV range), the largest for Ti2B (in the 3.9–4.7 eV range), while for TiB they are intermediate (in the 2.8–3.5 eV range). Calculations performed on hydrogenated Ti2B result in two energetically stable sites for two different starting environments, suggesting a possible soft mode solution. [Copyright &y& Elsevier]