  Using density-functional theory and a tight-binding approach we investigate
the physical origin of distinct favourable geometries of adsorbed hydrogen
atoms in various graphyne structures, and the relation with electronic
properties. In particular, H atoms are adsorbed in-plane for $\alpha$-graphyne,
and they assume an oblique configuration in all other graphynes, including
6,6,12-graphyne. The origin of different configurations is identified by means
of a simple tight-binding model and it is controlled by the tuning of the
hopping between sp$^2$-bonded C atoms and sp-bonded C atoms hybridized with the
H atoms. We discuss in details how the geometry change of the attached H atom
tunes the electronic properties like energy gap.
