  We theoretically study the electronic band structure of isolated unpaired and
paired dangling bonds (DB), DB wires and DB clusters on H:Si(100)-(2$\times$1)
surface using Extended H\"uckel Theory (EHT) and report their effect on the Si
band gap. An isolated unpaired DB introduces a near-midgap state, whereas a
paired DB leads to $\pi$ and $\pi^*$ states, similar to those introduced by an
unpassivated asymmetric dimer (AD) Si(100)-(2$\times$1) surface. Such induced
states have very small dispersion due to their isolation from the other states,
which reside in conduction and valence band. On the other hand, the surface
state induced due to an unpaired DB wire in the direction along the dimer row
(referred to as $[\bar{1}10]$), has large dispersion due to the strong coupling
between the adjacent DBs, being 3.84$\AA$ apart. However, in the direction
perpendicular to the dimer row (referred to as [110]), due to the reduced
coupling between the DBs being 7.68$\AA$ apart, the dispersion in the surface
state is similar to that of an isolated unpaired DB. Apart from this, a paired
DB wire in $[\bar{1}10]$ direction introduces $\pi$ and $\pi^*$ states similar
to those of an AD surface and a paired DB wire in [110] direction exhibits
surface states similar to those of an isolated paired DB, as expected. Besides
this, we report the electronic structure of different DB clusters, which
exhibit states inside the band gap that can be interpreted as superpositions of
states due to unpaired and paired DBs.
