  We studied the electronic properties of beta-platinum dioxide ({\beta}-PtO2),
a catalytic material, based on density functional theory. Using the GGA+U
method which reproduces the GW band structures and the experimental structural
parameters, we found that the creation of an oxygen vacancy will induce local
magnetic moment on the neighboring Pt and O atoms. The magnetism originates not
only from the unpaired electrons that occupy the vacancy induced gap state, but
also from the itinerant valence electrons. Because of antiferromagnetic (AF)
coupling and the localized nature of gap states, the total magnetic moment is
zero for charge-neutral state (V_o^0) and is ~ 1 \mu B for singly-charged
states (V_o^\mu). Calculation of grand potential shows that, the three charge
states (V_o^0, V_o^\pm) are of the same stability within a small region, and
the negatively charged state (V_o^-) is energetically favored within a wide
range of the band gap. On this basis we discussed the implication on catalytic
behavior.
