We present new [ Ne ii ] ( 12.8 \mu m ) IRTF /TEXES observations of the Galactic Center H ii regions H1 and H2 , which are at a projected distance of \sim 11 pc from the center of the Galaxy . The new observations allow to map the radial velocity distributions of ionized gas . The high spectroscopic resolution ( \sim 4 km s ^ { -1 } ) helps us to disentangle different velocity components and enables us to resolve previous ambiguity regarding the nature of these sources . The spatial distributions of the intensity and radial velocity of the [ Ne ii ] line are mapped . In H1 , the intensity distributions of the Paschen- \alpha ( 1.87 \mu m ) and [ Ne ii ] lines are significantly different , which suggests a strong variation of extinction across the H ii region of A _ { K } \sim 0.56 . The radial velocity distributions across these H ii regions are consistent with the predictions of a bow-shock model for H1 and the pressure-driven model for H2 . Furthermore , we find a concentration of bright stars in H2 . These stars have similar H - K _ { s } colors and can be explained as part of a 2 Myr old stellar cluster . H2 also falls on the orbit of the molecular clouds , suggested to be around Sgr A ^ { * } . Our new results confirm what we had previously suggested : the O supergiant P114 in H1 is a runaway star , moving towards us through the -30 - 0 km s ^ { -1 } molecular cloud , whereas the O If star P35 in H2 formed in-situ , and may mark the position of a so-far unknown small star cluster formed within the central 30 pc of the Galaxy .