  Aims. We have investigated neutral gas in the central cavity of the
circumnuclear disk (CND) at the Galactic Center, where the ionized minispiral
lies, to describe the H2 distribution and properties in this ionized
environment. Methods. This study was carried out through a spectro-imaging data
cube of the central cavity obtained with SPIFFI on the VLT. The observed field
of view is 36"x 29" , with a spectral resolution R = 1 300 in the
near-infrared. These observations cover several H2 lines. To preserve the
spatial resolution and avoid edge effects, we applied a new line-fitting method
that consists of a regularized 3D fitting. We also applied a more classical 1D
fitting to compare the relative strength of the H2 lines. Results. We present
high spatial and spectral resolution maps of the intensity, velocity, and width
of five H2 lines and an extinction map derived from H2. Molecular gas is
detected everywhere in the field. In particular, in addition to the known CND
features, we detected an emission from the northern arm cloud and from the
minicavity. The excitation diagrams allow us to estimate the temperature, mass,
and density of these features. Conclusions. We interpret the CND emission as
coming from a hot, thermalized, thin layer at the surface of the clouds. The
observed H2 corresponds only to a small fraction of the total H2 mass. The
emission remains fairly strong in the whole central cavity, but it is not
thermalized. A strong deviation from thermal equilibrium is detected near the
minicavity. We suggest that this emission is caused by constantly forming H2
that is destroyed again before it reaches ortho/para equilibrium.
