With the development of nano-technology and micro-electronic device, nano-scale titanium dioxide materials have been exploited in many application fields, such as solar energy storage, photocatalytic decomposition of organic molecules, etc. Among its polymorphs, anatase particles are preferentially used not only because of its higher catalytic activity, but also anatase particles are more stable than rutile particles in nanometer scale. Previous experimental data has shown that Ti-O bond lengths in titanium dioxide nanoparticles are significantly different from the bulk phase value of 1.94 � and can be as low as 1.79 �. At the same time, the coordination environment of the titanium dioxide decreases from the normal octahedral environment to an environment where it has a coordination number of 4 or 5. These unsaturated Ti atoms exposed in the surface of anatase nanoparticles has shown great potential attraction for the molecular adsorption. In this work, we study the anatase nanoparticles with the size scale ranging from 1nm to 3nm. We investigate the bond lengths, coordination environment and electronic structures of these nanoparticles via an ab intio tight-binding method (called FIREBALL), which is based on density-functional theory with a nonlocal pseudopotential scheme. This method has already been successfully applied to different systems, such as zeolites, clathrate structures, bulk-titanium dioxide and biomolecules. Based on the relaxed nanoparticles obtained in our simulation, we also study the water adsorption on the surface of the relative most stable nanoparticle in order to have a full knowledge of the photocatalytic mechanism and describe several possible photoreaction by potential curves along selected reaction coordinates.