We present time dependent chemical models for a dense and warm O-rich gas exposed to a strong far ultraviolet field aiming at exploring the formation of simple organic molecules in the inner regions of protoplanetary disks around T Tauri stars. An up-to-date chemical network is used to compute the evolution of molecular abundances. Reactions of H2 with small organic radicals such as C2 and C2H, which are not included in current astrochemical databases, overcome their moderate activation energies at warm temperatures and become very important for the gas phase synthesis of C-bearing molecules. The photodissociation of CO and release of C triggers the formation of simple organic species such as C2H2, HCN, and CH4. In timescales between 1 and 10,000 years, depending on the density and FUV field, a steady state is reached in the model in which molecules are continuously photodissociated but also formed, mainly through gas phase chemical reactions involving H2. The application of the model to the upper layers of inner protoplanetary disks predicts large gas phase abundances of C2H2 and HCN. The implied vertical column densities are as large as several 10^(16) cm^(-2) in the very inner disk (< 1 AU), in good agreement with the recent infrared observations of warm C2H2 and HCN in the inner regions of IRS 46 and GV Tau disks. We also compare our results with previous chemical models studying the photoprocessing in the outer disk regions, and find that the gas phase chemical composition in the upper layers of the inner terrestrial zone (a few AU) is predicted to be substantially different from that in the upper layers of the outer disk (> 50 AU).
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