Context : Aims : 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 . Methods : An up-to-date chemical network is used to compute the evolution of molecular abundances . Reactions of H _ { 2 } with small organic radicals such as C _ { 2 } and C _ { 2 } H , 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 . Results : The photodissociation of CO and release of C triggers the formation of simple organic species such as C _ { 2 } H _ { 2 } , HCN , and CH _ { 4 } . In timescales between 1 and 10 ^ { 4 } 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 H _ { 2 } . Conclusions : The application of the model to the upper layers of inner protoplanetary disks predicts large gas phase abundances of C _ { 2 } H _ { 2 } 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 C _ { 2 } H _ { 2 } 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 ) .