Context: T Tauri stars have X-ray luminosities ranging from L_X = 10^28-10^32 erg/s. These luminosities are similar to UV luminosities (L_UV 10^30-10^31 erg/s) and therefore X-rays are expected to affect the physics and chemistry of the upper layers of their surrounding protoplanetary disks. Aim: The effects and importance of X-rays on the chemical and hydrostatic structure of protoplanetary disks are investigated, species tracing X-ray irradiation (for L_X >= 10^29 erg/s) are identified and predictions for [OI], [CII] and [NII] fine structure line fluxes are provided. Methods: We have implemented X-ray physics and chemistry into the chemo-physical disk code ProDiMo. We include Coulomb heating and H2 ionization as heating processes and primary and secondary ionization due to X-rays in the chemistry. Results: X-rays heat up the gas causing it to expand in the optically thin surface layers. Neutral molecular species are not much affected in their abundance and spatial distribution, but charged species such as N+, OH+, H2O+ and H3O+ show enhanced abundances in the disk surface. Conclusions: Coulomb heating by X-rays changes the vertical structure of the disk, yielding temperatures of ~ 8000 K out to distances of 50 AU. The chemical structure is altered by the high electron abundance in the gas in the disk surface, causing an efficient ion-molecule chemistry. The products of this, OH+, H2O+ and H3O+, are of great interest for observations of low-mass young stellar objects with the Herschel Space Observatory. [OI] (at 63 and 145 mic) and [CII] (at 158 mic) fine structure emission are only affected for L_X > 10^30 erg/s.
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