We present the results of docking and quantum-chemical studies of the relationships between the electronic/molecular structure and the inhibitory activity against the mTOR kinase by a group of recently synthesized thienopyrimidine derivatives bearing a chromone moiety. The electronic structure, including full geometry optimization, was obtained at the DFT B3LYP/6-31G(d,p) level. All molecules were also docked to a simplified model of mTOR kinase. Good results relating electronic structure and inhibitory percentage against mTOR kinase at a concentration of 10μM in vitro were obtained and the corresponding pharmacophore is proposed. Docking results suggest that all molecules interact with the same site and that short-range interactions of the C-H…O kind predominate. The question of the relationships between QSAR and docking results is analyzed.