A theoretical study of the hydride bond complexes with tetrafluoro- and tetracyanoethylene, C2F4 and C2(CN)4, has been carried out by means of density functional theory (DFT) and ab initio methods, up to the MP2/aug-cc-pVTZ computational level. In addition, the ternary complexes formed by an additional standard hydrogen bond donor, such as hydrogen fluoride, have been explored. The results show that the hydride bond complexes are stable and an electron transfer took place from the hydride to the C2F4 and C2(CN)4 molecules. While these molecules are not able to form stable complexes between the pi-electrons and hydrogen bond donors, the presence of the hydrides in the opposite face of the pi-system of C2F4 stabilizes the ternary complexes showing cooperativity effects.