MP2 calculations with cc-pVTZ basis set were used to analyze intermolecular interactions in F(3)CX···HMgH···Y and F(3)CX···Y···HMgH triads (X = Cl, Br; Y = HCN, and HNC) which are connecting with three kinds of unusual weak interactions, namely halogen-hydride, dihydrogen, and σ-hole. To understand the properties of the systems better, the corresponding dyads are also studied. Molecular geometries, binding energies, and infrared spectra of monomers, dyads, and triads were investigated at the MP2/cc-pVTZ computational level. Particular attention is given to parameters such as cooperative energies, cooperative dipole moments, and many-body interaction energies. Those complexes with simultaneous presence of a σ-hole bond and a dihydrogen bond show cooperativity energy ranging between -1.02 and -2.31 kJ mol(-1), whereas those with a halogen-hydride bond and a dihydrogen bond are diminutive, with this energetic effect between 0.1 and 0.63 kJ mol(-1). The electronic properties of the complexes have been analyzed using the molecular electrostatic potential (MEP), the electron density shift maps, and the parameters derived from the atoms in molecules (AIM) methodology.